Interferogram conditioning for improved Fourier analysis and application to X-ray phase imaging by grating interferometry.

PubMed

Montaux-Lambert, Antoine; Mercère, Pascal; Primot, Jérôme

2015-11-02

An interferogram conditioning procedure, for subsequent phase retrieval by Fourier demodulation, is presented here as a fast iterative approach aiming at fulfilling the classical boundary conditions imposed by Fourier transform techniques. Interference fringe patterns with typical edge discontinuities were simulated in order to reveal the edge artifacts that classically appear in traditional Fourier analysis, and were consecutively used to demonstrate the correction efficiency of the proposed conditioning technique. Optimization of the algorithm parameters is also presented and discussed. Finally, the procedure was applied to grating-based interferometric measurements performed in the hard X-ray regime. The proposed algorithm enables nearly edge-artifact-free retrieval of the phase derivatives. A similar enhancement of the retrieved absorption and fringe visibility images is also achieved.

Near-common-path interferometer for imaging Fourier-transform spectroscopy in wide-field microscopy

PubMed Central

Wadduwage, Dushan N.; Singh, Vijay Raj; Choi, Heejin; Yaqoob, Zahid; Heemskerk, Hans; Matsudaira, Paul; So, Peter T. C.

2017-01-01

Imaging Fourier-transform spectroscopy (IFTS) is a powerful method for biological hyperspectral analysis based on various imaging modalities, such as fluorescence or Raman. Since the measurements are taken in the Fourier space of the spectrum, it can also take advantage of compressed sensing strategies. IFTS has been readily implemented in high-throughput, high-content microscope systems based on wide-field imaging modalities. However, there are limitations in existing wide-field IFTS designs. Non-common-path approaches are less phase-stable. Alternatively, designs based on the common-path Sagnac interferometer are stable, but incompatible with high-throughput imaging. They require exhaustive sequential scanning over large interferometric path delays, making compressive strategic data acquisition impossible. In this paper, we present a novel phase-stable, near-common-path interferometer enabling high-throughput hyperspectral imaging based on strategic data acquisition. Our results suggest that this approach can improve throughput over those of many other wide-field spectral techniques by more than an order of magnitude without compromising phase stability. PMID:29392168

Temporal Fourier analysis applied to equilibrium radionuclide cineangiography. Importance in the study of global and regional left ventricular wall motion.

PubMed

Cardot, J C; Berthout, P; Verdenet, J; Bidet, A; Faivre, R; Bassand, J P; Bidet, R; Maurat, J P

1982-01-01

Regional and global left ventricular wall motion was assessed in 120 patients using radionuclide cineangiography (RCA) and contrast angiography. Functional imaging procedures based on a temporal Fourier analysis of dynamic image sequences were applied to the study of cardiac contractility. Two images were constructed by taking the phase and amplitude values of the first harmonic in the Fourier transform for each pixel. These two images aided in determining the perimeter of the left ventricle to calculate the global ejection fraction. Regional left ventricular wall motion was studied by analyzing the phase value and by examining the distribution histogram of these values. The accuracy of global ejection fraction calculation was improved by the Fourier technique. This technique increased the sensitivity of RCA for determining segmental abnormalities especially in the left anterior oblique view (LAO).

Hypercomplex Fourier transforms of color images.

PubMed

Ell, Todd A; Sangwine, Stephen J

2007-01-01

Fourier transforms are a fundamental tool in signal and image processing, yet, until recently, there was no definition of a Fourier transform applicable to color images in a holistic manner. In this paper, hypercomplex numbers, specifically quaternions, are used to define a Fourier transform applicable to color images. The properties of the transform are developed, and it is shown that the transform may be computed using two standard complex fast Fourier transforms. The resulting spectrum is explained in terms of familiar phase and modulus concepts, and a new concept of hypercomplex axis. A method for visualizing the spectrum using color graphics is also presented. Finally, a convolution operational formula in the spectral domain is discussed.

Recognition of rotated images using the multi-valued neuron and rotation-invariant 2D Fourier descriptors

NASA Astrophysics Data System (ADS)

Aizenberg, Evgeni; Bigio, Irving J.; Rodriguez-Diaz, Eladio

2012-03-01

The Fourier descriptors paradigm is a well-established approach for affine-invariant characterization of shape contours. In the work presented here, we extend this method to images, and obtain a 2D Fourier representation that is invariant to image rotation. The proposed technique retains phase uniqueness, and therefore structural image information is not lost. Rotation-invariant phase coefficients were used to train a single multi-valued neuron (MVN) to recognize satellite and human face images rotated by a wide range of angles. Experiments yielded 100% and 96.43% classification rate for each data set, respectively. Recognition performance was additionally evaluated under effects of lossy JPEG compression and additive Gaussian noise. Preliminary results show that the derived rotation-invariant features combined with the MVN provide a promising scheme for efficient recognition of rotated images.

Efficient image projection by Fourier electroholography.

PubMed

Makowski, Michał; Ducin, Izabela; Kakarenko, Karol; Kolodziejczyk, Andrzej; Siemion, Agnieszka; Siemion, Andrzej; Suszek, Jaroslaw; Sypek, Maciej; Wojnowski, Dariusz

2011-08-15

An improved efficient projection of color images is presented. It uses a phase spatial light modulator with three iteratively optimized Fourier holograms displayed simultaneously--each for one primary color. This spatial division instead of time division provides stable images. A pixelated structure of the modulator and fluctuations of liquid crystal molecules cause a zeroth-order peak, eliminated by additional wavelength-dependent phase factors shifting it before the image plane, where it is blocked with a matched filter. Speckles are suppressed by time integration of variable speckle patterns generated by additional randomizations of an initial phase and minor changes of the signal. © 2011 Optical Society of America

Pixel-based speckle adjustment for noise reduction in Fourier-domain OCT images.

PubMed

Zhang, Anqi; Xi, Jiefeng; Sun, Jitao; Li, Xingde

2017-03-01

Speckle resides in OCT signals and inevitably effects OCT image quality. In this work, we present a novel method for speckle noise reduction in Fourier-domain OCT images, which utilizes the phase information of complex OCT data. In this method, speckle area is pre-delineated pixelwise based on a phase-domain processing method and then adjusted by the results of wavelet shrinkage of the original image. Coefficient shrinkage method such as wavelet or contourlet is applied afterwards for further suppressing the speckle noise. Compared with conventional methods without speckle adjustment, the proposed method demonstrates significant improvement of image quality.

Extending Single-Molecule Microscopy Using Optical Fourier Processing

PubMed Central

2015-01-01

This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules. PMID:24745862

Extending single-molecule microscopy using optical Fourier processing.

PubMed

Backer, Adam S; Moerner, W E

2014-07-17

This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules.

Algorithms and Array Design Criteria for Robust Imaging in Interferometry

NASA Astrophysics Data System (ADS)

Kurien, Binoy George

Optical interferometry is a technique for obtaining high-resolution imagery of a distant target by interfering light from multiple telescopes. Image restoration from interferometric measurements poses a unique set of challenges. The first challenge is that the measurement set provides only a sparse-sampling of the object's Fourier Transform and hence image formation from these measurements is an inherently ill-posed inverse problem. Secondly, atmospheric turbulence causes severe distortion of the phase of the Fourier samples. We develop array design conditions for unique Fourier phase recovery, as well as a comprehensive algorithmic framework based on the notion of redundant-spaced-calibration (RSC), which together achieve reliable image reconstruction in spite of these challenges. Within this framework, we see that classical interferometric observables such as the bispectrum and closure phase can limit sensitivity, and that generalized notions of these observables can improve both theoretical and empirical performance. Our framework leverages techniques from lattice theory to resolve integer phase ambiguities in the interferometric phase measurements, and from graph theory, to select a reliable set of generalized observables. We analyze the expected shot-noise-limited performance of our algorithm for both pairwise and Fizeau interferometric architectures and corroborate this analysis with simulation results. We apply techniques from the field of compressed sensing to perform image reconstruction from the estimates of the object's Fourier coefficients. The end result is a comprehensive strategy to achieve well-posed and easily-predictable reconstruction performance in optical interferometry.

Fourier Analysis and Structure Determination. Part II: Pulse NMR and NMR Imaging.

ERIC Educational Resources Information Center

Chesick, John P.

1989-01-01

Uses simple pulse NMR experiments to discuss Fourier transforms. Studies the generation of spin echoes used in the imaging procedure. Shows that pulse NMR experiments give signals that are additions of sinusoids of differing amplitudes, frequencies, and phases. (MVL)

Fourier power spectrum characteristics of face photographs: attractiveness perception depends on low-level image properties.

PubMed

Menzel, Claudia; Hayn-Leichsenring, Gregor U; Langner, Oliver; Wiese, Holger; Redies, Christoph

2015-01-01

We investigated whether low-level processed image properties that are shared by natural scenes and artworks - but not veridical face photographs - affect the perception of facial attractiveness and age. Specifically, we considered the slope of the radially averaged Fourier power spectrum in a log-log plot. This slope is a measure of the distribution of special frequency power in an image. Images of natural scenes and artworks possess - compared to face images - a relatively shallow slope (i.e., increased high spatial frequency power). Since aesthetic perception might be based on the efficient processing of images with natural scene statistics, we assumed that the perception of facial attractiveness might also be affected by these properties. We calculated Fourier slope and other beauty-associated measurements in face images and correlated them with ratings of attractiveness and age of the depicted persons (Study 1). We found that Fourier slope - in contrast to the other tested image properties - did not predict attractiveness ratings when we controlled for age. In Study 2A, we overlaid face images with random-phase patterns with different statistics. Patterns with a slope similar to those in natural scenes and artworks resulted in lower attractiveness and higher age ratings. In Studies 2B and 2C, we directly manipulated the Fourier slope of face images and found that images with shallower slopes were rated as more attractive. Additionally, attractiveness of unaltered faces was affected by the Fourier slope of a random-phase background (Study 3). Faces in front of backgrounds with statistics similar to natural scenes and faces were rated as more attractive. We conclude that facial attractiveness ratings are affected by specific image properties. An explanation might be the efficient coding hypothesis.

Fourier Power Spectrum Characteristics of Face Photographs: Attractiveness Perception Depends on Low-Level Image Properties

PubMed Central

Langner, Oliver; Wiese, Holger; Redies, Christoph

2015-01-01

We investigated whether low-level processed image properties that are shared by natural scenes and artworks – but not veridical face photographs – affect the perception of facial attractiveness and age. Specifically, we considered the slope of the radially averaged Fourier power spectrum in a log-log plot. This slope is a measure of the distribution of special frequency power in an image. Images of natural scenes and artworks possess – compared to face images – a relatively shallow slope (i.e., increased high spatial frequency power). Since aesthetic perception might be based on the efficient processing of images with natural scene statistics, we assumed that the perception of facial attractiveness might also be affected by these properties. We calculated Fourier slope and other beauty-associated measurements in face images and correlated them with ratings of attractiveness and age of the depicted persons (Study 1). We found that Fourier slope – in contrast to the other tested image properties – did not predict attractiveness ratings when we controlled for age. In Study 2A, we overlaid face images with random-phase patterns with different statistics. Patterns with a slope similar to those in natural scenes and artworks resulted in lower attractiveness and higher age ratings. In Studies 2B and 2C, we directly manipulated the Fourier slope of face images and found that images with shallower slopes were rated as more attractive. Additionally, attractiveness of unaltered faces was affected by the Fourier slope of a random-phase background (Study 3). Faces in front of backgrounds with statistics similar to natural scenes and faces were rated as more attractive. We conclude that facial attractiveness ratings are affected by specific image properties. An explanation might be the efficient coding hypothesis. PMID:25835539

Liquid-crystal projection image depixelization by spatial phase scrambling

NASA Astrophysics Data System (ADS)

Yang, Xiangyang; Jutamulia, Suganda; Li, Nan

1996-08-01

A technique that removes the pixel structure by scrambling the relative phases among multiple spatial spectra is described. Because of the pixel structure of the liquid-crystal-display (LCD) panel, multiple spectra are generated at the Fourier-spectrum plane (usually at the back focal plane of the imaging lens). A transparent phase mask is placed at the Fourier-spectrum plane such that each spectral order is modulated by one of the subareas of the phase mask, and the phase delay resulting from each pair of subareas is longer than the coherent length of the light source, which is approximately 1 m for the wideband white light sources used in most of LCD s. Such a phase-scrambling technique eliminates the coherence between different spectral orders; therefore, the reconstructed images from the multiple spectra will superimpose incoherently, and the pixel structure will not be observed in the projection image.

Construction of high frame rate images with Fourier transform

NASA Astrophysics Data System (ADS)

Peng, Hu; Lu, Jian-Yu

2002-05-01

Traditionally, images are constructed with a delay-and-sum method that adjusts the phases of received signals (echoes) scattered from the same point in space so that they are summed in phase. Recently, the relationship between the delay-and-sum method and the Fourier transform is investigated [Jian-yu Lu, Anjun Liu, and Hu Peng, ``High frame rate and delay-and-sum imaging methods,'' IEEE Trans. Ultrason. Ferroelectr. Freq. Control (submitted)]. In this study, a generic Fourier transform method is developed. Two-dimensional (2-D) or three-dimensional (3-D) high frame rate images can be constructed using the Fourier transform with a single transmission of an ultrasound pulse from an array as long as the transmission field of the array is known. To verify our theory, computer simulations have been performed with a linear array, a 2-D array, a convex curved array, and a spherical 2-D array. The simulation results are consistent with our theory. [Work supported in part by Grant 5RO1 HL60301 from NIH.

Pixel-based speckle adjustment for noise reduction in Fourier-domain OCT images

PubMed Central

Zhang, Anqi; Xi, Jiefeng; Sun, Jitao; Li, Xingde

2017-01-01

Speckle resides in OCT signals and inevitably effects OCT image quality. In this work, we present a novel method for speckle noise reduction in Fourier-domain OCT images, which utilizes the phase information of complex OCT data. In this method, speckle area is pre-delineated pixelwise based on a phase-domain processing method and then adjusted by the results of wavelet shrinkage of the original image. Coefficient shrinkage method such as wavelet or contourlet is applied afterwards for further suppressing the speckle noise. Compared with conventional methods without speckle adjustment, the proposed method demonstrates significant improvement of image quality. PMID:28663860

High-resolution wave-theory-based ultrasound reflection imaging using the split-step fourier and globally optimized fourier finite-difference methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Lianjie

Methods for enhancing ultrasonic reflection imaging are taught utilizing a split-step Fourier propagator in which the reconstruction is based on recursive inward continuation of ultrasonic wavefields in the frequency-space and frequency-wave number domains. The inward continuation within each extrapolation interval consists of two steps. In the first step, a phase-shift term is applied to the data in the frequency-wave number domain for propagation in a reference medium. The second step consists of applying another phase-shift term to data in the frequency-space domain to approximately compensate for ultrasonic scattering effects of heterogeneities within the tissue being imaged (e.g., breast tissue). Resultsmore » from various data input to the method indicate significant improvements are provided in both image quality and resolution.« less

Phase retrieval of images using Gaussian radial bases.

PubMed

Trahan, Russell; Hyland, David

2013-12-20

Here, the possibility of a noniterative solution to the phase retrieval problem is explored. A new look is taken at the phase retrieval problem that reveals that knowledge of a diffraction pattern's frequency components is enough to recover the image without projective iterations. This occurs when the image is formed using Gaussian bases that give the convenience of a continuous Fourier transform existing in a compact form where square pixels do not. The Gaussian bases are appropriate when circular apertures are used to detect the diffraction pattern because of their optical transfer functions, as discussed briefly. An algorithm is derived that is capable of recovering an image formed by Gaussian bases from only the Fourier transform's modulus, without background constraints. A practical example is shown.

Optical image encryption by random shifting in fractional Fourier domains

NASA Astrophysics Data System (ADS)

Hennelly, B.; Sheridan, J. T.

2003-02-01

A number of methods have recently been proposed in the literature for the encryption of two-dimensional information by use of optical systems based on the fractional Fourier transform. Typically, these methods require random phase screen keys for decrypting the data, which must be stored at the receiver and must be carefully aligned with the received encrypted data. A new technique based on a random shifting, or jigsaw, algorithm is proposed. This method does not require the use of phase keys. The image is encrypted by juxtaposition of sections of the image in fractional Fourier domains. The new method has been compared with existing methods and shows comparable or superior robustness to blind decryption. Optical implementation is discussed, and the sensitivity of the various encryption keys to blind decryption is examined.

Phase-image-based content-addressable holographic data storage

NASA Astrophysics Data System (ADS)

John, Renu; Joseph, Joby; Singh, Kehar

2004-03-01

We propose and demonstrate the use of phase images for content-addressable holographic data storage. Use of binary phase-based data pages with 0 and π phase changes, produces uniform spectral distribution at the Fourier plane. The absence of strong DC component at the Fourier plane and more intensity of higher order spatial frequencies facilitate better recording of higher spatial frequencies, and improves the discrimination capability of the content-addressable memory. This improves the results of the associative recall in a holographic memory system, and can give low number of false hits even for small search arguments. The phase-modulated pixels also provide an opportunity of subtraction among data pixels leading to better discrimination between similar data pages.

Fourier domain image fusion for differential X-ray phase-contrast breast imaging.

PubMed

Coello, Eduardo; Sperl, Jonathan I; Bequé, Dirk; Benz, Tobias; Scherer, Kai; Herzen, Julia; Sztrókay-Gaul, Anikó; Hellerhoff, Karin; Pfeiffer, Franz; Cozzini, Cristina; Grandl, Susanne

2017-04-01

X-Ray Phase-Contrast (XPC) imaging is a novel technology with a great potential for applications in clinical practice, with breast imaging being of special interest. This work introduces an intuitive methodology to combine and visualize relevant diagnostic features, present in the X-ray attenuation, phase shift and scattering information retrieved in XPC imaging, using a Fourier domain fusion algorithm. The method allows to present complementary information from the three acquired signals in one single image, minimizing the noise component and maintaining visual similarity to a conventional X-ray image, but with noticeable enhancement in diagnostic features, details and resolution. Radiologists experienced in mammography applied the image fusion method to XPC measurements of mastectomy samples and evaluated the feature content of each input and the fused image. This assessment validated that the combination of all the relevant diagnostic features, contained in the XPC images, was present in the fused image as well. Copyright © 2017 Elsevier B.V. All rights reserved.

Experimental determination of pore shapes using phase retrieval from q -space NMR diffraction

NASA Astrophysics Data System (ADS)

Demberg, Kerstin; Laun, Frederik Bernd; Bertleff, Marco; Bachert, Peter; Kuder, Tristan Anselm

2018-05-01

This paper presents an approach to solving the phase problem in nuclear magnetic resonance (NMR) diffusion pore imaging, a method that allows imaging the shape of arbitrary closed pores filled with an NMR-detectable medium for investigation of the microstructure of biological tissue and porous materials. Classical q -space imaging composed of two short diffusion-encoding gradient pulses yields, analogously to diffraction experiments, the modulus squared of the Fourier transform of the pore image which entails an inversion problem: An unambiguous reconstruction of the pore image requires both magnitude and phase. Here the phase information is recovered from the Fourier modulus by applying a phase retrieval algorithm. This allows omitting experimentally challenging phase measurements using specialized temporal gradient profiles. A combination of the hybrid input-output algorithm and the error reduction algorithm was used with dynamically adapting support (shrinkwrap extension). No a priori knowledge on the pore shape was fed to the algorithm except for a finite pore extent. The phase retrieval approach proved successful for simulated data with and without noise and was validated in phantom experiments with well-defined pores using hyperpolarized xenon gas.

Experimental determination of pore shapes using phase retrieval from q-space NMR diffraction.

PubMed

Demberg, Kerstin; Laun, Frederik Bernd; Bertleff, Marco; Bachert, Peter; Kuder, Tristan Anselm

2018-05-01

This paper presents an approach to solving the phase problem in nuclear magnetic resonance (NMR) diffusion pore imaging, a method that allows imaging the shape of arbitrary closed pores filled with an NMR-detectable medium for investigation of the microstructure of biological tissue and porous materials. Classical q-space imaging composed of two short diffusion-encoding gradient pulses yields, analogously to diffraction experiments, the modulus squared of the Fourier transform of the pore image which entails an inversion problem: An unambiguous reconstruction of the pore image requires both magnitude and phase. Here the phase information is recovered from the Fourier modulus by applying a phase retrieval algorithm. This allows omitting experimentally challenging phase measurements using specialized temporal gradient profiles. A combination of the hybrid input-output algorithm and the error reduction algorithm was used with dynamically adapting support (shrinkwrap extension). No a priori knowledge on the pore shape was fed to the algorithm except for a finite pore extent. The phase retrieval approach proved successful for simulated data with and without noise and was validated in phantom experiments with well-defined pores using hyperpolarized xenon gas.

Ghost imaging of phase objects with classical incoherent light

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shirai, Tomohiro; Setaelae, Tero; Friberg, Ari T.

2011-10-15

We describe an optical setup for performing spatial Fourier filtering in ghost imaging with classical incoherent light. This is achieved by a modification of the conventional geometry for lensless ghost imaging. It is shown on the basis of classical coherence theory that with this technique one can realize what we call phase-contrast ghost imaging to visualize pure phase objects.

Hypothesis on human eye perceiving optical spectrum rather than an image

NASA Astrophysics Data System (ADS)

Zheng, Yufeng; Szu, Harold

2015-05-01

It is a common knowledge that we see the world because our eyes can perceive an optical image. A digital camera seems a good example of simulating the eye imaging system. However, the signal sensing and imaging on human retina is very complicated. There are at least five layers (of neurons) along the signal pathway: photoreceptors (cones and rods), bipolar, horizontal, amacrine and ganglion cells. To sense an optical image, it seems that photoreceptors (as sensors) plus ganglion cells (converting to electrical signals for transmission) are good enough. Image sensing does not require ununiformed distribution of photoreceptors like fovea. There are some challenging questions, for example, why don't we feel the "blind spots" (never fibers exiting the eyes)? Similar situation happens to glaucoma patients who do not feel their vision loss until 50% or more nerves died. Now our hypothesis is that human retina initially senses optical (i.e., Fourier) spectrum rather than optical image. Due to the symmetric property of Fourier spectrum the signal loss from a blind spot or the dead nerves (for glaucoma patients) can be recovered. Eye logarithmic response to input light intensity much likes displaying Fourier magnitude. The optics and structures of human eyes satisfy the needs of optical Fourier spectrum sampling. It is unsure that where and how inverse Fourier transform is performed in human vision system to obtain an optical image. Phase retrieval technique in compressive sensing domain enables image reconstruction even without phase inputs. The spectrum-based imaging system can potentially tolerate up to 50% of bad sensors (pixels), adapt to large dynamic range (with logarithmic response), etc.

Fast non-interferometric iterative phase retrieval for holographic data storage.

PubMed

Lin, Xiao; Huang, Yong; Shimura, Tsutomu; Fujimura, Ryushi; Tanaka, Yoshito; Endo, Masao; Nishimoto, Hajimu; Liu, Jinpeng; Li, Yang; Liu, Ying; Tan, Xiaodi

2017-12-11

Fast non-interferometric phase retrieval is a very important technique for phase-encoded holographic data storage and other phase based applications due to its advantage of easy implementation, simple system setup, and robust noise tolerance. Here we present an iterative non-interferometric phase retrieval for 4-level phase encoded holographic data storage based on an iterative Fourier transform algorithm and known portion of the encoded data, which increases the storage code rate to two-times that of an amplitude based method. Only a single image at the Fourier plane of the beam is captured for the iterative reconstruction. Since beam intensity at the Fourier plane of the reconstructed beam is more concentrated than the reconstructed beam itself, the requirement of diffractive efficiency of the recording media is reduced, which will improve the dynamic range of recording media significantly. The phase retrieval only requires 10 iterations to achieve a less than 5% phase data error rate, which is successfully demonstrated by recording and reconstructing a test image data experimentally. We believe our method will further advance the holographic data storage technique in the era of big data.

Single Channel Quantum Color Image Encryption Algorithm Based on HSI Model and Quantum Fourier Transform

NASA Astrophysics Data System (ADS)

Gong, Li-Hua; He, Xiang-Tao; Tan, Ru-Chao; Zhou, Zhi-Hong

2018-01-01

In order to obtain high-quality color images, it is important to keep the hue component unchanged while emphasize the intensity or saturation component. As a public color model, Hue-Saturation Intensity (HSI) model is commonly used in image processing. A new single channel quantum color image encryption algorithm based on HSI model and quantum Fourier transform (QFT) is investigated, where the color components of the original color image are converted to HSI and the logistic map is employed to diffuse the relationship of pixels in color components. Subsequently, quantum Fourier transform is exploited to fulfill the encryption. The cipher-text is a combination of a gray image and a phase matrix. Simulations and theoretical analyses demonstrate that the proposed single channel quantum color image encryption scheme based on the HSI model and quantum Fourier transform is secure and effective.

Encoding plaintext by Fourier transform hologram in double random phase encoding using fingerprint keys

NASA Astrophysics Data System (ADS)

Takeda, Masafumi; Nakano, Kazuya; Suzuki, Hiroyuki; Yamaguchi, Masahiro

2012-09-01

It has been shown that biometric information can be used as a cipher key for binary data encryption by applying double random phase encoding. In such methods, binary data are encoded in a bit pattern image, and the decrypted image becomes a plain image when the key is genuine; otherwise, decrypted images become random images. In some cases, images decrypted by imposters may not be fully random, such that the blurred bit pattern can be partially observed. In this paper, we propose a novel bit coding method based on a Fourier transform hologram, which makes images decrypted by imposters more random. Computer experiments confirm that the method increases the randomness of images decrypted by imposters while keeping the false rejection rate as low as in the conventional method.

Optical image encryption system using nonlinear approach based on biometric authentication

NASA Astrophysics Data System (ADS)

Verma, Gaurav; Sinha, Aloka

2017-07-01

A nonlinear image encryption scheme using phase-truncated Fourier transform (PTFT) and natural logarithms is proposed in this paper. With the help of the PTFT, the input image is truncated into phase and amplitude parts at the Fourier plane. The phase-only information is kept as the secret key for the decryption, and the amplitude distribution is modulated by adding an undercover amplitude random mask in the encryption process. Furthermore, the encrypted data is kept hidden inside the face biometric-based phase mask key using the base changing rule of logarithms for secure transmission. This phase mask is generated through principal component analysis. Numerical experiments show the feasibility and the validity of the proposed nonlinear scheme. The performance of the proposed scheme has been studied against the brute force attacks and the amplitude-phase retrieval attack. Simulation results are presented to illustrate the enhanced system performance with desired advantages in comparison to the linear cryptosystem.

Novel Fourier-domain constraint for fast phase retrieval in coherent diffraction imaging.

PubMed

Latychevskaia, Tatiana; Longchamp, Jean-Nicolas; Fink, Hans-Werner

2011-09-26

Coherent diffraction imaging (CDI) for visualizing objects at atomic resolution has been realized as a promising tool for imaging single molecules. Drawbacks of CDI are associated with the difficulty of the numerical phase retrieval from experimental diffraction patterns; a fact which stimulated search for better numerical methods and alternative experimental techniques. Common phase retrieval methods are based on iterative procedures which propagate the complex-valued wave between object and detector plane. Constraints in both, the object and the detector plane are applied. While the constraint in the detector plane employed in most phase retrieval methods requires the amplitude of the complex wave to be equal to the squared root of the measured intensity, we propose a novel Fourier-domain constraint, based on an analogy to holography. Our method allows achieving a low-resolution reconstruction already in the first step followed by a high-resolution reconstruction after further steps. In comparison to conventional schemes this Fourier-domain constraint results in a fast and reliable convergence of the iterative reconstruction process. © 2011 Optical Society of America

Artefacts in geometric phase analysis of compound materials.

PubMed

Peters, Jonathan J P; Beanland, Richard; Alexe, Marin; Cockburn, John W; Revin, Dmitry G; Zhang, Shiyong Y; Sanchez, Ana M

2015-10-01

The geometric phase analysis (GPA) algorithm is known as a robust and straightforward technique that can be used to measure lattice strains in high resolution transmission electron microscope (TEM) images. It is also attractive for analysis of aberration-corrected scanning TEM (ac-STEM) images that resolve every atom column, since it uses Fourier transforms and does not require real-space peak detection and assignment to appropriate sublattices. Here it is demonstrated that, in ac-STEM images of compound materials with compositionally distinct atom columns, an additional geometric phase is present in the Fourier transform. If the structure changes from one area to another in the image (e.g. across an interface), the change in this additional phase will appear as a strain in conventional GPA, even if there is no lattice strain. Strategies to avoid this pitfall are outlined. Copyright © 2015 Elsevier B.V. All rights reserved.

SAVI: Synthetic apertures for long-range, subdiffraction-limited visible imaging using Fourier ptychography

PubMed Central

Holloway, Jason; Wu, Yicheng; Sharma, Manoj K.; Cossairt, Oliver; Veeraraghavan, Ashok

2017-01-01

Synthetic aperture radar is a well-known technique for improving resolution in radio imaging. Extending these synthetic aperture techniques to the visible light domain is not straightforward because optical receivers cannot measure phase information. We propose to use macroscopic Fourier ptychography (FP) as a practical means of creating a synthetic aperture for visible imaging to achieve subdiffraction-limited resolution. We demonstrate the first working prototype for macroscopic FP in a reflection imaging geometry that is capable of imaging optically rough objects. In addition, a novel image space denoising regularization is introduced during phase retrieval to reduce the effects of speckle and improve perceptual quality of the recovered high-resolution image. Our approach is validated experimentally where the resolution of various diffuse objects is improved sixfold. PMID:28439550

Single-pixel non-imaging object recognition by means of Fourier spectrum acquisition

NASA Astrophysics Data System (ADS)

Chen, Huichao; Shi, Jianhong; Liu, Xialin; Niu, Zhouzhou; Zeng, Guihua

2018-04-01

Single-pixel imaging has emerged over recent years as a novel imaging technique, which has significant application prospects. In this paper, we propose and experimentally demonstrate a scheme that can achieve single-pixel non-imaging object recognition by acquiring the Fourier spectrum. In an experiment, a four-step phase-shifting sinusoid illumination light is used to irradiate the object image, the value of the light intensity is measured with a single-pixel detection unit, and the Fourier coefficients of the object image are obtained by a differential measurement. The Fourier coefficients are first cast into binary numbers to obtain the hash value. We propose a new method of perceptual hashing algorithm, which is combined with a discrete Fourier transform to calculate the hash value. The hash distance is obtained by calculating the difference of the hash value between the object image and the contrast images. By setting an appropriate threshold, the object image can be quickly and accurately recognized. The proposed scheme realizes single-pixel non-imaging perceptual hashing object recognition by using fewer measurements. Our result might open a new path for realizing object recognition with non-imaging.

Monocular deprivation of Fourier phase information boosts the deprived eye's dominance during interocular competition but not interocular phase combination.

PubMed

Bai, Jianying; Dong, Xue; He, Sheng; Bao, Min

2017-06-03

Ocular dominance has been extensively studied, often with the goal to understand neuroplasticity, which is a key characteristic within the critical period. Recent work on monocular deprivation, however, demonstrates residual neuroplasticity in the adult visual cortex. After deprivation of patterned inputs by monocular patching, the patched eye becomes more dominant. Since patching blocks both the Fourier amplitude and phase information of the input image, it remains unclear whether deprivation of the Fourier phase information alone is able to reshape eye dominance. Here, for the first time, we show that removing of the phase regularity without changing the amplitude spectra of the input image induced a shift of eye dominance toward the deprived eye, but only if the eye dominance was measured with a binocular rivalry task rather than an interocular phase combination task. These different results indicate that the two measurements are supported by different mechanisms. Phase integration requires the fusion of monocular images. The fused percept highly relies on the weights of the phase-sensitive monocular neurons that respond to the two monocular images. However, binocular rivalry reflects the result of direct interocular competition that strongly weights the contour information transmitted along each monocular pathway. Monocular phase deprivation may not change the weights in the integration (fusion) mechanism much, but alters the balance in the rivalry (competition) mechanism. Our work suggests that ocular dominance plasticity may occur at different stages of visual processing, and that homeostatic compensation also occurs for the lack of phase regularity in natural scenes. Copyright © 2017 IBRO. Published by Elsevier Ltd. All rights reserved.

Electromagnetic Vortex-Based Radar Imaging Using a Single Receiving Antenna: Theory and Experimental Results

PubMed Central

Yuan, Tiezhu; Wang, Hongqiang; Cheng, Yongqiang; Qin, Yuliang

2017-01-01

Radar imaging based on electromagnetic vortex can achieve azimuth resolution without relative motion. The present paper investigates this imaging technique with the use of a single receiving antenna through theoretical analysis and experimental results. Compared with the use of multiple receiving antennas, the echoes from a single receiver cannot be used directly for image reconstruction using Fourier method. The reason is revealed by using the point spread function. An additional phase is compensated for each mode before imaging process based on the array parameters and the elevation of the targets. A proof-of-concept imaging system based on a circular phased array is created, and imaging experiments of corner-reflector targets are performed in an anechoic chamber. The azimuthal image is reconstructed by the use of Fourier transform and spectral estimation methods. The azimuth resolution of the two methods is analyzed and compared through experimental data. The experimental results verify the principle of azimuth resolution and the proposed phase compensation method. PMID:28335487

High-resolution electron microscope

NASA Technical Reports Server (NTRS)

Nathan, R.

1977-01-01

Employing scanning transmission electron microscope as interferometer, relative phases of diffraction maximums can be determined by analysis of dark field images. Synthetic aperture technique and Fourier-transform computer processing of amplitude and phase information provide high resolution images at approximately one angstrom.

Fourier ptychographic microscopy at telecommunication wavelengths using a femtosecond laser

NASA Astrophysics Data System (ADS)

Ahmed, Ishtiaque; Alotaibi, Maged; Skinner-Ramos, Sueli; Dominguez, Daniel; Bernussi, Ayrton A.; de Peralta, Luis Grave

2017-12-01

We report the implementation of the Fourier Ptychographic Microscopy (FPM) technique, a phase retrieval technique, at telecommunication wavelengths using a low-coherence ultrafast pulsed laser source. High quality images, near speckle-free, were obtained with the proposed approach. We demonstrate that FPM can also be used to image periodic features through a silicon wafer.

[Research on spatially modulated Fourier transform imaging spectrometer data processing method].

PubMed

Huang, Min; Xiangli, Bin; Lü, Qun-Bo; Zhou, Jin-Song; Jing, Juan-Juan; Cui, Yan

2010-03-01

Fourier transform imaging spectrometer is a new technic, and has been developed very rapidly in nearly ten years. The data catched by Fourier transform imaging spectrometer is indirect data, can not be used by user, and need to be processed by various approaches, including data pretreatment, apodization, phase correction, FFT, and spectral radicalization calibration. No paper so far has been found roundly to introduce this method. In the present paper, the author will give an effective method to process the interfering data to spectral data, and with this method we can obtain good result.

Randomly displaced phase distribution design and its advantage in page-data recording of Fourier transform holograms.

PubMed

Emoto, Akira; Fukuda, Takashi

2013-02-20

For Fourier transform holography, an effective random phase distribution with randomly displaced phase segments is proposed for obtaining a smooth finite optical intensity distribution in the Fourier transform plane. Since unitary phase segments are randomly distributed in-plane, the blanks give various spatial frequency components to an image, and thus smooth the spectrum. Moreover, by randomly changing the phase segment size, spike generation from the unitary phase segment size in the spectrum can be reduced significantly. As a result, a smooth spectrum including sidebands can be formed at a relatively narrow extent. The proposed phase distribution sustains the primary functions of a random phase mask for holographic-data recording and reconstruction. Therefore, this distribution is expected to find applications in high-density holographic memory systems, replacing conventional random phase mask patterns.

Optical character recognition of camera-captured images based on phase features

NASA Astrophysics Data System (ADS)

Diaz-Escobar, Julia; Kober, Vitaly

2015-09-01

Nowadays most of digital information is obtained using mobile devices specially smartphones. In particular, it brings the opportunity for optical character recognition in camera-captured images. For this reason many recognition applications have been recently developed such as recognition of license plates, business cards, receipts and street signal; document classification, augmented reality, language translator and so on. Camera-captured images are usually affected by geometric distortions, nonuniform illumination, shadow, noise, which make difficult the recognition task with existing systems. It is well known that the Fourier phase contains a lot of important information regardless of the Fourier magnitude. So, in this work we propose a phase-based recognition system exploiting phase-congruency features for illumination/scale invariance. The performance of the proposed system is tested in terms of miss classifications and false alarms with the help of computer simulation.

A half-blind color image hiding and encryption method in fractional Fourier domains

NASA Astrophysics Data System (ADS)

Ge, Fan; Chen, Linfei; Zhao, Daomu

2008-09-01

We have proposed a new technique for digital image encryption and hiding based on fractional Fourier transforms with double random phases. An original hidden image is encrypted two times and the keys are increased to strengthen information protection. Color image hiding and encryption with wavelength multiplexing is proposed by embedding and encryption in R, G and B three channels. The robustness against occlusion attacks and noise attacks are analyzed. And computer simulations are presented with the corresponding results.

Distributed Two-Dimensional Fourier Transforms on DSPs with an Application for Phase Retrieval

NASA Technical Reports Server (NTRS)

Smith, Jeffrey Scott

2006-01-01

Many applications of two-dimensional Fourier Transforms require fixed timing as defined by system specifications. One example is image-based wavefront sensing. The image-based approach has many benefits, yet it is a computational intensive solution for adaptive optic correction, where optical adjustments are made in real-time to correct for external (atmospheric turbulence) and internal (stability) aberrations, which cause image degradation. For phase retrieval, a type of image-based wavefront sensing, numerous two-dimensional Fast Fourier Transforms (FFTs) are used. To meet the required real-time specifications, a distributed system is needed, and thus, the 2-D FFT necessitates an all-to-all communication among the computational nodes. The 1-D floating point FFT is very efficient on a digital signal processor (DSP). For this study, several architectures and analysis of such are presented which address the all-to-all communication with DSPs. Emphasis of this research is on a 64-node cluster of Analog Devices TigerSharc TS-101 DSPs.

Mesh-based phase contrast Fourier transform imaging

NASA Astrophysics Data System (ADS)

Tahir, Sajjad; Bashir, Sajid; MacDonald, C. A.; Petruccelli, Jonathan C.

2017-04-01

Traditional x-ray radiography is limited by low attenuation contrast in materials of low electron density. Phase contrast imaging offers the potential to improve the contrast between such materials, but due to the requirements on the spatial coherence of the x-ray beam, practical implementation of such systems with tabletop (i.e. non-synchrotron) sources has been limited. One phase imaging technique employs multiple fine-pitched gratings. However, the strict manufacturing tolerances and precise alignment requirements have limited the widespread adoption of grating-based techniques. In this work, we have investigated a recently developed technique that utilizes a single grid of much coarser pitch. Our system consisted of a low power 100 μm spot Mo source, a CCD with 22 μm pixel pitch, and either a focused mammography linear grid or a stainless steel woven mesh. Phase is extracted from a single image by windowing and comparing data localized about harmonics of the mesh in the Fourier domain. The effects on the diffraction phase contrast and scattering amplitude images of varying grid types and periods, and of varying the width of the window function used to separate the harmonics were investigated. Using the wire mesh, derivatives of the phase along two orthogonal directions were obtained and combined to form improved phase contrast images.

Imaging through ground-level turbulence by Fourier telescopy: Simulations and preliminary experiments

NASA Astrophysics Data System (ADS)

Randunu Pathirannehelage, Nishantha

Fourier telescopy imaging is a recently-developed imaging method that relies on active structured-light illumination of the object. Reflected/scattered light is measured by a large "light bucket" detector; processing of the detected signal yields the magnitude and phase of spatial frequency components of the object reflectance or transmittance function. An inverse Fourier transform results in the image. In 2012 a novel method, known as time-average Fourier telescopy (TAFT), was introduced by William T. Rhodes as a means for diffraction-limited imaging through ground-level atmospheric turbulence. This method, which can be applied to long horizontal-path terrestrial imaging, addresses a need that is not solved by the adaptive optics methods being used in astronomical imaging. Field-experiment verification of the TAFT concept requires instrumentation that is not available at Florida Atlantic University. The objective of this doctoral research program is thus to demonstrate, in the absence of full-scale experimentation, the feasibility of time-average Fourier telescopy through (a) the design, construction, and testing of small-scale laboratory instrumentation capable of exploring basic Fourier telescopy data-gathering operations, and (b) the development of MATLAB-based software capable of demonstrating the effect of kilometer-scale passage of laser beams through ground-level turbulence in a numerical simulation of TAFT.

Phase and amplitude beam shaping with two deformable mirrors implementing input plane and Fourier plane phase modifications.

PubMed

Wu, Chensheng; Ko, Jonathan; Rzasa, John R; Paulson, Daniel A; Davis, Christopher C

2018-03-20

We find that ideas in optical image encryption can be very useful for adaptive optics in achieving simultaneous phase and amplitude shaping of a laser beam. An adaptive optics system with simultaneous phase and amplitude shaping ability is very desirable for atmospheric turbulence compensation. Atmospheric turbulence-induced beam distortions can jeopardize the effectiveness of optical power delivery for directed-energy systems and optical information delivery for free-space optical communication systems. In this paper, a prototype adaptive optics system is proposed based on a famous image encryption structure. The major change is to replace the two random phase plates at the input plane and Fourier plane of the encryption system, respectively, with two deformable mirrors that perform on-demand phase modulations. A Gaussian beam is used as an input to replace the conventional image input. We show through theory, simulation, and experiments that the slightly modified image encryption system can be used to achieve arbitrary phase and amplitude beam shaping within the limits of stroke range and influence function of the deformable mirrors. In application, the proposed technique can be used to perform mode conversion between optical beams, generate structured light signals for imaging and scanning, and compensate atmospheric turbulence-induced phase and amplitude beam distortions.

Image security based on iterative random phase encoding in expanded fractional Fourier transform domains

NASA Astrophysics Data System (ADS)

Liu, Zhengjun; Chen, Hang; Blondel, Walter; Shen, Zhenmin; Liu, Shutian

2018-06-01

A novel image encryption method is proposed by using the expanded fractional Fourier transform, which is implemented with a pair of lenses. Here the centers of two lenses are separated at the cross section of axis in optical system. The encryption system is addressed with Fresnel diffraction and phase modulation for the calculation of information transmission. The iterative process with the transform unit is utilized for hiding secret image. The structure parameters of a battery of lenses can be used for additional keys. The performance of encryption method is analyzed theoretically and digitally. The results show that the security of this algorithm is enhanced markedly by the added keys.

Radar imaging using electromagnetic wave carrying orbital angular momentum

NASA Astrophysics Data System (ADS)

Yuan, Tiezhu; Cheng, Yongqiang; Wang, Hongqiang; Qin, Yuliang; Fan, Bo

2017-03-01

The concept of radar imaging based on orbital angular momentum (OAM) modulation, which has the ability of azimuthal resolution without relative motion, has recently been proposed. We investigate this imaging technique further in greater detail. We first analyze the principle of the technique, accounting for its resolving ability physically. The phase and intensity distributions of the OAM-carrying fields produced by phased uniform circular array antenna, which have significant effects on the imaging results, are investigated. The imaging model shows that the received signal has the form of inverse discrete Fourier transform with the use of OAM and frequency diversities. The two-dimensional Fourier transform is employed to reconstruct the target images in the case of large and small elevation angles. Due to the peculiar phase and intensity characteristics, the small elevation is more suitable for practical application than the large one. The minimum elevation angle is then obtained given the array parameters. The imaging capability is analyzed by means of the point spread function. All results are verified through numerical simulations. The proposed staring imaging technique can achieve extremely high azimuthal resolution with the use of plentiful OAM modes.

Phase in Optical Image Processing

NASA Astrophysics Data System (ADS)

Naughton, Thomas J.

2010-04-01

The use of phase has a long standing history in optical image processing, with early milestones being in the field of pattern recognition, such as VanderLugt's practical construction technique for matched filters, and (implicitly) Goodman's joint Fourier transform correlator. In recent years, the flexibility afforded by phase-only spatial light modulators and digital holography, for example, has enabled many processing techniques based on the explicit encoding and decoding of phase. One application area concerns efficient numerical computations. Pushing phase measurement to its physical limits, designs employing the physical properties of phase have ranged from the sensible to the wonderful, in some cases making computationally easy problems easier to solve and in other cases addressing mathematics' most challenging computationally hard problems. Another application area is optical image encryption, in which, typically, a phase mask modulates the fractional Fourier transformed coefficients of a perturbed input image, and the phase of the inverse transform is then sensed as the encrypted image. The inherent linearity that makes the system so elegant mitigates against its use as an effective encryption technique, but we show how a combination of optical and digital techniques can restore confidence in that security. We conclude with the concept of digital hologram image processing, and applications of same that are uniquely suited to optical implementation, where the processing, recognition, or encryption step operates on full field information, such as that emanating from a coherently illuminated real-world three-dimensional object.

A Palmprint Recognition Algorithm Using Phase-Only Correlation

NASA Astrophysics Data System (ADS)

Ito, Koichi; Aoki, Takafumi; Nakajima, Hiroshi; Kobayashi, Koji; Higuchi, Tatsuo

This paper presents a palmprint recognition algorithm using Phase-Only Correlation (POC). The use of phase components in 2D (two-dimensional) discrete Fourier transforms of palmprint images makes it possible to achieve highly robust image registration and matching. In the proposed algorithm, POC is used to align scaling, rotation and translation between two palmprint images, and evaluate similarity between them. Experimental evaluation using a palmprint image database clearly demonstrates efficient matching performance of the proposed algorithm.

Missing texture reconstruction method based on error reduction algorithm using Fourier transform magnitude estimation scheme.

PubMed

Ogawa, Takahiro; Haseyama, Miki

2013-03-01

A missing texture reconstruction method based on an error reduction (ER) algorithm, including a novel estimation scheme of Fourier transform magnitudes is presented in this brief. In our method, Fourier transform magnitude is estimated for a target patch including missing areas, and the missing intensities are estimated by retrieving its phase based on the ER algorithm. Specifically, by monitoring errors converged in the ER algorithm, known patches whose Fourier transform magnitudes are similar to that of the target patch are selected from the target image. In the second approach, the Fourier transform magnitude of the target patch is estimated from those of the selected known patches and their corresponding errors. Consequently, by using the ER algorithm, we can estimate both the Fourier transform magnitudes and phases to reconstruct the missing areas.

Encoding methods for B1+ mapping in parallel transmit systems at ultra high field

NASA Astrophysics Data System (ADS)

Tse, Desmond H. Y.; Poole, Michael S.; Magill, Arthur W.; Felder, Jörg; Brenner, Daniel; Jon Shah, N.

2014-08-01

Parallel radiofrequency (RF) transmission, either in the form of RF shimming or pulse design, has been proposed as a solution to the B1+ inhomogeneity problem in ultra high field magnetic resonance imaging. As a prerequisite, accurate B1+ maps from each of the available transmit channels are required. In this work, four different encoding methods for B1+ mapping, namely 1-channel-on, all-channels-on-except-1, all-channels-on-1-inverted and Fourier phase encoding, were evaluated using dual refocusing acquisition mode (DREAM) at 9.4 T. Fourier phase encoding was demonstrated in both phantom and in vivo to be the least susceptible to artefacts caused by destructive RF interference at 9.4 T. Unlike the other two interferometric encoding schemes, Fourier phase encoding showed negligible dependency on the initial RF phase setting and therefore no prior B1+ knowledge is required. Fourier phase encoding also provides a flexible way to increase the number of measurements to increase SNR, and to allow further reduction of artefacts by weighted decoding. These advantages of Fourier phase encoding suggest that it is a good choice for B1+ mapping in parallel transmit systems at ultra high field.

MOSAIC - A space-multiplexing technique for optical processing of large images

NASA Technical Reports Server (NTRS)

Athale, Ravindra A.; Astor, Michael E.; Yu, Jeffrey

1993-01-01

A technique for Fourier processing of images larger than the space-bandwidth products of conventional or smart spatial light modulators and two-dimensional detector arrays is described. The technique involves a spatial combination of subimages displayed on individual spatial light modulators to form a phase-coherent image, which is subsequently processed with Fourier optical techniques. Because of the technique's similarity with the mosaic technique used in art, the processor used is termed an optical MOSAIC processor. The phase accuracy requirements of this system were studied by computer simulation. It was found that phase errors of less than lambda/8 did not degrade the performance of the system and that the system was relatively insensitive to amplitude nonuniformities. Several schemes for implementing the subimage combination are described. Initial experimental results demonstrating the validity of the mosaic concept are also presented.

Vibration measurement by temporal Fourier analyses of a digital hologram sequence.

PubMed

Fu, Yu; Pedrini, Giancarlo; Osten, Wolfgang

2007-08-10

A method for whole-field noncontact measurement of displacement, velocity, and acceleration of a vibrating object based on image-plane digital holography is presented. A series of digital holograms of a vibrating object are captured by use of a high-speed CCD camera. The result of the reconstruction is a three-dimensional complex-valued matrix with noise. We apply Fourier analysis and windowed Fourier analysis in both the spatial and the temporal domains to extract the displacement, the velocity, and the acceleration. The instantaneous displacement is obtained by temporal unwrapping of the filtered phase map, whereas the velocity and acceleration are evaluated by Fourier analysis and by windowed Fourier analysis along the time axis. The combination of digital holography and temporal Fourier analyses allows for evaluation of the vibration, without a phase ambiguity problem, and smooth spatial distribution of instantaneous displacement, velocity, and acceleration of each instant are obtained. The comparison of Fourier analysis and windowed Fourier analysis in velocity and acceleration measurements is also presented.

Double-resolution electron holography with simple Fourier transform of fringe-shifted holograms.

PubMed

Volkov, V V; Han, M G; Zhu, Y

2013-11-01

We propose a fringe-shifting holographic method with an appropriate image wave recovery algorithm leading to exact solution of holographic equations. With this new method the complex object image wave recovered from holograms appears to have much less traditional artifacts caused by the autocorrelation band present practically in all Fourier transformed holograms. The new analytical solutions make possible a double-resolution electron holography free from autocorrelation band artifacts and thus push the limits for phase resolution. The new image wave recovery algorithm uses a popular Fourier solution of the side band-pass filter technique, while the fringe-shifting holographic method is simple to implement in practice. Published by Elsevier B.V.

Speckless head-up display on two spatial light modulators

NASA Astrophysics Data System (ADS)

Siemion, Andrzej; Ducin, Izabela; Kakarenko, Karol; Makowski, Michał; Siemion, Agnieszka; Suszek, Jarosław; Sypek, Maciej; Wojnowski, Dariusz; Jaroszewicz, Zbigniew; Kołodziejczyk, Andrzej

2010-12-01

There is a continuous demand for the computer generated holograms to give an almost perfect reconstruction with a reasonable cost of manufacturing. One method of improving the image quality is to illuminate a Fourier hologram with a quasi-random, but well known, light field phase distribution. It can be achieved with a lithographically produced phase mask. Up to date, the implementation of the lithographic technique is relatively complex and time and money consuming, which is why we have decided to use two Spatial Light Modulators (SLM). For the correctly adjusted light polarization a SLM acts as a pure phase modulator with 256 adjustable phase levels between 0 and 2π. The two modulators give us an opportunity to use the whole surface of the device and to reduce the size of the experimental system. The optical system with one SLM can also be used but it requires dividing the active surface into halves (one for the Fourier hologram and the second for the quasi-random diffuser), which implies a more complicated optical setup. A larger surface allows to display three Fourier holograms, each for one primary colour: red, green and blue. This allows to reconstruct almost noiseless colourful dynamic images. In this work we present the results of numerical simulations of image reconstructions with the use of two SLM displays.

Why phase errors affect the electron function more than amplitude errors.

PubMed

Lattman, Eaton; DeRosier, David

2008-03-01

If Fexp(ialpha) are the set of structure factors for a structure f, the amplitudes can be converted to those of an uncorrelated structure g (amplitude swapping) by multiplying each F by the positive number G/F. Correspondingly, the image f is convoluted with k, the Fourier transform of G/F; k has a large peak at the origin, so that f * k approximately f. For swapped phases, the image f is convoluted with l, the Fourier transform of exp(iDeltaalpha), where Deltaalpha, the phase difference between F and G, is a random variable; l does not have a large peak at the origin, so that f * l does not resemble f. The paper provides quantitative descriptions of these arguments.

Algorithm for Wavefront Sensing Using an Extended Scene

NASA Technical Reports Server (NTRS)

Sidick, Erkin; Green, Joseph; Ohara, Catherine

2008-01-01

A recently conceived algorithm for processing image data acquired by a Shack-Hartmann (SH) wavefront sensor is not subject to the restriction, previously applicable in SH wavefront sensing, that the image be formed from a distant star or other equivalent of a point light source. That is to say, the image could be of an extended scene. (One still has the option of using a point source.) The algorithm can be implemented in commercially available software on ordinary computers. The steps of the algorithm are the following: 1. Suppose that the image comprises M sub-images. Determine the x,y Cartesian coordinates of the centers of these sub-images and store them in a 2xM matrix. 2. Within each sub-image, choose an NxN-pixel cell centered at the coordinates determined in step 1. For the ith sub-image, let this cell be denoted as si(x,y). Let the cell of another subimage (preferably near the center of the whole extended-scene image) be designated a reference cell, denoted r(x,y). 3. Calculate the fast Fourier transforms of the sub-sub-images in the central NxN portions (where N < N and both are preferably powers of 2) of r(x,y) and si(x,y). 4. Multiply the two transforms to obtain a cross-correlation function Ci(u,v), in the Fourier domain. Then let the phase of Ci(u, v) constitute a phase function, phi(u,v). 5. Fit u and v slopes to phi (u,v) over a small u,v subdomain. 6. Compute the fast Fourier transform, Si(u,v) of the full NxN cell si(x,y). Multiply this transform by the u and phase slopes obtained in step 4. Then compute the inverse fast Fourier transform of the product. 7. Repeat steps 4 through 6 in an iteration loop, cumulating the u and slopes, until a maximum iteration number is reached or the change in image shift becomes smaller than a predetermined tolerance. 8. Repeat steps 4 through 7 for the cells of all other sub-images.

A no-key-exchange secure image sharing scheme based on Shamir's three-pass cryptography protocol and the multiple-parameter fractional Fourier transform.

PubMed

Lang, Jun

2012-01-30

In this paper, we propose a novel secure image sharing scheme based on Shamir's three-pass protocol and the multiple-parameter fractional Fourier transform (MPFRFT), which can safely exchange information with no advance distribution of either secret keys or public keys between users. The image is encrypted directly by the MPFRFT spectrum without the use of phase keys, and information can be shared by transmitting the encrypted image (or message) three times between users. Numerical simulation results are given to verify the performance of the proposed algorithm.

Formation of Fourier phase shifts in the solar Ni I 6768 A line

NASA Technical Reports Server (NTRS)

Jones, Harrison P.

1989-01-01

A formalism is developed to understand better how Doppler shifts of spectrum lines as inferred from phase shifts in the Fourier transforms of line profiles are related to the underlying velocity structures which they are intended to measure. With a standard model atmosphere and a simplified, quasi-LTE treatment of line formation, the formalism is applied to the Ni I 6768 A line, which has been selected for use with a network of imaging interferometers under development by the Global Oscillations Network Group for research in helioseismology. Fourier phase shifts are found to be a remarkably linear measure of velocity even in the presence of gradients and unresolved lateral variations in the assumed velocity field. An assumed outward increase in amplitude of a model oscillatory velocity is noticeably reflected in the center-to-limb behavior of the simulated velocity measure, and a sample model of solar granulation is found to have a strong influence on the formation of the Fourier phase.

Evaluation of intrinsic respiratory signal determination methods for 4D CBCT adapted for mice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martin, Rachael; Pan, Tinsu, E-mail: tpan@mdanderson.org; Rubinstein, Ashley

Purpose: 4D CT imaging in mice is important in a variety of areas including studies of lung function and tumor motion. A necessary step in 4D imaging is obtaining a respiratory signal, which can be done through an external system or intrinsically through the projection images. A number of methods have been developed that can successfully determine the respiratory signal from cone-beam projection images of humans, however only a few have been utilized in a preclinical setting and most of these rely on step-and-shoot style imaging. The purpose of this work is to assess and make adaptions of several successfulmore » methods developed for humans for an image-guided preclinical radiation therapy system. Methods: Respiratory signals were determined from the projection images of free-breathing mice scanned on the X-RAD system using four methods: the so-called Amsterdam shroud method, a method based on the phase of the Fourier transform, a pixel intensity method, and a center of mass method. The Amsterdam shroud method was modified so the sharp inspiration peaks associated with anesthetized mouse breathing could be detected. Respiratory signals were used to sort projections into phase bins and 4D images were reconstructed. Error and standard deviation in the assignment of phase bins for the four methods compared to a manual method considered to be ground truth were calculated for a range of region of interest (ROI) sizes. Qualitative comparisons were additionally made between the 4D images obtained using each of the methods and the manual method. Results: 4D images were successfully created for all mice with each of the respiratory signal extraction methods. Only minimal qualitative differences were noted between each of the methods and the manual method. The average error (and standard deviation) in phase bin assignment was 0.24 ± 0.08 (0.49 ± 0.11) phase bins for the Fourier transform method, 0.09 ± 0.03 (0.31 ± 0.08) phase bins for the modified Amsterdam shroud method, 0.09 ± 0.02 (0.33 ± 0.07) phase bins for the intensity method, and 0.37 ± 0.10 (0.57 ± 0.08) phase bins for the center of mass method. Little dependence on ROI size was noted for the modified Amsterdam shroud and intensity methods while the Fourier transform and center of mass methods showed a noticeable dependence on the ROI size. Conclusions: The modified Amsterdam shroud, Fourier transform, and intensity respiratory signal methods are sufficiently accurate to be used for 4D imaging on the X-RAD system and show improvement over the existing center of mass method. The intensity and modified Amsterdam shroud methods are recommended due to their high accuracy and low dependence on ROI size.« less

Image registration under translation and rotation in two-dimensional planes using Fourier slice theorem.

PubMed

Pohit, M; Sharma, J

2015-05-10

Image recognition in the presence of both rotation and translation is a longstanding problem in correlation pattern recognition. Use of log polar transform gives a solution to this problem, but at a cost of losing the vital phase information from the image. The main objective of this paper is to develop an algorithm based on Fourier slice theorem for measuring the simultaneous rotation and translation of an object in a 2D plane. The algorithm is applicable for any arbitrary object shift for full 180° rotation.

An imaging method of wavefront coding system based on phase plate rotation

NASA Astrophysics Data System (ADS)

Yi, Rigui; Chen, Xi; Dong, Liquan; Liu, Ming; Zhao, Yuejin; Liu, Xiaohua

2018-01-01

Wave-front coding has a great prospect in extending the depth of the optical imaging system and reducing optical aberrations, but the image quality and noise performance are inevitably reduced. According to the theoretical analysis of the wave-front coding system and the phase function expression of the cubic phase plate, this paper analyzed and utilized the feature that the phase function expression would be invariant in the new coordinate system when the phase plate rotates at different angles around the z-axis, and we proposed a method based on the rotation of the phase plate and image fusion. First, let the phase plate rotated at a certain angle around the z-axis, the shape and distribution of the PSF obtained on the image surface remain unchanged, the rotation angle and direction are consistent with the rotation angle of the phase plate. Then, the middle blurred image is filtered by the point spread function of the rotation adjustment. Finally, the reconstruction images were fused by the method of the Laplacian pyramid image fusion and the Fourier transform spectrum fusion method, and the results were evaluated subjectively and objectively. In this paper, we used Matlab to simulate the images. By using the Laplacian pyramid image fusion method, the signal-to-noise ratio of the image is increased by 19% 27%, the clarity is increased by 11% 15% , and the average gradient is increased by 4% 9% . By using the Fourier transform spectrum fusion method, the signal-to-noise ratio of the image is increased by 14% 23%, the clarity is increased by 6% 11% , and the average gradient is improved by 2% 6%. The experimental results show that the image processing by the above method can improve the quality of the restored image, improving the image clarity, and can effectively preserve the image information.

A general theory of interference fringes in x-ray phase grating imaging.

PubMed

Yan, Aimin; Wu, Xizeng; Liu, Hong

2015-06-01

The authors note that the concept of the Talbot self-image distance in x-ray phase grating interferometry is indeed not well defined for polychromatic x-rays, because both the grating phase shift and the fractional Talbot distances are all x-ray wavelength-dependent. For x-ray interferometry optimization, there is a need for a quantitative theory that is able to predict if a good intensity modulation is attainable at a given grating-to-detector distance. In this work, the authors set out to meet this need. In order to apply Fourier analysis directly to the intensity fringe patterns of two-dimensional and one-dimensional phase grating interferometers, the authors start their derivation from a general phase space theory of x-ray phase-contrast imaging. Unlike previous Fourier analyses, the authors evolved the Wigner distribution to obtain closed-form expressions of the Fourier coefficients of the intensity fringes for any grating-to-detector distance, even if it is not a fractional Talbot distance. The developed theory determines the visibility of any diffraction order as a function of the grating-to-detector distance, the phase shift of the grating, and the x-ray spectrum. The authors demonstrate that the visibilities of diffraction orders can serve as the indicators of the underlying interference intensity modulation. Applying the theory to the conventional and inverse geometry configurations of single-grating interferometers, the authors demonstrated that the proposed theory provides a quantitative tool for the grating interferometer optimization with or without the Talbot-distance constraints. In this work, the authors developed a novel theory of the interference intensity fringes in phase grating x-ray interferometry. This theory provides a quantitative tool in design optimization of phase grating x-ray interferometers.

360-degrees profilometry using strip-light projection coupled to Fourier phase-demodulation.

PubMed

Servin, Manuel; Padilla, Moises; Garnica, Guillermo

2016-01-11

360 degrees (360°) digitalization of three dimensional (3D) solids using a projected light-strip is a well-established technique in academic and commercial profilometers. These profilometers project a light-strip over the digitizing solid while the solid is rotated a full revolution or 360-degrees. Then, a computer program typically extracts the centroid of this light-strip, and by triangulation one obtains the shape of the solid. Here instead of using intensity-based light-strip centroid estimation, we propose to use Fourier phase-demodulation for 360° solid digitalization. The advantage of Fourier demodulation over strip-centroid estimation is that the accuracy of phase-demodulation linearly-increases with the fringe density, while in strip-light the centroid-estimation errors are independent. Here we proposed first to construct a carrier-frequency fringe-pattern by closely adding the individual light-strip images recorded while the solid is being rotated. Next, this high-density fringe-pattern is phase-demodulated using the standard Fourier technique. To test the feasibility of this Fourier demodulation approach, we have digitized two solids with increasing topographic complexity: a Rubik's cube and a plastic model of a human-skull. According to our results, phase demodulation based on the Fourier technique is less noisy than triangulation based on centroid light-strip estimation. Moreover, Fourier demodulation also provides the amplitude of the analytic signal which is a valuable information for the visualization of surface details.

An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm

NASA Astrophysics Data System (ADS)

Zhang, B.; Sang, Jun; Alam, Mohammad S.

2013-03-01

An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm was proposed. Firstly, the original secret image was encrypted into two phase-only masks M1 and M2 via cascaded iterative Fourier transform (CIFT) algorithm. Then, the public-key encryption algorithm RSA was adopted to encrypt M2 into M2' . Finally, a host image was enlarged by extending one pixel into 2×2 pixels and each element in M1 and M2' was multiplied with a superimposition coefficient and added to or subtracted from two different elements in the 2×2 pixels of the enlarged host image. To recover the secret image from the stego-image, the two masks were extracted from the stego-image without the original host image. By applying public-key encryption algorithm, the key distribution was facilitated, and also compared with the image hiding method based on optical interference, the proposed method may reach higher robustness by employing the characteristics of the CIFT algorithm. Computer simulations show that this method has good robustness against image processing.

Quantitative phase imaging and complex field reconstruction by pupil modulation differential phase contrast

PubMed Central

Lu, Hangwen; Chung, Jaebum; Ou, Xiaoze; Yang, Changhuei

2016-01-01

Differential phase contrast (DPC) is a non-interferometric quantitative phase imaging method achieved by using an asymmetric imaging procedure. We report a pupil modulation differential phase contrast (PMDPC) imaging method by filtering a sample’s Fourier domain with half-circle pupils. A phase gradient image is captured with each half-circle pupil, and a quantitative high resolution phase image is obtained after a deconvolution process with a minimum of two phase gradient images. Here, we introduce PMDPC quantitative phase image reconstruction algorithm and realize it experimentally in a 4f system with an SLM placed at the pupil plane. In our current experimental setup with the numerical aperture of 0.36, we obtain a quantitative phase image with a resolution of 1.73μm after computationally removing system aberrations and refocusing. We also extend the depth of field digitally by 20 times to ±50μm with a resolution of 1.76μm. PMID:27828473

High resolution quantitative phase imaging of live cells with constrained optimization approach

NASA Astrophysics Data System (ADS)

Pandiyan, Vimal Prabhu; Khare, Kedar; John, Renu

2016-03-01

Quantitative phase imaging (QPI) aims at studying weakly scattering and absorbing biological specimens with subwavelength accuracy without any external staining mechanisms. Use of a reference beam at an angle is one of the necessary criteria for recording of high resolution holograms in most of the interferometric methods used for quantitative phase imaging. The spatial separation of the dc and twin images is decided by the reference beam angle and Fourier-filtered reconstructed image will have a very poor resolution if hologram is recorded below a minimum reference angle condition. However, it is always inconvenient to have a large reference beam angle while performing high resolution microscopy of live cells and biological specimens with nanometric features. In this paper, we treat reconstruction of digital holographic microscopy images as a constrained optimization problem with smoothness constraint in order to recover only complex object field in hologram plane even with overlapping dc and twin image terms. We solve this optimization problem by gradient descent approach iteratively and the smoothness constraint is implemented by spatial averaging with appropriate size. This approach will give excellent high resolution image recovery compared to Fourier filtering while keeping a very small reference angle. We demonstrate this approach on digital holographic microscopy of live cells by recovering the quantitative phase of live cells from a hologram recorded with nearly zero reference angle.

Onion cell imaging by using Talbot/self-imaging effect

NASA Astrophysics Data System (ADS)

Agarwal, Shilpi; Kumar, Varun; Shakher, Chandra

2017-08-01

This paper presents the amplitude and phase imaging of onion epidermis cell using the self-imaging capabilities of a grating (Talbot effect) in visible light region. In proposed method, the Fresnel diffraction pattern from the first grating and object is recorded at self-image plane. Fast Fourier Transform (FFT) is used for extracting the 3D amplitude and phase image of onion epidermis cell. The stability of the proposed system, from environmental perturbation as well as its compactness and portability give the proposed system a high potential for several clinical applications.

Speckle imaging for planetary research

NASA Technical Reports Server (NTRS)

Nisenson, P.; Goody, R.; Apt, J.; Papaliolios, C.

1983-01-01

The present study of speckle imaging technique effectiveness encompasses image reconstruction by means of a division algorithm for Fourier amplitudes, and the Knox-Thompson (1974) algorithm for Fourier phases. Results which have been obtained for Io, Titan, Pallas, Jupiter and Uranus indicate that spatial resolutions lower than the seeing limit by a factor of four are obtainable for objects brighter than Uranus. The resolutions obtained are well above the diffraction limit, due to inadequacies of the video camera employed. A photon-counting camera has been developed to overcome these difficulties, making possible the diffraction-limited resolution of objects as faint as Charon.

Terahertz holography for imaging amplitude and phase objects.

PubMed

Hack, Erwin; Zolliker, Peter

2014-06-30

A non-monochromatic THz Quantum Cascade Laser and an uncooled micro-bolometer array detector with VGA resolution are used in a beam-splitter free holographic set-up to measure amplitude and phase objects in transmission. Phase maps of the diffraction pattern are retrieved using the Fourier transform carrier fringe method; while a Fresnel-Kirchhoff back propagation algorithm is used to reconstruct the complex object image. A lateral resolution of 280 µm and a relative phase sensitivity of about 0.5 rad are estimated from reconstructed images of a metallic Siemens star and a polypropylene test structure, respectively. Simulations corroborate the experimental results.

Imaging vibration of the cochlear partition of an excised guinea pig cochlea using phase-sensitive Fourier domain optical coherence tomography

NASA Astrophysics Data System (ADS)

Choudhury, Niloy; Zeng, Yaguang; Fridberger, Anders; Chen, Fangyi; Zha, Dingjun; Nuttall, Alfred L.; Wang, Ruikang K.

2011-03-01

Studying the sound stimulated vibrations of various membranes that form the complex structure of the organ of Corti in the cochlea of the inner ear is essential for understanding how the travelling sound wave of the basilar membrane couples its energy to the organ structures. In this paper we report the feasibility of using phase-sensitive Fourier domain optical coherence tomography (FD-OCT) to image the vibration of various micro-structures of the cochlea at the same time. An excised cochlea of a guinea pig was stimulated using sounds at various frequencies and vibration image was obtained. When measuring the apex area, vibration signal from different turns, which have different best response frequencies are obtained in the same image. The method has the potential to measure the response from a much wider region of the cochlea than any other currently used method. The noise floor for vibration image for the system at 200 Hz was ~0.3nm.

Threshold multi-secret sharing scheme based on phase-shifting interferometry

NASA Astrophysics Data System (ADS)

Deng, Xiaopeng; Wen, Wei; Shi, Zhengang

2017-03-01

A threshold multi-secret sharing scheme is proposed based on phase-shifting interferometry. The K secret images to be shared are firstly encoded by using Fourier transformation, respectively. Then, these encoded images are shared into many shadow images based on recording principle of the phase-shifting interferometry. In the recovering stage, the secret images can be restored by combining any 2 K + 1 or more shadow images, while any 2 K or fewer shadow images cannot obtain any information about the secret images. As a result, a (2 K + 1 , N) threshold multi-secret sharing scheme can be implemented. Simulation results are presented to demonstrate the feasibility of the proposed method.

Absorption Mode FT-ICR Mass Spectrometry Imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Donald F.; Kilgour, David P.; Konijnenburg, Marco

2013-12-03

Fourier transform ion cyclotron resonance mass spectrometry offers the highest mass resolving power for molecular imaging experiments. This high mass resolving power ensures that closely spaced peaks at the same nominal mass are resolved for proper image generation. Typically higher magnetic fields are used to increase mass resolving power. However, a gain in mass resolving power can also be realized by phase correction of the data for absorption mode display. In addition to mass resolving power, absorption mode offers higher mass accuracy and signal-to-noise ratio over the conventional magnitude mode. Here we present the first use of absorption mode formore » Fourier transform ion cyclotron resonance mass spectrometry imaging. The Autophaser algorithm is used to phase correct each spectrum (pixel) in the image and then these parameters are used by the Chameleon work-flow based data processing software to generate absorption mode ?Datacubes? for image and spectral viewing. Absorption mode reveals new mass and spatial features that are not resolved in magnitude mode and results in improved selected ion image contrast.« less

Isotropic scalar image visualization of vector differential image data using the inverse Riesz transform.

PubMed

Larkin, Kieran G; Fletcher, Peter A

2014-03-01

X-ray Talbot moiré interferometers can now simultaneously generate two differential phase images of a specimen. The conventional approach to integrating differential phase is unstable and often leads to images with loss of visible detail. We propose a new reconstruction method based on the inverse Riesz transform. The Riesz approach is stable and the final image retains visibility of high resolution detail without directional bias. The outline Riesz theory is developed and an experimentally acquired X-ray differential phase data set is presented for qualitative visual appraisal. The inverse Riesz phase image is compared with two alternatives: the integrated (quantitative) phase and the modulus of the gradient of the phase. The inverse Riesz transform has the computational advantages of a unitary linear operator, and is implemented directly as a complex multiplication in the Fourier domain also known as the spiral phase transform.

Isotropic scalar image visualization of vector differential image data using the inverse Riesz transform

PubMed Central

Larkin, Kieran G.; Fletcher, Peter A.

2014-01-01

X-ray Talbot moiré interferometers can now simultaneously generate two differential phase images of a specimen. The conventional approach to integrating differential phase is unstable and often leads to images with loss of visible detail. We propose a new reconstruction method based on the inverse Riesz transform. The Riesz approach is stable and the final image retains visibility of high resolution detail without directional bias. The outline Riesz theory is developed and an experimentally acquired X-ray differential phase data set is presented for qualitative visual appraisal. The inverse Riesz phase image is compared with two alternatives: the integrated (quantitative) phase and the modulus of the gradient of the phase. The inverse Riesz transform has the computational advantages of a unitary linear operator, and is implemented directly as a complex multiplication in the Fourier domain also known as the spiral phase transform. PMID:24688823

Multiple template-based image matching using alpha-rooted quaternion phase correlation

NASA Astrophysics Data System (ADS)

DelMarco, Stephen

2010-04-01

In computer vision applications, image matching performed on quality-degraded imagery is difficult due to image content distortion and noise effects. State-of-the art keypoint based matchers, such as SURF and SIFT, work very well on clean imagery. However, performance can degrade significantly in the presence of high noise and clutter levels. Noise and clutter cause the formation of false features which can degrade recognition performance. To address this problem, previously we developed an extension to the classical amplitude and phase correlation forms, which provides improved robustness and tolerance to image geometric misalignments and noise. This extension, called Alpha-Rooted Phase Correlation (ARPC), combines Fourier domain-based alpha-rooting enhancement with classical phase correlation. ARPC provides tunable parameters to control the alpha-rooting enhancement. These parameter values can be optimized to tradeoff between high narrow correlation peaks, and more robust wider, but smaller peaks. Previously, we applied ARPC in the radon transform domain for logo image recognition in the presence of rotational image misalignments. In this paper, we extend ARPC to incorporate quaternion Fourier transforms, thereby creating Alpha-Rooted Quaternion Phase Correlation (ARQPC). We apply ARQPC to the logo image recognition problem. We use ARQPC to perform multiple-reference logo template matching by representing multiple same-class reference templates as quaternion-valued images. We generate recognition performance results on publicly-available logo imagery, and compare recognition results to results generated from standard approaches. We show that small deviations in reference templates of sameclass logos can lead to improved recognition performance using the joint matching inherent in ARQPC.

Digital Model of Fourier and Fresnel Quantized Holograms

NASA Astrophysics Data System (ADS)

Boriskevich, Anatoly A.; Erokhovets, Valery K.; Tkachenko, Vadim V.

Some models schemes of Fourier and Fresnel quantized protective holograms with visual effects are suggested. The condition to arrive at optimum relationship between the quality of reconstructed images, and the coefficient of data reduction about a hologram, and quantity of iterations in the reconstructing hologram process has been estimated through computer model. Higher protection level is achieved by means of greater number both bi-dimensional secret keys (more than 2128) in form of pseudorandom amplitude and phase encoding matrixes, and one-dimensional encoding key parameters for every image of single-layer or superimposed holograms.

Discrete Fourier Transform in a Complex Vector Space

NASA Technical Reports Server (NTRS)

Dean, Bruce H. (Inventor)

2015-01-01

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

Spatial Specificity in Spatiotemporal Encoding and Fourier Imaging

PubMed Central

Goerke, Ute

2015-01-01

Purpose Ultrafast imaging techniques based on spatiotemporal-encoding (SPEN), such as RASER (rapid acquisition with sequential excitation and refocusing), is a promising new class of sequences since they are largely insensitive to magnetic field variations which cause signal loss and geometric distortion in EPI. So far, attempts to theoretically describe the point-spread-function (PSF) for the original SPEN-imaging techniques have yielded limited success. To fill this gap a novel definition for an apparent PSF is proposed. Theory Spatial resolution in SPEN-imaging is determined by the spatial phase dispersion imprinted on the acquired signal by a frequency-swept excitation or refocusing pulse. The resulting signal attenuation increases with larger distance from the vertex of the quadratic phase profile. Methods Bloch simulations and experiments were performed to validate theoretical derivations. Results The apparent PSF quantifies the fractional contribution of magnetization to a voxel’s signal as a function of distance to the voxel. In contrast, the conventional PSF represents the signal intensity at various locations. Conclusion The definition of the conventional PSF fails for SPEN-imaging since only the phase of isochromats, but not the amplitude of the signal varies. The concept of the apparent PSF is shown to be generalizable to conventional Fourier- imaging techniques. PMID:26712657

Threshold secret sharing scheme based on phase-shifting interferometry.

PubMed

Deng, Xiaopeng; Shi, Zhengang; Wen, Wei

2016-11-01

We propose a new method for secret image sharing with the (3,N) threshold scheme based on phase-shifting interferometry. The secret image, which is multiplied with an encryption key in advance, is first encrypted by using Fourier transformation. Then, the encoded image is shared into N shadow images based on the recording principle of phase-shifting interferometry. Based on the reconstruction principle of phase-shifting interferometry, any three or more shadow images can retrieve the secret image, while any two or fewer shadow images cannot obtain any information of the secret image. Thus, a (3,N) threshold secret sharing scheme can be implemented. Compared with our previously reported method, the algorithm of this paper is suited for not only a binary image but also a gray-scale image. Moreover, the proposed algorithm can obtain a larger threshold value t. Simulation results are presented to demonstrate the feasibility of the proposed method.

A new phase encoding approach for a compact head-up display

NASA Astrophysics Data System (ADS)

Suszek, Jaroslaw; Makowski, Michal; Sypek, Maciej; Siemion, Andrzej; Kolodziejczyk, Andrzej; Bartosz, Andrzej

2008-12-01

The possibility of encoding multiple asymmetric symbols into a single thin binary Fourier hologram would have a practical application in the design of simple translucent holographic head-up displays. A Fourier hologram displays the encoded images at the infinity so this enables an observation without a time-consuming eye accommodation. Presenting a set of the most crucial signs for a driver in this way is desired, especially by older people with various eyesight disabilities. In this paper a method of holographic design is presented that assumes a combination of a spatial segmentation and carrier frequencies. It allows to achieve multiple reconstructed images selectable by the angle of the incident laser beam. In order to encode several binary symbols into a single Fourier hologram, the chessboard shaped segmentation function is used. An optimized sequence of phase encoding steps and a final direct phase binarization enables recording of asymmetric symbols into a binary hologram. The theoretical analysis is presented, verified numerically and confirmed in the optical experiment. We suggest and describe a practical and highly useful application of such holograms in an inexpensive HUD device for the use of the automotive industry. We present two alternative propositions of car viewing setups.

Simultaneous two-wavelength tri-window common-path digital holography

NASA Astrophysics Data System (ADS)

Liu, Lei; Shan, Mingguang; Zhong, Zhi

2018-06-01

Two-wavelength common-path off-axis digital holography is proposed with a tri-window in a single shot. It is established using a standard 4f optical image system with a 2D Ronchi grating placed outside the Fourier plane. The input plane consists of three windows: one for the object and the other two for reference. Aided by a spatial filter together with two orthogonal linear polarizers in the Fourier plane, the two-wavelength information is encoded into a multiplexed hologram with two orthogonal spatial frequencies that enable full separation of spectral information in the digital Fourier space without resolution loss. Theoretical analysis and experimental results illustrate that our approach can simultaneously perform quantitative phase imaging at two wavelengths.

Diffractive shear interferometry for extreme ultraviolet high-resolution lensless imaging

NASA Astrophysics Data System (ADS)

Jansen, G. S. M.; de Beurs, A.; Liu, X.; Eikema, K. S. E.; Witte, S.

2018-05-01

We demonstrate a novel imaging approach and associated reconstruction algorithm for far-field coherent diffractive imaging, based on the measurement of a pair of laterally sheared diffraction patterns. The differential phase profile retrieved from such a measurement leads to improved reconstruction accuracy, increased robustness against noise, and faster convergence compared to traditional coherent diffractive imaging methods. We measure laterally sheared diffraction patterns using Fourier-transform spectroscopy with two phase-locked pulse pairs from a high harmonic source. Using this approach, we demonstrate spectrally resolved imaging at extreme ultraviolet wavelengths between 28 and 35 nm.

Wave field restoration using three-dimensional Fourier filtering method.

PubMed

Kawasaki, T; Takai, Y; Ikuta, T; Shimizu, R

2001-11-01

A wave field restoration method in transmission electron microscopy (TEM) was mathematically derived based on a three-dimensional (3D) image formation theory. Wave field restoration using this method together with spherical aberration correction was experimentally confirmed in through-focus images of amorphous tungsten thin film, and the resolution of the reconstructed phase image was successfully improved from the Scherzer resolution limit to the information limit. In an application of this method to a crystalline sample, the surface structure of Au(110) was observed in a profile-imaging mode. The processed phase image showed quantitatively the atomic relaxation of the topmost layer.

Fourier transform digital holographic adaptive optics imaging system

PubMed Central

Liu, Changgeng; Yu, Xiao; Kim, Myung K.

2013-01-01

A Fourier transform digital holographic adaptive optics imaging system and its basic principles are proposed. The CCD is put at the exact Fourier transform plane of the pupil of the eye lens. The spherical curvature introduced by the optics except the eye lens itself is eliminated. The CCD is also at image plane of the target. The point-spread function of the system is directly recorded, making it easier to determine the correct guide-star hologram. Also, the light signal will be stronger at the CCD, especially for phase-aberration sensing. Numerical propagation is avoided. The sensor aperture has nothing to do with the resolution and the possibility of using low coherence or incoherent illumination is opened. The system becomes more efficient and flexible. Although it is intended for ophthalmic use, it also shows potential application in microscopy. The robustness and feasibility of this compact system are demonstrated by simulations and experiments using scattering objects. PMID:23262541

Calibration of the Geostationary Imaging Fourier Transform Spectrometer (GIFTS)

NASA Technical Reports Server (NTRS)

Best, F. A.; Revercomb, H. E.; Bingham, G. E.; Knuteson, R. O.; Tobin, D. C.; LaPorte, D. D.; Smith, W. L.

2001-01-01

The NASA New Millennium Program's Geostationary Imaging Fourier Transform Spectrometer (GIFTS) requires highly accurate radiometric and spectral calibration in order to carry out its mission to provide water vapor, wind, temperature, and trace gas profiling from geostationary orbit. A calibration concept has been developed for the GIFTS Phase A instrument design. The in-flight calibration is performed using views of two on-board blackbody sources along with cold space. A radiometric calibration uncertainty analysis has been developed and used to show that the expected performance for GIFTS exceeds its top level requirement to measure brightness temperature to better than 1 K. For the Phase A GIFTS design, the spectral calibration is established by the highly stable diode laser used as the reference for interferogram sampling, and verified with comparisons to atmospheric calculations.

Image encryption based on fractal-structured phase mask in fractional Fourier transform domain

NASA Astrophysics Data System (ADS)

Zhao, Meng-Dan; Gao, Xu-Zhen; Pan, Yue; Zhang, Guan-Lin; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

2018-04-01

We present an optical encryption approach based on the combination of fractal Fresnel lens (FFL) and fractional Fourier transform (FrFT). Our encryption approach is in fact a four-fold encryption scheme, including the random phase encoding produced by the Gerchberg–Saxton algorithm, a FFL, and two FrFTs. A FFL is composed of a Sierpinski carpet fractal plate and a Fresnel zone plate. In our encryption approach, the security is enhanced due to the more expandable key spaces and the use of FFL overcomes the alignment problem of the optical axis in optical system. Only using the perfectly matched parameters of the FFL and the FrFT, the plaintext can be recovered well. We present an image encryption algorithm that from the ciphertext we can get two original images by the FrFT with two different phase distribution keys, obtained by performing 100 iterations between the two plaintext and ciphertext, respectively. We test the sensitivity of our approach to various parameters such as the wavelength of light, the focal length of FFL, and the fractional orders of FrFT. Our approach can resist various attacks.

Image Reconstruction from Data Collected with an Imaging Interferometer

NASA Astrophysics Data System (ADS)

DeSantis, Z. J.; Thurman, S. T.; Hix, T. T.; Ogden, C. E.

The intensity distribution of an incoherent source and the spatial coherence function at some distance away are related by a Fourier transform, via the Van Cittert-Zernike theorem. Imaging interferometers measure the spatial coherence of light propagated from the incoherently illuminated object by combining light from spatially separated points to measure interference fringes. The contrast and phase of the fringe are the amplitude and phase of a Fourier component of the source’s intensity distribution. The Fiber-Coupled Interferometer (FCI) testbed is a visible light, lab-based imaging interferometer designed to test aspects of an envisioned ground-based interferometer for imaging geosynchronous satellites. The front half of the FCI testbed consists of the scene projection optics, which includes an incoherently backlit scene, located at the focus of a 1 m aperture f/100 telescope. The projected light was collected by the back half of the FCI testbed. The collection optics consisted of three 11 mm aperture fiber-coupled telescopes. Light in the fibers was combined pairwise and dispersed onto a sensor to measure the interference fringe as a function of wavelength, which produces a radial spoke of measurements in the Fourier domain. The visibility function was sampled throughout the Fourier domain by recording fringe data at many different scene rotations and collection telescope separations. Our image reconstruction algorithm successfully produced images for the three scenes we tested: asymmetric pair of pinholes, U.S. Air Force resolution bar target, and satellite scene. The bar target reconstruction shows detail and resolution near the predicted resolution limit. This research was developed with funding from the Defense Advanced Research Projects Agency (DARPA). The views, opinions and/or findings expressed are those of the author(s) and should not be interpreted as reflecting the official views or policies of the Department of Defense or the U.S. Government.

Comparison of different phase retrieval algorithms

NASA Astrophysics Data System (ADS)

Kaufmann, Rolf; Plamondon, Mathieu; Hofmann, Jürgen; Neels, Antonia

2017-09-01

X-ray phase contrast imaging is attracting more and more interest. Since the phase cannot be measured directly an indirect method using e.g. a grating interferometer has to be applied. This contribution compares three different approaches to calculate the phase from Talbot-Lau interferometer measurements using a phase-stepping approach. Besides the usually applied Fourier coefficient method also a linear fitting technique and Taylor series expansion method are applied and compared.

Multiple image encryption scheme based on pixel exchange operation and vector decomposition

NASA Astrophysics Data System (ADS)

Xiong, Y.; Quan, C.; Tay, C. J.

2018-02-01

We propose a new multiple image encryption scheme based on a pixel exchange operation and a basic vector decomposition in Fourier domain. In this algorithm, original images are imported via a pixel exchange operator, from which scrambled images and pixel position matrices are obtained. Scrambled images encrypted into phase information are imported using the proposed algorithm and phase keys are obtained from the difference between scrambled images and synthesized vectors in a charge-coupled device (CCD) plane. The final synthesized vector is used as an input in a random phase encoding (DRPE) scheme. In the proposed encryption scheme, pixel position matrices and phase keys serve as additional private keys to enhance the security of the cryptosystem which is based on a 4-f system. Numerical simulations are presented to demonstrate the feasibility and robustness of the proposed encryption scheme.

Moire measuring technology for three-dimensional profile of the object

NASA Astrophysics Data System (ADS)

Fu, Yanjun; Yang, Kuntao

2006-02-01

An optical system is designed to get projection of the transmission grating, the deformed grating is obtained on surface of the object. The image of the deformed grating is given by the lens, the reference grating is put on the place of the image, and then the moire fringe is obtained. The amplify principle of the moire fringe is used to measure the profile of the object. The optical principle of the projection is analyzed. And the relation between the phase and the height of object is deduced. From the different point of geometry optics and the physics opticsl, the optical system is analyzed, the factors that influence the image equality and the measuring result are obtained. So the betterment of improving the measuring precision is brought forward, and in the later information processing, because of the diffuse reflection, the image equality is not very well. In order to get a good image, the digital filter is used to filter the noise and smooth the image firstly. Then in order to improve the measure precision, the subdivision technology is applied. The Fourier transform profilometry and phase shifting technology is used in the calculation. A detail analyses is done both in time field and frequency field. And the method of improving the measuring precision is put forward. A good digital filter algorithm is brought forward in the Fourier transform profilometry. In the phase shifting technology, the detail formula of three-step and four-step is given. At last the phase that is relational with the high information of the object is get, but the phase is disconnected phase, after the unwrapping algorithm,the disconnected phase is changed to be the continuous phase. Taking use of the relation between the phase and height, the height is obtained. Then the three-dimensional profile of the measured object can be reconstructed. The system is very convenient for non-contact measure of profile of some objects.

Quantitative phase imaging of living cells with a swept laser source

NASA Astrophysics Data System (ADS)

Chen, Shichao; Zhu, Yizheng

2016-03-01

Digital holographic phase microscopy is a well-established quantitative phase imaging technique. However, interference artifacts from inside the system, typically induced by elements whose optical thickness are within the source coherence length, limit the imaging quality as well as sensitivity. In this paper, a swept laser source based technique is presented. Spectra acquired at a number of wavelengths, after Fourier Transform, can be used to identify the sources of the interference artifacts. With proper tuning of the optical pathlength difference between sample and reference arms, it is possible to avoid these artifacts and achieve sensitivity below 0.3nm. Performance of the proposed technique is examined in live cell imaging.

Biological applications of phase-contrast electron microscopy.

PubMed

Nagayama, Kuniaki

2014-01-01

Here, I review the principles and applications of phase-contrast electron microscopy using phase plates. First, I develop the principle of phase contrast based on a minimal model of microscopy, introducing a double Fourier-transform process to mathematically formulate the image formation. Next, I explain four phase-contrast (PC) schemes, defocus PC, Zernike PC, Hilbert differential contrast, and schlieren optics, as image-filtering processes in the context of the minimal model, with particular emphases on the Zernike PC and corresponding Zernike phase plates. Finally, I review applications of Zernike PC cryo-electron microscopy to biological systems such as protein molecules, virus particles, and cells, including single-particle analysis to delineate three-dimensional (3D) structures of protein and virus particles and cryo-electron tomography to reconstruct 3D images of complex protein systems and cells.

Experiments on sparsity assisted phase retrieval of phase objects

NASA Astrophysics Data System (ADS)

Gaur, Charu; Lochab, Priyanka; Khare, Kedar

2017-05-01

Iterative phase retrieval algorithms such as the Gerchberg-Saxton method and the Fienup hybrid input-output method are known to suffer from the twin image stagnation problem, particularly when the solution to be recovered is complex valued and has centrosymmetric support. Recently we showed that the twin image stagnation problem can be addressed using image sparsity ideas (Gaur et al 2015 J. Opt. Soc. Am. A 32 1922). In this work we test this sparsity assisted phase retrieval method with experimental single shot Fourier transform intensity data frames corresponding to phase objects displayed on a spatial light modulator. The standard iterative phase retrieval algorithms are combined with an image sparsity based penalty in an adaptive manner. Illustrations for both binary and continuous phase objects are provided. It is observed that image sparsity constraint has an important role to play in obtaining meaningful phase recovery without encountering the well-known stagnation problems. The results are valuable for enabling single shot coherent diffraction imaging of phase objects for applications involving illumination wavelengths over a wide range of electromagnetic spectrum.

Proposal of AAA-battery-size one-shot ATR Fourier spectroscopic imager for on-site analysis: Simultaneous measurement of multi-components with high accuracy

NASA Astrophysics Data System (ADS)

Hosono, Satsuki; Qi, Wei; Sato, Shun; Suzuki, Yo; Fujiwara, Masaru; Hiramatsu, Hiroyuki; Suzuki, Satoru; Abeygunawardhana, P. K. W.; Wada, Kenji; Nishiyama, Akira; Ishimaru, Ichiro

2015-03-01

For simultaneous measurement of multi-components on-site like factories, the ultra-compact (diameter: 9[mm], length: 45[mm], weight: 200[g]) one-shot ATR (Attenuated Total Reflection) Fourier spectroscopic imager was proposed. Because the proposed one-shot Fourier spectroscopic imaging is based on spatial-phase-shift interferometer, interferograms could be obtained with simple optical configurations. We introduced the transmission-type relativeinclined phase-shifter, that was constructed with a cuboid prism and a wedge prism, onto the optical Fourier transform plane of infinity corrected optical systems. And also, small light-sources and cameras in the mid-infrared light region, whose size are several millimeter on a side, are essential components for the ultra-compact spectroscopic configuration. We selected the Graphite light source (light source area: 1.7×1.7[mm], maker: Hawkeye technologies) whose radiation factor was high. Fortunately, in these days we could apply the cost-effective 2-dimensional light receiving device for smartphone (e.g. product name: LEPTON, maker: FLIR, price: around 400USD). In the case of alcoholic drinks factory, conventionally workers measure glucose and ethanol concentrations by bringing liquid solution back to laboratories every day. The high portable spectroscopy will make it possible to measure multi-components simultaneously on manufacturing scene. But we found experimentally that absorption spectrum of glucose and water and ethanol were overlapped each other in near infrared light region. But for mid-infrared light region, we could distinguish specific absorption peaks of glucose (@10.5[μm]) and ethanol (@11.5[μm]) independently from water absorption. We obtained standard curve between absorption (@9.6[μm]) and ethanol concentration with high correlation coefficient 0.98 successfully by ATR imaging-type 2-dimensional Fourier spectroscopy (wavelength resolution: 0.057[μm]) with the graphite light source (maker: Hawkeye technologies, type: IR-75).

Score-Level Fusion of Phase-Based and Feature-Based Fingerprint Matching Algorithms

NASA Astrophysics Data System (ADS)

Ito, Koichi; Morita, Ayumi; Aoki, Takafumi; Nakajima, Hiroshi; Kobayashi, Koji; Higuchi, Tatsuo

This paper proposes an efficient fingerprint recognition algorithm combining phase-based image matching and feature-based matching. In our previous work, we have already proposed an efficient fingerprint recognition algorithm using Phase-Only Correlation (POC), and developed commercial fingerprint verification units for access control applications. The use of Fourier phase information of fingerprint images makes it possible to achieve robust recognition for weakly impressed, low-quality fingerprint images. This paper presents an idea of improving the performance of POC-based fingerprint matching by combining it with feature-based matching, where feature-based matching is introduced in order to improve recognition efficiency for images with nonlinear distortion. Experimental evaluation using two different types of fingerprint image databases demonstrates efficient recognition performance of the combination of the POC-based algorithm and the feature-based algorithm.

Orbital angular momentum light in microscopy

PubMed Central

2017-01-01

Light with a helical phase has had an impact on optical imaging, pushing the limits of resolution or sensitivity. Here, special emphasis will be given to classical light microscopy of phase samples and to Fourier filtering techniques with a helical phase profile, such as the spiral phase contrast technique in its many variants and areas of application. This article is part of the themed issue ‘Optical orbital angular momentum’. PMID:28069768

Overlapped Fourier coding for optical aberration removal

PubMed Central

Horstmeyer, Roarke; Ou, Xiaoze; Chung, Jaebum; Zheng, Guoan; Yang, Changhuei

2014-01-01

We present an imaging procedure that simultaneously optimizes a camera’s resolution and retrieves a sample’s phase over a sequence of snapshots. The technique, termed overlapped Fourier coding (OFC), first digitally pans a small aperture across a camera’s pupil plane with a spatial light modulator. At each aperture location, a unique image is acquired. The OFC algorithm then fuses these low-resolution images into a full-resolution estimate of the complex optical field incident upon the detector. Simultaneously, the algorithm utilizes redundancies within the acquired dataset to computationally estimate and remove unknown optical aberrations and system misalignments via simulated annealing. The result is an imaging system that can computationally overcome its optical imperfections to offer enhanced resolution, at the expense of taking multiple snapshots over time. PMID:25321982

Digital double random amplitude image encryption method based on the symmetry property of the parametric discrete Fourier transform

NASA Astrophysics Data System (ADS)

Bekkouche, Toufik; Bouguezel, Saad

2018-03-01

We propose a real-to-real image encryption method. It is a double random amplitude encryption method based on the parametric discrete Fourier transform coupled with chaotic maps to perform the scrambling. The main idea behind this method is the introduction of a complex-to-real conversion by exploiting the inherent symmetry property of the transform in the case of real-valued sequences. This conversion allows the encrypted image to be real-valued instead of being a complex-valued image as in all existing double random phase encryption methods. The advantage is to store or transmit only one image instead of two images (real and imaginary parts). Computer simulation results and comparisons with the existing double random amplitude encryption methods are provided for peak signal-to-noise ratio, correlation coefficient, histogram analysis, and key sensitivity.

Imaging photonic crystals using hemispherical digital condensers and phase-recovery techniques.

PubMed

Alotaibi, Maged; Skinner-Ramos, Sueli; Farooq, Hira; Alharbi, Nouf; Alghasham, Hawra; de Peralta, Luis Grave

2018-05-10

We describe experiments where Fourier ptychographic microscopy (FPM) and dual-space microscopy (DSM) are implemented for imaging photonic crystals using a hemispherical digital condenser (HDC). Phase-recovery imaging simulations show that both techniques should be able to image photonic crystals with a period below the Rayleigh resolution limit. However, after processing the experimental images using both phase-recovery algorithms, we found that DSM can, but FPM cannot, image periodic structures with a period below the diffraction limit. We studied the origin of this apparent contradiction between simulations and experiments, and we concluded that the occurrence of unwanted reflections in the HDC is the source of the apparent failure of FPM. We thereafter solved the problem of reflections by using a single-directional illumination source and showed that FPM can image photonic crystals with a period below the Rayleigh resolution limit.

Genetic Algorithm Phase Retrieval for the Systematic Image-Based Optical Alignment Testbed

NASA Technical Reports Server (NTRS)

Taylor, Jaime; Rakoczy, John; Steincamp, James

2003-01-01

Phase retrieval requires calculation of the real-valued phase of the pupil fimction from the image intensity distribution and characteristics of an optical system. Genetic 'algorithms were used to solve two one-dimensional phase retrieval problem. A GA successfully estimated the coefficients of a polynomial expansion of the phase when the number of coefficients was correctly specified. A GA also successfully estimated the multiple p h e s of a segmented optical system analogous to the seven-mirror Systematic Image-Based Optical Alignment (SIBOA) testbed located at NASA s Marshall Space Flight Center. The SIBOA testbed was developed to investigate phase retrieval techniques. Tiphilt and piston motions of the mirrors accomplish phase corrections. A constant phase over each mirror can be achieved by an independent tip/tilt correction: the phase Conection term can then be factored out of the Discrete Fourier Tranform (DFT), greatly reducing computations.

Iterative pixelwise approach applied to computer-generated holograms and diffractive optical elements.

PubMed

Hsu, Wei-Feng; Lin, Shih-Chih

2018-01-01

This paper presents a novel approach to optimizing the design of phase-only computer-generated holograms (CGH) for the creation of binary images in an optical Fourier transform system. Optimization begins by selecting an image pixel with a temporal change in amplitude. The modulated image function undergoes an inverse Fourier transform followed by the imposition of a CGH constraint and the Fourier transform to yield an image function associated with the change in amplitude of the selected pixel. In iterations where the quality of the image is improved, that image function is adopted as the input for the next iteration. In cases where the image quality is not improved, the image function before the pixel changed is used as the input. Thus, the proposed approach is referred to as the pixelwise hybrid input-output (PHIO) algorithm. The PHIO algorithm was shown to achieve image quality far exceeding that of the Gerchberg-Saxton (GS) algorithm. The benefits were particularly evident when the PHIO algorithm was equipped with a dynamic range of image intensities equivalent to the amplitude freedom of the image signal. The signal variation of images reconstructed from the GS algorithm was 1.0223, but only 0.2537 when using PHIO, i.e., a 75% improvement. Nonetheless, the proposed scheme resulted in a 10% degradation in diffraction efficiency and signal-to-noise ratio.

Symmetric Phase-Only Filtering in Particle-Image Velocimetry

NASA Technical Reports Server (NTRS)

Wemet, Mark P.

2008-01-01

Symmetrical phase-only filtering (SPOF) can be exploited to obtain substantial improvements in the results of data processing in particle-image velocimetry (PIV). In comparison with traditional PIV data processing, SPOF PIV data processing yields narrower and larger amplitude correlation peaks, thereby providing more-accurate velocity estimates. The higher signal-to-noise ratios associated with the higher amplitude correlation peaks afford greater robustness and reliability of processing. SPOF also affords superior performance in the presence of surface flare light and/or background light. SPOF algorithms can readily be incorporated into pre-existing algorithms used to process digitized image data in PIV, without significantly increasing processing times. A summary of PIV and traditional PIV data processing is prerequisite to a meaningful description of SPOF PIV processing. In PIV, a pulsed laser is used to illuminate a substantially planar region of a flowing fluid in which particles are entrained. An electronic camera records digital images of the particles at two instants of time. The components of velocity of the fluid in the illuminated plane can be obtained by determining the displacements of particles between the two illumination pulses. The objective in PIV data processing is to compute the particle displacements from the digital image data. In traditional PIV data processing, to which the present innovation applies, the two images are divided into a grid of subregions and the displacements determined from cross-correlations between the corresponding sub-regions in the first and second images. The cross-correlation process begins with the calculation of the Fourier transforms (or fast Fourier transforms) of the subregion portions of the images. The Fourier transforms from the corresponding subregions are multiplied, and this product is inverse Fourier transformed, yielding the cross-correlation intensity distribution. The average displacement of the particles across a subregion results in a displacement of the correlation peak from the center of the correlation plane. The velocity is then computed from the displacement of the correlation peak and the time between the recording of the two images. The process as described thus far is performed for all the subregions. The resulting set of velocities in grid cells amounts to a velocity vector map of the flow field recorded on the image plane. In traditional PIV processing, surface flare light and bright background light give rise to a large, broad correlation peak, at the center of the correlation plane, that can overwhelm the true particle- displacement correlation peak. This has made it necessary to resort to tedious image-masking and background-subtraction procedures to recover the relatively small amplitude particle-displacement correlation peak. SPOF is a variant of phase-only filtering (POF), which, in turn, is a variant of matched spatial filtering (MSF). In MSF, one projects a first image (denoted the input image) onto a second image (denoted the filter) as part of a computation to determine how much and what part of the filter is present in the input image. MSF is equivalent to cross-correlation. In POF, the frequency-domain content of the MSF filter is modified to produce a unitamplitude (phase-only) object. POF is implemented by normalizing the Fourier transform of the filter by its magnitude. The advantage of POFs is that they yield correlation peaks that are sharper and have higher signal-to-noise ratios than those obtained through traditional MSF. In the SPOF, these benefits of POF can be extended to PIV data processing. The SPOF yields even better performance than the POF approach, which is uniquely applicable to PIV type image data. In SPOF as now applied to PIV data processing, a subregion of the first image is treated as the input image and the corresponding subregion of the second image is treated as the filter. The Fourier transforms from both the firs and second- image subregions are normalized by the square roots of their respective magnitudes. This scheme yields optimal performance because the amounts of normalization applied to the spatial-frequency contents of the input and filter scenes are just enough to enhance their high-spatial-frequency contents while reducing their spurious low-spatial-frequency content. As a result, in SPOF PIV processing, particle-displacement correlation peaks can readily be detected above spurious background peaks, without need for masking or background subtraction.

Joint transform correlator optical encryption system: Extensions of the recorded encrypted signal and its inverse Fourier transform

NASA Astrophysics Data System (ADS)

Galizzi, Gustavo E.; Cuadrado-Laborde, Christian

2015-10-01

In this work we study the joint transform correlator setup, finding two analytical expressions for the extensions of the joint power spectrum and its inverse Fourier transform. We found that an optimum efficiency is reached, when the bandwidth of the key code is equal to the sum of the bandwidths of the image plus the random phase mask (RPM). The quality of the decryption is also affected by the ratio between the bandwidths of the RPM and the input image, being better as this ratio increases. In addition, the effect on the decrypted image when the detection area is lower than the encrypted signal extension was analyzed. We illustrate these results through several numerical examples.

Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient.

PubMed

Bian, Liheng; Suo, Jinli; Chung, Jaebum; Ou, Xiaoze; Yang, Changhuei; Chen, Feng; Dai, Qionghai

2016-06-10

Fourier ptychographic microscopy (FPM) is a novel computational coherent imaging technique for high space-bandwidth product imaging. Mathematically, Fourier ptychographic (FP) reconstruction can be implemented as a phase retrieval optimization process, in which we only obtain low resolution intensity images corresponding to the sub-bands of the sample's high resolution (HR) spatial spectrum, and aim to retrieve the complex HR spectrum. In real setups, the measurements always suffer from various degenerations such as Gaussian noise, Poisson noise, speckle noise and pupil location error, which would largely degrade the reconstruction. To efficiently address these degenerations, we propose a novel FP reconstruction method under a gradient descent optimization framework in this paper. The technique utilizes Poisson maximum likelihood for better signal modeling, and truncated Wirtinger gradient for effective error removal. Results on both simulated data and real data captured using our laser-illuminated FPM setup show that the proposed method outperforms other state-of-the-art algorithms. Also, we have released our source code for non-commercial use.

An analytical SMASH procedure (ASP) for sensitivity-encoded MRI.

PubMed

Lee, R F; Westgate, C R; Weiss, R G; Bottomley, P A

2000-05-01

The simultaneous acquisition of spatial harmonics (SMASH) method of imaging with detector arrays can reduce the number of phase-encoding steps, and MRI scan time several-fold. The original approach utilized numerical gradient-descent fitting with the coil sensitivity profiles to create a set of composite spatial harmonics to replace the phase-encoding steps. Here, an analytical approach for generating the harmonics is presented. A transform is derived to project the harmonics onto a set of sensitivity profiles. A sequence of Fourier, Hilbert, and inverse Fourier transform is then applied to analytically eliminate spatially dependent phase errors from the different coils while fully preserving the spatial-encoding. By combining the transform and phase correction, the original numerical image reconstruction method can be replaced by an analytical SMASH procedure (ASP). The approach also allows simulation of SMASH imaging, revealing a criterion for the ratio of the detector sensitivity profile width to the detector spacing that produces optimal harmonic generation. When detector geometry is suboptimal, a group of quasi-harmonics arises, which can be corrected and restored to pure harmonics. The simulation also reveals high-order harmonic modulation effects, and a demodulation procedure is presented that enables application of ASP to a large numbers of detectors. The method is demonstrated on a phantom and humans using a standard 4-channel phased-array MRI system. Copyright 2000 Wiley-Liss, Inc.

Phase retrieval with Fourier-weighted projections.

PubMed

Guizar-Sicairos, Manuel; Fienup, James R

2008-03-01

In coherent lensless imaging, the presence of image sidelobes, which arise as a natural consequence of the finite nature of the detector array, was early recognized as a convergence issue for phase retrieval algorithms that rely on an object support constraint. To mitigate the problem of truncated far-field measurement, a controlled analytic continuation by means of an iterative transform algorithm with weighted projections is proposed and tested. This approach avoids the use of sidelobe reduction windows and achieves full-resolution reconstructions.

Algorithms for image recovery calculation in extended single-shot phase-shifting digital holography

NASA Astrophysics Data System (ADS)

Hasegawa, Shin-ya; Hirata, Ryo

2018-04-01

The single-shot phase-shifting method of image recovery using an inclined reference wave has the advantages of reducing the effects of vibration, being capable of operating in real time, and affording low-cost sensing. In this method, relatively low reference angles compared with that in the conventional method using phase shift between three or four pixels has been required. We propose an extended single-shot phase-shifting technique which uses the multiple-step phase-shifting algorithm and the corresponding multiple pixels which are the same as that of the period of an interference fringe. We have verified the theory underlying this recovery method by means of Fourier spectral analysis and its effectiveness by evaluating the visibility of the image using a high-resolution pattern. Finally, we have demonstrated high-contrast image recovery experimentally using a resolution chart. This method can be used in a variety of applications such as color holographic interferometry.

Color image encryption using random transforms, phase retrieval, chaotic maps, and diffusion

NASA Astrophysics Data System (ADS)

Annaby, M. H.; Rushdi, M. A.; Nehary, E. A.

2018-04-01

The recent tremendous proliferation of color imaging applications has been accompanied by growing research in data encryption to secure color images against adversary attacks. While recent color image encryption techniques perform reasonably well, they still exhibit vulnerabilities and deficiencies in terms of statistical security measures due to image data redundancy and inherent weaknesses. This paper proposes two encryption algorithms that largely treat these deficiencies and boost the security strength through novel integration of the random fractional Fourier transforms, phase retrieval algorithms, as well as chaotic scrambling and diffusion. We show through detailed experiments and statistical analysis that the proposed enhancements significantly improve security measures and immunity to attacks.

Coherent diffraction imaging by moving a lens.

PubMed

Shen, Cheng; Tan, Jiubin; Wei, Ce; Liu, Zhengjun

2016-07-25

A moveable lens is used for determining amplitude and phase on the object plane. The extended fractional Fourier transform is introduced to address the single lens imaging. We put forward a fast algorithm for the transform by convolution. Combined with parallel iterative phase retrieval algorithm, it is applied to reconstruct the complex amplitude of the object. Compared with inline holography, the implementation of our method is simple and easy. Without the oversampling operation, the computational load is less. Also the proposed method has a superiority of accuracy over the direct focusing measurement for the imaging of small size objects.

Phase Retrieval Using a Genetic Algorithm on the Systematic Image-Based Optical Alignment Testbed

NASA Technical Reports Server (NTRS)

Taylor, Jaime R.

2003-01-01

NASA s Marshall Space Flight Center s Systematic Image-Based Optical Alignment (SIBOA) Testbed was developed to test phase retrieval algorithms and hardware techniques. Individuals working with the facility developed the idea of implementing phase retrieval by breaking the determination of the tip/tilt of each mirror apart from the piston motion (or translation) of each mirror. Presented in this report is an algorithm that determines the optimal phase correction associated only with the piston motion of the mirrors. A description of the Phase Retrieval problem is first presented. The Systematic Image-Based Optical Alignment (SIBOA) Testbeb is then described. A Discrete Fourier Transform (DFT) is necessary to transfer the incoming wavefront (or estimate of phase error) into the spatial frequency domain to compare it with the image. A method for reducing the DFT to seven scalar/matrix multiplications is presented. A genetic algorithm is then used to search for the phase error. The results of this new algorithm on a test problem are presented.

A PRESTO-SENSE sequence with alternating partial-Fourier encoding for rapid susceptibility-weighted 3D MRI time series.

PubMed

Klarhöfer, Markus; Dilharreguy, Bixente; van Gelderen, Peter; Moonen, Chrit T W

2003-10-01

A 3D sequence for dynamic susceptibility imaging is proposed which combines echo-shifting principles (such as PRESTO), sensitivity encoding (SENSE), and partial-Fourier acquisition. The method uses a moderate SENSE factor of 2 and takes advantage of an alternating partial k-space acquisition in the "slow" phase encode direction allowing an iterative reconstruction using high-resolution phase estimates. Offering an isotropic spatial resolution of 4 x 4 x 4 mm(3), the novel sequence covers the whole brain including parts of the cerebellum in 0.5 sec. Its temporal signal stability is comparable to that of a full-Fourier, full-FOV EPI sequence having the same dynamic scan time but much less brain coverage. Initial functional MRI experiments showed consistent activation in the motor cortex with an average signal change slightly less than that of EPI. Copyright 2003 Wiley-Liss, Inc.

Holographic maps of quasiparticle interference

NASA Astrophysics Data System (ADS)

Dalla Torre, Emanuele G.; He, Yang; Demler, Eugene

2016-11-01

The analysis of Fourier-transformed scanning tunnelling microscopy images with subatomic resolution is a common tool for studying the properties of quasiparticle excitations in strongly correlated materials. Although Fourier amplitudes are generally complex valued, earlier analysis primarily focused on their absolute values. Their complex phases were often deemed random, and thus irrelevant, due to the unknown positions of the impurities in the sample. Here we show how to factor out these random phases by analysing overlaps between Fourier amplitudes that differ by reciprocal lattice vectors. The resulting holographic maps provide important and previously unknown information about the electronic structures. When applied to superconducting cuprates, our method solves a long-standing puzzle of the dichotomy between equivalent wavevectors. We show that d-wave Wannier functions of the conduction band provide a natural explanation for experimental results that were interpreted as evidence for competing unconventional charge modulations. Our work opens a new pathway to identify the nature of electronic states in scanning tunnelling microscopy.

Quantitative x-ray phase imaging at the nanoscale by multilayer Laue lenses

PubMed Central

Yan, Hanfei; Chu, Yong S.; Maser, Jörg; Nazaretski, Evgeny; Kim, Jungdae; Kang, Hyon Chol; Lombardo, Jeffrey J.; Chiu, Wilson K. S.

2013-01-01

For scanning x-ray microscopy, many attempts have been made to image the phase contrast based on a concept of the beam being deflected by a specimen, the so-called differential phase contrast imaging (DPC). Despite the successful demonstration in a number of representative cases at moderate spatial resolutions, these methods suffer from various limitations that preclude applications of DPC for ultra-high spatial resolution imaging, where the emerging wave field from the focusing optic tends to be significantly more complicated. In this work, we propose a highly robust and generic approach based on a Fourier-shift fitting process and demonstrate quantitative phase imaging of a solid oxide fuel cell (SOFC) anode by multilayer Laue lenses (MLLs). The high sensitivity of the phase to structural and compositional variations makes our technique extremely powerful in correlating the electrode performance with its buried nanoscale interfacial structures that may be invisible to the absorption and fluorescence contrasts. PMID:23419650

Iteration and superposition encryption scheme for image sequences based on multi-dimensional keys

NASA Astrophysics Data System (ADS)

Han, Chao; Shen, Yuzhen; Ma, Wenlin

2017-12-01

An iteration and superposition encryption scheme for image sequences based on multi-dimensional keys is proposed for high security, big capacity and low noise information transmission. Multiple images to be encrypted are transformed into phase-only images with the iterative algorithm and then are encrypted by different random phase, respectively. The encrypted phase-only images are performed by inverse Fourier transform, respectively, thus new object functions are generated. The new functions are located in different blocks and padded zero for a sparse distribution, then they propagate to a specific region at different distances by angular spectrum diffraction, respectively and are superposed in order to form a single image. The single image is multiplied with a random phase in the frequency domain and then the phase part of the frequency spectrums is truncated and the amplitude information is reserved. The random phase, propagation distances, truncated phase information in frequency domain are employed as multiple dimensional keys. The iteration processing and sparse distribution greatly reduce the crosstalk among the multiple encryption images. The superposition of image sequences greatly improves the capacity of encrypted information. Several numerical experiments based on a designed optical system demonstrate that the proposed scheme can enhance encrypted information capacity and make image transmission at a highly desired security level.

Phase Tomography Reconstructed by 3D TIE in Hard X-ray Microscope

NASA Astrophysics Data System (ADS)

Yin, Gung-Chian; Chen, Fu-Rong; Pyun, Ahram; Je, Jung Ho; Hwu, Yeukuang; Liang, Keng S.

2007-01-01

X-ray phase tomography and phase imaging are promising ways of investigation on low Z material. A polymer blend of PE/PS sample was used to test the 3D phase retrieval method in the parallel beam illuminated microscope. Because the polymer sample is thick, the phase retardation is quite mixed and the image can not be distinguished when the 2D transport intensity equation (TIE) is applied. In this study, we have provided a different approach for solving the phase in three dimensions for thick sample. Our method involves integration of 3D TIE/Fourier slice theorem for solving thick phase sample. In our experiment, eight sets of de-focal series image data sets were recorded covering the angular range of 0 to 180 degree. Only three set of image cubes were used in 3D TIE equation for solving the phase tomography. The phase contrast of the polymer blend in 3D is obviously enhanced, and the two different groups of polymer blend can be distinguished in the phase tomography.

Image Reconstruction in Radio Astronomy with Non-Coplanar Synthesis Arrays

NASA Astrophysics Data System (ADS)

Goodrick, L.

2015-03-01

Traditional radio astronomy imaging techniques assume that the interferometric array is coplanar, with a small field of view, and that the two-dimensional Fourier relationship between brightness and visibility remains valid, allowing the Fast Fourier Transform to be used. In practice, to acquire more accurate data, the non-coplanar baseline effects need to be incorporated, as small height variations in the array plane introduces the w spatial frequency component. This component adds an additional phase shift to the incoming signals. There are two approaches to account for the non-coplanar baseline effects: either the full three-dimensional brightness and visibility model can be used to reconstruct an image, or the non-coplanar effects can be removed, reducing the three dimensional relationship to that of the two-dimensional one. This thesis describes and implements the w-projection and w-stacking algorithms. The aim of these algorithms is to account for the phase error introduced by non-coplanar synthesis arrays configurations, making the recovered visibilities more true to the actual brightness distribution model. This is done by reducing the 3D visibilities to a 2D visibility model. The algorithms also have the added benefit of wide-field imaging, although w-stacking supports a wider field of view at the cost of more FFT bin support. For w-projection, the w-term is accounted for in the visibility domain by convolving it out of the problem with a convolution kernel, allowing the use of the two-dimensional Fast Fourier Transform. Similarly, the w-Stacking algorithm applies a phase correction in the image domain to image layers to produce an intensity model that accounts for the non-coplanar baseline effects. This project considers the KAT7 array for simulation and analysis of the limitations and advantages of both the algorithms. Additionally, a variant of the Högbom CLEAN algorithm was used which employs contour trimming for extended source emission flagging. The CLEAN algorithm is an iterative two-dimensional deconvolution method that can further improve image fidelity by removing the effects of the point spread function which can obscure source data.

MTF evaluation of in-line phase contrast imaging system

NASA Astrophysics Data System (ADS)

Sun, Xiaoran; Gao, Feng; Zhao, Huijuan; Zhang, Limin; Li, Jiao; Zhou, Zhongxing

2017-02-01

X-ray phase contrast imaging (XPCI) is a novel method that exploits the phase shift for the incident X-ray to form an image. Various XPCI methods have been proposed, among which, in-line phase contrast imaging (IL-PCI) is regarded as one of the most promising clinical methods. The contrast of the interface is enhanced due to the introduction of the boundary fringes in XPCI, thus it is generally used to evaluate the image quality of XPCI. But the contrast is a comprehensive index and it does not reflect the information of image quality in the frequency range. The modulation transfer function (MTF), which is the Fourier transform of the system point spread function, is recognized as the metric to characterize the spatial response of conventional X-ray imaging system. In this work, MTF is introduced into the image quality evaluation of the IL-PCI system. Numerous simulations based on Fresnel - Kirchhoff diffraction theory are performed with varying system settings and the corresponding MTFs were calculated for comparison. The results show that MTF can provide more comprehensive information of image quality comparing to contrast in IL-PCI.

Information security using multiple reference-based optical joint transform correlation and orthogonal code

NASA Astrophysics Data System (ADS)

Nazrul Islam, Mohammed; Karim, Mohammad A.; Vijayan Asari, K.

2013-09-01

Protecting and processing of confidential information, such as personal identification, biometrics, remains a challenging task for further research and development. A new methodology to ensure enhanced security of information in images through the use of encryption and multiplexing is proposed in this paper. We use orthogonal encoding scheme to encode multiple information independently and then combine them together to save storage space and transmission bandwidth. The encoded and multiplexed image is encrypted employing multiple reference-based joint transform correlation. The encryption key is fed into four channels which are relatively phase shifted by different amounts. The input image is introduced to all the channels and then Fourier transformed to obtain joint power spectra (JPS) signals. The resultant JPS signals are again phase-shifted and then combined to form a modified JPS signal which yields the encrypted image after having performed an inverse Fourier transformation. The proposed cryptographic system makes the confidential information absolutely inaccessible to any unauthorized intruder, while allows for the retrieval of the information to the respective authorized recipient without any distortion. The proposed technique is investigated through computer simulations under different practical conditions in order to verify its overall robustness.

Choice of optical system is critical for the security of double random phase encryption systems

NASA Astrophysics Data System (ADS)

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Cassidy, Derek; Zhao, Liang; Ryle, James P.; Healy, John J.; Sheridan, John T.

2017-06-01

The linear canonical transform (LCT) is used in modeling a coherent light-field propagation through first-order optical systems. Recently, a generic optical system, known as the quadratic phase encoding system (QPES), for encrypting a two-dimensional image has been reported. In such systems, two random phase keys and the individual LCT parameters (α,β,γ) serve as secret keys of the cryptosystem. It is important that such encryption systems also satisfy some dynamic security properties. We, therefore, examine such systems using two cryptographic evaluation methods, the avalanche effect and bit independence criterion, which indicate the degree of security of the cryptographic algorithms using QPES. We compared our simulation results with the conventional Fourier and the Fresnel transform-based double random phase encryption (DRPE) systems. The results show that the LCT-based DRPE has an excellent avalanche and bit independence characteristics compared to the conventional Fourier and Fresnel-based encryption systems.

A phase space model of Fourier ptychographic microscopy

PubMed Central

Horstmeyer, Roarke; Yang, Changhuei

2014-01-01

A new computational imaging technique, termed Fourier ptychographic microscopy (FPM), uses a sequence of low-resolution images captured under varied illumination to iteratively converge upon a high-resolution complex sample estimate. Here, we propose a mathematical model of FPM that explicitly connects its operation to conventional ptychography, a common procedure applied to electron and X-ray diffractive imaging. Our mathematical framework demonstrates that under ideal illumination conditions, conventional ptychography and FPM both produce datasets that are mathematically linked by a linear transformation. We hope this finding encourages the future cross-pollination of ideas between two otherwise unconnected experimental imaging procedures. In addition, the coherence state of the illumination source used by each imaging platform is critical to successful operation, yet currently not well understood. We apply our mathematical framework to demonstrate that partial coherence uniquely alters both conventional ptychography’s and FPM’s captured data, but up to a certain threshold can still lead to accurate resolution-enhanced imaging through appropriate computational post-processing. We verify this theoretical finding through simulation and experiment. PMID:24514995

Extremely simple holographic projection of color images

NASA Astrophysics Data System (ADS)

Makowski, Michal; Ducin, Izabela; Kakarenko, Karol; Suszek, Jaroslaw; Kolodziejczyk, Andrzej; Sypek, Maciej

2012-03-01

A very simple scheme of holographic projection is presented with some experimental results showing good quality image projection without any imaging lens. This technique can be regarded as an alternative to classic projection methods. It is based on the reconstruction real images from three phase iterated Fourier holograms. The illumination is performed with three laser beams of primary colors. A divergent wavefront geometry is used to achieve an increased throw angle of the projection, compared to plane wave illumination. Light fibers are used as light guidance in order to keep the setup as simple as possible and to provide point-like sources of high quality divergent wave-fronts at optimized position against the light modulator. Absorbing spectral filters are implemented to multiplex three holograms on a single phase-only spatial light modulator. Hence color mixing occurs without any time-division methods, which cause rainbow effects and color flicker. The zero diffractive order with divergent illumination is practically invisible and speckle field is effectively suppressed with phase optimization and time averaging techniques. The main advantages of the proposed concept are: a very simple and highly miniaturizable configuration; lack of lens; a single LCoS (Liquid Crystal on Silicon) modulator; a strong resistance to imperfections and obstructions of the spatial light modulator like dead pixels, dust, mud, fingerprints etc.; simple calculations based on Fast Fourier Transform (FFT) easily processed in real time mode with GPU (Graphic Programming).

Massively parallel X-ray holography

NASA Astrophysics Data System (ADS)

Marchesini, Stefano; Boutet, Sébastien; Sakdinawat, Anne E.; Bogan, Michael J.; Bajt, Saša; Barty, Anton; Chapman, Henry N.; Frank, Matthias; Hau-Riege, Stefan P.; Szöke, Abraham; Cui, Congwu; Shapiro, David A.; Howells, Malcolm R.; Spence, John C. H.; Shaevitz, Joshua W.; Lee, Joanna Y.; Hajdu, Janos; Seibert, Marvin M.

2008-09-01

Advances in the development of free-electron lasers offer the realistic prospect of nanoscale imaging on the timescale of atomic motions. We identify X-ray Fourier-transform holography as a promising but, so far, inefficient scheme to do this. We show that a uniformly redundant array placed next to the sample, multiplies the efficiency of X-ray Fourier transform holography by more than three orders of magnitude, approaching that of a perfect lens, and provides holographic images with both amplitude- and phase-contrast information. The experiments reported here demonstrate this concept by imaging a nano-fabricated object at a synchrotron source, and a bacterial cell with a soft-X-ray free-electron laser, where illumination by a single 15-fs pulse was successfully used in producing the holographic image. As X-ray lasers move to shorter wavelengths we expect to obtain higher spatial resolution ultrafast movies of transient states of matter.

Robust image registration for multiple exposure high dynamic range image synthesis

NASA Astrophysics Data System (ADS)

Yao, Susu

2011-03-01

Image registration is an important preprocessing technique in high dynamic range (HDR) image synthesis. This paper proposed a robust image registration method for aligning a group of low dynamic range images (LDR) that are captured with different exposure times. Illumination change and photometric distortion between two images would result in inaccurate registration. We propose to transform intensity image data into phase congruency to eliminate the effect of the changes in image brightness and use phase cross correlation in the Fourier transform domain to perform image registration. Considering the presence of non-overlapped regions due to photometric distortion, evolutionary programming is applied to search for the accurate translation parameters so that the accuracy of registration is able to be achieved at a hundredth of a pixel level. The proposed algorithm works well for under and over-exposed image registration. It has been applied to align LDR images for synthesizing high quality HDR images..

DHMI: dynamic holographic microscopy interface

NASA Astrophysics Data System (ADS)

He, Xuefei; Zheng, Yujie; Lee, Woei Ming

2016-12-01

Digital holographic microscopy (DHM) is a powerful in-vitro biological imaging tool. In this paper, we report a fully automated off-axis digital holographic microscopy system completed with a graphical user interface in the Matlab environment. The interface primarily includes Fourier domain processing, phase reconstruction, aberration compensation and autofocusing. A variety of imaging operations such as region of interest selection, de-noising mode (filtering and averaging), low frame rate imaging for immediate reconstruction and high frame rate imaging routine ( 27 fps) are implemented to facilitate ease of use.

High-speed Fourier ptychographic microscopy based on programmable annular illuminations.

PubMed

Sun, Jiasong; Zuo, Chao; Zhang, Jialin; Fan, Yao; Chen, Qian

2018-05-16

High-throughput quantitative phase imaging (QPI) is essential to cellular phenotypes characterization as it allows high-content cell analysis and avoids adverse effects of staining reagents on cellular viability and cell signaling. Among different approaches, Fourier ptychographic microscopy (FPM) is probably the most promising technique to realize high-throughput QPI by synthesizing a wide-field, high-resolution complex image from multiple angle-variably illuminated, low-resolution images. However, the large dataset requirement in conventional FPM significantly limits its imaging speed, resulting in low temporal throughput. Moreover, the underlying theoretical mechanism as well as optimum illumination scheme for high-accuracy phase imaging in FPM remains unclear. Herein, we report a high-speed FPM technique based on programmable annular illuminations (AIFPM). The optical-transfer-function (OTF) analysis of FPM reveals that the low-frequency phase information can only be correctly recovered if the LEDs are precisely located at the edge of the objective numerical aperture (NA) in the frequency space. By using only 4 low-resolution images corresponding to 4 tilted illuminations matching a 10×, 0.4 NA objective, we present the high-speed imaging results of in vitro Hela cells mitosis and apoptosis at a frame rate of 25 Hz with a full-pitch resolution of 655 nm at a wavelength of 525 nm (effective NA = 0.8) across a wide field-of-view (FOV) of 1.77 mm 2 , corresponding to a space-bandwidth-time product of 411 megapixels per second. Our work reveals an important capability of FPM towards high-speed high-throughput imaging of in vitro live cells, achieving video-rate QPI performance across a wide range of scales, both spatial and temporal.

Real time en face Fourier-domain optical coherence tomography with direct hardware frequency demodulation

PubMed Central

Biedermann, Benjamin R.; Wieser, Wolfgang; Eigenwillig, Christoph M.; Palte, Gesa; Adler, Desmond C.; Srinivasan, Vivek J.; Fujimoto, James G.; Huber, Robert

2009-01-01

We demonstrate en face swept source optical coherence tomography (ss-OCT) without requiring a Fourier transformation step. The electronic optical coherence tomography (OCT) interference signal from a k-space linear Fourier domain mode-locked laser is mixed with an adjustable local oscillator, yielding the analytic reflectance signal from one image depth for each frequency sweep of the laser. Furthermore, a method for arbitrarily shaping the spectral intensity profile of the laser is presented, without requiring the step of numerical apodization. In combination, these two techniques enable sampling of the in-phase and quadrature signal with a slow analog-to-digital converter and allow for real-time display of en face projections even for highest axial scan rates. Image data generated with this technique is compared to en face images extracted from a three-dimensional OCT data set. This technique can allow for real-time visualization of arbitrarily oriented en face planes for the purpose of alignment, registration, or operator-guided survey scans while simultaneously maintaining the full capability of high-speed volumetric ss-OCT functionality. PMID:18978919

Numerical phase retrieval from beam intensity measurements in three planes

NASA Astrophysics Data System (ADS)

Bruel, Laurent

2003-05-01

A system and method have been developed at CEA to retrieve phase information from multiple intensity measurements along a laser beam. The device has been patented. Commonly used devices for beam measurement provide phase and intensity information separately or with a rather poor resolution whereas the MIROMA method provides both at the same time, allowing direct use of the results in numerical models. Usual phase retrieval algorithms use two intensity measurements, typically the image plane and the focal plane (Gerschberg-Saxton algorithm) related by a Fourier transform, or the image plane and a lightly defocus plane (D.L. Misell). The principal drawback of such iterative algorithms is their inability to provide unambiguous convergence in all situations. The algorithms can stagnate on bad solutions and the error between measured and calculated intensities remains unacceptable. If three planes rather than two are used, the data redundancy created confers to the method good convergence capability and noise immunity. It provides an excellent agreement between intensity determined from the retrieved phase data set in the image plane and intensity measurements in any diffraction plane. The method employed for MIROMA is inspired from GS algorithm, replacing Fourier transforms by a beam-propagating kernel with gradient search accelerating techniques and special care for phase branch cuts. A fast one dimensional algorithm provides an initial guess for the iterative algorithm. Applications of the algorithm on synthetic data find out the best reconstruction planes that have to be chosen. Robustness and sensibility are evaluated. Results on collimated and distorted laser beams are presented.

Optical spatial heterodyne interferometric Fourier transform technique (OSHIFT) and a resulting interferometer

NASA Astrophysics Data System (ADS)

Georges, James A., III

2007-09-01

This article reports on the novel patent pending Optical Spatial Heterodyne Interferometric Fourier Transform Technique (the OSHIFT technique), the resulting interferometer also referred to as OSHIFT, and its preliminary results. OSHIFT was borne out of the following requirements: wavefront sensitivity on the order of 1/100 waves, high-frequency wavefront spatial sampling, snapshot 100Hz operation, and the ability to deal with discontinuous wavefronts. The first two capabilities lend themselves to the use of traditional interferometric techniques; however, the last two prove difficult for standard techniques, e.g., phase shifting interferometry tends to take a time sequence of images and most interferometers require estimation of a center fringe across wavefront discontinuities. OSHIFT overcomes these challenges by employing a spatial heterodyning concept in the Fourier (image) plane of the optic-under-test. This concept, the mathematical theory, an autocorrelation view of operation, and the design with results of OSHIFT will be discussed. Also discussed will be future concepts such as a sensor that could interrogate an entire imaging system as well as a methodology to create innovative imaging systems that encode wavefront information onto the image. Certain techniques and systems described in this paper are the subject of a patent application currently pending in the United States Patent Office.

Interleaved diffusion-weighted EPI improved by adaptive partial-Fourier and multi-band multiplexed sensitivity-encoding reconstruction

PubMed Central

Chang, Hing-Chiu; Guhaniyogi, Shayan; Chen, Nan-kuei

2014-01-01

Purpose We report a series of techniques to reliably eliminate artifacts in interleaved echo-planar imaging (EPI) based diffusion weighted imaging (DWI). Methods First, we integrate the previously reported multiplexed sensitivity encoding (MUSE) algorithm with a new adaptive Homodyne partial-Fourier reconstruction algorithm, so that images reconstructed from interleaved partial-Fourier DWI data are free from artifacts even in the presence of either a) motion-induced k-space energy peak displacement, or b) susceptibility field gradient induced fast phase changes. Second, we generalize the previously reported single-band MUSE framework to multi-band MUSE, so that both through-plane and in-plane aliasing artifacts in multi-band multi-shot interleaved DWI data can be effectively eliminated. Results The new adaptive Homodyne-MUSE reconstruction algorithm reliably produces high-quality and high-resolution DWI, eliminating residual artifacts in images reconstructed with previously reported methods. Furthermore, the generalized MUSE algorithm is compatible with multi-band and high-throughput DWI. Conclusion The integration of the multi-band and adaptive Homodyne-MUSE algorithms significantly improves the spatial-resolution, image quality, and scan throughput of interleaved DWI. We expect that the reported reconstruction framework will play an important role in enabling high-resolution DWI for both neuroscience research and clinical uses. PMID:24925000

Dynamic measurements of flowing cells labeled by gold nanoparticles using full-field photothermal interferometric imaging

NASA Astrophysics Data System (ADS)

Turko, Nir A.; Roitshtain, Darina; Blum, Omry; Kemper, Björn; Shaked, Natan T.

2017-06-01

We present highly dynamic photothermal interferometric phase microscopy for quantitative, selective contrast imaging of live cells during flow. Gold nanoparticles can be biofunctionalized to bind to specific cells, and stimulated for local temperature increase due to plasmon resonance, causing a rapid change of the optical phase. These phase changes can be recorded by interferometric phase microscopy and analyzed to form an image of the binding sites of the nanoparticles in the cells, gaining molecular specificity. Since the nanoparticle excitation frequency might overlap with the sample dynamics frequencies, photothermal phase imaging was performed on stationary or slowly dynamic samples. Furthermore, the computational analysis of the photothermal signals is time consuming. This makes photothermal imaging unsuitable for applications requiring dynamic imaging or real-time analysis, such as analyzing and sorting cells during fast flow. To overcome these drawbacks, we utilized an external interferometric module and developed new algorithms, based on discrete Fourier transform variants, enabling fast analysis of photothermal signals in highly dynamic live cells. Due to the self-interference module, the cells are imaged with and without excitation in video-rate, effectively increasing signal-to-noise ratio. Our approach holds potential for using photothermal cell imaging and depletion in flow cytometry.

Optimized phase mask to realize retro-reflection reduction for optical systems

NASA Astrophysics Data System (ADS)

He, Sifeng; Gong, Mali

2017-10-01

Aiming at the threats to the active laser detection systems of electro-optical devices due to the cat-eye effect, a novel solution is put forward to realize retro-reflection reduction in this paper. According to the demands of both cat-eye effect reduction and the image quality maintenance of electro-optical devices, a symmetric phase mask is achieved from a stationary phase method and a fast Fourier transform algorithm. Then, based on a comparison of peak normalized cross-correlation (PNCC) between the different defocus parameters, the optimal imaging position can be obtained. After modification with the designed phase mask, the cat-eye effect peak intensity can be reduced by two orders of magnitude while maintaining good image quality and high modulation transfer function (MTF). Furthermore, a practical design example is introduced to demonstrate the feasibility of our proposed approach.

Fourier removal of stripe artifacts in IRAS images

NASA Technical Reports Server (NTRS)

Van Buren, Dave

1987-01-01

By working in the Fourier plane, approximate removal of stripe artifacts in IRAS images can be effected. The image of interest is smoothed and subtracted from the original, giving the high-spatial-frequency part. This 'filtered' image is then clipped to remove point sources and then Fourier transformed. Subtracting the Fourier components contributing to the stripes in this image from the Fourier transform of the original and transforming back to the image plane yields substantial removal of the stripes.

Experimental geometry for simultaneous beam characterization and sample imaging allowing for pink beam Fourier transform holography or coherent diffractive imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Flewett, Samuel; Eisebitt, Stefan

2011-02-20

One consequence of the self-amplified stimulated emission process used to generate x rays in free electron lasers (FELs) is the intrinsic shot-to-shot variance in the wavelength and temporal coherence. In order to optimize the results from diffractive imaging experiments at FEL sources, it will be advantageous to acquire a means of collecting coherence and spectral information simultaneously with the diffraction pattern from the sample we wish to study. We present a holographic mask geometry, including a grating structure, which can be used to extract both temporal and spatial coherence information alongside the sample scatter from each individual FEL shot andmore » also allows for the real space reconstruction of the sample using either Fourier transform holography or iterative phase retrieval.« less

High resolution imaging and wavefront aberration correction in plenoptic systems.

PubMed

Trujillo-Sevilla, J M; Rodríguez-Ramos, L F; Montilla, I; Rodríguez-Ramos, J M

2014-09-01

Plenoptic imaging systems are becoming more common since they provide capabilities unattainable in conventional imaging systems, but one of their main limitations is the poor bidimensional resolution. Combining the wavefront phase measurement and the plenoptic image deconvolution, we propose a system capable of improving the resolution when a wavefront aberration is present and the image is blurred. In this work, a plenoptic system is simulated using Fourier optics, and the results show that an improved resolution is achieved, even in the presence of strong wavefront aberrations.

Global Data for Ecology and Epidemiology: A Novel Algorithm for Temporal Fourier Processing MODIS Data

PubMed Central

Scharlemann, Jörn P. W.; Benz, David; Hay, Simon I.; Purse, Bethan V.; Tatem, Andrew J.; Wint, G. R. William; Rogers, David J.

2008-01-01

Background Remotely-sensed environmental data from earth-orbiting satellites are increasingly used to model the distribution and abundance of both plant and animal species, especially those of economic or conservation importance. Time series of data from the MODerate-resolution Imaging Spectroradiometer (MODIS) sensors on-board NASA's Terra and Aqua satellites offer the potential to capture environmental thermal and vegetation seasonality, through temporal Fourier analysis, more accurately than was previously possible using the NOAA Advanced Very High Resolution Radiometer (AVHRR) sensor data. MODIS data are composited over 8- or 16-day time intervals that pose unique problems for temporal Fourier analysis. Applying standard techniques to MODIS data can introduce errors of up to 30% in the estimation of the amplitudes and phases of the Fourier harmonics. Methodology/Principal Findings We present a novel spline-based algorithm that overcomes the processing problems of composited MODIS data. The algorithm is tested on artificial data generated using randomly selected values of both amplitudes and phases, and provides an accurate estimate of the input variables under all conditions. The algorithm was then applied to produce layers that capture the seasonality in MODIS data for the period from 2001 to 2005. Conclusions/Significance Global temporal Fourier processed images of 1 km MODIS data for Middle Infrared Reflectance, day- and night-time Land Surface Temperature (LST), Normalised Difference Vegetation Index (NDVI), and Enhanced Vegetation Index (EVI) are presented for ecological and epidemiological applications. The finer spatial and temporal resolution, combined with the greater geolocational and spectral accuracy of the MODIS instruments, compared with previous multi-temporal data sets, mean that these data may be used with greater confidence in species' distribution modelling. PMID:18183289

Global data for ecology and epidemiology: a novel algorithm for temporal Fourier processing MODIS data.

PubMed

Scharlemann, Jörn P W; Benz, David; Hay, Simon I; Purse, Bethan V; Tatem, Andrew J; Wint, G R William; Rogers, David J

2008-01-09

Remotely-sensed environmental data from earth-orbiting satellites are increasingly used to model the distribution and abundance of both plant and animal species, especially those of economic or conservation importance. Time series of data from the MODerate-resolution Imaging Spectroradiometer (MODIS) sensors on-board NASA's Terra and Aqua satellites offer the potential to capture environmental thermal and vegetation seasonality, through temporal Fourier analysis, more accurately than was previously possible using the NOAA Advanced Very High Resolution Radiometer (AVHRR) sensor data. MODIS data are composited over 8- or 16-day time intervals that pose unique problems for temporal Fourier analysis. Applying standard techniques to MODIS data can introduce errors of up to 30% in the estimation of the amplitudes and phases of the Fourier harmonics. We present a novel spline-based algorithm that overcomes the processing problems of composited MODIS data. The algorithm is tested on artificial data generated using randomly selected values of both amplitudes and phases, and provides an accurate estimate of the input variables under all conditions. The algorithm was then applied to produce layers that capture the seasonality in MODIS data for the period from 2001 to 2005. Global temporal Fourier processed images of 1 km MODIS data for Middle Infrared Reflectance, day- and night-time Land Surface Temperature (LST), Normalised Difference Vegetation Index (NDVI), and Enhanced Vegetation Index (EVI) are presented for ecological and epidemiological applications. The finer spatial and temporal resolution, combined with the greater geolocational and spectral accuracy of the MODIS instruments, compared with previous multi-temporal data sets, mean that these data may be used with greater confidence in species' distribution modelling.

Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects.

PubMed

Sidorenko, Pavel; Kfir, Ofer; Shechtman, Yoav; Fleischer, Avner; Eldar, Yonina C; Segev, Mordechai; Cohen, Oren

2015-09-08

Phase-retrieval problems of one-dimensional (1D) signals are known to suffer from ambiguity that hampers their recovery from measurements of their Fourier magnitude, even when their support (a region that confines the signal) is known. Here we demonstrate sparsity-based coherent diffraction imaging of 1D objects using extreme-ultraviolet radiation produced from high harmonic generation. Using sparsity as prior information removes the ambiguity in many cases and enhances the resolution beyond the physical limit of the microscope. Our approach may be used in a variety of problems, such as diagnostics of defects in microelectronic chips. Importantly, this is the first demonstration of sparsity-based 1D phase retrieval from actual experiments, hence it paves the way for greatly improving the performance of Fourier-based measurement systems where 1D signals are inherent, such as diagnostics of ultrashort laser pulses, deciphering the complex time-dependent response functions (for example, time-dependent permittivity and permeability) from spectral measurements and vice versa.

Wide-field Fourier ptychographic microscopy using laser illumination source

PubMed Central

Chung, Jaebum; Lu, Hangwen; Ou, Xiaoze; Zhou, Haojiang; Yang, Changhuei

2016-01-01

Fourier ptychographic (FP) microscopy is a coherent imaging method that can synthesize an image with a higher bandwidth using multiple low-bandwidth images captured at different spatial frequency regions. The method’s demand for multiple images drives the need for a brighter illumination scheme and a high-frame-rate camera for a faster acquisition. We report the use of a guided laser beam as an illumination source for an FP microscope. It uses a mirror array and a 2-dimensional scanning Galvo mirror system to provide a sample with plane-wave illuminations at diverse incidence angles. The use of a laser presents speckles in the image capturing process due to reflections between glass surfaces in the system. They appear as slowly varying background fluctuations in the final reconstructed image. We are able to mitigate these artifacts by including a phase image obtained by differential phase contrast (DPC) deconvolution in the FP algorithm. We use a 1-Watt laser configured to provide a collimated beam with 150 mW of power and beam diameter of 1 cm to allow for the total capturing time of 0.96 seconds for 96 raw FPM input images in our system, with the camera sensor’s frame rate being the bottleneck for speed. We demonstrate a factor of 4 resolution improvement using a 0.1 NA objective lens over the full camera field-of-view of 2.7 mm by 1.5 mm. PMID:27896016

PASSIVELY ESTIMATING INDEX OF REFRACTION FOR SPECULAR REFLECTORS USING POLARIMETRIC HYPERSPECTRAL IMAGING

DTIC Science & Technology

2016-12-22

23 6 Band-averaged radiance image with checkerboard is shown in the upper left. The 2-D Fourier transform of the image is...red is 1) that is multiplied by the Fourier transform of the original image. The inverse Fourier transform is then taken to get the final image with...Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 IFTS Imaging Fourier Transform Spectrometer

Uncomfortable images in art and nature.

PubMed

Fernandez, Dominic; Wilkins, Arnold J

2008-01-01

The ratings of discomfort from a wide variety of images can be predicted from the energy at different spatial scales in the image, as measured by the Fourier amplitude spectrum of the luminance. Whereas comfortable images show the regression of Fourier amplitude against spatial frequency common in natural scenes, uncomfortable images show a regression with disproportionately greater amplitude at spatial frequencies within two octaves of 3 cycles deg(-1). In six studies, the amplitude in this spatial frequency range relative to that elsewhere in the spectrum explains variance in judgments of discomfort from art, from images constructed from filtered noise, and from art in which the phase or amplitude spectra have been altered. Striped patterns with spatial frequency within the above range are known to be uncomfortable and capable of provoking headaches and seizures in susceptible persons. The present findings show for the first time that, even in more complex images, the energy in this spatial-frequency range is associated with aversion. We propose a simple measurement that can predict aversion to those works of art that have reached the national media because of negative public reaction.

Uncomfortable images in art and nature

PubMed Central

Fernandez, Dominic; Wilkins, Arnold J.

2008-01-01

We find that the ratings of discomfort from a wide variety of images can be predicted from the energy at different spatial scales in the image, as measured by the Fourier amplitude spectrum of the luminance. Whereas comfortable images show the regression of Fourier amplitude against spatial frequency common in natural scenes, uncomfortable images show a regression with disproportionately greater amplitude at spatial frequencies within two octaves of 3 cycles per degree. In six studies, the amplitude at this spatial frequency relative to that 3 octaves below explains variance in judgments of discomfort from art, from images constructed from filtered noise and from art in which the phase or amplitude spectra have been altered. Striped patterns with spatial frequency within the above range are known to be uncomfortable and capable of provoking headaches and seizures in susceptible persons. The present findings show for the first time that even in more complex images the energy in this spatial frequency range is associated with aversion. We propose a simple measurement that can predict aversion to those works of art that have reached the national media because of negative public reaction. PMID:18773732

Light field measurement based on the single-lens coherent diffraction imaging

NASA Astrophysics Data System (ADS)

Shen, Cheng; Tan, Jiubin; Liu, Zhengjun

2018-01-01

Plenoptic camera and holography are popular light field measurement techniques. However, the low resolution or the complex apparatus hinders their widespread application. In this paper, we put forward a new light field measurement scheme. The lens is introduced into coherent diffraction imaging to operate an optical transform, extended fractional Fourier transform. Combined with the multi-image phase retrieval algorithm, the scheme is proved to hold several advantages. It gets rid of the support requirement and is much easier to implement while keeping a high resolution by making full use of the detector plane. Also, it is verified that our scheme has a superiority over the direct lens focusing imaging in amplitude measurement accuracy and phase retrieval ability.

Development of Michelson interferometer based spatial phase-shift digital shearography

NASA Astrophysics Data System (ADS)

Xie, Xin

Digital shearography is a non-contact, full field, optical measurement method, which has the capability of directly measuring the gradient of deformation. For high measurement sensitivity, phase evaluation method has to be introduced into digital shearography by phase-shift technique. Catalog by phase-shift method, digital phase-shift shearography can be divided into Temporal Phase-Shift Digital Shearography (TPS-DS) and Spatial Phase-Shift Digital Shearography (SPS-DS). TPS-DS is the most widely used phase-shift shearography system, due to its simple algorithm, easy operation and good phase-map quality. However, the application of TPS-DS is only limited in static/step-by-step loading measurement situation, due to its multi-step shifting process. In order to measure the strain under dynamic/continuous loading situation, a SPS-DS system has to be developed. This dissertation aims to develop a series of Michelson Interferometer based SPS-DS measurement methods to achieve the strain measurement by using only a single pair of speckle pattern images. The Michelson Interferometer based SPS-DS systems utilize special designed optical setup to introduce extra carrier frequency into the laser wavefront. The phase information corresponds to the strain field can be separated on the Fourier domain using a Fourier Transform and can further be evaluated with a Windowed Inverse Fourier Transform. With different optical setups and carrier frequency arrangements, the Michelson Interferometer based SPS-DS method is capable to achieve a variety of measurement tasks using only single pair of speckle pattern images. Catalog by the aimed measurand, these capable measurement tasks can be divided into five categories: 1) measurement of out-of-plane strain field with small shearing amount; 2) measurement of relative out-of-plane deformation field with big shearing amount; 3) simultaneous measurement of relative out-of-plane deformation field and deformation gradient field by using multiple carrier frequencies; 4) simultaneous measurement of two directional strain field using dual measurement channels 5) measurement of pure in-plane strain and pure out-of-plane strain with multiple carrier frequencies. The basic theory, optical path analysis, preliminary studies, results analysis and research plan are shown in detail in this dissertation.

Going through a quantum phase

NASA Technical Reports Server (NTRS)

Shapiro, Jeffrey H.

1992-01-01

Phase measurements on a single-mode radiation field are examined from a system-theoretic viewpoint. Quantum estimation theory is used to establish the primacy of the Susskind-Glogower (SG) phase operator; its phase eigenkets generate the probability operator measure (POM) for maximum likelihood phase estimation. A commuting observables description for the SG-POM on a signal x apparatus state space is derived. It is analogous to the signal-band x image-band formulation for optical heterodyne detection. Because heterodyning realizes the annihilation operator POM, this analogy may help realize the SG-POM. The wave function representation associated with the SG POM is then used to prove the duality between the phase measurement and the number operator measurement, from which a number-phase uncertainty principle is obtained, via Fourier theory, without recourse to linearization. Fourier theory is also employed to establish the principle of number-ket causality, leading to a Paley-Wiener condition that must be satisfied by the phase-measurement probability density function (PDF) for a single-mode field in an arbitrary quantum state. Finally, a two-mode phase measurement is shown to afford phase-conjugate quantum communication at zero error probability with finite average photon number. Application of this construct to interferometric precision measurements is briefly discussed.

Effects of illumination on image reconstruction via Fourier ptychography

NASA Astrophysics Data System (ADS)

Cao, Xinrui; Sinzinger, Stefan

2017-12-01

The Fourier ptychographic microscopy (FPM) technique provides high-resolution images by combining a traditional imaging system, e.g. a microscope or a 4f-imaging system, with a multiplexing illumination system, e.g. an LED array and numerical image processing for enhanced image reconstruction. In order to numerically combine images that are captured under varying illumination angles, an iterative phase-retrieval algorithm is often applied. However, in practice, the performance of the FPM algorithm degrades due to the imperfections of the optical system, the image noise caused by the camera, etc. To eliminate the influence of the aberrations of the imaging system, an embedded pupil function recovery (EPRY)-FPM algorithm has been proposed [Opt. Express 22, 4960-4972 (2014)]. In this paper, we study how the performance of FPM and EPRY-FPM algorithms are affected by imperfections of the illumination system using both numerical simulations and experiments. The investigated imperfections include varying and non-uniform intensities, and wavefront aberrations. Our study shows that the aberrations of the illumination system significantly affect the performance of both FPM and EPRY-FPM algorithms. Hence, in practice, aberrations in the illumination system gain significant influence on the resulting image quality.

Frequency domain phase-shifted confocal microscopy (FDPCM) with array detection

NASA Astrophysics Data System (ADS)

Ge, Baoliang; Huang, Yujia; Fang, Yue; Kuang, Cuifang; Xiu, Peng; Liu, Xu

2017-09-01

We proposed a novel method to reconstruct images taken by array detected confocal microscopy without prior knowledge about its detector distribution. The proposed frequency domain phase-shifted confocal microscopy (FDPCM) shifts the image from each detection channel to its corresponding place by substituting the phase information in Fourier domain. Theoretical analysis shows that our method could approach the resolution nearly twofold of wide-field microscopy. Simulation and experiment results are also shown to verify the applicability and effectiveness of our method. Compared to Airyscan, our method holds the advantage of simplicity and convenience to be applied to array detectors with different structure, which makes FDPCM have great potential in the application of biomedical observation in the future.

Multi-template image matching using alpha-rooted biquaternion phase correlation with application to logo recognition

NASA Astrophysics Data System (ADS)

DelMarco, Stephen

2011-06-01

Hypercomplex approaches are seeing increased application to signal and image processing problems. The use of multicomponent hypercomplex numbers, such as quaternions, enables the simultaneous co-processing of multiple signal or image components. This joint processing capability can provide improved exploitation of the information contained in the data, thereby leading to improved performance in detection and recognition problems. In this paper, we apply hypercomplex processing techniques to the logo image recognition problem. Specifically, we develop an image matcher by generalizing classical phase correlation to the biquaternion case. We further incorporate biquaternion Fourier domain alpha-rooting enhancement to create Alpha-Rooted Biquaternion Phase Correlation (ARBPC). We present the mathematical properties which justify use of ARBPC as an image matcher. We present numerical performance results of a logo verification problem using real-world logo data, demonstrating the performance improvement obtained using the hypercomplex approach. We compare results of the hypercomplex approach to standard multi-template matching approaches.

Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings.

PubMed

Márquez, Andrés; Neipp, Cristian; Beléndez, Augusto; Gallego, Sergi; Ortuño, Manuel; Pascual, Inmaculada

2003-09-01

We demonstrate edge-enhanced imaging produced by volume phase gratings recorded on a polyvinyl alcohol/acrylamide photopolymer. Bragg diffraction, exhibited by volume gratings, modifies the impulse response of the imaging system, facilitating spatial filtering operations with no need for a physical Fourier plane. We demonstrate that Kogelnik's coupled-wave theory can be used to calculate the transfer function for the transmitted and the diffracted orders. The experimental and simulated results agree, and they demonstrate the feasibility of our proposal.

Strategies to improve phase-stability of ultrafast swept source optical coherence tomography for single shot imaging of transient mechanical waves at 16 kHz frame rate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Shaozhen; Wei, Wei; Hsieh, Bao-Yu

We present single-shot phase-sensitive imaging of propagating mechanical waves within tissue, enabled by an ultrafast optical coherence tomography (OCT) system powered by a 1.628 MHz Fourier domain mode-locked (FDML) swept laser source. We propose a practical strategy for phase-sensitive measurement by comparing the phases between adjacent OCT B-scans, where the B-scan contains a number of A-scans equaling an integer number of FDML buffers. With this approach, we show that micro-strain fields can be mapped with ∼3.0 nm sensitivity at ∼16 000 fps. The system's capabilities are demonstrated on porcine cornea by imaging mechanical wave propagation launched by a pulsed UV laser beam, promisingmore » non-contact, real-time, and high-resolution optical coherence elastography.« less

Security analysis of quadratic phase based cryptography

NASA Astrophysics Data System (ADS)

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Healy, John J.; Sheridan, John T.

2016-09-01

The linear canonical transform (LCT) is essential in modeling a coherent light field propagation through first-order optical systems. Recently, a generic optical system, known as a Quadratic Phase Encoding System (QPES), for encrypting a two-dimensional (2D) image has been reported. It has been reported together with two phase keys the individual LCT parameters serve as keys of the cryptosystem. However, it is important that such the encryption systems also satisfies some dynamic security properties. Therefore, in this work, we examine some cryptographic evaluation methods, such as Avalanche Criterion and Bit Independence, which indicates the degree of security of the cryptographic algorithms on QPES. We compare our simulation results with the conventional Fourier and the Fresnel transform based DRPE systems. The results show that the LCT based DRPE has an excellent avalanche and bit independence characteristics than that of using the conventional Fourier and Fresnel based encryption systems.

Improvement of coda phase detectability and reconstruction of global seismic data using frequency-wavenumber methods

NASA Astrophysics Data System (ADS)

Schneider, Simon; Thomas, Christine; Dokht, Ramin M. H.; Gu, Yu Jeffrey; Chen, Yunfeng

2018-02-01

Due to uneven earthquake source and receiver distributions, our abilities to isolate weak signals from interfering phases and reconstruct missing data are fundamental to improving the resolution of seismic imaging techniques. In this study, we introduce a modified frequency-wavenumber (fk) domain based approach using a `Projection Onto Convex Sets' (POCS) algorithm. POCS takes advantage of the sparsity of the dominating energies of phase arrivals in the fk domain, which enables an effective detection and reconstruction of the weak seismic signals. Moreover, our algorithm utilizes the 2-D Fourier transform to perform noise removal, interpolation and weak-phase extraction. To improve the directional resolution of the reconstructed data, we introduce a band-stop 2-D Fourier filter to remove the energy of unwanted, interfering phases in the fk domain, which significantly increases the robustness of the signal of interest. The effectiveness and benefits of this method are clearly demonstrated using both simulated and actual broadband recordings of PP precursors from an array located in Tanzania. When used properly, this method could significantly enhance the resolution of weak crust and mantle seismic phases.

Image reconstruction: an overview for clinicians.

PubMed

Hansen, Michael S; Kellman, Peter

2015-03-01

Image reconstruction plays a critical role in the clinical use of magnetic resonance imaging (MRI). The MRI raw data is not acquired in image space and the role of the image reconstruction process is to transform the acquired raw data into images that can be interpreted clinically. This process involves multiple signal processing steps that each have an impact on the image quality. This review explains the basic terminology used for describing and quantifying image quality in terms of signal-to-noise ratio and point spread function. In this context, several commonly used image reconstruction components are discussed. The image reconstruction components covered include noise prewhitening for phased array data acquisition, interpolation needed to reconstruct square pixels, raw data filtering for reducing Gibbs ringing artifacts, Fourier transforms connecting the raw data with image space, and phased array coil combination. The treatment of phased array coils includes a general explanation of parallel imaging as a coil combination technique. The review is aimed at readers with no signal processing experience and should enable them to understand what role basic image reconstruction steps play in the formation of clinical images and how the resulting image quality is described. © 2014 Wiley Periodicals, Inc.

Specific coil design for SENSE: a six-element cardiac array.

PubMed

Weiger, M; Pruessmann, K P; Leussler, C; Röschmann, P; Boesiger, P

2001-03-01

In sensitivity encoding (SENSE), the effects of inhomogeneous spatial sensitivity of surface coils are utilized for signal localization in addition to common Fourier encoding using magnetic field gradients. Unlike standard Fourier MRI, SENSE images exhibit an inhomogeneous noise distribution, which crucially depends on the geometrical sensitivity relations of the coils used. Thus, for optimum signal-to-noise-ratio (SNR) and noise homogeneity, specialized coil configurations are called for. In this article we study the implications of SENSE imaging for coil layout by means of simulations and imaging experiments in a phantom and in vivo. New, specific design principles are identified. For SENSE imaging, the elements of a coil array should be smaller than for common phased-array imaging. Furthermore, adjacent coil elements should not overlap. Based on the findings of initial investigations, a configuration of six coils was designed and built specifically for cardiac applications. The in vivo evaluation of this array showed a considerable SNR increase in SENSE images, as compared with a conventional array. Magn Reson Med 45:495-504, 2001. Copyright 2001 Wiley-Liss, Inc.

Research on Wide-field Imaging Technologies for Low-frequency Radio Array

NASA Astrophysics Data System (ADS)

Lao, B. Q.; An, T.; Chen, X.; Wu, X. C.; Lu, Y.

2017-09-01

Wide-field imaging of low-frequency radio telescopes are subject to a number of difficult problems. One particularly pernicious problem is the non-coplanar baseline effect. It will lead to distortion of the final image when the phase of w direction called w-term is ignored. The image degradation effects are amplified for telescopes with the wide field of view. This paper summarizes and analyzes several w-term correction methods and their technical principles. Their advantages and disadvantages have been analyzed after comparing their computational cost and computational complexity. We conduct simulations with two of these methods, faceting and w-projection, based on the configuration of the first-phase Square Kilometre Array (SKA) low frequency array. The resulted images are also compared with the two-dimensional Fourier transform method. The results show that image quality and correctness derived from both faceting and w-projection are better than the two-dimensional Fourier transform method in wide-field imaging. The image quality and run time affected by the number of facets and w steps have been evaluated. The results indicate that the number of facets and w steps must be reasonable. Finally, we analyze the effect of data size on the run time of faceting and w-projection. The results show that faceting and w-projection need to be optimized before the massive amounts of data processing. The research of the present paper initiates the analysis of wide-field imaging techniques and their application in the existing and future low-frequency array, and fosters the application and promotion to much broader fields.

High-speed and high-resolution quantitative phase imaging with digital-micromirror device-based illumination (Conference Presentation)

NASA Astrophysics Data System (ADS)

Zhou, Renjie; Jin, Di; Yaqoob, Zahid; So, Peter T. C.

2017-02-01

Due to the large number of available mirrors, the patterning speed, low-cost, and compactness, digital-micromirror devices (DMDs) have been extensively used in biomedical imaging system. Recently, DMDs have been brought to the quantitative phase microscopy (QPM) field to achieve synthetic-aperture imaging and tomographic imaging. Last year, our group demonstrated using DMD for QPM, where the phase-retrieval is based on a recently developed Fourier ptychography algorithm. In our previous system, the illumination angle was varied through coding the aperture plane of the illumination system, which has a low efficiency on utilizing the laser power. In our new DMD-based QPM system, we use the Lee-holograms, which is conjugated to the sample plane, to change the illumination angles for much higher power efficiency. Multiple-angle illumination can also be achieved with this method. With this versatile system, we can achieve FPM-based high-resolution phase imaging with 250 nm lateral resolution using the Rayleigh criteria. Due to the use of a powerful laser, the imaging speed would only be limited by the camera acquisition speed. With a fast camera, we expect to achieve close to 100 fps phase imaging speed that has not been achieved in current FPM imaging systems. By adding reference beam, we also expect to achieve synthetic-aperture imaging while directly measuring the phase of the sample fields. This would reduce the phase-retrieval processing time to allow for real-time imaging applications in the future.

Information verification and encryption based on phase retrieval with sparsity constraints and optical inference

NASA Astrophysics Data System (ADS)

Zhong, Shenlu; Li, Mengjiao; Tang, Xiajie; He, Weiqing; Wang, Xiaogang

2017-01-01

A novel optical information verification and encryption method is proposed based on inference principle and phase retrieval with sparsity constraints. In this method, a target image is encrypted into two phase-only masks (POMs), which comprise sparse phase data used for verification. Both of the two POMs need to be authenticated before being applied for decrypting. The target image can be optically reconstructed when the two authenticated POMs are Fourier transformed and convolved by the correct decryption key, which is also generated in encryption process. No holographic scheme is involved in the proposed optical verification and encryption system and there is also no problem of information disclosure in the two authenticable POMs. Numerical simulation results demonstrate the validity and good performance of this new proposed method.

THz holography in reflection using a high resolution microbolometer array.

PubMed

Zolliker, Peter; Hack, Erwin

2015-05-04

We demonstrate a digital holographic setup for Terahertz imaging of surfaces in reflection. The set-up is based on a high-power continuous wave (CW) THz laser and a high-resolution (640 × 480 pixel) bolometer detector array. Wave propagation to non-parallel planes is used to reconstruct the object surface that is rotated relative to the detector plane. In addition we implement synthetic aperture methods for resolution enhancement and compare Fourier transform phase retrieval to phase stepping methods. A lateral resolution of 200 μm and a relative phase sensitivity of about 0.4 rad corresponding to a depth resolution of 6 μm are estimated from reconstructed images of two specially prepared test targets, respectively. We highlight the use of digital THz holography for surface profilometry as well as its potential for video-rate imaging.

Applications of wavelets in interferometry and artificial vision

NASA Astrophysics Data System (ADS)

Escalona Z., Rafael A.

2001-08-01

In this paper we present a different point of view of phase measurements performed in interferometry, image processing and intelligent vision using Wavelet Transform. In standard and white-light interferometry, the phase function is retrieved by using phase-shifting, Fourier-Transform, cosinus-inversion and other known algorithms. Our novel technique presented here is faster, robust and shows excellent accuracy in phase determinations. Finally, in our second application, fringes are no more generate by some light interaction but result from the observation of adapted strip set patterns directly printed on the target of interest. The moving target is simply observed by a conventional vision system and usual phase computation algorithms are adapted to an image processing by wavelet transform, in order to sense target position and displacements with a high accuracy. In general, we have determined that wavelet transform presents properties of robustness, relative speed of calculus and very high accuracy in phase computations.

Shape Measurement by Means of Phase Retrieval using a Spatial Light Modulator

NASA Astrophysics Data System (ADS)

Agour, Mostafa; Huke, Philipp; Kopylow, Christoph V.; Falldorf, Claas

2010-04-01

We present a novel approach to investigate the shape of a diffusely reflecting technical object. It is based on a combination of a multiple-illumination contouring procedure and phase retrieval from a set of intensity measurements. Special consideration is given to the design of the experimental configuration for phase retrieval and the iterative algorithm to extract the 3D phase map. It is mainly based on a phase-only spatial light modulator (SLM) in the Fourier domain of a 4f-imaging system. The SLM is used to modulate the light incident in the Fourier plane with the transfer function of propagation. Thus, a set of consecutive intensity measurements of the wave field scattered by the investigated object in various propagation states can be realized in a common recording plane. In contrast to already existing methods, no mechanical adjustment is required during the recording process and thus the measuring time is considerably reduced. The method is applied to investigate the shape of micro-objects obtained from a metalforming process. Finally, the experimental results are compared to those provided by a standard interferometric contouring procedure.

Phase-Image Encryption Based on 3D-Lorenz Chaotic System and Double Random Phase Encoding

NASA Astrophysics Data System (ADS)

Sharma, Neha; Saini, Indu; Yadav, AK; Singh, Phool

2017-12-01

In this paper, an encryption scheme for phase-images based on 3D-Lorenz chaotic system in Fourier domain under the 4f optical system is presented. The encryption scheme uses a random amplitude mask in the spatial domain and a random phase mask in the frequency domain. Its inputs are phase-images, which are relatively more secure as compared to the intensity images because of non-linearity. The proposed scheme further derives its strength from the use of 3D-Lorenz transform in the frequency domain. Although the experimental setup for optical realization of the proposed scheme has been provided, the results presented here are based on simulations on MATLAB. It has been validated for grayscale images, and is found to be sensitive to the encryption parameters of the Lorenz system. The attacks analysis shows that the key-space is large enough to resist brute-force attack, and the scheme is also resistant to the noise and occlusion attacks. Statistical analysis and the analysis based on correlation distribution of adjacent pixels have been performed to test the efficacy of the encryption scheme. The results have indicated that the proposed encryption scheme possesses a high level of security.

Imaging through scattering media by Fourier filtering and single-pixel detection

NASA Astrophysics Data System (ADS)

Jauregui-Sánchez, Y.; Clemente, P.; Lancis, J.; Tajahuerce, E.

2018-02-01

We present a novel imaging system that combines the principles of Fourier spatial filtering and single-pixel imaging in order to recover images of an object hidden behind a turbid medium by transillumination. We compare the performance of our single-pixel imaging setup with that of a conventional system. We conclude that the introduction of Fourier gating improves the contrast of images in both cases. Furthermore, we show that the combination of single-pixel imaging and Fourier spatial filtering techniques is particularly well adapted to provide images of objects transmitted through scattering media.

Improvements in low-cost label-free QPI microscope for live cell imaging

NASA Astrophysics Data System (ADS)

Seniya, C.; Towers, C. E.; Towers, D. P.

2017-07-01

This paper reports an improvement in the development of a low-cost QPI microscope offering new capabilities in term of phase measurement accuracy for label-free live samples in the longer term (i.e., hours to days). The spatially separated scattered and non-scattered image light fields are reshaped in the Fourier plane and modulated to form an interference image at a CCD camera. The apertures that enable these two beams to be generated have been optimised by means of laser-cut apertures placed on the mirrors of a Michelson interferometer and has improved the phase measuring and reconstruction capability of the QPI microscope. The microscope was tested with transparent onion cells as an object of interest.

Robust interferometric imaging via prior-less phase recovery: redundant spacing calibration with generalized-closure phases

NASA Astrophysics Data System (ADS)

Kurien, Binoy G.; Ashcom, Jonathan B.; Shah, Vinay N.; Rachlin, Yaron; Tarokh, Vahid

2017-01-01

Atmospheric turbulence presents a fundamental challenge to Fourier phase recovery in optical interferometry. Typical reconstruction algorithms employ Bayesian inference techniques which rely on prior knowledge of the scene under observation. In contrast, redundant spacing calibration (RSC) algorithms employ redundancy in the baselines of the interferometric array to directly expose the contribution of turbulence, thereby enabling phase recovery for targets of arbitrary and unknown complexity. Traditionally RSC algorithms have been applied directly to single-exposure measurements, which are reliable only at high photon flux in general. In scenarios of low photon flux, such as those arising in the observation of dim objects in space, one must instead rely on time-averaged, atmosphere-invariant quantities such as the bispectrum. In this paper, we develop a novel RSC-based algorithm for prior-less phase recovery in which we generalize the bispectrum to higher order atmosphere-invariants (n-spectra) for improved sensitivity. We provide a strategy for selection of a high-signal-to-noise ratio set of n-spectra using the graph-theoretic notion of the minimum cycle basis. We also discuss a key property of this set (wrap-invariance), which then enables reliable application of standard linear estimation techniques to recover the Fourier phases from the 2π-wrapped n-spectra phases. For validation, we analyse the expected shot-noise-limited performance of our algorithm for both pairwise and Fizeau interferometric architectures, and corroborate this analysis with simulation results showing performance near an atmosphere-oracle Cramer-Rao bound. Lastly, we apply techniques from the field of compressed sensing to perform image reconstruction from the estimated complex visibilities.

A new imaging technique on strength and phase of pulsatile tissue-motion in brightness-mode ultrasonogram

NASA Astrophysics Data System (ADS)

Fukuzawa, Masayuki; Yamada, Masayoshi; Nakamori, Nobuyuki; Kitsunezuka, Yoshiki

2007-03-01

A new imaging technique has been developed for observing both strength and phase of pulsatile tissue-motion in a movie of brightness-mode ultrasonogram. The pulsatile tissue-motion is determined by evaluating the heartbeat-frequency component in Fourier transform of a series of pixel value as a function of time at each pixel in a movie of ultrasonogram (640x480pixels/frame, 8bit/pixel, 33ms/frame) taken by a conventional ultrasonograph apparatus (ATL HDI5000). In order to visualize both the strength and the phase of the pulsatile tissue-motion, we propose a pulsatile-phase image that is obtained by superimposition of color gradation proportional to the motion phase on the original ultrasonogram only at which the motion strength exceeds a proper threshold. The pulsatile-phase image obtained from a cranial ultrasonogram of normal neonate clearly reveals that the motion region gives good agreement with the anatomical shape and position of the middle cerebral artery and the corpus callosum. The motion phase is fluctuated with the shape of arteries revealing local obstruction of blood flow. The pulsatile-phase images in the neonates with asphyxia at birth reveal decreases of the motion region and increases of the phase fluctuation due to the weakness and local disturbance of blood flow, which is useful for pediatric diagnosis.

A method of solving tilt illumination for multiple distance phase retrieval

NASA Astrophysics Data System (ADS)

Guo, Cheng; Li, Qiang; Tan, Jiubin; Liu, Shutian; Liu, Zhengjun

2018-07-01

Multiple distance phase retrieval is a technique of using a series of intensity patterns to reconstruct a complex-valued image of object. However, tilt illumination originating from the off-axis displacement of incident light significantly impairs its imaging quality. To eliminate this affection, we use cross-correlation calibration to estimate oblique angle of incident light and a Fourier-based strategy to correct tilted illumination effect. Compared to other methods, binary and biological object are both stably reconstructed in simulation and experiment. This work provides a simple but beneficial method to solve the problem of tilt illumination for lens-free multi-distance system.

Topography of hidden objects using THz digital holography with multi-beam interferences.

PubMed

Valzania, Lorenzo; Zolliker, Peter; Hack, Erwin

2017-05-15

We present a method for the separation of the signal scattered from an object hidden behind a THz-transparent sample in the framework of THz digital holography in reflection. It combines three images of different interference patterns to retrieve the amplitude and phase distribution of the object beam. Comparison of simulated with experimental images obtained from a metallic resolution target behind a Teflon plate demonstrates that the interference patterns can be described in the simple form of three-beam interference. Holographic reconstructions after the application of the method show a considerable improvement compared to standard reconstructions exclusively based on Fourier transform phase retrieval.

Approximating SIR-B response characteristics and estimating wave height and wavelength for ocean imagery

NASA Technical Reports Server (NTRS)

Tilley, David G.

1987-01-01

NASA Space Shuttle Challenger SIR-B ocean scenes are used to derive directional wave spectra for which speckle noise is modeled as a function of Rayleigh random phase coherence downrange and Poisson random amplitude errors inherent in the Doppler measurement of along-track position. A Fourier filter that preserves SIR-B image phase relations is used to correct the stationary and dynamic response characteristics of the remote sensor and scene correlator, as well as to subtract an estimate of the speckle noise component. A two-dimensional map of sea surface elevation is obtained after the filtered image is corrected for both random and deterministic motions.

On the role of spatial phase and phase correlation in vision, illusion, and cognition

PubMed Central

Gladilin, Evgeny; Eils, Roland

2015-01-01

Numerous findings indicate that spatial phase bears an important cognitive information. Distortion of phase affects topology of edge structures and makes images unrecognizable. In turn, appropriately phase-structured patterns give rise to various illusions of virtual image content and apparent motion. Despite a large body of phenomenological evidence not much is known yet about the role of phase information in neural mechanisms of visual perception and cognition. Here, we are concerned with analysis of the role of spatial phase in computational and biological vision, emergence of visual illusions and pattern recognition. We hypothesize that fundamental importance of phase information for invariant retrieval of structural image features and motion detection promoted development of phase-based mechanisms of neural image processing in course of evolution of biological vision. Using an extension of Fourier phase correlation technique, we show that the core functions of visual system such as motion detection and pattern recognition can be facilitated by the same basic mechanism. Our analysis suggests that emergence of visual illusions can be attributed to presence of coherently phase-shifted repetitive patterns as well as the effects of acuity compensation by saccadic eye movements. We speculate that biological vision relies on perceptual mechanisms effectively similar to phase correlation, and predict neural features of visual pattern (dis)similarity that can be used for experimental validation of our hypothesis of “cognition by phase correlation.” PMID:25954190

On the role of spatial phase and phase correlation in vision, illusion, and cognition.

PubMed

Gladilin, Evgeny; Eils, Roland

2015-01-01

Numerous findings indicate that spatial phase bears an important cognitive information. Distortion of phase affects topology of edge structures and makes images unrecognizable. In turn, appropriately phase-structured patterns give rise to various illusions of virtual image content and apparent motion. Despite a large body of phenomenological evidence not much is known yet about the role of phase information in neural mechanisms of visual perception and cognition. Here, we are concerned with analysis of the role of spatial phase in computational and biological vision, emergence of visual illusions and pattern recognition. We hypothesize that fundamental importance of phase information for invariant retrieval of structural image features and motion detection promoted development of phase-based mechanisms of neural image processing in course of evolution of biological vision. Using an extension of Fourier phase correlation technique, we show that the core functions of visual system such as motion detection and pattern recognition can be facilitated by the same basic mechanism. Our analysis suggests that emergence of visual illusions can be attributed to presence of coherently phase-shifted repetitive patterns as well as the effects of acuity compensation by saccadic eye movements. We speculate that biological vision relies on perceptual mechanisms effectively similar to phase correlation, and predict neural features of visual pattern (dis)similarity that can be used for experimental validation of our hypothesis of "cognition by phase correlation."

Detection of physiological noise in resting state fMRI using machine learning.

PubMed

Ash, Tom; Suckling, John; Walter, Martin; Ooi, Cinly; Tempelmann, Claus; Carpenter, Adrian; Williams, Guy

2013-04-01

We present a technique for predicting cardiac and respiratory phase on a time point by time point basis, from fMRI image data. These predictions have utility in attempts to detrend effects of the physiological cycles from fMRI image data. We demonstrate the technique both in the case where it can be trained on a subject's own data, and when it cannot. The prediction scheme uses a multiclass support vector machine algorithm. Predictions are demonstrated to have a close fit to recorded physiological phase, with median Pearson correlation scores between recorded and predicted values of 0.99 for the best case scenario (cardiac cycle trained on a subject's own data) down to 0.83 for the worst case scenario (respiratory predictions trained on group data), as compared to random chance correlation score of 0.70. When predictions were used with RETROICOR--a popular physiological noise removal tool--the effects are compared to using recorded phase values. Using Fourier transforms and seed based correlation analysis, RETROICOR is shown to produce similar effects whether recorded physiological phase values are used, or they are predicted using this technique. This was seen by similar levels of noise reduction noise in the same regions of the Fourier spectra, and changes in seed based correlation scores in similar regions of the brain. This technique has a use in situations where data from direct monitoring of the cardiac and respiratory cycles are incomplete or absent, but researchers still wish to reduce this source of noise in the image data. Copyright © 2011 Wiley Periodicals, Inc.

An optical Fourier transform coprocessor with direct phase determination.

PubMed

Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D

2017-10-20

The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.

Accelerated Slice Encoding for Metal Artifact Correction

PubMed Central

Hargreaves, Brian A.; Chen, Weitian; Lu, Wenmiao; Alley, Marcus T.; Gold, Garry E.; Brau, Anja C. S.; Pauly, John M.; Pauly, Kim Butts

2010-01-01

Purpose To demonstrate accelerated imaging with artifact reduction near metallic implants and different contrast mechanisms. Materials and Methods Slice-encoding for metal artifact correction (SEMAC) is a modified spin echo sequence that uses view-angle tilting and slice-direction phase encoding to correct both in-plane and through-plane artifacts. Standard spin echo trains and short-TI inversion recovery (STIR) allow efficient PD-weighted imaging with optional fat suppression. A completely linear reconstruction allows incorporation of parallel imaging and partial Fourier imaging. The SNR effects of all reconstructions were quantified in one subject. 10 subjects with different metallic implants were scanned using SEMAC protocols, all with scan times below 11 minutes, as well as with standard spin echo methods. Results The SNR using standard acceleration techniques is unaffected by the linear SEMAC reconstruction. In all cases with implants, accelerated SEMAC significantly reduced artifacts compared with standard imaging techniques, with no additional artifacts from acceleration techniques. The use of different contrast mechanisms allowed differentiation of fluid from other structures in several subjects. Conclusion SEMAC imaging can be combined with standard echo-train imaging, parallel imaging, partial-Fourier imaging and inversion recovery techniques to offer flexible image contrast with a dramatic reduction of metal-induced artifacts in scan times under 11 minutes. PMID:20373445

Accelerated slice encoding for metal artifact correction.

PubMed

Hargreaves, Brian A; Chen, Weitian; Lu, Wenmiao; Alley, Marcus T; Gold, Garry E; Brau, Anja C S; Pauly, John M; Pauly, Kim Butts

2010-04-01

To demonstrate accelerated imaging with both artifact reduction and different contrast mechanisms near metallic implants. Slice-encoding for metal artifact correction (SEMAC) is a modified spin echo sequence that uses view-angle tilting and slice-direction phase encoding to correct both in-plane and through-plane artifacts. Standard spin echo trains and short-TI inversion recovery (STIR) allow efficient PD-weighted imaging with optional fat suppression. A completely linear reconstruction allows incorporation of parallel imaging and partial Fourier imaging. The signal-to-noise ratio (SNR) effects of all reconstructions were quantified in one subject. Ten subjects with different metallic implants were scanned using SEMAC protocols, all with scan times below 11 minutes, as well as with standard spin echo methods. The SNR using standard acceleration techniques is unaffected by the linear SEMAC reconstruction. In all cases with implants, accelerated SEMAC significantly reduced artifacts compared with standard imaging techniques, with no additional artifacts from acceleration techniques. The use of different contrast mechanisms allowed differentiation of fluid from other structures in several subjects. SEMAC imaging can be combined with standard echo-train imaging, parallel imaging, partial-Fourier imaging, and inversion recovery techniques to offer flexible image contrast with a dramatic reduction of metal-induced artifacts in scan times under 11 minutes. (c) 2010 Wiley-Liss, Inc.

Structural characterization and gas reactions of small metal particles by high resolution in-situ TEM (Transmission Electron Microscopy) and TED (Transmission Electron Diffraction)

NASA Technical Reports Server (NTRS)

Heinemann, K.

1987-01-01

The detection and size analysis of small metal particles supported on amorphous substrates becomes increasingly difficult when the particle size approaches that of the phase contrast background structures of the support. An approach of digital image analysis, involving Fourier transformation of the original image, filtering, and image reconstruction was studied with respect to the likelihood of unambiguously detecting particles of less than 1 nm diameter on amorphous substrates from a single electron micrograph.

Multi-oriented windowed harmonic phase reconstruction for robust cardiac strain imaging.

PubMed

Cordero-Grande, Lucilio; Royuela-del-Val, Javier; Sanz-Estébanez, Santiago; Martín-Fernández, Marcos; Alberola-López, Carlos

2016-04-01

The purpose of this paper is to develop a method for direct estimation of the cardiac strain tensor by extending the harmonic phase reconstruction on tagged magnetic resonance images to obtain more precise and robust measurements. The extension relies on the reconstruction of the local phase of the image by means of the windowed Fourier transform and the acquisition of an overdetermined set of stripe orientations in order to avoid the phase interferences from structures outside the myocardium and the instabilities arising from the application of a gradient operator. Results have shown that increasing the number of acquired orientations provides a significant improvement in the reproducibility of the strain measurements and that the acquisition of an extended set of orientations also improves the reproducibility when compared with acquiring repeated samples from a smaller set of orientations. Additionally, biases in local phase estimation when using the original harmonic phase formulation are greatly diminished by the one here proposed. The ideas here presented allow the design of new methods for motion sensitive magnetic resonance imaging, which could simultaneously improve the resolution, robustness and accuracy of motion estimates. Copyright © 2015 Elsevier B.V. All rights reserved.

Ultrasonic backscatter imaging by shear-wave-induced echo phase encoding of target locations.

PubMed

McAleavey, Stephen

2011-01-01

We present a novel method for ultrasound backscatter image formation wherein lateral resolution of the target is obtained by using traveling shear waves to encode the lateral position of targets in the phase of the received echo. We demonstrate that the phase modulation as a function of shear wavenumber can be expressed in terms of a Fourier transform of the lateral component of the target echogenicity. The inverse transform, obtained by measurements of the phase modulation over a range of shear wave spatial frequencies, yields the lateral scatterer distribution. Range data are recovered from time of flight as in conventional ultrasound, yielding a B-mode-like image. In contrast to conventional ultrasound imaging, where mechanical or electronic focusing is used and lateral resolution is determined by aperture size and wavelength, we demonstrate that lateral resolution using the proposed method is independent of the properties of the aperture. Lateral resolution of the target is achieved using a stationary, unfocused, single-element transducer. We present simulated images of targets of uniform and non-uniform shear modulus. Compounding for speckle reduction is demonstrated. Finally, we demonstrate image formation with an unfocused transducer in gelatin phantoms of uniform shear modulus.

Application of the windowed-Fourier-transform-based fringe analysis technique for investigating temperature and concentration fields in fluids.

PubMed

Mohanan, Sharika; Srivastava, Atul

2014-04-10

The present work is concerned with the development and application of a novel fringe analysis technique based on the principles of the windowed-Fourier-transform (WFT) for the determination of temperature and concentration fields from interferometric images for a range of heat and mass transfer applications. Based on the extent of the noise level associated with the experimental data, the technique has been coupled with two different phase unwrapping methods: the Itoh algorithm and the quality guided phase unwrapping technique for phase extraction. In order to generate the experimental data, a range of experiments have been carried out which include cooling of a vertical flat plate in free convection conditions, combustion of mono-propellant flames, and growth of organic as well as inorganic crystals from their aqueous solutions. The flat plate and combustion experiments are modeled as heat transfer applications wherein the interest is to determine the whole-field temperature distribution. Aqueous-solution-based crystal growth experiments are performed to simulate the mass transfer phenomena and the interest is to determine the two-dimensional solute concentration field around the growing crystal. A Mach-Zehnder interferometer has been employed to record the path-integrated quantity of interest (temperature and/or concentration) in the form of interferometric images in the experiments. The potential of the WFT method has also been demonstrated on numerically simulated phase data for varying noise levels, and the accuracy in phase extraction have been quantified in terms of the root mean square errors. Three levels of noise, i.e., 0%, 10%, and 20% have been considered. Results of the present study show that the WFT technique allows an accurate extraction of phase values that can subsequently be converted into two-dimensional temperature and/or concentration distribution fields. Moreover, since WFT is a local processing technique, speckle patterns and the inherent noise in the interferometric data do not affect the resultant phase values. Brief comparisons of the accuracy of the WFT with other standard techniques such as conventional Fourier-filtering methods are also presented.

Fast Fourier single-pixel imaging via binary illumination.

PubMed

Zhang, Zibang; Wang, Xueying; Zheng, Guoan; Zhong, Jingang

2017-09-20

Fourier single-pixel imaging (FSI) employs Fourier basis patterns for encoding spatial information and is capable of reconstructing high-quality two-dimensional and three-dimensional images. Fourier-domain sparsity in natural scenes allows FSI to recover sharp images from undersampled data. The original FSI demonstration, however, requires grayscale Fourier basis patterns for illumination. This requirement imposes a limitation on the imaging speed as digital micro-mirror devices (DMDs) generate grayscale patterns at a low refreshing rate. In this paper, we report a new strategy to increase the speed of FSI by two orders of magnitude. In this strategy, we binarize the Fourier basis patterns based on upsampling and error diffusion dithering. We demonstrate a 20,000 Hz projection rate using a DMD and capture 256-by-256-pixel dynamic scenes at a speed of 10 frames per second. The reported technique substantially accelerates image acquisition speed of FSI. It may find broad imaging applications at wavebands that are not accessible using conventional two-dimensional image sensors.

Rotational-translational fourier imaging system

NASA Technical Reports Server (NTRS)

Campbell, Jonathan W. (Inventor)

2004-01-01

This invention has the ability to create Fourier-based images with only two grid pairs. The two grid pairs are manipulated in a manner that allows (1) a first grid pair to provide multiple real components of the Fourier-based image and (2) a second grid pair to provide multiple imaginary components of the Fourier-based image. The novelty of this invention resides in the use of only two grid pairs to provide the same imaging information that has been traditionally collected with multiple grid pairs.

Middle infrared (wavelength range: 8 μm-14 μm) 2-dimensional spectroscopy (total weight with electrical controller: 1.7 kg, total cost: less than 10,000 USD) so-called hyperspectral camera for unmanned air vehicles like drones

NASA Astrophysics Data System (ADS)

Yamamoto, Naoyuki; Saito, Tsubasa; Ogawa, Satoru; Ishimaru, Ichiro

2016-05-01

We developed the palm size (optical unit: 73[mm]×102[mm]×66[mm]) and light weight (total weight with electrical controller: 1.7[kg]) middle infrared (wavelength range: 8[μm]-14[μm]) 2-dimensional spectroscopy for UAV (Unmanned Air Vehicle) like drone. And we successfully demonstrated the flights with the developed hyperspectral camera mounted on the multi-copter so-called drone in 15/Sep./2015 at Kagawa prefecture in Japan. We had proposed 2 dimensional imaging type Fourier spectroscopy that was the near-common path temporal phase-shift interferometer. We install the variable phase shifter onto optical Fourier transform plane of infinity corrected imaging optical systems. The variable phase shifter was configured with a movable mirror and a fixed mirror. The movable mirror was actuated by the impact drive piezo-electric device (stroke: 4.5[mm], resolution: 0.01[μm], maker: Technohands Co.,Ltd., type:XDT50-45, price: around 1,000USD). We realized the wavefront division type and near common path interferometry that has strong robustness against mechanical vibrations. Without anti-mechanical vibration systems, the palm-size Fourier spectroscopy was realized. And we were able to utilize the small and low-cost middle infrared camera that was the micro borometer array (un-cooled VOxMicroborometer, pixel array: 336×256, pixel pitch: 17[μm], frame rate 60[Hz], maker: FLIR, type: Quark 336, price: around 5,000USD). And this apparatus was able to be operated by single board computer (Raspberry Pi.). Thus, total cost was less than 10,000 USD. We joined with KAMOME-PJ (Kanagawa Advanced MOdule for Material Evaluation Project) with DRONE FACTORY Corp., KUUSATSU Corp., Fuji Imvac Inc. And we successfully obtained the middle infrared spectroscopic imaging with multi-copter drone.

Cryptosystem for Securing Image Encryption Using Structured Phase Masks in Fresnel Wavelet Transform Domain

NASA Astrophysics Data System (ADS)

Singh, Hukum

2016-12-01

A cryptosystem for securing image encryption is considered by using double random phase encoding in Fresnel wavelet transform (FWT) domain. Random phase masks (RPMs) and structured phase masks (SPMs) based on devil's vortex toroidal lens (DVTL) are used in spatial as well as in Fourier planes. The images to be encrypted are first Fresnel transformed and then single-level discrete wavelet transform (DWT) is apply to decompose LL,HL, LH and HH matrices. The resulting matrices from the DWT are multiplied by additional RPMs and the resultants are subjected to inverse DWT for the encrypted images. The scheme is more secure because of many parameters used in the construction of SPM. The original images are recovered by using the correct parameters of FWT and SPM. Phase mask SPM based on DVTL increases security that enlarges the key space for encryption and decryption. The proposed encryption scheme is a lens-less optical system and its digital implementation has been performed using MATLAB 7.6.0 (R2008a). The computed value of mean-squared-error between the retrieved and the input images shows the efficacy of scheme. The sensitivity to encryption parameters, robustness against occlusion, entropy and multiplicative Gaussian noise attacks have been analysed.

Key management of the double random-phase-encoding method using public-key encryption

NASA Astrophysics Data System (ADS)

Saini, Nirmala; Sinha, Aloka

2010-03-01

Public-key encryption has been used to encode the key of the encryption process. In the proposed technique, an input image has been encrypted by using the double random-phase-encoding method using extended fractional Fourier transform. The key of the encryption process have been encoded by using the Rivest-Shamir-Adelman (RSA) public-key encryption algorithm. The encoded key has then been transmitted to the receiver side along with the encrypted image. In the decryption process, first the encoded key has been decrypted using the secret key and then the encrypted image has been decrypted by using the retrieved key parameters. The proposed technique has advantage over double random-phase-encoding method because the problem associated with the transmission of the key has been eliminated by using public-key encryption. Computer simulation has been carried out to validate the proposed technique.

Femtosecond X-ray Fourier holography imaging of free-flying nanoparticles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorkhover, Tais; Ulmer, Anatoli; Ferguson, Ken

Ultrafast X-ray imaging on individual fragile specimens such as aerosols, metastable particles, superfluid quantum systems and live biospecimens provides high-resolution information that is inaccessible with conventional imaging techniques. Coherent X-ray diffractive imaging, however, suffers from intrinsic loss of phase, and therefore structure recovery is often complicated and not always uniquely defined. Here in this paper, we introduce the method of in-flight holography, where we use nanoclusters as reference X-ray scatterers to encode relative phase information into diffraction patterns of a virus. The resulting hologram contains an unambiguous three-dimensional map of a virus and two nanoclusters with the highest lateral resolutionmore » so far achieved via single shot X-ray holography. Our approach unlocks the benefits of holography for ultrafast X-ray imaging of nanoscale, non-periodic systems and paves the way to direct observation of complex electron dynamics down to the attosecond timescale.« less

Femtosecond X-ray Fourier holography imaging of free-flying nanoparticles

NASA Astrophysics Data System (ADS)

Gorkhover, Tais; Ulmer, Anatoli; Ferguson, Ken; Bucher, Max; Maia, Filipe R. N. C.; Bielecki, Johan; Ekeberg, Tomas; Hantke, Max F.; Daurer, Benedikt J.; Nettelblad, Carl; Andreasson, Jakob; Barty, Anton; Bruza, Petr; Carron, Sebastian; Hasse, Dirk; Krzywinski, Jacek; Larsson, Daniel S. D.; Morgan, Andrew; Mühlig, Kerstin; Müller, Maria; Okamoto, Kenta; Pietrini, Alberto; Rupp, Daniela; Sauppe, Mario; van der Schot, Gijs; Seibert, Marvin; Sellberg, Jonas A.; Svenda, Martin; Swiggers, Michelle; Timneanu, Nicusor; Westphal, Daniel; Williams, Garth; Zani, Alessandro; Chapman, Henry N.; Faigel, Gyula; Möller, Thomas; Hajdu, Janos; Bostedt, Christoph

2018-03-01

Ultrafast X-ray imaging on individual fragile specimens such as aerosols1, metastable particles2, superfluid quantum systems3 and live biospecimens4 provides high-resolution information that is inaccessible with conventional imaging techniques. Coherent X-ray diffractive imaging, however, suffers from intrinsic loss of phase, and therefore structure recovery is often complicated and not always uniquely defined4,5. Here, we introduce the method of in-flight holography, where we use nanoclusters as reference X-ray scatterers to encode relative phase information into diffraction patterns of a virus. The resulting hologram contains an unambiguous three-dimensional map of a virus and two nanoclusters with the highest lateral resolution so far achieved via single shot X-ray holography. Our approach unlocks the benefits of holography for ultrafast X-ray imaging of nanoscale, non-periodic systems and paves the way to direct observation of complex electron dynamics down to the attosecond timescale.

Femtosecond X-ray Fourier holography imaging of free-flying nanoparticles

DOE PAGES

Gorkhover, Tais; Ulmer, Anatoli; Ferguson, Ken; ...

2018-02-26

Ultrafast X-ray imaging on individual fragile specimens such as aerosols, metastable particles, superfluid quantum systems and live biospecimens provides high-resolution information that is inaccessible with conventional imaging techniques. Coherent X-ray diffractive imaging, however, suffers from intrinsic loss of phase, and therefore structure recovery is often complicated and not always uniquely defined. Here in this paper, we introduce the method of in-flight holography, where we use nanoclusters as reference X-ray scatterers to encode relative phase information into diffraction patterns of a virus. The resulting hologram contains an unambiguous three-dimensional map of a virus and two nanoclusters with the highest lateral resolutionmore » so far achieved via single shot X-ray holography. Our approach unlocks the benefits of holography for ultrafast X-ray imaging of nanoscale, non-periodic systems and paves the way to direct observation of complex electron dynamics down to the attosecond timescale.« less

Dual tree fractional quaternion wavelet transform for disparity estimation.

PubMed

Kumar, Sanoj; Kumar, Sanjeev; Sukavanam, Nagarajan; Raman, Balasubramanian

2014-03-01

This paper proposes a novel phase based approach for computing disparity as the optical flow from the given pair of consecutive images. A new dual tree fractional quaternion wavelet transform (FrQWT) is proposed by defining the 2D Fourier spectrum upto a single quadrant. In the proposed FrQWT, each quaternion wavelet consists of a real part (a real DWT wavelet) and three imaginary parts that are organized according to the quaternion algebra. First two FrQWT phases encode the shifts of image features in the absolute horizontal and vertical coordinate system, while the third phase has the texture information. The FrQWT allowed a multi-scale framework for calculating and adjusting local disparities and executing phase unwrapping from coarse to fine scales with linear computational efficiency. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Optimization of magnetic flux density for fast MREIT conductivity imaging using multi-echo interleaved partial fourier acquisitions.

PubMed

Chauhan, Munish; Jeong, Woo Chul; Kim, Hyung Joong; Kwon, Oh In; Woo, Eung Je

2013-08-27

Magnetic resonance electrical impedance tomography (MREIT) has been introduced as a non-invasive method for visualizing the internal conductivity and/or current density of an electrically conductive object by externally injected currents. The injected current through a pair of surface electrodes induces a magnetic flux density distribution inside the imaging object, which results in additional magnetic flux density. To measure the magnetic flux density signal in MREIT, the phase difference approach in an interleaved encoding scheme cancels out the systematic artifacts accumulated in phase signals and also reduces the random noise effect by doubling the measured magnetic flux density signal. For practical applications of in vivo MREIT, it is essential to reduce the scan duration maintaining spatial-resolution and sufficient contrast. In this paper, we optimize the magnetic flux density by using a fast gradient multi-echo MR pulse sequence. To recover the one component of magnetic flux density Bz, we use a coupled partial Fourier acquisitions in the interleaved sense. To prove the proposed algorithm, we performed numerical simulations using a two-dimensional finite-element model. For a real experiment, we designed a phantom filled with a calibrated saline solution and located a rubber balloon inside the phantom. The rubber balloon was inflated by injecting the same saline solution during the MREIT imaging. We used the multi-echo fast low angle shot (FLASH) MR pulse sequence for MRI scan, which allows the reduction of measuring time without a substantial loss in image quality. Under the assumption of a priori phase artifact map from a reference scan, we rigorously investigated the convergence ratio of the proposed method, which was closely related with the number of measured phase encode set and the frequency range of the background field inhomogeneity. In the phantom experiment with a partial Fourier acquisition, the total scan time was less than 6 seconds to measure the magnetic flux density Bz data with 128×128 spacial matrix size, where it required 10.24 seconds to fill the complete k-space region. Numerical simulation and experimental results demonstrated that the proposed method reduces the scanning time and provides the recovered Bz data comparable to what we obtained by measuring complete k-space data.

Development of a High-Throughput Microwave Imaging System for Concealed Weapons Detection

DTIC Science & Technology

2016-07-15

hardware. Index Terms—Microwave imaging, multistatic radar, Fast Fourier Transform (FFT). I. INTRODUCTION Near-field microwave imaging is a non-ionizing...configuration, but its computational demands are extreme. Fast Fourier Transform (FFT) imaging has long been used to efficiently construct images sampled with...Simulated image of 25 point scatterers imaged at range 1.5m, with array layout depicted in Fig. 3. Left: image formed with Equation (5) ( Fourier

Functional imaging of hemodynamic stimulus response in the rat retina with ultrahigh-speed spectral / Fourier domain OCT

NASA Astrophysics Data System (ADS)

Choi, WooJhon; Baumann, Bernhard; Clermont, Allen C.; Feener, Edward P.; Boas, David A.; Fujimoto, James G.

2013-03-01

Measuring retinal hemodynamics in response to flicker stimulus is important for investigating pathophysiology in small animal models of diabetic retinopathy, because a reduction in the hyperemic response is thought to be one of the earliest changes in diabetic retinopathy. In this study, we investigated functional imaging of retinal hemodynamics in response to flicker stimulus in the rat retina using an ultrahigh speed spectral / Fourier domain OCT system at 840nm with an axial scan rate of 244kHz. At 244kHz the nominal axial velocity range that could be measured without phase wrapping was +/-37.7mm/s. Pulsatile total retinal arterial blood flow as a function of time was measured using an en face Doppler approach where a 200μm × 200μm area centered at the central retinal artery was repeatedly raster scanned at a volume acquisition rate of 55Hz. Three-dimensional capillary imaging was performed using speckle decorrelation which has minimal angle dependency compared to other angiography techniques based on OCT phase information. During OCT imaging, a flicker stimulus could be applied to the retina synchronously by inserting a dichroic mirror in the imaging interface. An acute transient increase in total retinal blood flow could be detected. At the capillary level, an increase in the degree of speckle decorrelation in capillary OCT angiography images could also be observed, which indicates an increase in the velocity of blood at the capillary level. This method promises to be useful for the investigation of small animal models of ocular diseases.

The Importance of Information Localization in Scene Gist Recognition

ERIC Educational Resources Information Center

Loschky, Lester C.; Sethi, Amit; Simons, Daniel J.; Pydimarri, Tejaswi N.; Ochs, Daniel; Corbeille, Jeremy L.

2007-01-01

People can recognize the meaning or gist of a scene from a single glance, and a few recent studies have begun to examine the sorts of information that contribute to scene gist recognition. The authors of the present study used visual masking coupled with image manipulations (randomizing phase while maintaining the Fourier amplitude spectrum;…

Limitations in imaging common conjunctival and corneal pathologies with fourier-domain optical coherence tomography.

PubMed

Demirci, Hakan; Steen, Daniel W

2014-01-01

To describe the limitations of Fourier-domain optical coherence tomography (OCT) in imaging common conjunctival and corneal pathology. Retrospective, single-center case series of 40 patients with conjunctival and cornea pathology. Fourier-domain OCT imaged laser in situ keratomileusis (LASIK) flaps in detail, including its relation to other corneal structures and abnormalities. Similarly, in infectious or degenerative corneal disorders, Fourier-domain OCT successfully showed the extent of infiltration or material deposition, which appeared as hyper-reflective areas. In cases with pterygium, the underlying cornea could not be imaged. All cases of common conjunctival pathologies, such as nevus or pinguecula, were successfully imaged in detail. Nevi, scleritis, pterygium, pinguecula, and subconjunctival hemorrhage were hyper-reflective lesions, while cysts and lymphangiectasia were hyporeflective. The details of the underlying sclera were not uniformly imaged in conjunctival pathologies. Fourier-domain OCT imaged the trabeculectomy bleb in detail, whereas the details of structures of the anterior chamber angle were not routinely visualized in all cases. Light scatter through vascularized, densely inflamed, or thick lesions limits the imaging capabilities of Fourier-domain anterior segment OCT.

A positional misalignment correction method for Fourier ptychographic microscopy based on simulated annealing

NASA Astrophysics Data System (ADS)

Sun, Jiasong; Zhang, Yuzhen; Chen, Qian; Zuo, Chao

2017-02-01

Fourier ptychographic microscopy (FPM) is a newly developed super-resolution technique, which employs angularly varying illuminations and a phase retrieval algorithm to surpass the diffraction limit of a low numerical aperture (NA) objective lens. In current FPM imaging platforms, accurate knowledge of LED matrix's position is critical to achieve good recovery quality. Furthermore, considering such a wide field-of-view (FOV) in FPM, different regions in the FOV have different sensitivity of LED positional misalignment. In this work, we introduce an iterative method to correct position errors based on the simulated annealing (SA) algorithm. To improve the efficiency of this correcting process, large number of iterations for several images with low illumination NAs are firstly implemented to estimate the initial values of the global positional misalignment model through non-linear regression. Simulation and experimental results are presented to evaluate the performance of the proposed method and it is demonstrated that this method can both improve the quality of the recovered object image and relax the LED elements' position accuracy requirement while aligning the FPM imaging platforms.

Devil's vortex Fresnel lens phase masks on an asymmetric cryptosystem based on phase-truncation in gyrator wavelet transform domain

NASA Astrophysics Data System (ADS)

Singh, Hukum

2016-06-01

An asymmetric scheme has been proposed for optical double images encryption in the gyrator wavelet transform (GWT) domain. Grayscale and binary images are encrypted separately using double random phase encoding (DRPE) in the GWT domain. Phase masks based on devil's vortex Fresnel Lens (DVFLs) and random phase masks (RPMs) are jointly used in spatial as well as in the Fourier plane. The images to be encrypted are first gyrator transformed and then single-level discrete wavelet transformed (DWT) to decompose LL , HL , LH and HH matrices of approximation, horizontal, vertical and diagonal coefficients. The resulting coefficients from the DWT are multiplied by other RPMs and the results are applied to inverse discrete wavelet transform (IDWT) for obtaining the encrypted images. The images are recovered from their corresponding encrypted images by using the correct parameters of the GWT, DVFL and its digital implementation has been performed using MATLAB 7.6.0 (R2008a). The mother wavelet family, DVFL and gyrator transform orders associated with the GWT are extra keys that cause difficulty to an attacker. Thus, the scheme is more secure as compared to conventional techniques. The efficacy of the proposed scheme is verified by computing mean-squared-error (MSE) between recovered and the original images. The sensitivity of the proposed scheme is verified with encryption parameters and noise attacks.

Wide-Field Imaging Interferometry Spatial-Spectral Image Synthesis Algorithms

NASA Technical Reports Server (NTRS)

Lyon, Richard G.; Leisawitz, David T.; Rinehart, Stephen A.; Memarsadeghi, Nargess; Sinukoff, Evan J.

2012-01-01

Developed is an algorithmic approach for wide field of view interferometric spatial-spectral image synthesis. The data collected from the interferometer consists of a set of double-Fourier image data cubes, one cube per baseline. These cubes are each three-dimensional consisting of arrays of two-dimensional detector counts versus delay line position. For each baseline a moving delay line allows collection of a large set of interferograms over the 2D wide field detector grid; one sampled interferogram per detector pixel per baseline. This aggregate set of interferograms, is algorithmically processed to construct a single spatial-spectral cube with angular resolution approaching the ratio of the wavelength to longest baseline. The wide field imaging is accomplished by insuring that the range of motion of the delay line encompasses the zero optical path difference fringe for each detector pixel in the desired field-of-view. Each baseline cube is incoherent relative to all other baseline cubes and thus has only phase information relative to itself. This lost phase information is recovered by having point, or otherwise known, sources within the field-of-view. The reference source phase is known and utilized as a constraint to recover the coherent phase relation between the baseline cubes and is key to the image synthesis. Described will be the mathematical formalism, with phase referencing and results will be shown using data collected from NASA/GSFC Wide-Field Imaging Interferometry Testbed (WIIT).

Super-Resolution of Multi-Pixel and Sub-Pixel Images for the SDI

DTIC Science & Technology

1993-06-08

where the phase of the transmitted signal is not needed. The Wigner - Ville distribution ( WVD ) of a real signal s(t), associated with the complex...B. Boashash, 0. P. Kenny and H. J. Whitehouse, "Radar imaging using the Wigner - Ville distribution ", in Real-Time Signal Processing, J. P. Letellier...analytic signal z(t), is a time- frequency distribution defined as-’- 00 W(tf) Z (~t + ) t- -)exp(-i2nft) . (45) Note that the WVD is the double Fourier

Leakage radiation interference microscopy.

PubMed

Descrovi, Emiliano; Barakat, Elsie; Angelini, Angelo; Munzert, Peter; De Leo, Natascia; Boarino, Luca; Giorgis, Fabrizio; Herzig, Hans Peter

2013-09-01

We present a proof of principle for a new imaging technique combining leakage radiation microscopy with high-resolution interference microscopy. By using oil immersion optics it is demonstrated that amplitude and phase can be retrieved from optical fields, which are evanescent in air. This technique is illustratively applied for mapping a surface mode propagating onto a planar dielectric multilayer on a thin glass substrate. The surface mode propagation constant estimated after Fourier transformation of the measured complex field is well matched with an independent measurement based on back focal plane imaging.

Fractional Talbot field and of finite gratings: compact analytical formulation.

PubMed

Arrizón, V; Rojo-Velázquez, G

2001-06-01

We present a compact analytical formulation for the fractional Talbot effect at the paraxial domain of a finite grating. Our results show that laterally shifted distorted images of the grating basic cell form the Fresnel field at a fractional Talbot plane of the grating. Our formulas give the positions of those images and show that they are given by the convolution of the nondistorted cells (modulated by a quadratic phase factor) with the Fourier transform of the finite-grating pupil.

Extreme ultraviolet interferometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goldberg, Kenneth A.

EUV lithography is a promising and viable candidate for circuit fabrication with 0.1-micron critical dimension and smaller. In order to achieve diffraction-limited performance, all-reflective multilayer-coated lithographic imaging systems operating near 13-nm wavelength and 0.1 NA have system wavefront tolerances of 0.27 nm, or 0.02 waves RMS. Owing to the highly-sensitive resonant reflective properties of multilayer mirrors and extraordinarily tight tolerances set forth for their fabrication, EUV optical systems require at-wavelength EUV interferometry for final alignment and qualification. This dissertation discusses the development and successful implementation of high-accuracy EUV interferometric techniques. Proof-of-principle experiments with a prototype EUV point-diffraction interferometer for themore » measurement of Fresnel zoneplate lenses first demonstrated sub-wavelength EUV interferometric capability. These experiments spurred the development of the superior phase-shifting point-diffraction interferometer (PS/PDI), which has been implemented for the testing of an all-reflective lithographic-quality EUV optical system. Both systems rely on pinhole diffraction to produce spherical reference wavefronts in a common-path geometry. Extensive experiments demonstrate EUV wavefront-measuring precision beyond 0.02 waves RMS. EUV imaging experiments provide verification of the high-accuracy of the point-diffraction principle, and demonstrate the utility of the measurements in successfully predicting imaging performance. Complementary to the experimental research, several areas of theoretical investigation related to the novel PS/PDI system are presented. First-principles electromagnetic field simulations of pinhole diffraction are conducted to ascertain the upper limits of measurement accuracy and to guide selection of the pinhole diameter. Investigations of the relative merits of different PS/PDI configurations accompany a general study of the most significant sources of systematic measurement errors. To overcome a variety of experimental difficulties, several new methods in interferogram analysis and phase-retrieval were developed: the Fourier-Transform Method of Phase-Shift Determination, which uses Fourier-domain analysis to improve the accuracy of phase-shifting interferometry; the Fourier-Transform Guided Unwrap Method, which was developed to overcome difficulties associated with a high density of mid-spatial-frequency blemishes and which uses a low-spatial-frequency approximation to the measured wavefront to guide the phase unwrapping in the presence of noise; and, finally, an expedient method of Gram-Schmidt orthogonalization which facilitates polynomial basis transformations in wave-front surface fitting procedures.« less

Facing the phase problem in Coherent Diffractive Imaging via Memetic Algorithms.

PubMed

Colombo, Alessandro; Galli, Davide Emilio; De Caro, Liberato; Scattarella, Francesco; Carlino, Elvio

2017-02-09

Coherent Diffractive Imaging is a lensless technique that allows imaging of matter at a spatial resolution not limited by lens aberrations. This technique exploits the measured diffraction pattern of a coherent beam scattered by periodic and non-periodic objects to retrieve spatial information. The diffracted intensity, for weak-scattering objects, is proportional to the modulus of the Fourier Transform of the object scattering function. Any phase information, needed to retrieve its scattering function, has to be retrieved by means of suitable algorithms. Here we present a new approach, based on a memetic algorithm, i.e. a hybrid genetic algorithm, to face the phase problem, which exploits the synergy of deterministic and stochastic optimization methods. The new approach has been tested on simulated data and applied to the phasing of transmission electron microscopy coherent electron diffraction data of a SrTiO 3 sample. We have been able to quantitatively retrieve the projected atomic potential, and also image the oxygen columns, which are not directly visible in the relevant high-resolution transmission electron microscopy images. Our approach proves to be a new powerful tool for the study of matter at atomic resolution and opens new perspectives in those applications in which effective phase retrieval is necessary.

Rotational-translational fourier imaging system requiring only one grid pair

NASA Technical Reports Server (NTRS)

Campbell, Jonathan W. (Inventor)

2006-01-01

The sky contains many active sources that emit X-rays, gamma rays, and neutrons. Unfortunately hard X-rays, gamma rays, and neutrons cannot be imaged by conventional optics. This obstacle led to the development of Fourier imaging systems. In early approaches, multiple grid pairs were necessary in order to create rudimentary Fourier imaging systems. At least one set of grid pairs was required to provide multiple real components of a Fourier derived image, and another set was required to provide multiple imaginary components of the image. It has long been recognized that the expense associated with the physical production of the numerous grid pairs required for Fourier imaging was a drawback. Herein one grid pair (two grids), with accompanying rotation and translation, can be used if one grid has one more slit than the other grid, and if the detector is modified.

Electro-Optical Imaging Fourier-Transform Spectrometer

NASA Technical Reports Server (NTRS)

Chao, Tien-Hsin; Zhou, Hanying

2006-01-01

An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.

Multispectral high-resolution hologram generation using orthographic projection images

NASA Astrophysics Data System (ADS)

Muniraj, I.; Guo, C.; Sheridan, J. T.

2016-08-01

We present a new method of synthesizing a digital hologram of three-dimensional (3D) real-world objects from multiple orthographic projection images (OPI). A high-resolution multiple perspectives of 3D objects (i.e., two dimensional elemental image array) are captured under incoherent white light using synthetic aperture integral imaging (SAII) technique and their OPIs are obtained respectively. The reference beam is then multiplied with the corresponding OPI and integrated to form a Fourier hologram. Eventually, a modified phase retrieval algorithm (GS/HIO) is applied to reconstruct the hologram. The principle is validated experimentally and the results support the feasibility of the proposed method.

SU-E-T-56: A Novel Approach to Computing Expected Value and Variance of Point Dose From Non-Gated Radiotherapy Delivery

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, S; Zhu, X; Zhang, M

Purpose: Randomness in patient internal organ motion phase at the beginning of non-gated radiotherapy delivery may introduce uncertainty to dose received by the patient. Concerns of this dose deviation from the planned one has motivated many researchers to study this phenomenon although unified theoretical framework for computing it is still missing. This study was conducted to develop such framework for analyzing the effect. Methods: Two reasonable assumptions were made: a) patient internal organ motion is stationary and periodic; b) no special arrangement is made to start a non -gated radiotherapy delivery at any specific phase of patient internal organ motion.more » A statistical ensemble was formed consisting of patient’s non-gated radiotherapy deliveries at all equally possible initial organ motion phases. To characterize the patient received dose, statistical ensemble average method is employed to derive formulae for two variables: expected value and variance of dose received by a patient internal point from a non-gated radiotherapy delivery. Fourier Series was utilized to facilitate our analysis. Results: According to our formulae, the two variables can be computed from non-gated radiotherapy generated dose rate time sequences at the point’s corresponding locations on fixed phase 3D CT images sampled evenly in time over one patient internal organ motion period. The expected value of point dose is simply the average of the doses to the point’s corresponding locations on the fixed phase CT images. The variance can be determined by time integration in terms of Fourier Series coefficients of the dose rate time sequences on the same fixed phase 3D CT images. Conclusion: Given a non-gated radiotherapy delivery plan and patient’s 4D CT study, our novel approach can predict the expected value and variance of patient radiation dose. We expect it to play a significant role in determining both quality and robustness of patient non-gated radiotherapy plan.« less

Two-harmonic complex spectral-domain optical coherence tomography using achromatic sinusoidal phase modulation

NASA Astrophysics Data System (ADS)

Lu, Sheng-Hua; Huang, Siang-Ru; Chou, Che-Chung

2018-03-01

We resolve the complex conjugate ambiguity in spectral-domain optical coherence tomography (SD-OCT) by using achromatic two-harmonic method. Unlike previous researches, the optical phase of the fiber interferometer is modulated by an achromatic phase shifter based on an optical delay line. The achromatic phase modulation leads to a wavelength-independent scaling coefficient for the two harmonics. Dividing the mean absolute value of the first harmonic by that of the second harmonic in a B-scan interferogram directly gives the scaling coefficient. It greatly simplifies the determination of the magnitude ratio between the two harmonics without the need of third harmonic and cumbersome iterative calculations. The inverse fast Fourier transform of the complex-valued interferogram constructed with the scaling coefficient, first and second harmonics yields a full-range OCT image. Experimental results confirm the effectiveness of the proposed achromatic two-harmonic technique for suppressing the mirror artifacts in SD-OCT images.

Effect of noise on modulation amplitude and phase in frequency-domain diffusive imaging

PubMed Central

Kupinski, Matthew A.

2012-01-01

Abstract. We theoretically investigate the effect of noise on frequency-domain heterodyne and/or homodyne measurements of intensity-modulated beams propagating through diffusive media, such as a photon density wave. We assumed that the attenuated amplitude and delayed phase are estimated by taking the Fourier transform of the noisy, modulated output data. We show that the estimated amplitude and phase are biased when the number of output photons is small. We also show that the use of image intensifiers for photon amplification in heterodyne or homodyne measurements increases the amount of biases. Especially, it turns out that the biased estimation is independent of AC-dependent noise in sinusoidal heterodyne or homodyne outputs. Finally, the developed theory indicates that the previously known variance model of modulation amplitude and phase is not valid in low light situations. Monte-Carlo simulations with varied numbers of input photons verify our theoretical trends of the bias. PMID:22352660

Microscopy illumination engineering using a low-cost liquid crystal display.

PubMed

Guo, Kaikai; Bian, Zichao; Dong, Siyuan; Nanda, Pariksheet; Wang, Ying Min; Zheng, Guoan

2015-02-01

Illumination engineering is critical for obtaining high-resolution, high-quality images in microscope settings. In a typical microscope, the condenser lens provides sample illumination that is uniform and free from glare. The associated condenser diaphragm can be manually adjusted to obtain the optimal illumination numerical aperture. In this paper, we report a programmable condenser lens for active illumination control. In our prototype setup, we used a $15 liquid crystal display as a transparent spatial light modulator and placed it at the back focal plane of the condenser lens. By setting different binary patterns on the display, we can actively control the illumination and the spatial coherence of the microscope platform. We demonstrated the use of such a simple scheme for multimodal imaging, including bright-field microscopy, darkfield microscopy, phase-contrast microscopy, polarization microscopy, 3D tomographic imaging, and super-resolution Fourier ptychographic imaging. The reported illumination engineering scheme is cost-effective and compatible with most existing platforms. It enables a turnkey solution with high flexibility for researchers in various communities. From the engineering point-of-view, the reported illumination scheme may also provide new insights for the development of multimodal microscopy and Fourier ptychographic imaging.

The New Physical Optics Notebook: Tutorials in Fourier Optics.

ERIC Educational Resources Information Center

Reynolds, George O.; And Others

This is a textbook of Fourier optics for the classroom or self-study. Major topics included in the 38 chapters are: Huygens' principle and Fourier transforms; image formation; optical coherence theory; coherent imaging; image analysis; coherent noise; interferometry; holography; communication theory techniques; analog optical computing; phase…

Analysis and measurement of the modulation transfer function of harmonic shear wave induced phase encoding imaging.

PubMed

McAleavey, Stephen A

2014-05-01

Shear wave induced phase encoding (SWIPE) imaging generates ultrasound backscatter images of tissue-like elastic materials by using traveling shear waves to encode the lateral position of the scatters in the phase of the received echo. In contrast to conventional ultrasound B-scan imaging, SWIPE offers the potential advantages of image formation without beam focusing or steering from a single transducer element, lateral resolution independent of aperture size, and the potential to achieve relatively high lateral resolution with low frequency ultrasound. Here a Fourier series description of the phase modulated echo signal is developed, demonstrating that echo harmonics at multiples of the shear wave frequency reveal target k-space data at identical multiples of the shear wavenumber. Modulation transfer functions of SWIPE imaging systems are calculated for maximum shear wave acceleration and maximum shear constraints, and compared with a conventionally focused aperture. The relative signal-to-noise ratio of the SWIPE method versus a conventionally focused aperture is found through these calculations. Reconstructions of wire targets in a gelatin phantom using 1 and 3.5 MHz ultrasound and a cylindrical shear wave source are presented, generated from the fundamental and second harmonic of the shear wave modulation frequency, demonstrating weak dependence of lateral resolution with ultrasound frequency.

Imaging Organ of Corti Vibration Using Fourier-Domain OCT

NASA Astrophysics Data System (ADS)

Choudhury, Niloy; Chen, Fangyi; Fridberger, Anders; Zha, Dingjun; Jacques, Steven L.; Wang, Ruikang K.; Nuttall, Alfred L.

2011-11-01

Measuring the sound stimulated vibration from various structures in the organ of Corti is important in understanding how the small vibrations are amplified and detected. In this study we examine the feasibility of using phase-sensitive Fourier domain optical coherence tomography (PSFD-OCT) to measure vibration of the cellular structures of the organ of Corti. PSFD-OCT is a low coherence interferrometry system where the interferrogram is detected as a function of wavelength. The phase of the Fourier transformation of the detected spectra contains path deference (between the sample arm and the reference arm) information of the interferometer. In PSFD-OCT this phase is measured as a function of time and thus any time dependent change in the path difference between the sample arm and the reference arm can be detected. In the experiment, we used an in vitro preparation of the guinea pig cochlea and made a surgical opening at the apical end to access the organ of Corti. By applying tones with different frequencies via the intact middle ear, we recorded the structural vibration inside the organ of Corti. Vibration amplitude and phase of different substructures were mapped on a cross-section view of the organ of Corti. Although the measurements were made at the apical turn of the cochlea, it will be possible to make vibration measurement from various turns of the cochlea. The noise floor of the system was 0.3 nm, calibrated using a piezo stack as a calibrator.

High resolution human diffusion tensor imaging using 2-D navigated multi-shot SENSE EPI at 7 Tesla

PubMed Central

Jeong, Ha-Kyu; Gore, John C.; Anderson, Adam W.

2012-01-01

The combination of parallel imaging with partial Fourier acquisition has greatly improved the performance of diffusion-weighted single-shot EPI and is the preferred method for acquisitions at low to medium magnetic field strength such as 1.5 or 3 Tesla. Increased off-resonance effects and reduced transverse relaxation times at 7 Tesla, however, generate more significant artifacts than at lower magnetic field strength and limit data acquisition. Additional acceleration of k-space traversal using a multi-shot approach, which acquires a subset of k-space data after each excitation, reduces these artifacts relative to conventional single-shot acquisitions. However, corrections for motion-induced phase errors are not straightforward in accelerated, diffusion-weighted multi-shot EPI because of phase aliasing. In this study, we introduce a simple acquisition and corresponding reconstruction method for diffusion-weighted multi-shot EPI with parallel imaging suitable for use at high field. The reconstruction uses a simple modification of the standard SENSE algorithm to account for shot-to-shot phase errors; the method is called Image Reconstruction using Image-space Sampling functions (IRIS). Using this approach, reconstruction from highly aliased in vivo image data using 2-D navigator phase information is demonstrated for human diffusion-weighted imaging studies at 7 Tesla. The final reconstructed images show submillimeter in-plane resolution with no ghosts and much reduced blurring and off-resonance artifacts. PMID:22592941

Classification of footwear outsole patterns using Fourier transform and local interest points.

PubMed

Richetelli, Nicole; Lee, Mackenzie C; Lasky, Carleen A; Gump, Madison E; Speir, Jacqueline A

2017-06-01

Successful classification of questioned footwear has tremendous evidentiary value; the result can minimize the potential suspect pool and link a suspect to a victim, a crime scene, or even multiple crime scenes to each other. With this in mind, several different automated and semi-automated classification models have been applied to the forensic footwear recognition problem, with superior performance commonly associated with two different approaches: correlation of image power (magnitude) or phase, and the use of local interest points transformed using the Scale Invariant Feature Transform (SIFT) and compared using Random Sample Consensus (RANSAC). Despite the distinction associated with each of these methods, all three have not been cross-compared using a single dataset, of limited quality (i.e., characteristic of crime scene-like imagery), and created using a wide combination of image inputs. To address this question, the research presented here examines the classification performance of the Fourier-Mellin transform (FMT), phase-only correlation (POC), and local interest points (transformed using SIFT and compared using RANSAC), as a function of inputs that include mixed media (blood and dust), transfer mechanisms (gel lifters), enhancement techniques (digital and chemical) and variations in print substrate (ceramic tiles, vinyl tiles and paper). Results indicate that POC outperforms both FMT and SIFT+RANSAC, regardless of image input (type, quality and totality), and that the difference in stochastic dominance detected for POC is significant across all image comparison scenarios evaluated in this study. Copyright © 2017 Elsevier B.V. All rights reserved.

New developments in photoacoustics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosencwaig, A.

1981-07-01

There have been several important new developments in the fields of photoacoustics and photoacoustic spectroscopy. Photoactoustic techniques are now being used in ferromagnetic and electron spin resonance experiments, and there have been rapid advances in Fourier-transform infrared photoacoustic spectroscopy. In addition, the calorimetric aspects of photoacoustics are now being extensively exploited for phase transition studies, and to perform thermal-wave imaging and microscopy.

3D homogeneity study in PMMA layers using a Fourier domain OCT system

NASA Astrophysics Data System (ADS)

Briones-R., Manuel de J.; Torre-Ibarra, Manuel H. De La; Tavera, Cesar G.; Luna H., Juan M.; Mendoza-Santoyo, Fernando

2016-11-01

Micro-metallic particles embedded in polymers are now widely used in several industrial applications in order to modify the mechanical properties of the bulk. A uniform distribution of these particles inside the polymers is highly desired for instance, when a biological backscattering is simulated or a bio-framework is designed. A 3D Fourier domain optical coherence tomography system to detect the polymer's internal homogeneity is proposed. This optical system has a 2D camera sensor array that records a fringe pattern used to reconstruct with a single shot the tomographic image of the sample. The system gathers the full 3D tomographic and optical phase information during a controlled deformation by means of a motion linear stage. This stage avoids the use of expensive tilting stages, which in addition are commonly controlled by piezo drivers. As proof of principle, a series of different deformations were proposed to detect the uniform or non-uniform internal deposition of copper micro particles. The results are presented as images coming from the 3D tomographic micro reconstruction of the samples, and the 3D optical phase information that identifies the in-homogeneity regions within the Poly methyl methacrylate (PMMA) volume.

Methods for coherent lensless imaging and X-ray wavefront measurements

NASA Astrophysics Data System (ADS)

Guizar Sicairos, Manuel

X-ray diffractive imaging is set apart from other high-resolution imaging techniques (e.g. scanning electron or atomic force microscopy) for its high penetration depth, which enables tomographic 3D imaging of thick samples and buried structures. Furthermore, using short x-ray pulses, it enables the capability to take ultrafast snapshots, giving a unique opportunity to probe nanoscale dynamics at femtosecond time scales. In this thesis we present improvements to phase retrieval algorithms, assess their performance through numerical simulations, and develop new methods for both imaging and wavefront measurement. Building on the original work by Faulkner and Rodenburg, we developed an improved reconstruction algorithm for phase retrieval with transverse translations of the object relative to the illumination beam. Based on gradient-based nonlinear optimization, this algorithm is capable of estimating the object, and at the same time refining the initial knowledge of the incident illumination and the object translations. The advantages of this algorithm over the original iterative transform approach are shown through numerical simulations. Phase retrieval has already shown substantial success in wavefront sensing at optical wavelengths. Although in principle the algorithms can be used at any wavelength, in practice the focus-diversity mechanism that makes optical phase retrieval robust is not practical to implement for x-rays. In this thesis we also describe the novel application of phase retrieval with transverse translations to the problem of x-ray wavefront sensing. This approach allows the characterization of the complex-valued x-ray field in-situ and at-wavelength and has several practical and algorithmic advantages over conventional focused beam measurement techniques. A few of these advantages include improved robustness through diverse measurements, reconstruction from far-field intensity measurements only, and significant relaxation of experimental requirements over other beam characterization approaches. Furthermore, we show that a one-dimensional version of this technique can be used to characterize an x-ray line focus produced by a cylindrical focusing element. We provide experimental demonstrations of the latter at hard x-ray wavelengths, where we have characterized the beams focused by a kinoform lens and an elliptical mirror. In both experiments the reconstructions exhibited good agreement with independent measurements, and in the latter a small mirror misalignment was inferred from the phase retrieval reconstruction. These experiments pave the way for the application of robust phase retrieval algorithms for in-situ alignment and performance characterization of x-ray optics for nanofocusing. We also present a study on how transverse translations help with the well-known uniqueness problem of one-dimensional phase retrieval. We also present a novel method for x-ray holography that is capable of reconstructing an image using an off-axis extended reference in a non-iterative computation, greatly generalizing an earlier approach by Podorov et al. The approach, based on the numerical application of derivatives on the field autocorrelation, was developed from first mathematical principles. We conducted a thorough theoretical study to develop technical and intuitive understanding of this technique and derived sufficient separation conditions required for an artifact-free reconstruction. We studied the effects of missing information in the Fourier domain, and of an imperfect reference, and we provide a signal-to-noise ratio comparison with the more traditional approach of Fourier transform holography. We demonstrated this new holographic approach through proof-of-principle optical experiments and later experimentally at soft x-ray wavelengths, where we compared its performance to Fourier transform holography, iterative phase retrieval and state-of-the-art zone-plate x-ray imaging techniques (scanning and full-field). Finally, we present a demonstration of the technique using a single 20 fs pulse from a high-harmonic table-top source. Holography with an extended reference is shown to provide fast, good quality images that are robust to noise and artifacts that arise from missing information due to a beam stop. (Abstract shortened by UMI.)

A laboratory demonstration of high-resolution hard X-ray and gamma-ray imaging using Fourier-transform techniques

NASA Technical Reports Server (NTRS)

Palmer, David; Prince, Thomas A.

1987-01-01

A laboratory imaging system has been developed to study the use of Fourier-transform techniques in high-resolution hard X-ray and gamma-ray imaging, with particular emphasis on possible applications to high-energy astronomy. Considerations for the design of a Fourier-transform imager and the instrumentation used in the laboratory studies is described. Several analysis methods for image reconstruction are discussed including the CLEAN algorithm and maximum entropy methods. Images obtained using these methods are presented.

DMD-based quantitative phase microscopy and optical diffraction tomography

NASA Astrophysics Data System (ADS)

Zhou, Renjie

2018-02-01

Digital micromirror devices (DMDs), which offer high speed and high degree of freedoms in steering light illuminations, have been increasingly applied to optical microscopy systems in recent years. Lately, we introduced DMDs into digital holography to enable new imaging modalities and break existing imaging limitations. In this paper, we will first present our progress in using DMDs for demonstrating laser-illumination Fourier ptychographic microscopy (FPM) with shotnoise limited detection. After that, we will present a novel common-path quantitative phase microscopy (QPM) system based on using a DMD. Building on those early developments, a DMD-based high speed optical diffraction tomography (ODT) system has been recently demonstrated, and the results will also be presented. This ODT system is able to achieve video-rate 3D refractive-index imaging, which can potentially enable observations of high-speed 3D sample structural changes.

Simulation of the modulation transfer function dependent on the partial Fourier fraction in dynamic contrast enhancement magnetic resonance imaging.

PubMed

Takatsu, Yasuo; Ueyama, Tsuyoshi; Miyati, Tosiaki; Yamamura, Kenichirou

2016-12-01

The image characteristics in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) depend on the partial Fourier fraction and contrast medium concentration. These characteristics were assessed and the modulation transfer function (MTF) was calculated by computer simulation. A digital phantom was created from signal intensity data acquired at different contrast medium concentrations on a breast model. The frequency images [created by fast Fourier transform (FFT)] were divided into 512 parts and rearranged to form a new image. The inverse FFT of this image yielded the MTF. From the reference data, three linear models (low, medium, and high) and three exponential models (slow, medium, and rapid) of the signal intensity were created. Smaller partial Fourier fractions, and higher gradients in the linear models, corresponded to faster MTF decline. The MTF more gradually decreased in the exponential models than in the linear models. The MTF, which reflects the image characteristics in DCE-MRI, was more degraded as the partial Fourier fraction decreased.

Satellite on-board real-time SAR processor prototype

NASA Astrophysics Data System (ADS)

Bergeron, Alain; Doucet, Michel; Harnisch, Bernd; Suess, Martin; Marchese, Linda; Bourqui, Pascal; Desnoyers, Nicholas; Legros, Mathieu; Guillot, Ludovic; Mercier, Luc; Châteauneuf, François

2017-11-01

A Compact Real-Time Optronic SAR Processor has been successfully developed and tested up to a Technology Readiness Level of 4 (TRL4), the breadboard validation in a laboratory environment. SAR, or Synthetic Aperture Radar, is an active system allowing day and night imaging independent of the cloud coverage of the planet. The SAR raw data is a set of complex data for range and azimuth, which cannot be compressed. Specifically, for planetary missions and unmanned aerial vehicle (UAV) systems with limited communication data rates this is a clear disadvantage. SAR images are typically processed electronically applying dedicated Fourier transformations. This, however, can also be performed optically in real-time. Originally the first SAR images were optically processed. The optical Fourier processor architecture provides inherent parallel computing capabilities allowing real-time SAR data processing and thus the ability for compression and strongly reduced communication bandwidth requirements for the satellite. SAR signal return data are in general complex data. Both amplitude and phase must be combined optically in the SAR processor for each range and azimuth pixel. Amplitude and phase are generated by dedicated spatial light modulators and superimposed by an optical relay set-up. The spatial light modulators display the full complex raw data information over a two-dimensional format, one for the azimuth and one for the range. Since the entire signal history is displayed at once, the processor operates in parallel yielding real-time performances, i.e. without resulting bottleneck. Processing of both azimuth and range information is performed in a single pass. This paper focuses on the onboard capabilities of the compact optical SAR processor prototype that allows in-orbit processing of SAR images. Examples of processed ENVISAT ASAR images are presented. Various SAR processor parameters such as processing capabilities, image quality (point target analysis), weight and size are reviewed.

Regional distribution of ventilation assessed by Kr-81m scintigraphy employing temporal Fourier transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slosman, D.; Susskind, H.; Cinotti, L.

1986-01-01

Temporal Fourier analysis was applied to Kr-81m ventilation scintigraphy to determine the amplitude (AMP1) and phase (PHA1) of the first harmonic of a single composite respiratory cycle and to compare regional patterns in subjects with obstructive pulmonary disease (COPD) and nonobstructed subjects. Six nonobstructed subjects, three subjects with small airway disease, six subjects with COPD, and one subject with restrictive disease were investigated. The mean value of the functional PHA1 image (PHA1m) correlated negatively with 1-second forced expiratory volume (FEV1) (r = -0.801, P less than .001), with %FEV1/FVC (r = -0.636, P less than .01) and maximum midexpiratory flowmore » rate (FEF25-75%) (r = -0.723, P less than .002), and correlated positively with residual volume (r = 0.640, P less than .01). PHA1m values for the six subjects with COPD were significantly higher (t = 2.359, P less than .05) than for the ten nonobstructed subjects. Display of phase and amplitude functional images permits a visual evaluation of the regional distribution of ventilation to be made. Regional abnormalities of air flow were detected in obstructed subjects, and the presence of airway obstruction could be predicted. Dynamic ventilation imaging, therefore, appears to be a potentially useful noninvasive technique to assess lung impairment on a localized level.« less

Micro Fourier Transform Profilometry (μFTP): 3D shape measurement at 10,000 frames per second

NASA Astrophysics Data System (ADS)

Zuo, Chao; Tao, Tianyang; Feng, Shijie; Huang, Lei; Asundi, Anand; Chen, Qian

2018-03-01

Fringe projection profilometry is a well-established technique for optical 3D shape measurement. However, in many applications, it is desirable to make 3D measurements at very high speed, especially with fast moving or shape changing objects. In this work, we demonstrate a new 3D dynamic imaging technique, Micro Fourier Transform Profilometry (μFTP), which can realize an acquisition rate up to 10,000 3D frame per second (fps). The high measurement speed is achieved by the number of patterns reduction as well as high-speed fringe projection hardware. In order to capture 3D information in such a short period of time, we focus on the improvement of the phase recovery, phase unwrapping, and error compensation algorithms, allowing to reconstruct an accurate, unambiguous, and distortion-free 3D point cloud with every two projected patterns. We also develop a high-frame-rate fringe projection hardware by pairing a high-speed camera and a DLP projector, enabling binary pattern switching and precisely synchronized image capture at a frame rate up to 20,000 fps. Based on this system, we demonstrate high-quality textured 3D imaging of 4 transient scenes: vibrating cantilevers, rotating fan blades, flying bullet, and bursting balloon, which were previously difficult or even unable to be captured with conventional approaches.

Micro Fourier Transform Profilometry (μFTP): 3D shape measurement at 10,000 frames per second

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zuo, Chao; Tao, Tianyang; Feng, Shijie

We report that fringe projection profilometry is a well-established technique for optical 3D shape measurement. However, in many applications, it is desirable to make 3D measurements at very high speed, especially with fast moving or shape changing objects. In this work, we demonstrate a new 3D dynamic imaging technique, Micro Fourier Transform Profilometry (μFTP), which can realize an acquisition rate up to 10,000 3D frame per second (fps). The high measurement speed is achieved by the number of patterns reduction as well as high-speed fringe projection hardware. In order to capture 3D information in such a short period of time,more » we focus on the improvement of the phase recovery, phase unwrapping, and error compensation algorithms, allowing to reconstruct an accurate, unambiguous, and distortion-free 3D point cloud with every two projected patterns. We also develop a high-frame-rate fringe projection hardware by pairing a high-speed camera and a DLP projector, enabling binary pattern switching and precisely synchronized image capture at a frame rate up to 20,000 fps. Lastly, based on this system, we demonstrate high-quality textured 3D imaging of 4 transient scenes: vibrating cantilevers, rotating fan blades, flying bullet, and bursting balloon, which were previously difficult or even unable to be captured with conventional approaches.« less

Transformation of light double cones in the human retina: the origin of trichromatism, of 4D-spatiotemporal vision, and of patchwise 4D Fourier transformation in Talbot imaging

NASA Astrophysics Data System (ADS)

Lauinger, Norbert

1997-09-01

The interpretation of the 'inverted' retina of primates as an 'optoretina' (a light cones transforming diffractive cellular 3D-phase grating) integrates the functional, structural, and oscillatory aspects of a cortical layer. It is therefore relevant to consider prenatal developments as a basis of the macro- and micro-geometry of the inner eye. This geometry becomes relevant for the postnatal trichromatic synchrony organization (TSO) as well as the adaptive levels of human vision. It is shown that the functional performances, the trichromatism in photopic vision, the monocular spatiotemporal 3D- and 4D-motion detection, as well as the Fourier optical image transformation with extraction of invariances all become possible. To transform light cones into reciprocal gratings especially the spectral phase conditions in the eikonal of the geometrical optical imaging before the retinal 3D-grating become relevant first, then in the von Laue resp. reciprocal von Laue equation for 3D-grating optics inside the grating and finally in the periodicity of Talbot-2/Fresnel-planes in the near-field behind the grating. It is becoming possible to technically realize -- at least in some specific aspects -- such a cortical optoretina sensor element with its typical hexagonal-concentric structure which leads to these visual functions.

Micro Fourier Transform Profilometry (μFTP): 3D shape measurement at 10,000 frames per second

DOE PAGES

Zuo, Chao; Tao, Tianyang; Feng, Shijie; ...

2017-11-06

We report that fringe projection profilometry is a well-established technique for optical 3D shape measurement. However, in many applications, it is desirable to make 3D measurements at very high speed, especially with fast moving or shape changing objects. In this work, we demonstrate a new 3D dynamic imaging technique, Micro Fourier Transform Profilometry (μFTP), which can realize an acquisition rate up to 10,000 3D frame per second (fps). The high measurement speed is achieved by the number of patterns reduction as well as high-speed fringe projection hardware. In order to capture 3D information in such a short period of time,more » we focus on the improvement of the phase recovery, phase unwrapping, and error compensation algorithms, allowing to reconstruct an accurate, unambiguous, and distortion-free 3D point cloud with every two projected patterns. We also develop a high-frame-rate fringe projection hardware by pairing a high-speed camera and a DLP projector, enabling binary pattern switching and precisely synchronized image capture at a frame rate up to 20,000 fps. Lastly, based on this system, we demonstrate high-quality textured 3D imaging of 4 transient scenes: vibrating cantilevers, rotating fan blades, flying bullet, and bursting balloon, which were previously difficult or even unable to be captured with conventional approaches.« less

Direct single-shot phase retrieval from the diffraction pattern of separated objects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leshem, Ben; Xu, Rui; Dallal, Yehonatan

The non-crystallographic phase problem arises in numerous scientific and technological fields. An important application is coherent diffractive imaging. Recent advances in X-ray free-electron lasers allow capturing of the diffraction pattern from a single nanoparticle before it disintegrates, in so-called ‘diffraction before destruction’ experiments. Presently, the phase is reconstructed by iterative algorithms, imposing a non-convex computational challenge, or by Fourier holography, requiring a well-characterized reference field. Here we present a convex scheme for single-shot phase retrieval for two (or more) sufficiently separated objects, demonstrated in two dimensions. In our approach, the objects serve as unknown references to one another, reducing themore » phase problem to a solvable set of linear equations. We establish our method numerically and experimentally in the optical domain and demonstrate a proof-of-principle single-shot coherent diffractive imaging using X-ray free-electron lasers pulses. Lastly, our scheme alleviates several limitations of current methods, offering a new pathway towards direct reconstruction of complex objects.« less

Direct single-shot phase retrieval from the diffraction pattern of separated objects

DOE PAGES

Leshem, Ben; Xu, Rui; Dallal, Yehonatan; ...

2016-02-22

The non-crystallographic phase problem arises in numerous scientific and technological fields. An important application is coherent diffractive imaging. Recent advances in X-ray free-electron lasers allow capturing of the diffraction pattern from a single nanoparticle before it disintegrates, in so-called ‘diffraction before destruction’ experiments. Presently, the phase is reconstructed by iterative algorithms, imposing a non-convex computational challenge, or by Fourier holography, requiring a well-characterized reference field. Here we present a convex scheme for single-shot phase retrieval for two (or more) sufficiently separated objects, demonstrated in two dimensions. In our approach, the objects serve as unknown references to one another, reducing themore » phase problem to a solvable set of linear equations. We establish our method numerically and experimentally in the optical domain and demonstrate a proof-of-principle single-shot coherent diffractive imaging using X-ray free-electron lasers pulses. Lastly, our scheme alleviates several limitations of current methods, offering a new pathway towards direct reconstruction of complex objects.« less

Femtosecond X-ray Fourier holography imaging of freeflying nanoparticles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorkhover, Tais; Ulmer, Anatoli; Ferguson, Ken R.

Ultrafast X-ray imaging on individual fragile specimens such as aerosols1, metastable particles2, superfluid quantum systems3 and live biospecimen4 provides high resolution information, which is inaccessible with conventional imaging techniques. Coherent X-ray diffractive imag- 2 ing, however, suffers from intrinsic loss of phase, and therefore structure recovery is often complicated and not always uniquely-defined4, 5. Here, we introduce the method of in-flight holography, where we use nanoclusters as reference X-ray scatterers in order to encode relative phase information into diffraction patterns of a virus. The resulting hologram contains an unambiguous three-dimensional map of a virus and two nanoclusters with the highestmore » lateral resolution so far achieved via single shot X-ray holography. Our approach unlocks the benefits of holography for ultrafast X-ray imaging of nanoscale, non-periodic systems and paves the way to direct observation of complex electron dynamics down to the attosecond time scale.« less

Simulation of pattern and defect detection in periodic amplitude and phase structures using photorefractive four-wave mixing

NASA Astrophysics Data System (ADS)

Nehmetallah, Georges; Banerjee, Partha; Khoury, Jed

2015-03-01

The nonlinearity inherent in four-wave mixing in photorefractive (PR) materials is used for adaptive filtering. Examples include script enhancement on a periodic pattern, scratch and defect cluster enhancement, periodic pattern dislocation enhancement, etc. through intensity filtering image manipulation. Organic PR materials have large space-bandwidth product, which makes them useful in adaptive filtering techniques in quality control systems. For instance, in the case of edge enhancement, phase conjugation via four-wave mixing suppresses the low spatial frequencies of the Fourier spectrum of an aperiodic image and consequently leads to image edge enhancement. In this work, we model, numerically verify, and simulate the performance of a four wave mixing setup used for edge, defect and pattern detection in periodic amplitude and phase structures. The results show that this technique successfully detects the slightest defects clearly even with no enhancement. This technique should facilitate improvements in applications such as image display sharpness utilizing edge enhancement, production line defect inspection of fabrics, textiles, e-beam lithography masks, surface inspection, and materials characterization.

Development of imaging FTS for astronomy

NASA Astrophysics Data System (ADS)

Grandmont, Frederic

2002-05-01

The Next Generation Space Telescope project in its early definition phases has given birth to many innovations in instrumentation for astronomy by providing funding for industries in an area often considered less lucrative and hence of lower interest. New alliances were formed with universities and institutions and the knowledge exchange lead to very interesting new concepts. The Imaging version of the Fourier Transform Spectrometer (IFTS), a derivative of the classical Michelson interferometer that has been used successfully in spectroscopy for decades, was introduced in military applications in the mid 80's with small FPA (- 2 X 4).

Automated vessel segmentation using cross-correlation and pooled covariance matrix analysis.

PubMed

Du, Jiang; Karimi, Afshin; Wu, Yijing; Korosec, Frank R; Grist, Thomas M; Mistretta, Charles A

2011-04-01

Time-resolved contrast-enhanced magnetic resonance angiography (CE-MRA) provides contrast dynamics in the vasculature and allows vessel segmentation based on temporal correlation analysis. Here we present an automated vessel segmentation algorithm including automated generation of regions of interest (ROIs), cross-correlation and pooled sample covariance matrix analysis. The dynamic images are divided into multiple equal-sized regions. In each region, ROIs for artery, vein and background are generated using an iterative thresholding algorithm based on the contrast arrival time map and contrast enhancement map. Region-specific multi-feature cross-correlation analysis and pooled covariance matrix analysis are performed to calculate the Mahalanobis distances (MDs), which are used to automatically separate arteries from veins. This segmentation algorithm is applied to a dual-phase dynamic imaging acquisition scheme where low-resolution time-resolved images are acquired during the dynamic phase followed by high-frequency data acquisition at the steady-state phase. The segmented low-resolution arterial and venous images are then combined with the high-frequency data in k-space and inverse Fourier transformed to form the final segmented arterial and venous images. Results from volunteer and patient studies demonstrate the advantages of this automated vessel segmentation and dual phase data acquisition technique. Copyright © 2011 Elsevier Inc. All rights reserved.

Experimental image alignment system

NASA Technical Reports Server (NTRS)

Moyer, A. L.; Kowel, S. T.; Kornreich, P. G.

1980-01-01

A microcomputer-based instrument for image alignment with respect to a reference image is described which uses the DEFT sensor (Direct Electronic Fourier Transform) for image sensing and preprocessing. The instrument alignment algorithm which uses the two-dimensional Fourier transform as input is also described. It generates signals used to steer the stage carrying the test image into the correct orientation. This algorithm has computational advantages over algorithms which use image intensity data as input and is suitable for a microcomputer-based instrument since the two-dimensional Fourier transform is provided by the DEFT sensor.

Optical Correlation of Images With Signal-Dependent Noise Using Constrained-Modulation Filter Devices

NASA Technical Reports Server (NTRS)

Downie, John D.

1995-01-01

Images with signal-dependent noise present challenges beyond those of images with additive white or colored signal-independent noise in terms of designing the optimal 4-f correlation filter that maximizes correlation-peak signal-to-noise ratio, or combinations of correlation-peak metrics. Determining the proper design becomes more difficult when the filter is to be implemented on a constrained-modulation spatial light modulator device. The design issues involved for updatable optical filters for images with signal-dependent film-grain noise and speckle noise are examined. It is shown that although design of the optimal linear filter in the Fourier domain is impossible for images with signal-dependent noise, proper nonlinear preprocessing of the images allows the application of previously developed design rules for optimal filters to be implemented on constrained-modulation devices. Thus the nonlinear preprocessing becomes necessary for correlation in optical systems with current spatial light modulator technology. These results are illustrated with computer simulations of images with signal-dependent noise correlated with binary-phase-only filters and ternary-phase-amplitude filters.

Two-Lens, Anamorphic, Brewster-Angle, Fourier-Transform Relay

NASA Astrophysics Data System (ADS)

Berggren, Ralph R.

1987-06-01

A two-lens system provides a simple and versatile means to relay a laser beam. The pair of lenses can provide true volume imaging, reproducing both amplitude and phase of the input beam. By using cylindrical lenses it is possible to change the aspect ratio of the beam. By adjusting the cylindrical curvatures, it is possible to minimize reflections by tilting the lenses at the Brewster angle.

Computer-assisted techniques to evaluate fringe patterns

NASA Astrophysics Data System (ADS)

Sciammarella, Cesar A.; Bhat, Gopalakrishna K.

1992-01-01

Strain measurement using interferometry requires an efficient way to extract the desired information from interferometric fringes. Availability of digital image processing systems makes it possible to use digital techniques for the analysis of fringes. In the past, there have been several developments in the area of one dimensional and two dimensional fringe analysis techniques, including the carrier fringe method (spatial heterodyning) and the phase stepping (quasi-heterodyning) technique. This paper presents some new developments in the area of two dimensional fringe analysis, including a phase stepping technique supplemented by the carrier fringe method and a two dimensional Fourier transform method to obtain the strain directly from the discontinuous phase contour map.

Off-resonance artifacts correction with convolution in k-space (ORACLE).

PubMed

Lin, Wei; Huang, Feng; Simonotto, Enrico; Duensing, George R; Reykowski, Arne

2012-06-01

Off-resonance artifacts hinder the wider applicability of echo-planar imaging and non-Cartesian MRI methods such as radial and spiral. In this work, a general and rapid method is proposed for off-resonance artifacts correction based on data convolution in k-space. The acquired k-space is divided into multiple segments based on their acquisition times. Off-resonance-induced artifact within each segment is removed by applying a convolution kernel, which is the Fourier transform of an off-resonance correcting spatial phase modulation term. The field map is determined from the inverse Fourier transform of a basis kernel, which is calibrated from data fitting in k-space. The technique was demonstrated in phantom and in vivo studies for radial, spiral and echo-planar imaging datasets. For radial acquisitions, the proposed method allows the self-calibration of the field map from the imaging data, when an alternating view-angle ordering scheme is used. An additional advantage for off-resonance artifacts correction based on data convolution in k-space is the reusability of convolution kernels to images acquired with the same sequence but different contrasts. Copyright © 2011 Wiley-Liss, Inc.

Diffraction-limited imaging with very large telescopes; Proceedings of the NATO Advanced Study Institute, Cargese, France, Sept. 13-23, 1988

NASA Astrophysics Data System (ADS)

Alloin, D. M.; Mariotti, J.-M.

Recent advances in optics and observation techniques for very large astronomical telescopes are discussed in reviews and reports. Topics addressed include Fourier optics and coherence, optical propagation and image formation through a turbulent atmosphere, radio telescopes, continuously deformable telescopes for optical interferometry (I), amplitude estimation from speckle I, noise calibration of speckle imagery, and amplitude estimation from diluted-array I. Consideration is given to first-order imaging methods, speckle imaging with the PAPA detector and the Knox-Thompson algorithm, phase-closure imaging, real-time wavefront sensing and adaptive optics, differential I, astrophysical programs for high-angular-resolution optical I, cophasing telescope arrays, aperture synthesis for space observatories, and lunar occultations for marcsec resolution.

Intensity correlation imaging with sunlight-like source

NASA Astrophysics Data System (ADS)

Wang, Wentao; Tang, Zhiguo; Zheng, Huaibin; Chen, Hui; Yuan, Yuan; Liu, Jinbin; Liu, Yanyan; Xu, Zhuo

2018-05-01

We show a method of intensity correlation imaging of targets illuminated by a sunlight-like source both theoretically and experimentally. With a Faraday anomalous dispersion optical filter (FADOF), we have modulated the coherence time of a thermal source up to 0.167 ns. And we carried out measurements of temporal and spatial correlations, respectively, with an intensity interferometer setup. By skillfully using the even Fourier fitting on the very sparse sampling data, the images of targets are successfully reconstructed from the low signal-noise-ratio(SNR) interference pattern by applying an iterative phase retrieval algorithm. The resulting imaging quality is as well as the one obtained by the theoretical fitting. The realization of such a case will bring this technique closer to geostationary satellite imaging illuminated by sunlight.

Generalized Fourier slice theorem for cone-beam image reconstruction.

PubMed

Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang

2015-01-01

The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).

Observations on the effects of image processing functions on fingermark data in the Fourier domain

NASA Astrophysics Data System (ADS)

Bramble, Simon K.; Fabrizi, Paola M.

1995-09-01

One of the image processing functions used for the enhancement of laten fingermark images is the Fourier transform. This paper describes some effects of spatial resolution, zero-filling and windowing on fingermark data in the Fourier domain. It is shown that with an understanding of the fingermark structure it is possible to determine the approximate prosition of the frequency data in the Fourier domain corresponding to the fingermark image detail. The effect of attenuation of frequency data on a zero-filled image is shown to be different to the same attenuation on a non-zero-filled image. The effects of windowing spatial data on the frequency data are also highlighted and compared with the same data after the application of a Hanning window.

A 2D Fourier tool for the analysis of photo-elastic effect in large granular assemblies

NASA Astrophysics Data System (ADS)

Leśniewska, Danuta

2017-06-01

Fourier transforms are the basic tool in constructing different types of image filters, mainly those reducing optical noise. Some DIC or PIV software also uses frequency space to obtain displacement fields from a series of digital images of a deforming body. The paper presents series of 2D Fourier transforms of photo-elastic transmission images, representing large pseudo 2D granular assembly, deforming under varying boundary conditions. The images related to different scales were acquired using the same image resolution, but taken at different distance from the sample. Fourier transforms of images, representing different stages of deformation, reveal characteristic features at the three (`macro-`, `meso-` and `micro-`) scales, which can serve as a data to study internal order-disorder transition within granular materials.

Single-shot EPI with Nyquist ghost compensation: Interleaved Dual-Echo with Acceleration (IDEA) EPI

PubMed Central

Poser, Benedikt A; Barth, Markus; Goa, Pål-Erik; Deng, Weiran; Stenger, V Andrew

2012-01-01

Echo planar imaging is most commonly used for BOLD fMRI, owing to its sensitivity and acquisition speed. A major problem with EPI is Nyquist (N/2) ghosting, most notably at high field. EPI data are acquired under an oscillating readout gradient and hence vulnerable to gradient imperfections such as eddy current delays and off-resonance effects, as these cause inconsistencies between odd and even k-space lines after time reversal. We propose a straightforward and pragmatic method herein termed Interleaved Dual Echo with Acceleration (IDEA) EPI: Two k-spaces (echoes) are acquired under the positive and negative readout lobes, respectively, by performing phase blips only before alternate readout gradients. From these two k-spaces, two almost entirely ghost free images per shot can be constructed, without need for phase correction. The doubled echo train length can be compensated by parallel imaging and/or partial Fourier acquisition. The two k-spaces can either be complex-averaged during reconstruction, which results in near-perfect cancellation of residual phase errors, or reconstructed into separate images. We demonstrate the efficacy of IDEA EPI and show phantom and in vivo images at both 3 and 7 Tesla. PMID:22411762

Complete fourier direct magnetic resonance imaging (CFD-MRI) for diffusion MRI

PubMed Central

Özcan, Alpay

2013-01-01

The foundation for an accurate and unifying Fourier-based theory of diffusion weighted magnetic resonance imaging (DW–MRI) is constructed by carefully re-examining the first principles of DW–MRI signal formation and deriving its mathematical model from scratch. The derivations are specifically obtained for DW–MRI signal by including all of its elements (e.g., imaging gradients) using complex values. Particle methods are utilized in contrast to conventional partial differential equations approach. The signal is shown to be the Fourier transform of the joint distribution of number of the magnetic moments (at a given location at the initial time) and magnetic moment displacement integrals. In effect, the k-space is augmented by three more dimensions, corresponding to the frequency variables dual to displacement integral vectors. The joint distribution function is recovered by applying the Fourier transform to the complete high-dimensional data set. In the process, to obtain a physically meaningful real valued distribution function, phase corrections are applied for the re-establishment of Hermitian symmetry in the signal. Consequently, the method is fully unconstrained and directly presents the distribution of displacement integrals without any assumptions such as symmetry or Markovian property. The joint distribution function is visualized with isosurfaces, which describe the displacement integrals, overlaid on the distribution map of the number of magnetic moments with low mobility. The model provides an accurate description of the molecular motion measurements via DW–MRI. The improvement of the characterization of tissue microstructure leads to a better localization, detection and assessment of biological properties such as white matter integrity. The results are demonstrated on the experimental data obtained from an ex vivo baboon brain. PMID:23596401

The application of an optical Fourier spectrum analyzer on detecting defects in mass-produced satellite photographs

NASA Technical Reports Server (NTRS)

Athale, R.; Lee, S. H.

1976-01-01

Various defects in mass-produced pictures transmitted to earth from a satellite are investigated. It is found that the following defects are readily detectable via Fourier spectrum analysis: (1) bit slip, (2) breakup causing loss of image, and (3) disabled track at the top of the imagery. The scratches made on the film during mass production, which are difficult to detect by visual observation, also show themselves readily in Fourier spectrum analysis. A relation is established between the number of scratches, their width and depth and the intensity of their Fourier spectra. Other defects that are found to be equally suitable for Fourier spectrum analysis or visual (image analysis) detection are synchronous loss without blurring of image, and density variation in gray scale. However, the Fourier spectrum analysis is found to be unsuitable for detection of such defects as pin holes, annotation error, synchronous loss with blurring of images, and missing image in the beginning of the work order. The design of an automated, real time system, which will reject defective films, is treated.

Reduction and coding of synthetic aperture radar data with Fourier transforms

NASA Technical Reports Server (NTRS)

Tilley, David G.

1995-01-01

Recently, aboard the Space Radar Laboratory (SRL), the two roles of Fourier Transforms for ocean image synthesis and surface wave analysis have been implemented with a dedicated radar processor to significantly reduce Synthetic Aperture Radar (SAR) ocean data before transmission to the ground. The object was to archive the SAR image spectrum, rather than the SAR image itself, to reduce data volume and capture the essential descriptors of the surface wave field. SAR signal data are usually sampled and coded in the time domain for transmission to the ground where Fourier Transforms are applied both to individual radar pulses and to long sequences of radar pulses to form two-dimensional images. High resolution images of the ocean often contain no striking features and subtle image modulations by wind generated surface waves are only apparent when large ocean regions are studied, with Fourier transforms, to reveal periodic patterns created by wind stress over the surface wave field. Major ocean currents and atmospheric instability in coastal environments are apparent as large scale modulations of SAR imagery. This paper explores the possibility of computing complex Fourier spectrum codes representing SAR images, transmitting the coded spectra to Earth for data archives and creating scenes of surface wave signatures and air-sea interactions via inverse Fourier transformations with ground station processors.

Comparison with the horizontal phase velocity distribution of gravity waves observed airglow imaging data of different sampling periods

NASA Astrophysics Data System (ADS)

Matsuda, T. S.; Nakamura, T.; Ejiri, M. K.; Tsutsumi, M.; Shiokawa, K.

2014-12-01

Atmospheric gravity waves (AGWs), which are generated in the lower atmosphere, transport significant amount of energy and momentum into the mesosphere and lower thermosphere. Among many parameters to characterize AGWs, horizontal phase velocity is very important to discuss the vertical propagation. Airglow imaging is a useful technique for investigating the horizontal structures of AGWs around mesopause. There are many airglow imagers operated all over the world, and a large amount of data which could improve our understanding of AGWs propagation direction and source distribution in the MLT region. We have developed a new statistical analysis method for obtaining the power spectrum in the horizontal phase velocity domain (phase velocity spectrum), from airglow image data, so as to deal with huge amounts of imaging data obtained on different years and at various observation sites, without bias caused by different event extraction criteria for the observer. From a series of images projected onto the geographic coordinates, 3-D Fourier transform is applied and 3-D power spectrum in horizontal wavenumber and frequency domain is obtained. Then, it is converted into phase velocity and frequency domain. Finally, the spectrum is integrated along the frequency for the range of interest and 2-D spectrum in horizontal phase velocity is calculated. This method was applied to the data obtained at Syowa Station (69ºS, 40ºE), Antarctica, in 2011 and compared with a conventional event analysis in which the phase fronts were traced manually in order to estimate horizontal propagation characteristics. This comparison shows that our new method is adequate to deriving the horizontal phase velocity characteristics of AGWs observed by airglow imaging technique. Airglow imaging observation has been operated with various sampling intervals. We also presents how the images with different sample interval should be treated.

Robust Global Image Registration Based on a Hybrid Algorithm Combining Fourier and Spatial Domain Techniques

DTIC Science & Technology

2012-09-01

Robust global image registration based on a hybrid algorithm combining Fourier and spatial domain techniques Peter N. Crabtree, Collin Seanor...00-00-2012 to 00-00-2012 4. TITLE AND SUBTITLE Robust global image registration based on a hybrid algorithm combining Fourier and spatial domain...demonstrate performance of a hybrid algorithm . These results are from analysis of a set of images of an ISO 12233 [12] resolution chart captured in the

Optical image encryption using triplet of functions

NASA Astrophysics Data System (ADS)

Yatish; Fatima, Areeba; Nishchal, Naveen Kumar

2018-03-01

We propose an image encryption scheme that brings into play a technique using a triplet of functions to manipulate complex-valued functions. Optical cryptosystems using this method are an easier approach toward the ciphertext generation that avoids the use of holographic setup to record phase. The features of this method were shown in the context of double random phase encoding and phase-truncated Fourier transform-based cryptosystems using gyrator transform. In the first step, the complex function is split into two matrices. These matrices are separated, so they contain the real and imaginary parts. In the next step, these two matrices and a random distribution function are acted upon by one of the functions in the triplet. During decryption, the other two functions in the triplet help us retrieve the complex-valued function. The simulation results demonstrate the effectiveness of the proposed idea. To check the robustness of the proposed scheme, attack analyses were carried out.

Atmospheric limb sounding with imaging FTS

NASA Astrophysics Data System (ADS)

Friedl-Vallon, Felix; Riese, Martin; Preusse, Peter; Oelhaf, Hermann; Fischer, Herbert

Imaging Fourier transform spectrometers in the thermal infrared are a promising new class of sensors for atmospheric science. The availability of fast and sensitive large focal plane arrays with appropriate spectral coverage in the infrared region allows the conception and construction of innovative sensors for Nadir and Limb geometry. Instruments in Nadir geometry have already reached prototype status (e.g. Geostationary Imaging Fourier Transform Spectrometer / U. Wisconsin and NASA) or are in Phase A study (infrared sounding mission on Meteosat third generation / ESA and EUMETSAT). The first application of the new technical possibilities to atmospheric limb sounding from space, the Imaging Michelson Interferometer for Passive Atmospheric Sounding (IMIPAS), is currently studied by industry in the context of preparatory work for the next set of ESA earth explorers. The scientific focus of the instrument is on the processes controlling the composition of the mid/upper troposphere and lower stratosphere. The instrument concept of IMIPAS has been conceived at the research centres Karlsruhe and J¨lich. The development of a precursor instrument (GLORIA-AB) at these research institutions u started already in 2005. The instrument will be able to fly on board of various airborne platforms. First scientific missions are planned for the second half of the year 2009 on board the new German research aircraft HALO. This airborne sensor serves its own scientific purpose, but it also provides a test bed to learn about this new instrument class and its peculiarities and to learn to exploit and interpret the wealth of information provided by a limb imaging IR Fourier transform spectrometer. The presentation will discuss design considerations and challenges for GLORIA-AB and put them in the context of the planned satellite application. It will describe the solutions found, present first laboratory figures of merit for the prototype instrument and outline the new scientific possibilities.

Inflection Points in Magnetic Resonance Imaging Technology-35 Years of Collaborative Research and Development.

PubMed

Wood, Michael L; Griswold, Mark A; Henkelman, Mark; Hennig, Jürgen

2015-09-01

The technology for clinical magnetic resonance imaging (MRI) has advanced with remarkable speed and in such a manner reflecting the influence of 3 forces-collaboration between disciplines, collaboration between academia and industry, and the enabling of software applications by hardware. The forces are evident in the key developments from the past and emerging trends for the future highlighted in this review article. These developments are associated with MRI system attributes, such as wider, shorter, and stronger magnets; specialty magnets and hybrid devices; k space; and the notion that magnetic field gradients perform a Fourier transform on the spatial distribution of magnetization, phased-array coils and parallel imaging, the user interface, the wide range of contrast possible, and applications that exploit motion-induced phase shifts. An attempt is made to show connections between these developments and how the 3 forces mentioned previously will continue to shape the technology used so productively in clinical MRI.

Analytic reconstruction of magnetic resonance imaging signal obtained from a periodic encoding field.

PubMed

Rybicki, F J; Hrovat, M I; Patz, S

2000-09-01

We have proposed a two-dimensional PERiodic-Linear (PERL) magnetic encoding field geometry B(x,y) = g(y)y cos(q(x)x) and a magnetic resonance imaging pulse sequence which incorporates two fields to image a two-dimensional spin density: a standard linear gradient in the x dimension, and the PERL field. Because of its periodicity, the PERL field produces a signal where the phase of the two dimensions is functionally different. The x dimension is encoded linearly, but the y dimension appears as the argument of a sinusoidal phase term. Thus, the time-domain signal and image spin density are not related by a two-dimensional Fourier transform. They are related by a one-dimensional Fourier transform in the x dimension and a new Bessel function integral transform (the PERL transform) in the y dimension. The inverse of the PERL transform provides a reconstruction algorithm for the y dimension of the spin density from the signal space. To date, the inverse transform has been computed numerically by a Bessel function expansion over its basis functions. This numerical solution used a finite sum to approximate an infinite summation and thus introduced a truncation error. This work analytically determines the basis functions for the PERL transform and incorporates them into the reconstruction algorithm. The improved algorithm is demonstrated by (1) direct comparison between the numerically and analytically computed basis functions, and (2) reconstruction of a known spin density. The new solution for the basis functions also lends proof of the system function for the PERL transform under specific conditions.

Single-Grid-Pair Fourier Telescope for Imaging in Hard-X Rays and gamma Rays

NASA Technical Reports Server (NTRS)

Campbell, Jonathan

2008-01-01

This instrument, a proposed Fourier telescope for imaging in hard-x rays and gamma rays, would contain only one pair of grids made of an appropriate radiation-absorpting/ scattering material, in contradistinction to multiple pairs of such as grids in prior Fourier x- and gamma-ray telescopes. This instrument would also include a relatively coarse gridlike image detector appropriate to the radiant flux to be imaged. Notwithstanding the smaller number of grids and the relative coarseness of the imaging detector, the images produced by the proposed instrument would be of higher quality.

Fourier plane imaging microscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dominguez, Daniel, E-mail: daniel.dominguez@ttu.edu; Peralta, Luis Grave de; Nano Tech Center, Texas Tech University, Lubbock, Texas 79409

We show how the image of an unresolved photonic crystal can be reconstructed using a single Fourier plane (FP) image obtained with a second camera that was added to a traditional compound microscope. We discuss how Fourier plane imaging microscopy is an application of a remarkable property of the obtained FP images: they contain more information about the photonic crystals than the images recorded by the camera commonly placed at the real plane of the microscope. We argue that the experimental results support the hypothesis that surface waves, contributing to enhanced resolution abilities, were optically excited in the studied photonicmore » crystals.« less

Fan beam image reconstruction with generalized Fourier slice theorem.

PubMed

Zhao, Shuangren; Yang, Kang; Yang, Kevin

2014-01-01

For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension.

Theory of Remote Image Formation

NASA Astrophysics Data System (ADS)

Blahut, Richard E.

2004-11-01

In many applications, images, such as ultrasonic or X-ray signals, are recorded and then analyzed with digital or optical processors in order to extract information. Such processing requires the development of algorithms of great precision and sophistication. This book presents a unified treatment of the mathematical methods that underpin the various algorithms used in remote image formation. The author begins with a review of transform and filter theory. He then discusses two- and three-dimensional Fourier transform theory, the ambiguity function, image construction and reconstruction, tomography, baseband surveillance systems, and passive systems (where the signal source might be an earthquake or a galaxy). Information-theoretic methods in image formation are also covered, as are phase errors and phase noise. Throughout the book, practical applications illustrate theoretical concepts, and there are many homework problems. The book is aimed at graduate students of electrical engineering and computer science, and practitioners in industry. Presents a unified treatment of the mathematical methods that underpin the algorithms used in remote image formation Illustrates theoretical concepts with reference to practical applications Provides insights into the design parameters of real systems

An Asymmetric Image Encryption Based on Phase Truncated Hybrid Transform

NASA Astrophysics Data System (ADS)

Khurana, Mehak; Singh, Hukum

2017-09-01

To enhance the security of the system and to protect it from the attacker, this paper proposes a new asymmetric cryptosystem based on hybrid approach of Phase Truncated Fourier and Discrete Cosine Transform (PTFDCT) which adds non linearity by including cube and cube root operation in the encryption and decryption path respectively. In this cryptosystem random phase masks are used as encryption keys and phase masks generated after the cube operation in encryption process are reserved as decryption keys and cube root operation is required to decrypt image in decryption process. The cube and cube root operation introduced in the encryption and decryption path makes system resistant against standard attacks. The robustness of the proposed cryptosystem has been analysed and verified on the basis of various parameters by simulating on MATLAB 7.9.0 (R2008a). The experimental results are provided to highlight the effectiveness and suitability of the proposed cryptosystem and prove the system is secure.

Off-axis digital holographic camera for quantitative phase microscopy.

PubMed

Monemhaghdoust, Zahra; Montfort, Frédéric; Emery, Yves; Depeursinge, Christian; Moser, Christophe

2014-06-01

We propose and experimentally demonstrate a digital holographic camera which can be attached to the camera port of a conventional microscope for obtaining digital holograms in a self-reference configuration, under short coherence illumination and in a single shot. A thick holographic grating filters the beam containing the sample information in two dimensions through diffraction. The filtered beam creates the reference arm of the interferometer. The spatial filtering method, based on the high angular selectivity of the thick grating, reduces the alignment sensitivity to angular displacements compared with pinhole based Fourier filtering. The addition of a thin holographic grating alters the coherence plane tilt introduced by the thick grating so as to create high-visibility interference over the entire field of view. The acquired full-field off-axis holograms are processed to retrieve the amplitude and phase information of the sample. The system produces phase images of cheek cells qualitatively similar to phase images extracted with a standard commercial DHM.

Implementations of three OCT angiography (OCTA) methods with 1.7 MHz A-scan rate OCT system on imaging of human retinal and choroidal vasculature

NASA Astrophysics Data System (ADS)

Poddar, Raju; Werner, John S.

2018-06-01

We present noninvasive depth-resolved imaging of human retinal and choroidal microcirculation with an ultrahigh-speed (1.7 MHz A-scans/s), Fourier-domain mode locked (FDML) swept-source optical coherence tomography (SS-OCT) system having a central wavelength of 1065 nm. Three OCT angiography (OCTA) motion based contrast methods, namely phase variance (PV), amplitude decorrelation (AD) and Joint Spectral and Time domain OCT (STdOCT) were implemented. The OCTA imaging was performed with a field of view of 16° (5 mm × 5 mm) and 30° (9 mm × 9 mm), on the retina. A qualitative comparison of images obtained with all three OCTA methods is demonstrated using the same eye of a healthy volunteer. Different parameters, namely acquisition time, scanning area, and scanning density, are discussed. The phase-variance OCTA (PV-OCTA) method produced relatively better results than the other two. Different features regarding the retinal and choroidal vessels are described in different subjects.

In-plane "superresolution" MRI with phaseless sub-pixel encoding.

PubMed

Hennel, Franciszek; Tian, Rui; Engel, Maria; Pruessmann, Klaas P

2018-04-15

Acquisition of high-resolution imaging data using multiple excitations without the sensitivity to fluctuations of the transverse magnetization phase, which is a major problem of multi-shot MRI. The concept of superresolution MRI based on microscopic tagging is analyzed using an analogy with the optical method of structured illumination. Sinusoidal tagging is shown to provide subpixel resolution by mixing of neighboring spatial frequency (k-space) bands. It represents a phaseless modulation added on top of the standard Fourier encoding, which allows the phase fluctuations to be discarded at an intermediate reconstruction step. Improvements are proposed to correct for tag distortions due to magnetic field inhomogeneity and to avoid the propagation of Gibbs ringing from intermediate low-resolution images to the final image. The method was applied to diffusion-weighted EPI. Artifact-free superresolution images can be obtained despite a finite duration of the tagging sequence and related pattern distortions by a field map based phase correction of band-wise reconstructed images. The ringing effect present in the intermediate images can be suppressed by partial overlapping of the mixed k-space bands in combination with an adapted filter. High-resolution diffusion-weighted images of the human head were obtained with a three-shot EPI sequence despite motion-related phase fluctuations between the shots. Due to its phaseless character, tagging-based sub-pixel encoding is an alternative to k-space segmenting in the presence of unknown phase fluctuations, in particular those due to motion under strong diffusion gradients. Proposed improvements render the method practicable in realistic conditions. © 2018 International Society for Magnetic Resonance in Medicine.

Isotropic Backward Waves Supported by a Spiral Array Metasurface.

PubMed

Tremain, Ben; Hooper, Ian R; Sambles, J Roy; Hibbins, Alastair P

2018-05-08

A planar metallic metasurface formed of spiral elements is shown to support an isotropic backward wave over a narrow band of microwave frequencies. The magnetic field of this left-handed mode is mapped experimentally using a near-field scanning technique, allowing the anti-parallel group and phase velocities to be directly visualised. The corresponding dispersion relation and isofrequency contours are obtained through Fourier transformation of the field images.

Laser induced periodic surface structuring on Si by temporal shaped femtosecond pulses.

PubMed

Almeida, G F B; Martins, R J; Otuka, A J G; Siqueira, J P; Mendonca, C R

2015-10-19

We investigated the effect of temporal shaped femtosecond pulses on silicon laser micromachining. By using sinusoidal spectral phases, pulse trains composed of sub-pulses with distinct temporal separations were generated and applied to the silicon surface to produce Laser Induced Periodic Surface Structures (LIPSS). The LIPSS obtained with different sub-pulse separation were analyzed by comparing the intensity of the two-dimensional fast Fourier Transform (2D-FFT) of the AFM images of the ripples (LIPSS). It was observed that LIPSS amplitude is more emphasized for the pulse train with sub-pulses separation of 128 fs, even when compared with the Fourier transform limited pulse. By estimating the carrier density achieved at the end of each pulse train, we have been able to interpret our results with the Sipe-Drude model, that predicts that LIPSS efficacy is higher for a specific induced carrier density. Hence, our results indicate that temporal shaping of the excitation pulse, performed by spectral phase modulation, can be explored in fs-laser microstructuring.

Contrast computation methods for interferometric measurement of sensor modulation transfer function

NASA Astrophysics Data System (ADS)

Battula, Tharun; Georgiev, Todor; Gille, Jennifer; Goma, Sergio

2018-01-01

Accurate measurement of image-sensor frequency response over a wide range of spatial frequencies is very important for analyzing pixel array characteristics, such as modulation transfer function (MTF), crosstalk, and active pixel shape. Such analysis is especially significant in computational photography for the purposes of deconvolution, multi-image superresolution, and improved light-field capture. We use a lensless interferometric setup that produces high-quality fringes for measuring MTF over a wide range of frequencies (here, 37 to 434 line pairs per mm). We discuss the theoretical framework, involving Michelson and Fourier contrast measurement of the MTF, addressing phase alignment problems using a moiré pattern. We solidify the definition of Fourier contrast mathematically and compare it to Michelson contrast. Our interferometric measurement method shows high detail in the MTF, especially at high frequencies (above Nyquist frequency). We are able to estimate active pixel size and pixel pitch from measurements. We compare both simulation and experimental MTF results to a lens-free slanted-edge implementation using commercial software.

3D cine magnetic resonance imaging of rat lung ARDS using gradient-modulated SWIFT with retrospective respiratory gating

NASA Astrophysics Data System (ADS)

Kobayashi, Naoharu; Lei, Jianxun; Utecht, Lynn; Garwood, Michael; Ingbar, David H.; Bhargava, Maneesh

2015-03-01

SWeep Imaging with Fourier Transformation (SWIFT) with gradient modulation and DC navigator retrospective gating is introduced as a 3D cine magnetic resonance imaging (MRI) method for the lung. In anesthetized normal rats, the quasi-simultaneous excitation and acquisition in SWIFT enabled extremely high sensitivity to the fast-decaying parenchymal signals (TE=~4 μs), which are invisible with conventional MRI techniques. Respiratory motion information was extracted from DC navigator signals and the SWIFT data were reconstructed to 3D cine images with 16 respiratory phases. To test this technique's capabilities, rats exposed to > 95% O2 for 60 hours for induction of acute respiratory distress syndrome (ARDS), were imaged and compared with normal rat lungs (N=7 and 5 for ARDS and normal groups, respectively). SWIFT images showed lung tissue density differences along the gravity direction. In the cine SWIFT images, a parenchymal signal drop at the inhalation phase was consistently observed for both normal and ARDS rats due to lung inflation (i.e. decrease of the proton density), but the drop was less for ARDS rats. Depending on the respiratory phase and lung region, the lungs from the ARDS rats showed 1-24% higher parenchymal signal intensities relative to the normal rat lungs, likely due to accumulated extravascular water (EVLW). Those results demonstrate that SWIFT has high enough sensitivity for detecting the lung proton density changes due to gravity, different phases of respiration and accumulation of EVLW in the rat ARDS lungs.

Three-dimensional image display system using stereogram and holographic optical memory techniques

NASA Astrophysics Data System (ADS)

Kim, Cheol S.; Kim, Jung G.; Shin, Chang-Mok; Kim, Soo-Joong

2001-09-01

In this paper, we implemented a three dimensional image display system using stereogram and holographic optical memory techniques which can store many images and reconstruct them automatically. In this system, to store and reconstruct stereo images, incident angle of reference beam must be controlled in real time, so we used BPH (binary phase hologram) and LCD (liquid crystal display) for controlling reference beam. And input images are represented on the LCD without polarizer/analyzer for maintaining uniform beam intensities regardless of the brightness of input images. The input images and BPHs are edited using application software with having the same recording scheduled time interval in storing. The reconstructed stereo images are acquired by capturing the output images with CCD camera at the behind of the analyzer which transforms phase information into brightness information of images. The reference beams are acquired by Fourier transform of BPH which designed with SA (simulated annealing) algorithm, and represented on the LCD with the 0.05 seconds time interval using application software for reconstructing the stereo images. In output plane, we used a LCD shutter that is synchronized to a monitor that displays alternate left and right eye images for depth perception. We demonstrated optical experiment which store and reconstruct four stereo images in BaTiO3 repeatedly using holographic optical memory techniques.

Optimized doppler optical coherence tomography for choroidal capillary vasculature imaging

NASA Astrophysics Data System (ADS)

Liu, Gangjun; Qi, Wenjuan; Yu, Lingfeng; Chen, Zhongping

2011-03-01

In this paper, we analyzed the retinal and choroidal blood vasculature in the posterior segment of the human eye with optimized color Doppler and Doppler variance optical coherence tomography. Depth-resolved structure, color Doppler and Doppler variance images were compared. Blood vessels down to capillary level were able to be obtained with the optimized optical coherence color Doppler and Doppler variance method. For in-vivo imaging of human eyes, bulkmotion induced bulk phase must be identified and removed before using color Doppler method. It was found that the Doppler variance method is not sensitive to bulk motion and the method can be used without removing the bulk phase. A novel, simple and fast segmentation algorithm to indentify retinal pigment epithelium (RPE) was proposed and used to segment the retinal and choroidal layer. The algorithm was based on the detected OCT signal intensity difference between different layers. A spectrometer-based Fourier domain OCT system with a central wavelength of 890 nm and bandwidth of 150nm was used in this study. The 3-dimensional imaging volume contained 120 sequential two dimensional images with 2048 A-lines per image. The total imaging time was 12 seconds and the imaging area was 5x5 mm2.

Null test fourier domain alignment technique for phase-shifting point diffraction interferometer

DOEpatents

Naulleau, Patrick; Goldberg, Kenneth Alan

2000-01-01

Alignment technique for calibrating a phase-shifting point diffraction interferometer involves three independent steps where the first two steps independently align the image points and pinholes in rotation and separation to a fixed reference coordinate system, e.g, CCD. Once the two sub-elements have been properly aligned to the reference in two parameters (separation and orientation), the third step is to align the two sub-element coordinate systems to each other in the two remaining parameters (x,y) using standard methods of locating the pinholes relative to some easy to find reference point.

Fourier Spectral Filter Array for Optimal Multispectral Imaging.

PubMed

Jia, Jie; Barnard, Kenneth J; Hirakawa, Keigo

2016-04-01

Limitations to existing multispectral imaging modalities include speed, cost, range, spatial resolution, and application-specific system designs that lack versatility of the hyperspectral imaging modalities. In this paper, we propose a novel general-purpose single-shot passive multispectral imaging modality. Central to this design is a new type of spectral filter array (SFA) based not on the notion of spatially multiplexing narrowband filters, but instead aimed at enabling single-shot Fourier transform spectroscopy. We refer to this new SFA pattern as Fourier SFA, and we prove that this design solves the problem of optimally sampling the hyperspectral image data.

On-axis programmable microscope using liquid crystal spatial light modulator

NASA Astrophysics Data System (ADS)

García-Martínez, Pascuala; Martínez, José Luís.; Moreno, Ignacio

2017-06-01

Spatial light modulators (SLM) are currently used in many applications in optical microscopy and imaging. One of the most promising methods is the use of liquid crystal displays (LCD) as programmable phase diffractive optical elements (DOE) placed in the Fourier plane giving access to the spatial frequencies which can be phased shifted individually, allowing to emulate a wealth of contrast enhancing methods for both amplitude and phase samples. We use phase and polarization modulation of LCD to implement an on-axis microscope optical system. The LCD used are Hamamatsu liquid crystal on silicon (LCOS) SLM free of flicker, thus showing a full profit of the SLM space bandwidth, as opposed to optical systems in the literature forced to work off-axis due to the strong zero-order component. Taking benefits of the phase modulation of the LCOS we have implemented different microscopic imaging operations, such as high-pass and low-pass filtering in parallel using programmable blazed gratings. Moreover, we are able to control polarization modulation to display two orthogonal linear state of polarization images than can be subtracted or added by changing the period of the blazed grating. In that sense, Differential Interference Contrast (DIC) microscopy can be easily done by generating two images exploiting the polarization splitting properties when a blazed grating is displayed in the SLM. Biological microscopy samples are also used.

Multi-Shot Sensitivity-Encoded Diffusion Data Recovery Using Structured Low-Rank Matrix Completion (MUSSELS)

PubMed Central

Mani, Merry; Jacob, Mathews; Kelley, Douglas; Magnotta, Vincent

2017-01-01

Purpose To introduce a novel method for the recovery of multi-shot diffusion weighted (MS-DW) images from echo-planar imaging (EPI) acquisitions. Methods Current EPI-based MS-DW reconstruction methods rely on the explicit estimation of the motion-induced phase maps to recover artifact-free images. In the new formulation, the k-space data of the artifact-free DWI is recovered using a structured low-rank matrix completion scheme, which does not require explicit estimation of the phase maps. The structured matrix is obtained as the lifting of the multi-shot data. The smooth phase-modulations between shots manifest as null-space vectors of this matrix, which implies that the structured matrix is low-rank. The missing entries of the structured matrix are filled in using a nuclear-norm minimization algorithm subject to the data-consistency. The formulation enables the natural introduction of smoothness regularization, thus enabling implicit motion-compensated recovery of the MS-DW data. Results Our experiments on in-vivo data show effective removal of artifacts arising from inter-shot motion using the proposed method. The method is shown to achieve better reconstruction than the conventional phase-based methods. Conclusion We demonstrate the utility of the proposed method to effectively recover artifact-free images from Cartesian fully/under-sampled and partial Fourier acquired data without the use of explicit phase estimates. PMID:27550212

Complex dark-field contrast and its retrieval in x-ray phase contrast imaging implemented with Talbot interferometry.

PubMed

Yang, Yi; Tang, Xiangyang

2014-10-01

Under the existing theoretical framework of x-ray phase contrast imaging methods implemented with Talbot interferometry, the dark-field contrast refers to the reduction in interference fringe visibility due to small-angle x-ray scattering of the subpixel microstructures of an object to be imaged. This study investigates how an object's subpixel microstructures can also affect the phase of the intensity oscillations. Instead of assuming that the object's subpixel microstructures distribute in space randomly, the authors' theoretical derivation starts by assuming that an object's attenuation projection and phase shift vary at a characteristic size that is not smaller than the period of analyzer grating G₂ and a characteristic length dc. Based on the paraxial Fresnel-Kirchhoff theory, the analytic formulae to characterize the zeroth- and first-order Fourier coefficients of the x-ray irradiance recorded at each detector cell are derived. Then the concept of complex dark-field contrast is introduced to quantify the influence of the object's microstructures on both the interference fringe visibility and the phase of intensity oscillations. A method based on the phase-attenuation duality that holds for soft tissues and high x-ray energies is proposed to retrieve the imaginary part of the complex dark-field contrast for imaging. Through computer simulation study with a specially designed numerical phantom, they evaluate and validate the derived analytic formulae and the proposed retrieval method. Both theoretical analysis and computer simulation study show that the effect of an object's subpixel microstructures on x-ray phase contrast imaging method implemented with Talbot interferometry can be fully characterized by a complex dark-field contrast. The imaginary part of complex dark-field contrast quantifies the influence of the object's subpixel microstructures on the phase of intensity oscillations. Furthermore, at relatively high energies, for soft tissues it can be retrieved for imaging with a method based on the phase-attenuation duality. The analytic formulae derived in this work to characterize the complex dark-field contrast in x-ray phase contrast imaging method implemented with Talbot interferometry are of significance, which may initiate more activities in the research and development of x-ray differential phase contrast imaging for extensive biomedical applications.

Invited Article: Mask-modulated lensless imaging with multi-angle illuminations

NASA Astrophysics Data System (ADS)

Zhang, Zibang; Zhou, You; Jiang, Shaowei; Guo, Kaikai; Hoshino, Kazunori; Zhong, Jingang; Suo, Jinli; Dai, Qionghai; Zheng, Guoan

2018-06-01

The use of multiple diverse measurements can make lensless phase retrieval more robust. Conventional diversity functions include aperture diversity, wavelength diversity, translational diversity, and defocus diversity. Here we discuss a lensless imaging scheme that employs multiple spherical-wave illuminations from a light-emitting diode array as diversity functions. In this scheme, we place a binary mask between the sample and the detector for imposing support constraints for the phase retrieval process. This support constraint enforces the light field to be zero at certain locations and is similar to the aperture constraint in Fourier ptychographic microscopy. We use a self-calibration algorithm to correct the misalignment of the binary mask. The efficacy of the proposed scheme is first demonstrated by simulations where we evaluate the reconstruction quality using mean square error and structural similarity index. The scheme is then experimentally tested by recovering images of a resolution target and biological samples. The proposed scheme may provide new insights for developing compact and large field-of-view lensless imaging platforms. The use of the binary mask can also be combined with other diversity functions for better constraining the phase retrieval solution space. We provide the open-source implementation code for the broad research community.

Comparative analysis of imaging configurations and objectives for Fourier microscopy.

PubMed

Kurvits, Jonathan A; Jiang, Mingming; Zia, Rashid

2015-11-01

Fourier microscopy is becoming an increasingly important tool for the analysis of optical nanostructures and quantum emitters. However, achieving quantitative Fourier space measurements requires a thorough understanding of the impact of aberrations introduced by optical microscopes that have been optimized for conventional real-space imaging. Here we present a detailed framework for analyzing the performance of microscope objectives for several common Fourier imaging configurations. To this end, we model objectives from Nikon, Olympus, and Zeiss using parameters that were inferred from patent literature and confirmed, where possible, by physical disassembly. We then examine the aberrations most relevant to Fourier microscopy, including the alignment tolerances of apodization factors for different objective classes, the effect of magnification on the modulation transfer function, and vignetting-induced reductions of the effective numerical aperture for wide-field measurements. Based on this analysis, we identify an optimal objective class and imaging configuration for Fourier microscopy. In addition, the Zemax files for the objectives and setups used in this analysis have been made publicly available as a resource for future studies.

Tomographic phase analysis to detect the site of accessory conduction pathway in Wolff-Parkinson-White syndrome

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakajima, K.; Bunko, H.; Tada, A.

1984-01-01

Phase analysis has been applied to Wolff-Parkinson-White syndrome (WPW) to detect the site of accessory conduction pathway (ACP); however, there was a limitation to estimate the precise location of ACP by planar phase analysis. In this study, the authors applied phase analysis to gated blood pool tomography. Twelve patients with WPW who underwent epicardial mapping and surgical division of ACP were studied by both of gated emission computed tomography (GECT) and routine gated blood pool study (GBPS). The GBPS was performed with Tc-99m red blood cells in multiple projections; modified left anterior oblique, right anterior oblique and/or left lateral views.more » In GECT, short axial, horizontal and vertical long axial blood pool images were reconstructed. Phase analysis was performed using fundamental frequency of the Fourier transform in both GECT and GBPS images, and abnormal initial contractions on both the planar and tomographic phase analysis were compared with the location of surgically confirmed ACPs. In planar phase analysis, abnormal initial phase was identified in 7 out of 12 (58%) patients, while in tomographic phase analysis, the localization of ACP was predicted in 11 out of 12 (92%) patients. Tomographic phase analysis is superior to planar phase images in 8 out of 12 patients to estimate the location of ACP. Phase analysis by GECT can avoid overlap of blood pool in cardiac chambers and has advantage to identify the propagation of phase three-dimensionally. Tomographic phase analysis is a good adjunctive method for patients with WPW to estimate the site of ACP.« less

Implementation and assessment of diffusion-weighted partial Fourier readout-segmented echo-planar imaging.

PubMed

Frost, Robert; Porter, David A; Miller, Karla L; Jezzard, Peter

2012-08-01

Single-shot echo-planar imaging has been used widely in diffusion magnetic resonance imaging due to the difficulties in correcting motion-induced phase corruption in multishot data. Readout-segmented EPI has addressed the multishot problem by introducing a two-dimensional nonlinear navigator correction with online reacquisition of uncorrectable data to enable acquisition of high-resolution diffusion data with reduced susceptibility artifact and T*(2) blurring. The primary shortcoming of readout-segmented EPI in its current form is its long acquisition time (longer than similar resolution single-shot echo-planar imaging protocols by approximately the number of readout segments), which limits the number of diffusion directions. By omitting readout segments at one side of k-space and using partial Fourier reconstruction, readout-segmented EPI imaging times could be reduced. In this study, the effects of homodyne and projection onto convex sets reconstructions on estimates of the fractional anisotropy, mean diffusivity, and diffusion orientation in fiber tracts and raw T(2)- and trace-weighted signal are compared, along with signal-to-noise ratio results. It is found that projections onto convex sets reconstruction with 3/5 segments in a 2 mm isotropic diffusion tensor image acquisition and 9/13 segments in a 0.9 × 0.9 × 4.0 mm(3) diffusion-weighted image acquisition provide good fidelity relative to the full k-space parameters. This allows application of readout-segmented EPI to tractography studies, and clinical stroke and oncology protocols. Copyright © 2011 Wiley-Liss, Inc.

General solution of undersampling frequency conversion and its optimization for parallel photodisplacement imaging.

PubMed

Nakata, Toshihiko; Ninomiya, Takanori

2006-10-10

A general solution of undersampling frequency conversion and its optimization for parallel photodisplacement imaging is presented. Phase-modulated heterodyne interference light generated by a linear region of periodic displacement is captured by a charge-coupled device image sensor, in which the interference light is sampled at a sampling rate lower than the Nyquist frequency. The frequencies of the components of the light, such as the sideband and carrier (which include photodisplacement and topography information, respectively), are downconverted and sampled simultaneously based on the integration and sampling effects of the sensor. A general solution of frequency and amplitude in this downconversion is derived by Fourier analysis of the sampling procedure. The optimal frequency condition for the heterodyne beat signal, modulation signal, and sensor gate pulse is derived such that undesirable components are eliminated and each information component is converted into an orthogonal function, allowing each to be discretely reproduced from the Fourier coefficients. The optimal frequency parameters that maximize the sideband-to-carrier amplitude ratio are determined, theoretically demonstrating its high selectivity over 80 dB. Preliminary experiments demonstrate that this technique is capable of simultaneous imaging of reflectivity, topography, and photodisplacement for the detection of subsurface lattice defects at a speed corresponding to an acquisition time of only 0.26 s per 256 x 256 pixel area.

Characterization of Viscoelastic Materials Using Group Shear Wave Speeds.

PubMed

Rouze, Ned C; Deng, Yufeng; Trutna, Courtney A; Palmeri, Mark L; Nightingale, Kathryn R

2018-05-01

Recent investigations of viscoelastic properties of materials have been performed by observing shear wave propagation following localized, impulsive excitations, and Fourier decomposing the shear wave signal to parameterize the frequency-dependent phase velocity using a material model. This paper describes a new method to characterize viscoelastic materials using group shear wave speeds , , and determined from the shear wave displacement, velocity, and acceleration signals, respectively. Materials are modeled using a two-parameter linear attenuation model with phase velocity and dispersion slope at a reference frequency of 200 Hz. Analytically calculated lookup tables are used to determine the two material parameters from pairs of measured group shear wave speeds. Green's function calculations are used to validate the analytic model. Results are reported for measurements in viscoelastic and approximately elastic phantoms and demonstrate good agreement with phase velocities measured using Fourier analysis of the measured shear wave signals. The calculated lookup tables are relatively insensitive to the excitation configuration. While many commercial shear wave elasticity imaging systems report group shear wave speeds as the measures of material stiffness, this paper demonstrates that differences , , and of group speeds are first-order measures of the viscous properties of materials.

Deblurring of Class-Averaged Images in Single-Particle Electron Microscopy.

PubMed

Park, Wooram; Madden, Dean R; Rockmore, Daniel N; Chirikjian, Gregory S

2010-03-01

This paper proposes a method for deblurring of class-averaged images in single-particle electron microscopy (EM). Since EM images of biological samples are very noisy, the images which are nominally identical projection images are often grouped, aligned and averaged in order to cancel or reduce the background noise. However, the noise in the individual EM images generates errors in the alignment process, which creates an inherent limit on the accuracy of the resulting class averages. This inaccurate class average due to the alignment errors can be viewed as the result of a convolution of an underlying clear image with a blurring function. In this work, we develop a deconvolution method that gives an estimate for the underlying clear image from a blurred class-averaged image using precomputed statistics of misalignment. Since this convolution is over the group of rigid body motions of the plane, SE(2), we use the Fourier transform for SE(2) in order to convert the convolution into a matrix multiplication in the corresponding Fourier space. For practical implementation we use a Hermite-function-based image modeling technique, because Hermite expansions enable lossless Cartesian-polar coordinate conversion using the Laguerre-Fourier expansions, and Hermite expansion and Laguerre-Fourier expansion retain their structures under the Fourier transform. Based on these mathematical properties, we can obtain the deconvolution of the blurred class average using simple matrix multiplication. Tests of the proposed deconvolution method using synthetic and experimental EM images confirm the performance of our method.

THE PHASE COHERENCE OF INTERSTELLAR DENSITY FLUCTUATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burkhart, Blakesley; Lazarian, A.

2016-08-10

Studies of MHD turbulence often investigate the Fourier power spectrum to provide information on the nature of the turbulence cascade. However, the Fourier power spectrum only contains the Fourier amplitudes and rejects all information regarding the Fourier phases. Here, we investigate the utility of two statistical diagnostics for recovering information on Fourier phases in ISM column density maps: the averaged amplitudes of the bispectrum and the phase coherence index (PCI), a new phase technique for the ISM. We create three-dimensional density and two-dimensional column density maps using a set of simulations of isothermal ideal MHD turbulence with a wide rangemore » of sonic and Alfvénic Mach numbers. We find that the bispectrum averaged along different angles with respect to either the k {sub 1} or k {sub 2} axis is primarily sensitive to the sonic Mach number while averaging the bispectral amplitudes over different annuli is sensitive to both the sonic and Alfvénic Mach numbers. The PCI of density suggests that the most correlated phases occur in supersonic sub-Alfvénic turbulence and near the shock scale. This suggests that nonlinear interactions with correlated phases are strongest in shock-dominated regions, in agreement with findings from the solar wind. Our results suggest that the phase information contained in the bispectrum and PCI can be used to find the turbulence parameters in column density maps.« less

Off-axis phase-only holograms of 3D objects using accelerated point-based Fresnel diffraction algorithm

NASA Astrophysics Data System (ADS)

Zeng, Zhenxiang; Zheng, Huadong; Yu, Yingjie; Asundi, Anand K.

2017-06-01

A method for calculating off-axis phase-only holograms of three-dimensional (3D) object using accelerated point-based Fresnel diffraction algorithm (PB-FDA) is proposed. The complex amplitude of the object points on the z-axis in hologram plane is calculated using Fresnel diffraction formula, called principal complex amplitudes (PCAs). The complex amplitudes of those off-axis object points of the same depth can be obtained by 2D shifting of PCAs. In order to improve the calculating speed of the PB-FDA, the convolution operation based on fast Fourier transform (FFT) is used to calculate the holograms rather than using the point-by-point spatial 2D shifting of the PCAs. The shortest recording distance of the PB-FDA is analyzed in order to remove the influence of multiple-order images in reconstructed images. The optimal recording distance of the PB-FDA is also analyzed to improve the quality of reconstructed images. Numerical reconstructions and optical reconstructions with a phase-only spatial light modulator (SLM) show that holographic 3D display is feasible with the proposed algorithm. The proposed PB-FDA can also avoid the influence of the zero-order image introduced by SLM in optical reconstructed images.

Imaging properties and its improvements of scanning/imaging x-ray microscope

DOE Office of Scientific and Technical Information (OSTI.GOV)

Takeuchi, Akihisa, E-mail: take@spring8.or.jp; Uesugi, Kentaro; Suzuki, Yoshio

A scanning / imaging X-ray microscope (SIXM) system has been developed at SPring-8. The SIXM consists of a scanning X-ray microscope with a one-dimensional (1D) X-ray focusing device and an imaging (full-field) X-ray microscope with a 1D X-ray objective. The motivation of the SIXM system is to realize a quantitative and highly-sensitive multimodal 3D X-ray tomography by taking advantages of both the scanning X-ray microscope using multi-pixel detector and the imaging X-ray microscope. Data acquisition process of a 2D image is completely different between in the horizontal direction and in the vertical direction; a 1D signal is obtained with themore » linear-scanning while the other dimensional signal is obtained with the imaging optics. Such condition have caused a serious problem on the imaging properties that the imaging quality in the vertical direction has been much worse than that in the horizontal direction. In this paper, two approaches to solve this problem will be presented. One is introducing a Fourier transform method for phase retrieval from one phase derivative image, and the other to develop and employ a 1D diffuser to produce an asymmetrical coherent illumination.« less

Robust generation of Fourier-synthesized laser fields and their estimation of the optical phase by using quantum control of molecular tunneling ionization

NASA Astrophysics Data System (ADS)

Yoshida, Tsuyoshi; Saito, Naoaki; Ohmura, Hideki

2018-03-01

Intense (5.0 × 1012 W cm-2) nanosecond Fourier-synthesized laser fields consisting of fundamental, second-, third-, and fourth-harmonic light generated by an interferometer-free Fourier-synthesized laser field generator induce orientation-selective ionization based on directionally asymmetric molecular tunneling ionization (TI). The laser field generator ensures adjustment-free operation, high stability, and high reproducibility. Phase-sensitive, orientation-selective molecular TI provides a simple way to estimate the relative phase differences between the fundamental light and each harmonic by data-fitting analysis. This application of Fourier-synthesized laser fields will facilitate not only lightwave engineering but also the control of matter.

Method for determining and displaying the spacial distribution of a spectral pattern of received light

DOEpatents

Bennett, C.L.

1996-07-23

An imaging Fourier transform spectrometer is described having a Fourier transform infrared spectrometer providing a series of images to a focal plane array camera. The focal plane array camera is clocked to a multiple of zero crossing occurrences as caused by a moving mirror of the Fourier transform infrared spectrometer and as detected by a laser detector such that the frame capture rate of the focal plane array camera corresponds to a multiple of the zero crossing rate of the Fourier transform infrared spectrometer. The images are transmitted to a computer for processing such that representations of the images as viewed in the light of an arbitrary spectral ``fingerprint`` pattern can be displayed on a monitor or otherwise stored and manipulated by the computer. 2 figs.

Deep vein thrombosis using noncontrast-enhanced MR venography with electrocardiographically gated three-dimensional half-Fourier FSE: preliminary experience.

PubMed

Ono, Atsushi; Murase, Kenya; Taniguchi, Toshitaka; Shibutani, Osamu; Takata, Satoru; Kobashi, Yasuyuki; Miyazaki, Mitsue

2009-04-01

Three noncontrast-enhanced MR venography techniques are presented for assessing deep vein thrombosis (DVT) at 0.5 T in patients with metallic implants. Two cardiac-gated 3D half-Fourier FSE fresh blood imaging sequences with flow-refocusing pulses (FR-FBI) in the read-out (RO) direction and without FR pulses (non-FR-FBI) were developed for slower-flowing blood. For faster flowing blood, a swap phase-encode arterial double-subtraction elimination (SPADE) technique was developed. The three techniques were assessed both quantitatively using signal-to-noise (SNR) and contrast-noise-ratio (CNR) measurements and qualitatively by subjective image analysis in 15 volunteers. SPADE was compared to FR-FBI in the pelvic veins and FR-FBI was compared to non-FR-FBI in the thigh and calf veins. Both SPADE and FR-FBI techniques produced significantly higher SNRs, CNRs, and image quality in each comparative study (P<0.001). Five patients with metallic implants and confirmed DVT underwent SPADE (pelvic veins) and FR-FBI (thigh and calf veins) examinations and the results were compared to conventional venography. The SPADE and FR-FBI images showed all DVTs from all five patients without interference from implant susceptibility artifacts. The excellent image quality produced by both SPADE and FR-FBI throughout peripheral vasculature demonstrates their promise for detecting DVT in postsurgery patients.

Development and Application of Multifunctional Optical Coherence Tomography

NASA Astrophysics Data System (ADS)

Zhi, Zhongwei

Microcirculation refers to the functions of capillaries and the neighboring lymphatic vessels. It plays a vital role in the pathophysiology of disorders in many clinical areas including cardiology, dermatology, neurology and ophthalmology, and so forth. It is crucial to develop imaging technologies that can provide both qualitative and quantitative information as to how microcirculation responds to certain injury and/or disease, and its treatment. Optical coherence tomography (OCT) is a non-invasive optical imaging technique for high-resolution cross-sectional imaging of specimens, with many applications in clinical medicine. Current state-of-the-art OCT systems operate in the Fourier domain, using either a broadband light source with a spectrometer, known as spectral domain OCT (SDOCT), or a rapidly tunable laser, known as swept source OCT (SSOCT). The current Fourier domain OCT systems have dramatically improvement in sensitivity, resolution and speed compared to time domain OCT. In addition to the improvement in the OCT system hardware, different methods for functional measurements of tissue beds have been developed and demonstrated. This includes but not limited to, i) Phase-resolved Doppler OCT for quantifying the blood flow, ii) OCT angiography for visualization of microvasculature, iii) Polarization sensitive OCT for measuring the intrinsic optical property/ birefringence of tissue, iv) spectroscopic OCT for measuring blood oxygenation, etc. Functional OCT can provide important clinical information that is not available in the typical intensity based structural OCT images. Among these functional OCT modalities, Doppler OCT and OCT angiography attract great interests as they show high capability for in vivo study of microvascular pathology. By analyzing the Doppler effect of a flowing particle on light frequency, Doppler OCT allows the quantification of the blood flow speed and blood flow rate. The most popular approach for Doppler OCT is achieved through analysis of the phase term in complex OCT signal which termed as Phase-resolved Doppler OCT. However, as limited by the phase noise and motion, Phase-resolved Doppler OCT can only be applied for relative large blood vessels, such as arterioles and venules. On the other hand, in order to visualize the microcirculation network, a number of strategies to enable better contrast of microvasculature components, which we termed OCT angiography, have been introduced during recent years. As a variation of Fourier domain OCT, optical microangiography (OMAG) is one of earliest proposed OCT angiography technique which is capable of generating 3D images of dynamic blood perfusion distribution within microcirculatory tissue beds. The OMAG algorithm works by separating the static and moving elements by high pass filtering on complex valued interferometric data after Fourier transform. Based on the conventional OMAG algorithm, we further developed ultra-high sensitive OMAG (UHS-OMAG) by switching the high-pass filtering from fast scan direction (adjacent A-lines within one B-frame) to slow scan direction (adjacent B-frames), which has a dramatically improved performance for capillary network imaging and analysis. Apart from the microvascular study with current available functional OCT for, visualization of the lymphatic system (lymph nodes and lymphatic vessels) plays a significant role in assessing patients with various malignancies and lymphedema. However, there is a lack of label-free and noninvasive method for lymphangiography. Hence, a cutting edge research to investigate the capability of OCT as a tool for non-invasive and label-free lymphangiography would be highly desired. The objective of my thesis is to develop a multiple-functional SDOCT system to image the microcirculation and quantify the several important parameters of microcirculation within microcirculatory tissue beds, and further apply it for pre-clinical research applications. The multifunctional OCT system provides modalities including structural OCT, OCT angiography, Doppler OCT and Optical lymphangiography, for multi-parametric study of tissue microstructure, blood vessel morphology, blood flow and lymphatic vessel all together. The thesis mainly focus on two parts: first, development of multi-functional OCT/optical microangiography (OMAG) system and methods for volumetric imaging of microvasculature and quantitative measurement of blood flow, and its application for pathological research in ophthalmology on rodent eye models; second, development of ultra-high resolution OCT system and algorithm for simultaneous label free imaging of blood and lymphatic vessel, and its application in wound healing study on mouse ear flap model. Objectives of my research are achieved through the following specific aims: Aim 1: Improve the sensitivity of OMAG for microvasculature imaging; perform volumetric and quantitative imaging of vasculature with combined OMAG and Phase-resolved Doppler OCT for in vivo study of vascular physiology. Aim 2: Develop high speed high resolution OCT system and method for rodent eye imaging. Apply the combined OMAG and Phase-resolved Doppler OCT approach to investigate the impact of elevated intraocular pressure on retinal, choroidal and optic nerve head blood flow in rat eye model, which aids to the better understanding of the mechanism and development of glaucoma. Aim 3: Apply the developed OCT system and ultra-high sensitive OMAG algorithm for noninvasive imaging of retinal morphology and microvasculature in obese mice, which may play an important role in early diagnosis of Diabetic retinopathy. Aim 4: Developing an ultra-high resolution SDOCT system using broadband Supercontinuum light source to achieve ultra-high resolution microvasculature imaging of biological tissue. Aim 5: Develop methods for simultaneous label free optical imaging of blood and lymphatic vessel and demonstrate its capability by monitoring the blood and lymph response to wound healing on mouse ear pinna model.

Fourier-Mellin moment-based intertwining map for image encryption

NASA Astrophysics Data System (ADS)

Kaur, Manjit; Kumar, Vijay

2018-03-01

In this paper, a robust image encryption technique that utilizes Fourier-Mellin moments and intertwining logistic map is proposed. Fourier-Mellin moment-based intertwining logistic map has been designed to overcome the issue of low sensitivity of an input image. Multi-objective Non-Dominated Sorting Genetic Algorithm (NSGA-II) based on Reinforcement Learning (MNSGA-RL) has been used to optimize the required parameters of intertwining logistic map. Fourier-Mellin moments are used to make the secret keys more secure. Thereafter, permutation and diffusion operations are carried out on input image using secret keys. The performance of proposed image encryption technique has been evaluated on five well-known benchmark images and also compared with seven well-known existing encryption techniques. The experimental results reveal that the proposed technique outperforms others in terms of entropy, correlation analysis, a unified average changing intensity and the number of changing pixel rate. The simulation results reveal that the proposed technique provides high level of security and robustness against various types of attacks.

Strategy for reliable strain measurement in InAs/GaAs materials from high-resolution Z-contrast STEM images

NASA Astrophysics Data System (ADS)

Vatanparast, Maryam; Vullum, Per Erik; Nord, Magnus; Zuo, Jian-Min; Reenaas, Turid W.; Holmestad, Randi

2017-09-01

Geometric phase analysis (GPA), a fast and simple Fourier space method for strain analysis, can give useful information on accumulated strain and defect propagation in multiple layers of semiconductors, including quantum dot materials. In this work, GPA has been applied to high resolution Z-contrast scanning transmission electron microscopy (STEM) images. Strain maps determined from different g vectors of these images are compared to each other, in order to analyze and assess the GPA technique in terms of accuracy. The SmartAlign tool has been used to improve the STEM image quality getting more reliable results. Strain maps from template matching as a real space approach are compared with strain maps from GPA, and it is discussed that a real space analysis is a better approach than GPA for aberration corrected STEM images.

Evaluation of mechanical dyssynchrony and myocardial perfusion using phase analysis of gated SPECT imaging in patients with left ventricular dysfunction

PubMed Central

Trimble, Mark A.; Borges-Neto, Salvador; Honeycutt, Emily F.; Shaw, Linda K.; Pagnanelli, Robert; Chen, Ji; Iskandrian, Ami E.; Garcia, Ernest V.; Velazquez, Eric J.

2010-01-01

Background Using phase analysis of gated single photon emission computed tomography (SPECT) imaging, we examined the relation between myocardial perfusion, degree of electrical dyssynchrony, and degree of SPECT-derived mechanical dyssynchrony in patients with left ventricular (LV) dysfunction. Methods and Results We retrospectively examined 125 patients with LV dysfunction and ejection fraction of 35% or lower. Fourier analysis converts regional myocardial counts into a continuous thickening function, allowing resolution of phase of onset of myocardial thickening. The SD of LV phase distribution (phase SD) and histogram bandwidth describe LV phase dispersion as a measure of dyssynchrony. Heart failure (HF) patients with perfusion abnormalities ities have higher degrees of dyssynchrony measured by median phase SD (45.5° vs 27.7°, P < .0001) and bandwidth (117.0° vs 73.0°, P = .0006). HF patients with prolonged QRS durations have higher degrees of dyssynchrony measured by median phase SD (54.1° vs 34.7°, P < .0001) and bandwidth (136.5° vs 99.0°, P = .0005). Mild to moderate correlations exist between QRS duration and phase analysis indices of phase SD (r = 0.50) and bandwidth (r = 0.40). Mechanical dyssynchrony (phase SD >43°) was 43.2%. Conclusions HF patients with perfusion abnormalities or prolonged QRS durations QRS durations have higher degrees of mechanical dyssynchrony. Gated SPECT myocardial perfusion imaging can quantify myocardial function, perfusion, and dyssynchrony and may help in evaluating patients for cardiac resynchronization therapy. PMID:18761269

Phase retrieval for crystalline specimens

NASA Astrophysics Data System (ADS)

Arnal, Romain A.; Millane, Rick P.

2017-09-01

The recent availability of ultra-bright and ultra-short X-rays pulses from new sources called x-ray free-electron lasers (XFELs) has introduced a new paradigm in X-ray crystallography. Called "diffraction-before-destruction," this paradigm addresses the main problems that plague crystallography using synchrotron sources. However, the phase problem of coherent diffraction imaging remains: one has to retrieve the phase of the measured diffraction amplitude in order to reconstruct the object. Fibrous and membrane proteins that crystallize in 1D and 2D crystals can now potentially be used for data collection with free-electron lasers. The crystallographic phase problem with such crystalline specimens is eased as the Fourier amplitude can be sampled more finely than at the Bragg sampling along one or two directions. Here we characterise uniqueness of the phase problem for different types of crystalline specimen. Simulated ab initio phase retrieval using iterative projection algorithms for 2D crystals is presented.

Edge-augmented Fourier partial sums with applications to Magnetic Resonance Imaging (MRI)

NASA Astrophysics Data System (ADS)

Larriva-Latt, Jade; Morrison, Angela; Radgowski, Alison; Tobin, Joseph; Iwen, Mark; Viswanathan, Aditya

2017-08-01

Certain applications such as Magnetic Resonance Imaging (MRI) require the reconstruction of functions from Fourier spectral data. When the underlying functions are piecewise-smooth, standard Fourier approximation methods suffer from the Gibbs phenomenon - with associated oscillatory artifacts in the vicinity of edges and an overall reduced order of convergence in the approximation. This paper proposes an edge-augmented Fourier reconstruction procedure which uses only the first few Fourier coefficients of an underlying piecewise-smooth function to accurately estimate jump information and then incorporate it into a Fourier partial sum approximation. We provide both theoretical and empirical results showing the improved accuracy of the proposed method, as well as comparisons demonstrating superior performance over existing state-of-the-art sparse optimization-based methods.

Dynamic half Fourier acquisition, single shot turbo spin-echo magnetic resonance imaging for evaluating the female pelvis.

PubMed

Gousse, A E; Barbaric, Z L; Safir, M H; Madjar, S; Marumoto, A K; Raz, S

2000-11-01

We assessed the merit of dynamic half Fourier acquisition, single shot turbo spin-echo sequence T2-weighted magnetic resonance imaging (MRI) for evaluating pelvic organ prolapse and all other female pelvic pathology by prospectively correlating clinical with imaging findings. From September 1997 to April 1998, 100 consecutive women 23 to 88 years old with (65) and without (35) pelvic organ prolapse underwent half Fourier acquisition, single shot turbo spin-echo sequence dynamic pelvic T2-weighted MRI at our institution using a 1.5 Tesla magnet with phased array coils. Mid sagittal and parasagittal views with the patient supine, relaxed and straining were obtained using no pre-examination preparation or instrumentation. We evaluated the anterior vaginal wall, bladder, urethra, posterior vaginal wall, rectum, pelvic floor musculature, perineum, uterus, vaginal cuff, ovaries, ureters and intraperitoneal organs for all pathological conditions, including pelvic prolapse. Patients underwent a prospective physical examination performed by a female urologist, and an experienced radiologist blinded to pre-imaging clinical findings interpreted all studies. Physical examination, MRI and intraoperative findings were statistically correlated. Total image acquisition time was 2.5 minutes, room time 10 minutes and cost American $540. Half Fourier acquisition, single shot turbo spin-echo T2-weighted MRI revealed pathological entities other than pelvic prolapse in 55 cases, including uterine fibroids in 11, ovarian cysts in 9, bilateral ureteronephrosis in 3, nabothian cyst in 7, Bartholin's gland cyst in 4, urethral diverticulum in 3, polytetrafluoroethylene graft abscess in 3, bladder diverticulum in 2, sacral spinal abnormalities in 2, bladder tumor in 1, sigmoid diverticulosis in 1 and other in 9. Intraoperative findings were considered the gold standard against which physical examination and MRI were compared. Using these criteria the sensitivity, specificity and positive predictive value of MRI were 100%, 83% and 97% for cystocele; 100%, 75% and 94% for urethrocele; 100%, 54% and 33% for vaginal vault prolapse; 83%, 100% and 100% for uterine prolapse; 87%, 80% and 91% for enterocele; and 76%, 50% and 96% for rectocele. Dynamic half Fourier acquisition, single shot turbo spin-echo MRI appears to be an important adjunct in the comprehensive evaluation of the female pelvis. Except for rectocele, pelvic floor prolapse is accurately staged and pelvic organ pathology reliably detected. The technique is rapid, noninvasive and cost-effective, and it allows the clinician to visualize the whole pelvis using a single dynamic study that provides superb anatomical detail.

The influence of statistical properties of Fourier coefficients on random Gaussian surfaces.

PubMed

de Castro, C P; Luković, M; Andrade, R F S; Herrmann, H J

2017-05-16

Many examples of natural systems can be described by random Gaussian surfaces. Much can be learned by analyzing the Fourier expansion of the surfaces, from which it is possible to determine the corresponding Hurst exponent and consequently establish the presence of scale invariance. We show that this symmetry is not affected by the distribution of the modulus of the Fourier coefficients. Furthermore, we investigate the role of the Fourier phases of random surfaces. In particular, we show how the surface is affected by a non-uniform distribution of phases.

Optimization of sampling pattern and the design of Fourier ptychographic illuminator.

PubMed

Guo, Kaikai; Dong, Siyuan; Nanda, Pariksheet; Zheng, Guoan

2015-03-09

Fourier ptychography (FP) is a recently developed imaging approach that facilitates high-resolution imaging beyond the cutoff frequency of the employed optics. In the original FP approach, a periodic LED array is used for sample illumination, and therefore, the scanning pattern is a uniform grid in the Fourier space. Such a uniform sampling scheme leads to 3 major problems for FP, namely: 1) it requires a large number of raw images, 2) it introduces the raster grid artefacts in the reconstruction process, and 3) it requires a high-dynamic-range detector. Here, we investigate scanning sequences and sampling patterns to optimize the FP approach. For most biological samples, signal energy is concentrated at low-frequency region, and as such, we can perform non-uniform Fourier sampling in FP by considering the signal structure. In contrast, conventional ptychography perform uniform sampling over the entire real space. To implement the non-uniform Fourier sampling scheme in FP, we have designed and built an illuminator using LEDs mounted on a 3D-printed plastic case. The advantages of this illuminator are threefold in that: 1) it reduces the number of image acquisitions by at least 50% (68 raw images versus 137 in the original FP setup), 2) it departs from the translational symmetry of sampling to solve the raster grid artifact problem, and 3) it reduces the dynamic range of the captured images 6 fold. The results reported in this paper significantly shortened acquisition time and improved quality of FP reconstructions. It may provide new insights for developing Fourier ptychographic imaging platforms and find important applications in digital pathology.

Jitter Correction

NASA Technical Reports Server (NTRS)

Waegell, Mordecai J.; Palacios, David M.

2011-01-01

Jitter_Correct.m is a MATLAB function that automatically measures and corrects inter-frame jitter in an image sequence to a user-specified precision. In addition, the algorithm dynamically adjusts the image sample size to increase the accuracy of the measurement. The Jitter_Correct.m function takes an image sequence with unknown frame-to-frame jitter and computes the translations of each frame (column and row, in pixels) relative to a chosen reference frame with sub-pixel accuracy. The translations are measured using a Cross Correlation Fourier transformation method in which the relative phase of the two transformed images is fit to a plane. The measured translations are then used to correct the inter-frame jitter of the image sequence. The function also dynamically expands the image sample size over which the cross-correlation is measured to increase the accuracy of the measurement. This increases the robustness of the measurement to variable magnitudes of inter-frame jitter

Full range line-field parallel swept source imaging utilizing digital refocusing

NASA Astrophysics Data System (ADS)

Fechtig, Daniel J.; Kumar, Abhishek; Drexler, Wolfgang; Leitgeb, Rainer A.

2015-12-01

We present geometric optics-based refocusing applied to a novel off-axis line-field parallel swept source imaging (LPSI) system. LPSI is an imaging modality based on line-field swept source optical coherence tomography, which permits 3-D imaging at acquisition speeds of up to 1 MHz. The digital refocusing algorithm applies a defocus-correcting phase term to the Fourier representation of complex-valued interferometric image data, which is based on the geometrical optics information of the LPSI system. We introduce the off-axis LPSI system configuration, the digital refocusing algorithm and demonstrate the effectiveness of our method for refocusing volumetric images of technical and biological samples. An increase of effective in-focus depth range from 255 μm to 4.7 mm is achieved. The recovery of the full in-focus depth range might be especially valuable for future high-speed and high-resolution diagnostic applications of LPSI in ophthalmology.

Imaging RF Phased Array Receivers using Optically-Coherent Up-conversion for High Beam-Bandwidth Processing

DTIC Science & Technology

2017-03-01

It does so by using an optical lens to perform an inverse spatial Fourier Transform on the up-converted RF signals, thereby rendering a real-time... simultaneous beams or other engineered beam patterns. There are two general approaches to array-based beam forming: digital and analog. In digital beam...of significantly limiting the number of beams that can be formed simultaneously and narrowing the operational bandwidth. An alternate approach that

Fractional-order Fourier analysis for ultrashort pulse characterization.

PubMed

Brunel, Marc; Coetmellec, Sébastien; Lelek, Mickael; Louradour, Frédéric

2007-06-01

We report what we believe to be the first experimental demonstration of ultrashort pulse characterization using fractional-order Fourier analysis. The analysis is applied to the interpretation of spectral interferometry resolved in time (SPIRIT) traces [which are spectral phase interferometry for direct electric field reconstruction (SPIDER)-like interferograms]. First, the fractional-order Fourier transformation is shown to naturally allow the determination of the cubic spectral phase coefficient of pulses to be analyzed. A simultaneous determination of both cubic and quadratic spectral phase coefficients of the pulses using the fractional-order Fourier series expansion is further demonstrated. This latter technique consists of localizing relative maxima in a 2D cartography representing decomposition coefficients. It is further used to reconstruct or filter SPIRIT traces.

Effect of random phase mask on input plane in photorefractive authentic memory with two-wave encryption method

NASA Astrophysics Data System (ADS)

Mita, Akifumi; Okamoto, Atsushi; Funakoshi, Hisatoshi

2004-06-01

We have proposed an all-optical authentic memory with the two-wave encryption method. In the recording process, the image data are encrypted to a white noise by the random phase masks added on the input beam with the image data and the reference beam. Only reading beam with the phase-conjugated distribution of the reference beam can decrypt the encrypted data. If the encrypted data are read out with an incorrect phase distribution, the output data are transformed into a white noise. Moreover, during read out, reconstructions of the encrypted data interfere destructively resulting in zero intensity. Therefore our memory has a merit that we can detect unlawful accesses easily by measuring the output beam intensity. In our encryption method, the random phase mask on the input plane plays important roles in transforming the input image into a white noise and prohibiting to decrypt a white noise to the input image by the blind deconvolution method. Without this mask, when unauthorized users observe the output beam by using CCD in the readout with the plane wave, the completely same intensity distribution as that of Fourier transform of the input image is obtained. Therefore the encrypted image will be decrypted easily by using the blind deconvolution method. However in using this mask, even if unauthorized users observe the output beam using the same method, the encrypted image cannot be decrypted because the observed intensity distribution is dispersed at random by this mask. Thus it can be said the robustness is increased by this mask. In this report, we compare two correlation coefficients, which represents the degree of a white noise of the output image, between the output image and the input image in using this mask or not. We show that the robustness of this encryption method is increased as the correlation coefficient is improved from 0.3 to 0.1 by using this mask.

Aperture shape dependencies in extended depth of focus for imaging camera by wavefront coding

NASA Astrophysics Data System (ADS)

Sakita, Koichi; Ohta, Mitsuhiko; Shimano, Takeshi; Sakemoto, Akito

2015-02-01

Optical transfer functions (OTFs) on various directional spatial frequency axes for cubic phase mask (CPM) with circular and square apertures are investigated. Although OTF has no zero points, it has a very close value to zero for a circular aperture at low frequencies on diagonal axis, which results in degradation of restored images. The reason for close-to-zero value in OTF is also analyzed in connection with point spread function profiles using Fourier slice theorem. To avoid close-to-zero condition, square aperture with CPM is indispensable in WFC. We optimized cubic coefficient α of CPM and coefficients of digital filter, and succeeded to get excellent de-blurred images at large depth of field.

A fast discrete S-transform for biomedical signal processing.

PubMed

Brown, Robert A; Frayne, Richard

2008-01-01

Determining the frequency content of a signal is a basic operation in signal and image processing. The S-transform provides both the true frequency and globally referenced phase measurements characteristic of the Fourier transform and also generates local spectra, as does the wavelet transform. Due to this combination, the S-transform has been successfully demonstrated in a variety of biomedical signal and image processing tasks. However, the computational demands of the S-transform have limited its application in medicine to this point in time. This abstract introduces the fast S-transform, a more efficient discrete implementation of the classic S-transform with dramatically reduced computational requirements.

Superfast 3D shape measurement of a flapping flight process with motion based segmentation

NASA Astrophysics Data System (ADS)

Li, Beiwen

2018-02-01

Flapping flight has drawn interests from different fields including biology, aerodynamics and robotics. For such research, the digital fringe projection technology using defocused binary image projection has superfast (e.g. several kHz) measurement capabilities with digital-micromirror-device, yet its measurement quality is still subject to the motion of flapping flight. This research proposes a novel computational framework for dynamic 3D shape measurement of a flapping flight process. The fast and slow motion parts are separately reconstructed with Fourier transform and phase shifting. Experiments demonstrate its success by measuring a flapping wing robot (image acquisition rate: 5000 Hz; flapping speed: 25 cycles/second).

Face recognition system using multiple face model of hybrid Fourier feature under uncontrolled illumination variation.

PubMed

Hwang, Wonjun; Wang, Haitao; Kim, Hyunwoo; Kee, Seok-Cheol; Kim, Junmo

2011-04-01

The authors present a robust face recognition system for large-scale data sets taken under uncontrolled illumination variations. The proposed face recognition system consists of a novel illumination-insensitive preprocessing method, a hybrid Fourier-based facial feature extraction, and a score fusion scheme. First, in the preprocessing stage, a face image is transformed into an illumination-insensitive image, called an "integral normalized gradient image," by normalizing and integrating the smoothed gradients of a facial image. Then, for feature extraction of complementary classifiers, multiple face models based upon hybrid Fourier features are applied. The hybrid Fourier features are extracted from different Fourier domains in different frequency bandwidths, and then each feature is individually classified by linear discriminant analysis. In addition, multiple face models are generated by plural normalized face images that have different eye distances. Finally, to combine scores from multiple complementary classifiers, a log likelihood ratio-based score fusion scheme is applied. The proposed system using the face recognition grand challenge (FRGC) experimental protocols is evaluated; FRGC is a large available data set. Experimental results on the FRGC version 2.0 data sets have shown that the proposed method shows an average of 81.49% verification rate on 2-D face images under various environmental variations such as illumination changes, expression changes, and time elapses.

Efficient phase contrast imaging in STEM using a pixelated detector. Part 1: Experimental demonstration at atomic resolution

DOE PAGES

Pennycook, Timothy J.; Lupini, Andrew R.; Yang, Hao; ...

2014-10-15

In this paper, we demonstrate a method to achieve high efficiency phase contrast imaging in aberration corrected scanning transmission electron microscopy (STEM) with a pixelated detector. The pixelated detector is used to record the Ronchigram as a function of probe position which is then analyzed with ptychography. Ptychography has previously been used to provide super-resolution beyond the diffraction limit of the optics, alongside numerically correcting for spherical aberration. Here we rely on a hardware aberration corrector to eliminate aberrations, but use the pixelated detector data set to utilize the largest possible volume of Fourier space to create high efficiency phasemore » contrast images. The use of ptychography to diagnose the effects of chromatic aberration is also demonstrated. In conclusion, the four dimensional dataset is used to compare different bright field detector configurations from the same scan for a sample of bilayer graphene. Our method of high efficiency ptychography produces the clearest images, while annular bright field produces almost no contrast for an in-focus aberration-corrected probe.« less

In-situ monitoring of blood glucose level for dialysis machine by AAA-battery-size ATR Fourier spectroscopy

NASA Astrophysics Data System (ADS)

Hosono, Satsuki; Sato, Shun; Ishida, Akane; Suzuki, Yo; Inohara, Daichi; Nogo, Kosuke; Abeygunawardhana, Pradeep K.; Suzuki, Satoru; Nishiyama, Akira; Wada, Kenji; Ishimaru, Ichiro

2015-07-01

For blood glucose level measurement of dialysis machines, we proposed AAA-battery-size ATR (Attenuated total reflection) Fourier spectroscopy in middle infrared light region. The proposed one-shot Fourier spectroscopic imaging is a near-common path and spatial phase-shift interferometer with high time resolution. Because numerous number of spectral data that is 60 (= camera frame rare e.g. 60[Hz]) multiplied by pixel number could be obtained in 1[sec.], statistical-averaging improvement realize high-accurate spectral measurement. We evaluated the quantitative accuracy of our proposed method for measuring glucose concentration in near-infrared light region with liquid cells. We confirmed that absorbance at 1600[nm] had high correlations with glucose concentrations (correlation coefficient: 0.92). But to measure whole-blood, complex light phenomenon caused from red blood cells, that is scattering and multiple reflection or so, deteriorate spectral data. Thus, we also proposed the ultrasound-assisted spectroscopic imaging that traps particles at standing-wave node. Thus, if ATR prism is oscillated mechanically, anti-node area is generated around evanescent light field on prism surface. By elimination complex light phenomenon of red blood cells, glucose concentration in whole-blood will be quantify with high accuracy. In this report, we successfully trapped red blood cells in normal saline solution with ultrasonic standing wave (frequency: 2[MHz]).

Scaled nonuniform Fourier transform for image reconstruction in swept source optical coherence tomography

NASA Astrophysics Data System (ADS)

Mezgebo, Biniyam; Nagib, Karim; Fernando, Namal; Kordi, Behzad; Sherif, Sherif

2018-02-01

Swept Source optical coherence tomography (SS-OCT) is an important imaging modality for both medical and industrial diagnostic applications. A cross-sectional SS-OCT image is obtained by applying an inverse discrete Fourier transform (DFT) to axial interferograms measured in the frequency domain (k-space). This inverse DFT is typically implemented as a fast Fourier transform (FFT) that requires the data samples to be equidistant in k-space. As the frequency of light produced by a typical wavelength-swept laser is nonlinear in time, the recorded interferogram samples will not be uniformly spaced in k-space. Many image reconstruction methods have been proposed to overcome this problem. Most such methods rely on oversampling the measured interferogram then use either hardware, e.g., Mach-Zhender interferometer as a frequency clock module, or software, e.g., interpolation in k-space, to obtain equally spaced samples that are suitable for the FFT. To overcome the problem of nonuniform sampling in k-space without any need for interferogram oversampling, an earlier method demonstrated the use of the nonuniform discrete Fourier transform (NDFT) for image reconstruction in SS-OCT. In this paper, we present a more accurate method for SS-OCT image reconstruction from nonuniform samples in k-space using a scaled nonuniform Fourier transform. The result is demonstrated using SS-OCT images of Axolotl salamander eggs.

Tilt-effect of holograms and images displayed on a spatial light modulator.

PubMed

Harm, Walter; Roider, Clemens; Bernet, Stefan; Ritsch-Marte, Monika

2015-11-16

We show that a liquid crystal spatial light modulator (LCOS-SLM) can be used to display amplitude images, or phase holograms, which change in a pre-determined way when the display is tilted, i.e. observed under different angles. This is similar to the tilt-effect (also called "latent image effect") known from various security elements ("kinegrams") on credit cards or bank notes. The effect is achieved without any specialized optical components, simply by using the large phase shifting capability of a "thick" SLM, which extends over several multiples of 2π, in combination with the angular dependence of the phase shift. For hologram projection one can use the fact that the phase of a monochromatic wave is only defined modulo 2π. Thus one can design a phase pattern extending over several multiples of 2π, which transforms at different readout angles into different 2π-wrapped phase structures, due to the angular dependence of the modulo 2π operation. These different beams then project different holograms at the respective readout angles. In amplitude modulation mode (with inserted polarizer) the intensity of each SLM pixel oscillates over several periods when tuning its control voltage. Since the oscillation period depends on the readout angle, it is possible to find a certain control voltage which produces two (or more) selectable gray levels at a corresponding number of pre-determined readout angles. This is done with all SLM pixels individually, thus constructing different images for the selected angles. We experimentally demonstrate the reconstruction of multiple (Fourier- and Fresnel-) holograms, and of different amplitude images, by readout of static diffractive patterns in a variable angular range between 0° and 60°.

The Fresnel Diffraction: A Story of Light and Darkness

NASA Astrophysics Data System (ADS)

Aime, C.; Aristidi, É.; Rabbia, Y.

2013-03-01

In a first part of the paper we give a simple introduction to the free space propagation of light at the level of a Master degree in Physics. The presentation promotes linear filtering aspects at the expense of fundamental physics. Following the Huygens-Fresnel approach, the propagation of the wave writes as a convolution relationship, the impulse response being a quadratic phase factor. We give the corresponding filter in the Fourier plane. As an illustration, we describe the propagation of wave with a spatial sinusoidal amplitude, introduce lenses as quadratic phase transmissions, discuss their Fourier transform properties and give some properties of Soret screens. Classical diffractions of rectangular diaphragms are also given here. In a second part of the paper, the presentation turns into the use of external occulters in coronagraphy for the detection of exoplanets and the study of the solar corona. Making use of Lommel series expansions, we obtain the analytical expression for the diffraction of a circular opaque screen, giving thereby the complete formalism for the Arago-Poisson spot. We include there shaped occulters. The paper ends up with a brief application to incoherent imaging in astronomy.

Fourier-transform and global contrast interferometer alignment methods

DOEpatents

Goldberg, Kenneth A.

2001-01-01

Interferometric methods are presented to facilitate alignment of image-plane components within an interferometer and for the magnified viewing of interferometer masks in situ. Fourier-transforms are performed on intensity patterns that are detected with the interferometer and are used to calculate pseudo-images of the electric field in the image plane of the test optic where the critical alignment of various components is being performed. Fine alignment is aided by the introduction and optimization of a global contrast parameter that is easily calculated from the Fourier-transform.

Method for determining and displaying the spacial distribution of a spectral pattern of received light

DOEpatents

Bennett, Charles L.

1996-01-01

An imaging Fourier transform spectrometer (10, 210) having a Fourier transform infrared spectrometer (12) providing a series of images (40) to a focal plane array camera (38). The focal plane array camera (38) is clocked to a multiple of zero crossing occurrences as caused by a moving mirror (18) of the Fourier transform infrared spectrometer (12) and as detected by a laser detector (50) such that the frame capture rate of the focal plane array camera (38) corresponds to a multiple of the zero crossing rate of the Fourier transform infrared spectrometer (12). The images (40) are transmitted to a computer (45) for processing such that representations of the images (40) as viewed in the light of an arbitrary spectral "fingerprint" pattern can be displayed on a monitor (60) or otherwise stored and manipulated by the computer (45).

Spatial-Heterodyne Interferometry For Reflection And Transm Ission (Shirt) Measurements

DOEpatents

Hanson, Gregory R [Clinton, TN; Bingham, Philip R [Knoxville, TN; Tobin, Ken W [Harriman, TN

2006-02-14

Systems and methods are described for spatial-heterodyne interferometry for reflection and transmission (SHIRT) measurements. A method includes digitally recording a first spatially-heterodyned hologram using a first reference beam and a first object beam; digitally recording a second spatially-heterodyned hologram using a second reference beam and a second object beam; Fourier analyzing the digitally recorded first spatially-heterodyned hologram to define a first analyzed image; Fourier analyzing the digitally recorded second spatially-heterodyned hologram to define a second analyzed image; digitally filtering the first analyzed image to define a first result; and digitally filtering the second analyzed image to define a second result; performing a first inverse Fourier transform on the first result, and performing a second inverse Fourier transform on the second result. The first object beam is transmitted through an object that is at least partially translucent, and the second object beam is reflected from the object.

In-line phase contrast micro-CT reconstruction for biomedical specimens.

PubMed

Fu, Jian; Tan, Renbo

2014-01-01

X-ray phase contrast micro computed tomography (micro-CT) can non-destructively provide the internal structure information of soft tissues and low atomic number materials. It has become an invaluable analysis tool for biomedical specimens. Here an in-line phase contrast micro-CT reconstruction technique is reported, which consists of a projection extraction method and the conventional filter back-projection (FBP) reconstruction algorithm. The projection extraction is implemented by applying the Fourier transform to the forward projections of in-line phase contrast micro-CT. This work comprises a numerical study of the method and its experimental verification using a biomedical specimen dataset measured at an X-ray tube source micro-CT setup. The numerical and experimental results demonstrate that the presented technique can improve the imaging contrast of biomedical specimens. It will be of interest for a wide range of in-line phase contrast micro-CT applications in medicine and biology.

Symmetric Phase Only Filtering for Improved DPIV Data Processing

NASA Technical Reports Server (NTRS)

Wernet, Mark P.

2006-01-01

The standard approach in Digital Particle Image Velocimetry (DPIV) data processing is to use Fast Fourier Transforms to obtain the cross-correlation of two single exposure subregions, where the location of the cross-correlation peak is representative of the most probable particle displacement across the subregion. This standard DPIV processing technique is analogous to Matched Spatial Filtering, a technique commonly used in optical correlators to perform the crosscorrelation operation. Phase only filtering is a well known variation of Matched Spatial Filtering, which when used to process DPIV image data yields correlation peaks which are narrower and up to an order of magnitude larger than those obtained using traditional DPIV processing. In addition to possessing desirable correlation plane features, phase only filters also provide superior performance in the presence of DC noise in the correlation subregion. When DPIV image subregions contaminated with surface flare light or high background noise levels are processed using phase only filters, the correlation peak pertaining only to the particle displacement is readily detected above any signal stemming from the DC objects. Tedious image masking or background image subtraction are not required. Both theoretical and experimental analyses of the signal-to-noise ratio performance of the filter functions are presented. In addition, a new Symmetric Phase Only Filtering (SPOF) technique, which is a variation on the traditional phase only filtering technique, is described and demonstrated. The SPOF technique exceeds the performance of the traditionally accepted phase only filtering techniques and is easily implemented in standard DPIV FFT based correlation processing with no significant computational performance penalty. An "Automatic" SPOF algorithm is presented which determines when the SPOF is able to provide better signal to noise results than traditional PIV processing. The SPOF based optical correlation processing approach is presented as a new paradigm for more robust cross-correlation processing of low signal-to-noise ratio DPIV image data."

Design of wavefront coding optical system with annular aperture

NASA Astrophysics Data System (ADS)

Chen, Xinhua; Zhou, Jiankang; Shen, Weimin

2016-10-01

Wavefront coding can extend the depth of field of traditional optical system by inserting a phase mask into the pupil plane. In this paper, the point spread function (PSF) of wavefront coding system with annular aperture are analyzed. Stationary phase method and fast Fourier transform (FFT) method are used to compute the diffraction integral respectively. The OTF invariance is analyzed for the annular aperture with cubic phase mask under different obscuration ratio. With these analysis results, a wavefront coding system using Maksutov-Cassegrain configuration is designed finally. It is an F/8.21 catadioptric system with annular aperture, and its focal length is 821mm. The strength of the cubic phase mask is optimized with user-defined operand in Zemax. The Wiener filtering algorithm is used to restore the images and the numerical simulation proves the validity of the design.

Correction for Eddy Current-Induced Echo-Shifting Effect in Partial-Fourier Diffusion Tensor Imaging.

PubMed

Truong, Trong-Kha; Song, Allen W; Chen, Nan-Kuei

2015-01-01

In most diffusion tensor imaging (DTI) studies, images are acquired with either a partial-Fourier or a parallel partial-Fourier echo-planar imaging (EPI) sequence, in order to shorten the echo time and increase the signal-to-noise ratio (SNR). However, eddy currents induced by the diffusion-sensitizing gradients can often lead to a shift of the echo in k-space, resulting in three distinct types of artifacts in partial-Fourier DTI. Here, we present an improved DTI acquisition and reconstruction scheme, capable of generating high-quality and high-SNR DTI data without eddy current-induced artifacts. This new scheme consists of three components, respectively, addressing the three distinct types of artifacts. First, a k-space energy-anchored DTI sequence is designed to recover eddy current-induced signal loss (i.e., Type 1 artifact). Second, a multischeme partial-Fourier reconstruction is used to eliminate artificial signal elevation (i.e., Type 2 artifact) associated with the conventional partial-Fourier reconstruction. Third, a signal intensity correction is applied to remove artificial signal modulations due to eddy current-induced erroneous T2(∗) -weighting (i.e., Type 3 artifact). These systematic improvements will greatly increase the consistency and accuracy of DTI measurements, expanding the utility of DTI in translational applications where quantitative robustness is much needed.

Correction for Eddy Current-Induced Echo-Shifting Effect in Partial-Fourier Diffusion Tensor Imaging

PubMed Central

Truong, Trong-Kha; Song, Allen W.; Chen, Nan-kuei

2015-01-01

In most diffusion tensor imaging (DTI) studies, images are acquired with either a partial-Fourier or a parallel partial-Fourier echo-planar imaging (EPI) sequence, in order to shorten the echo time and increase the signal-to-noise ratio (SNR). However, eddy currents induced by the diffusion-sensitizing gradients can often lead to a shift of the echo in k-space, resulting in three distinct types of artifacts in partial-Fourier DTI. Here, we present an improved DTI acquisition and reconstruction scheme, capable of generating high-quality and high-SNR DTI data without eddy current-induced artifacts. This new scheme consists of three components, respectively, addressing the three distinct types of artifacts. First, a k-space energy-anchored DTI sequence is designed to recover eddy current-induced signal loss (i.e., Type 1 artifact). Second, a multischeme partial-Fourier reconstruction is used to eliminate artificial signal elevation (i.e., Type 2 artifact) associated with the conventional partial-Fourier reconstruction. Third, a signal intensity correction is applied to remove artificial signal modulations due to eddy current-induced erroneous T 2 ∗-weighting (i.e., Type 3 artifact). These systematic improvements will greatly increase the consistency and accuracy of DTI measurements, expanding the utility of DTI in translational applications where quantitative robustness is much needed. PMID:26413505

Least squares reconstruction of non-linear RF phase encoded MR data.

PubMed

Salajeghe, Somaie; Babyn, Paul; Sharp, Jonathan C; Sarty, Gordon E

2016-09-01

The numerical feasibility of reconstructing MRI signals generated by RF coils that produce B1 fields with a non-linearly varying spatial phase is explored. A global linear spatial phase variation of B1 is difficult to produce from current confined to RF coils. Here we use regularized least squares inversion, in place of the usual Fourier transform, to reconstruct signals generated in B1 fields with non-linear phase variation. RF encoded signals were simulated for three RF coil configurations: ideal linear, parallel conductors and, circular coil pairs. The simulated signals were reconstructed by Fourier transform and by regularized least squares. The Fourier reconstruction of simulated RF encoded signals from the parallel conductor coil set showed minor distortions over the reconstruction of signals from the ideal linear coil set but the Fourier reconstruction of signals from the circular coil set produced severe geometric distortion. Least squares inversion in all cases produced reconstruction errors comparable to the Fourier reconstruction of the simulated signal from the ideal linear coil set. MRI signals encoded in B1 fields with non-linearly varying spatial phase may be accurately reconstructed using regularized least squares thus pointing the way to the use of simple RF coil designs for RF encoded MRI. Crown Copyright © 2016. Published by Elsevier Inc. All rights reserved.

Dual-wavelength common-path digital holographic microscopy for quantitative phase imaging of biological cells

NASA Astrophysics Data System (ADS)

Di, Jianglei; Song, Yu; Xi, Teli; Zhang, Jiwei; Li, Ying; Ma, Chaojie; Wang, Kaiqiang; Zhao, Jianlin

2017-11-01

Biological cells are usually transparent with a small refractive index gradient. Digital holographic interferometry can be used in the measurement of biological cells. We propose a dual-wavelength common-path digital holographic microscopy for the quantitative phase imaging of biological cells. In the proposed configuration, a parallel glass plate is inserted in the light path to create the lateral shearing, and two lasers with different wavelengths are used as the light source to form the dual-wavelength composite digital hologram. The information of biological cells for different wavelengths is separated and extracted in the Fourier domain of the hologram, and then combined to a shorter wavelength in the measurement process. This method could improve the system's temporal stability and reduce speckle noises simultaneously. Mouse osteoblastic cells and peony pollens are measured to show the feasibility of this method.

Near infrared bioluminescence resonance energy transfer from firefly luciferase—quantum dot bionanoconjugates

NASA Astrophysics Data System (ADS)

Alam, Rabeka; Karam, Liliana M.; Doane, Tennyson L.; Zylstra, Joshua; Fontaine, Danielle M.; Branchini, Bruce R.; Maye, Mathew M.

2014-12-01

The bioluminescence resonance energy transfer (BRET) between firefly luciferase enzymes and semiconductive quantum dots (QDs) with near infrared emission is described. The QD were phase transferred to aqueous buffers using a histidine mediated phase transfer route, and incubated with a hexahistidine tagged, green emitting variant of firefly luciferase from Photinus pyralis (PPyGRTS). The PPyGRTS were bound to the QD interface via the hexahistidine tag, which effectively displaces the histidine layer and binds directly to the QD interfaces, allowing for short donor-acceptor distances (˜5.5 nm). Due to this, high BRET efficiency ratios of ˜5 were obtained. These PPyGRTS-QD bio-nano conjugates were characterized by transmission electron microscopy, thermal gravimetric analysis, Fourier transform infrared spectroscopy and BRET emission studies. The final optimized conjugate was easily observable by night vision imaging, demonstrating the potential of these materials in imaging and signaling/sensing applications.

Angle-resolved light scattering of individual rod-shaped bacteria based on Fourier transform light scattering

NASA Astrophysics Data System (ADS)

Jo, Youngju; Jung, Jaehwang; Lee, Jee Woong; Shin, Della; Park, Hyunjoo; Nam, Ki Tae; Park, Ji-Ho; Park, Yongkeun

2014-05-01

Two-dimensional angle-resolved light scattering maps of individual rod-shaped bacteria are measured at the single-cell level. Using quantitative phase imaging and Fourier transform light scattering techniques, the light scattering patterns of individual bacteria in four rod-shaped species (Bacillus subtilis, Lactobacillus casei, Synechococcus elongatus, and Escherichia coli) are measured with unprecedented sensitivity in a broad angular range from -70° to 70°. The measured light scattering patterns are analyzed along the two principal axes of rod-shaped bacteria in order to systematically investigate the species-specific characteristics of anisotropic light scattering. In addition, the cellular dry mass of individual bacteria is calculated and used to demonstrate that the cell-to-cell variations in light scattering within bacterial species is related to the cellular dry mass and growth.

A new Fourier transform based CBIR scheme for mammographic mass classification: a preliminary invariance assessment

NASA Astrophysics Data System (ADS)

Gundreddy, Rohith Reddy; Tan, Maxine; Qui, Yuchen; Zheng, Bin

2015-03-01

The purpose of this study is to develop and test a new content-based image retrieval (CBIR) scheme that enables to achieve higher reproducibility when it is implemented in an interactive computer-aided diagnosis (CAD) system without significantly reducing lesion classification performance. This is a new Fourier transform based CBIR algorithm that determines image similarity of two regions of interest (ROI) based on the difference of average regional image pixel value distribution in two Fourier transform mapped images under comparison. A reference image database involving 227 ROIs depicting the verified soft-tissue breast lesions was used. For each testing ROI, the queried lesion center was systematically shifted from 10 to 50 pixels to simulate inter-user variation of querying suspicious lesion center when using an interactive CAD system. The lesion classification performance and reproducibility as the queried lesion center shift were assessed and compared among the three CBIR schemes based on Fourier transform, mutual information and Pearson correlation. Each CBIR scheme retrieved 10 most similar reference ROIs and computed a likelihood score of the queried ROI depicting a malignant lesion. The experimental results shown that three CBIR schemes yielded very comparable lesion classification performance as measured by the areas under ROC curves with the p-value greater than 0.498. However, the CBIR scheme using Fourier transform yielded the highest invariance to both queried lesion center shift and lesion size change. This study demonstrated the feasibility of improving robustness of the interactive CAD systems by adding a new Fourier transform based image feature to CBIR schemes.

Off-axis low coherence digital holographic interferometry for quantitative phase imaging with an LED

NASA Astrophysics Data System (ADS)

Guo, Rongli; Wang, Fan; Hu, Xiaoying; Yang, Wenqian

2017-11-01

Off-axis digital holographic interferometry with the light source of a light emitting diode (LED) is presented and its application for quantitative phase imaging in a large range with low noise is demonstrated. The scheme is implemented in a grating based Mach-Zehnder interferometer. To achieve off-axis interferometry, firstly, the collimated beam emitted from an LED is diffracted into multiple orders by a grating and they are split into two copies by a beam splitter; secondly, in the object arm the zero order of one copy is filtered in the Fourier plane and is reshaped to illuminate the sample, while in the reference arm one of its first order of another copy is selected to serve as the reference beam, and then an off-axis hologram can be obtained at the image plane. The main advantage stemming from an LED illumination is its high spatial phase resolution, due to the subdued speckle effect. The off-axis geometry enables one-shot recording of the hologram in the millisecond scale. The utility of the proposed setup is illustrated with measurements of a resolution target and part of a wing of green-lacewing, and dynamic evaporation process of an ethanol film.

MR imaging of the inner ear: comparison of a three-dimensional fast spin-echo sequence with use of a dedicated quadrature-surface coil with a gadolinium-enhanced spoiled gradient-recalled sequence.

PubMed

Naganawa, S; Ito, T; Fukatsu, H; Ishigaki, T; Nakashima, T; Ichinose, N; Kassai, Y; Miyazaki, M

1998-09-01

To prospectively evaluate the sensitivity and specificity of magnetic resonance (MR) imaging in the inner ear with a long echo train, three-dimensional (3D), asymmetric Fourier-transform, fast spin-echo (SE) sequence with use of a dedicated quadrature-surface phased-array coil to detect vestibular schwannoma in the cerebellopontine angle and the internal auditory canal. In 205 patients (410 ears) with ear symptoms, 1.5-T MR imaging was performed with unenhanced 3D asymmetric fast SE and gadolinium-enhanced 3D gradient-recalled (SPGR) sequences with use of a quadrature surface phased-array coil. The 3D asymmetric fast SE images were reviewed by two radiologists, with the gadolinium-enhanced 3D SPGR images used as the standard of reference. Nineteen lesions were detected in the 410 ears (diameter range, 2-30 mm; mean, 10.5 mm +/- 6.4 [standard deviation]; five lesions were smaller than 5 mm). With 3D asymmetric fast SE, sensitivity, specificity, and accuracy, respectively, were 100%, 99.5%, and 99.5% for observer 1 and 100%, 99.7%, and 99.8% for observer 2. The unenhanced 3D asymmetric fast SE sequence with a quadrature-surface phased-array coli allows the reliable detection of vestibular schwannoma in the cerebellopontine angle and internal auditory canal.

Fabrication and Testing of Binary-Phase Fourier Gratings for Nonuniform Array Generation

NASA Technical Reports Server (NTRS)

Keys, Andrew S.; Crow, Robert W.; Ashley, Paul R.; Nelson, Tom R., Jr.; Parker, Jack H.; Beecher, Elizabeth A.

2004-01-01

This effort describes the fabrication and testing of binary-phase Fourier gratings designed to generate an incoherent array of output source points with nonuniform user-defined intensities, symmetric about the zeroth order. Like Dammann fanout gratings, these binary-phase Fourier gratings employ only two phase levels to generate a defined output array. Unlike Dammann fanout gratings, these gratings generate an array of nonuniform, user-defined intensities when projected into the far-field regime. The paper describes the process of design, fabrication, and testing for two different version of the binary-phase grating; one designed for a 12 micron wavelength, referred to as the Long-Wavelength Infrared (LWIR) grating, and one designed for a 5 micron wavelength, referred to as the Mid-Wavelength Infrared Grating (MWIR).

Ballistic Signature Identification System Study

NASA Technical Reports Server (NTRS)

1976-01-01

The first phase of a research project directed toward development of a high speed automatic process to be used to match gun barrel signatures imparted to fired bullets was documented. An optical projection technique has been devised to produce and photograph a planar image of the entire signature, and the phototransparency produced is subjected to analysis using digital Fourier transform techniques. The success of this approach appears to be limited primarily by the accuracy of the photographic step since no significant processing limitations have been encountered.

Direct-to-digital holography reduction of reference hologram noise and fourier space smearing

DOEpatents

Voelkl, Edgar

2006-06-27

Systems and methods are described for reduction of reference hologram noise and reduction of Fourier space smearing, especially in the context of direct-to-digital holography (off-axis interferometry). A method of reducing reference hologram noise includes: recording a plurality of reference holograms; processing the plurality of reference holograms into a corresponding plurality of reference image waves; and transforming the corresponding plurality of reference image waves into a reduced noise reference image wave. A method of reducing smearing in Fourier space includes: recording a plurality of reference holograms; processing the plurality of reference holograms into a corresponding plurality of reference complex image waves; transforming the corresponding plurality of reference image waves into a reduced noise reference complex image wave; recording a hologram of an object; processing the hologram of the object into an object complex image wave; and dividing the complex image wave of the object by the reduced noise reference complex image wave to obtain a reduced smearing object complex image wave.

Mathematical Investigation of Gamma Ray and Neutron Absorption Grid Patterns for Homeland Defense Related Fourier Imaging Systems

NASA Technical Reports Server (NTRS)

Boccio, Dona

2003-01-01

Terrorist suitcase nuclear devices typically using converted Soviet tactical nuclear warheads contain several kilograms of plutonium. This quantity of plutonium emits a significant number of gamma rays and neutrons as it undergoes radioactive decay. These gamma rays and neutrons normally penetrate ordinary matter to a significant distance. Unfortunately this penetrating quality of the radiation makes imaging with classical optics impractical. However, this radiation signature emitted by the nuclear source may be sufficient to be imaged from low-flying aerial platforms carrying Fourier imaging systems. The Fourier imaging system uses a pair of co-aligned absorption grids to measure a selected range of spatial frequencies from an object. These grids typically measure the spatial frequency in only one direction at a time. A grid pair that looks in all directions simultaneously would be an improvement over existing technology. A number of grid pairs governed by various parameters were investigated to solve this problem. By examining numerous configurations, it became apparent that an appropriate spiral pattern could be made to work. A set of equations was found to describe a grid pattern that produces straight fringes. Straight fringes represent a Fourier transform of a point source at infinity. An inverse Fourier transform of this fringe pattern would provide an accurate image (location and intensity) of a point source.

A Fourier-based compressed sensing technique for accelerated CT image reconstruction using first-order methods.

PubMed

Choi, Kihwan; Li, Ruijiang; Nam, Haewon; Xing, Lei

2014-06-21

As a solution to iterative CT image reconstruction, first-order methods are prominent for the large-scale capability and the fast convergence rate [Formula: see text]. In practice, the CT system matrix with a large condition number may lead to slow convergence speed despite the theoretically promising upper bound. The aim of this study is to develop a Fourier-based scaling technique to enhance the convergence speed of first-order methods applied to CT image reconstruction. Instead of working in the projection domain, we transform the projection data and construct a data fidelity model in Fourier space. Inspired by the filtered backprojection formalism, the data are appropriately weighted in Fourier space. We formulate an optimization problem based on weighted least-squares in the Fourier space and total-variation (TV) regularization in image space for parallel-beam, fan-beam and cone-beam CT geometry. To achieve the maximum computational speed, the optimization problem is solved using a fast iterative shrinkage-thresholding algorithm with backtracking line search and GPU implementation of projection/backprojection. The performance of the proposed algorithm is demonstrated through a series of digital simulation and experimental phantom studies. The results are compared with the existing TV regularized techniques based on statistics-based weighted least-squares as well as basic algebraic reconstruction technique. The proposed Fourier-based compressed sensing (CS) method significantly improves both the image quality and the convergence rate compared to the existing CS techniques.

Metasurface Enabled Wide-Angle Fourier Lens.

PubMed

Liu, Wenwei; Li, Zhancheng; Cheng, Hua; Tang, Chengchun; Li, Junjie; Zhang, Shuang; Chen, Shuqi; Tian, Jianguo

2018-06-01

Fourier optics, the principle of using Fourier transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and it has been widely applied to optical information processing, imaging, holography, etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e., the paraxial approximation, which puts a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution information of an image. Other high numerical aperture Fourier lenses usually suffer from the bulky size and costly designs. Here, a dielectric metasurface consisting of high-aspect-ratio silicon waveguide array is demonstrated experimentally, which is capable of performing 1D Fourier transform for a large incident angle range and a broad operating bandwidth. Thus, the device significantly expands the operational Fourier space, benefitting from the large numerical aperture and negligible angular dispersion at large incident angles. The Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free-space optical wavefront, but also be readily integrated into micro-optical platforms due to its compact size. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Fourier-based linear systems description of free-breathing pulmonary magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Capaldi, D. P. I.; Svenningsen, S.; Cunningham, I. A.; Parraga, G.

2015-03-01

Fourier-decomposition of free-breathing pulmonary magnetic resonance imaging (FDMRI) was recently piloted as a way to provide rapid quantitative pulmonary maps of ventilation and perfusion without the use of exogenous contrast agents. This method exploits fast pulmonary MRI acquisition of free-breathing proton (1H) pulmonary images and non-rigid registration to compensate for changes in position and shape of the thorax associated with breathing. In this way, ventilation imaging using conventional MRI systems can be undertaken but there has been no systematic evaluation of fundamental image quality measurements based on linear systems theory. We investigated the performance of free-breathing pulmonary ventilation imaging using a Fourier-based linear system description of each operation required to generate FDMRI ventilation maps. Twelve subjects with chronic obstructive pulmonary disease (COPD) or bronchiectasis underwent pulmonary function tests and MRI. Non-rigid registration was used to co-register the temporal series of pulmonary images. Pulmonary voxel intensities were aligned along a time axis and discrete Fourier transforms were performed on the periodic signal intensity pattern to generate frequency spectra. We determined the signal-to-noise ratio (SNR) of the FDMRI ventilation maps using a conventional approach (SNRC) and using the Fourier-based description (SNRF). Mean SNR was 4.7 ± 1.3 for subjects with bronchiectasis and 3.4 ± 1.8, for COPD subjects (p>.05). SNRF was significantly different than SNRC (p<.01). SNRF was approximately 50% of SNRC suggesting that the linear system model well-estimates the current approach.

Fast data reconstructed method of Fourier transform imaging spectrometer based on multi-core CPU

NASA Astrophysics Data System (ADS)

Yu, Chunchao; Du, Debiao; Xia, Zongze; Song, Li; Zheng, Weijian; Yan, Min; Lei, Zhenggang

2017-10-01

Imaging spectrometer can gain two-dimensional space image and one-dimensional spectrum at the same time, which shows high utility in color and spectral measurements, the true color image synthesis, military reconnaissance and so on. In order to realize the fast reconstructed processing of the Fourier transform imaging spectrometer data, the paper designed the optimization reconstructed algorithm with OpenMP parallel calculating technology, which was further used for the optimization process for the HyperSpectral Imager of `HJ-1' Chinese satellite. The results show that the method based on multi-core parallel computing technology can control the multi-core CPU hardware resources competently and significantly enhance the calculation of the spectrum reconstruction processing efficiency. If the technology is applied to more cores workstation in parallel computing, it will be possible to complete Fourier transform imaging spectrometer real-time data processing with a single computer.

A method to perform a fast fourier transform with primitive image transformations.

PubMed

Sheridan, Phil

2007-05-01

The Fourier transform is one of the most important transformations in image processing. A major component of this influence comes from the ability to implement it efficiently on a digital computer. This paper describes a new methodology to perform a fast Fourier transform (FFT). This methodology emerges from considerations of the natural physical constraints imposed by image capture devices (camera/eye). The novel aspects of the specific FFT method described include: 1) a bit-wise reversal re-grouping operation of the conventional FFT is replaced by the use of lossless image rotation and scaling and 2) the usual arithmetic operations of complex multiplication are replaced with integer addition. The significance of the FFT presented in this paper is introduced by extending a discrete and finite image algebra, named Spiral Honeycomb Image Algebra (SHIA), to a continuous version, named SHIAC.

Picosecond imaging of sprays

NASA Technical Reports Server (NTRS)

Breisacher, Kevin; Liou, Larry; Wang, L.; Liang, X.; Galland, P.; Ho, P. P.; Alfano, R. R.

1994-01-01

Preliminary results from applying a Kerr-Fourier imaging system to a water/air spray produced by a shear coaxial element are presented. The physics behind ultrafast time-gated optical techniques is discussed briefly. A typical setup of a Kerr-Fourier time gating system is presented.

The angular difference function and its application to image registration.

PubMed

Keller, Yosi; Shkolnisky, Yoel; Averbuch, Amir

2005-06-01

The estimation of large motions without prior knowledge is an important problem in image registration. In this paper, we present the angular difference function (ADF) and demonstrate its applicability to rotation estimation. The ADF of two functions is defined as the integral of their spectral difference along the radial direction. It is efficiently computed using the pseudopolar Fourier transform, which computes the discrete Fourier transform of an image on a near spherical grid. Unlike other Fourier-based registration schemes, the suggested approach does not require any interpolation. Thus, it is more accurate and significantly faster.

Mapping agroecological zones and time lag in vegetation growth by means of Fourier analysis of time series of NDVI images

NASA Technical Reports Server (NTRS)

Menenti, M.; Azzali, S.; Verhoef, W.; Van Swol, R.

1993-01-01

Examples are presented of applications of a fast Fourier transform algorithm to analyze time series of images of Normalized Difference Vegetation Index values. The results obtained for a case study on Zambia indicated that differences in vegetation development among map units of an existing agroclimatic map were not significant, while reliable differences were observed among the map units obtained using the Fourier analysis.

Physical Modeling for Processing Geosynchronous Imaging Fourier Transform Spectrometer-Indian Ocean METOC Imager (GIFTS-IOMI) Hyperspectral Data

DTIC Science & Technology

2002-09-30

Physical Modeling for Processing Geosynchronous Imaging Fourier Transform Spectrometer-Indian Ocean METOC Imager ( GIFTS -IOMI) Hyperspectral Data...water quality assessment. OBJECTIVES The objective of this DoD research effort is to develop and demonstrate a fully functional GIFTS - IOMI...environment once GIFTS -IOMI is stationed over the Indian Ocean. The system will provide specialized methods for the characterization of the atmospheric

Partial fourier and parallel MR image reconstruction with integrated gradient nonlinearity correction.

PubMed

Tao, Shengzhen; Trzasko, Joshua D; Shu, Yunhong; Weavers, Paul T; Huston, John; Gray, Erin M; Bernstein, Matt A

2016-06-01

To describe how integrated gradient nonlinearity (GNL) correction can be used within noniterative partial Fourier (homodyne) and parallel (SENSE and GRAPPA) MR image reconstruction strategies, and demonstrate that performing GNL correction during, rather than after, these routines mitigates the image blurring and resolution loss caused by postreconstruction image domain based GNL correction. Starting from partial Fourier and parallel magnetic resonance imaging signal models that explicitly account for GNL, noniterative image reconstruction strategies for each accelerated acquisition technique are derived under the same core mathematical assumptions as their standard counterparts. A series of phantom and in vivo experiments on retrospectively undersampled data were performed to investigate the spatial resolution benefit of integrated GNL correction over conventional postreconstruction correction. Phantom and in vivo results demonstrate that the integrated GNL correction reduces the image blurring introduced by the conventional GNL correction, while still correcting GNL-induced coarse-scale geometrical distortion. Images generated from undersampled data using the proposed integrated GNL strategies offer superior depiction of fine image detail, for example, phantom resolution inserts and anatomical tissue boundaries. Noniterative partial Fourier and parallel imaging reconstruction methods with integrated GNL correction reduce the resolution loss that occurs during conventional postreconstruction GNL correction while preserving the computational efficiency of standard reconstruction techniques. Magn Reson Med 75:2534-2544, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

A coherent through-wall MIMO phased array imaging radar based on time-duplexed switching

NASA Astrophysics Data System (ADS)

Chen, Qingchao; Chetty, Kevin; Brennan, Paul; Lok, Lai Bun; Ritchie, Matthiew; Woodbridge, Karl

2017-05-01

Through-the-Wall (TW) radar sensors are gaining increasing interest for security, surveillance and search and rescue applications. Additionally, the integration of Multiple-Input, Multiple-Output (MIMO) techniques with phased array radar is allowing higher performance at lower cost. In this paper we present a 4-by-4 TW MIMO phased array imaging radar operating at 2.4 GHz with 200 MHz bandwidth. To achieve high imaging resolution in a cost-effective manner, the 4 Tx and 4 Rx elements are used to synthesize a uniform linear array (ULA) of 16 virtual elements. Furthermore, the transmitter is based on a single-channel 4-element time-multiplexed switched array. In transmission, the radar utilizes frequency modulated continuous wave (FMCW) waveforms that undergo de-ramping on receive to allow digitization at relatively low sampling rates, which then simplifies the imaging process. This architecture has been designed for the short-range TW scenarios envisaged, and permits sufficient time to switch between antenna elements. The paper first outlines the system characteristics before describing the key signal processing and imaging algorithms which are based on traditional Fast Fourier Transform (FFT) processing. These techniques are implemented in LabVIEW software. Finally, we report results from an experimental campaign that investigated the imaging capabilities of the system and demonstrated the detection of personnel targets. Moreover, we show that multiple targets within a room with greater than approximately 1 meter separation can be distinguished from one another.

[Spatial domain display for interference image dataset].

PubMed

Wang, Cai-Ling; Li, Yu-Shan; Liu, Xue-Bin; Hu, Bing-Liang; Jing, Juan-Juan; Wen, Jia

2011-11-01

The requirements of imaging interferometer visualization is imminent for the user of image interpretation and information extraction. However, the conventional researches on visualization only focus on the spectral image dataset in spectral domain. Hence, the quick show of interference spectral image dataset display is one of the nodes in interference image processing. The conventional visualization of interference dataset chooses classical spectral image dataset display method after Fourier transformation. In the present paper, the problem of quick view of interferometer imager in image domain is addressed and the algorithm is proposed which simplifies the matter. The Fourier transformation is an obstacle since its computation time is very large and the complexion would be even deteriorated with the size of dataset increasing. The algorithm proposed, named interference weighted envelopes, makes the dataset divorced from transformation. The authors choose three interference weighted envelopes respectively based on the Fourier transformation, features of interference data and human visual system. After comparing the proposed with the conventional methods, the results show the huge difference in display time.

Fourier rebinning and consistency equations for time-of-flight PET planograms

PubMed Central

Li, Yusheng; Defrise, Michel; Matej, Samuel; Metzler, Scott D

2016-01-01

Due to the unique geometry, dual-panel PET scanners have many advantages in dedicated breast imaging and on-board imaging applications since the compact scanners can be combined with other imaging and treatment modalities. The major challenges of dual-panel PET imaging are the limited-angle problem and data truncation, which can cause artifacts due to incomplete data sampling. The time-of-flight (TOF) information can be a promising solution to reduce these artifacts. The TOF planogram is the native data format for dual-panel TOF PET scanners, and the non-TOF planogram is the 3D extension of linogram. The TOF planograms is five-dimensional while the objects are three-dimensional, and there are two degrees of redundancy. In this paper, we derive consistency equations and Fourier-based rebinning algorithms to provide a complete understanding of the rich structure of the fully 3D TOF planograms. We first derive two consistency equations and John's equation for 3D TOF planograms. By taking the Fourier transforms, we obtain two Fourier consistency equations and the Fourier-John equation, which are the duals of the consistency equations and John's equation, respectively. We then solve the Fourier consistency equations and Fourier-John equation using the method of characteristics. The two degrees of entangled redundancy of the 3D TOF data can be explicitly elicited and exploited by the solutions along the characteristic curves. As the special cases of the general solutions, we obtain Fourier rebinning and consistency equations (FORCEs), and thus we obtain a complete scheme to convert among different types of PET planograms: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF planograms. The FORCEs can be used as Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. As a byproduct, we show the two consistency equations are necessary and sufficient for 3D TOF planograms. Finally, we give numerical examples of implementation of a fast 2D TOF planogram projector and Fourier-based rebinning for a 2D TOF planograms using the FORCEs to show the efficacy of the Fourier-based solutions. PMID:28255191

Fourier rebinning and consistency equations for time-of-flight PET planograms.

PubMed

Li, Yusheng; Defrise, Michel; Matej, Samuel; Metzler, Scott D

2016-01-01

Due to the unique geometry, dual-panel PET scanners have many advantages in dedicated breast imaging and on-board imaging applications since the compact scanners can be combined with other imaging and treatment modalities. The major challenges of dual-panel PET imaging are the limited-angle problem and data truncation, which can cause artifacts due to incomplete data sampling. The time-of-flight (TOF) information can be a promising solution to reduce these artifacts. The TOF planogram is the native data format for dual-panel TOF PET scanners, and the non-TOF planogram is the 3D extension of linogram. The TOF planograms is five-dimensional while the objects are three-dimensional, and there are two degrees of redundancy. In this paper, we derive consistency equations and Fourier-based rebinning algorithms to provide a complete understanding of the rich structure of the fully 3D TOF planograms. We first derive two consistency equations and John's equation for 3D TOF planograms. By taking the Fourier transforms, we obtain two Fourier consistency equations and the Fourier-John equation, which are the duals of the consistency equations and John's equation, respectively. We then solve the Fourier consistency equations and Fourier-John equation using the method of characteristics. The two degrees of entangled redundancy of the 3D TOF data can be explicitly elicited and exploited by the solutions along the characteristic curves. As the special cases of the general solutions, we obtain Fourier rebinning and consistency equations (FORCEs), and thus we obtain a complete scheme to convert among different types of PET planograms: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF planograms. The FORCEs can be used as Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. As a byproduct, we show the two consistency equations are necessary and sufficient for 3D TOF planograms. Finally, we give numerical examples of implementation of a fast 2D TOF planogram projector and Fourier-based rebinning for a 2D TOF planograms using the FORCEs to show the efficacy of the Fourier-based solutions.

Direct generation of abruptly focusing vortex beams using a 3/2 radial phase-only pattern.

PubMed

Davis, Jeffrey A; Cottrell, Don M; Zinn, Jonathan M

2013-03-20

Abruptly focusing Airy beams have previously been generated using a radial cubic phase pattern that represents the Fourier transform of the Airy beam. The Fourier transform of this pattern is formed using a system length of 2f, where f is the focal length of the Fourier transform lens. In this work, we directly generate these abruptly focusing Airy beams using a 3/2 radial phase pattern encoded onto a liquid crystal display. The resulting optical system is much shorter. In addition, we can easily produce vortex patterns at the focal point of these beams. Experimental results match theoretical predictions.

Optical information-processing systems and architectures II; Proceedings of the Meeting, San Diego, CA, July 9-13, 1990

NASA Astrophysics Data System (ADS)

Javidi, Bahram

The present conference discusses topics in the fields of neural networks, acoustooptic signal processing, pattern recognition, phase-only processing, nonlinear signal processing, image processing, optical computing, and optical information processing. Attention is given to the optical implementation of an inner-product neural associative memory, optoelectronic associative recall via motionless-head/parallel-readout optical disk, a compact real-time acoustooptic image correlator, a multidimensional synthetic estimation filter, and a light-efficient joint transform optical correlator. Also discussed are a high-resolution spatial light modulator, compact real-time interferometric Fourier-transform processors, a fast decorrelation algorithm for permutation arrays, the optical interconnection of optical modules, and carry-free optical binary adders.

Encrypted optical storage with wavelength-key and random phase codes.

PubMed

Matoba, O; Javidi, B

1999-11-10

An encrypted optical memory system that uses a wavelength code as well as input and Fourier-plane random phase codes is proposed. Original data are illuminated by a coherent light source with a specified wavelength and are then encrypted with two random phase codes before being stored holographically in a photorefractive material. Successful decryption requires the use of a readout beam with the same wavelength as that used in the recording, in addition to the correct phase key in the Fourier plane. The wavelength selectivity of the proposed system is evaluated numerically. We show that the number of available wavelength keys depends on the correlation length of the phase key in the Fourier plane. Preliminary experiments of encryption and decryption of optical memory in a LiNbO(3):Fe photorefractive crystal are demonstrated.

Diamond-Based Magnetic Imaging with Fourier Optical Processing

NASA Astrophysics Data System (ADS)

Backlund, Mikael P.; Kehayias, Pauli; Walsworth, Ronald L.

2017-11-01

Diamond-based magnetic field sensors have attracted great interest in recent years. In particular, wide-field magnetic imaging using nitrogen-vacancy (NV) centers in diamond has been previously demonstrated in condensed matter, biological, and paleomagnetic applications. Vector magnetic imaging with NV ensembles typically requires a significant applied field (>10 G ) to resolve the contributions from four crystallographic orientations, hindering studies of magnetic samples that require measurement in low or independently specified bias fields. Here we model and measure the complex amplitude distribution of NV emission at the microscope's Fourier plane and show that by modulating this collected light at the Fourier plane, one can decompose the NV ensemble magnetic resonance spectrum into its constituent orientations by purely optical means. This decomposition effectively extends the dynamic range at a given bias field and enables wide-field vector magnetic imaging at arbitrarily low bias fields, thus broadening potential applications of NV imaging and sensing. Our results demonstrate that NV-based microscopy stands to benefit greatly from Fourier optical approaches, which have already found widespread utility in other branches of microscopy.

Wavelength-encoded tomography based on optical temporal Fourier transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Chi; Wong, Kenneth K. Y., E-mail: kywong@eee.hku.hk

We propose and demonstrate a technique called wavelength-encoded tomography (WET) for non-invasive optical cross-sectional imaging, particularly beneficial in biological system. The WET utilizes time-lens to perform the optical Fourier transform, and the time-to-wavelength conversion generates a wavelength-encoded image of optical scattering from internal microstructures, analogous to the interferometery-based imaging such as optical coherence tomography. Optical Fourier transform, in principle, comes with twice as good axial resolution over the electrical Fourier transform, and will greatly simplify the digital signal processing after the data acquisition. As a proof-of-principle demonstration, a 150 -μm (ideally 36 μm) resolution is achieved based on a 7.5-nm bandwidth swept-pump,more » using a conventional optical spectrum analyzer. This approach can potentially achieve up to 100-MHz or even higher frame rate with some proven ultrafast spectrum analyzer. We believe that this technique is innovative towards the next-generation ultrafast optical tomographic imaging application.« less

Predictive searching algorithm for Fourier ptychography

NASA Astrophysics Data System (ADS)

Li, Shunkai; Wang, Yifan; Wu, Weichen; Liang, Yanmei

2017-12-01

By capturing a set of low-resolution images under different illumination angles and stitching them together in the Fourier domain, Fourier ptychography (FP) is capable of providing high-resolution image with large field of view. Despite its validity, long acquisition time limits its real-time application. We proposed an incomplete sampling scheme in this paper, termed the predictive searching algorithm to shorten the acquisition and recovery time. Informative sub-regions of the sample’s spectrum are searched and the corresponding images of the most informative directions are captured for spectrum expansion. Its effectiveness is validated by both simulated and experimental results, whose data requirement is reduced by ˜64% to ˜90% without sacrificing image reconstruction quality compared with the conventional FP method.

Fourier dimension of random images

NASA Astrophysics Data System (ADS)

Ekström, Fredrik

2016-10-01

Given a compact set of real numbers, a random C^{m + α}-diffeomorphism is constructed such that the image of any measure concentrated on the set and satisfying a certain condition involving a real number s, almost surely has Fourier dimension greater than or equal to s / (m + α). This is used to show that every Borel subset of the real numbers of Hausdorff dimension s is C^{m + α}-equivalent to a set of Fourier dimension greater than or equal to s / (m + α ). In particular every Borel set is diffeomorphic to a Salem set, and the Fourier dimension is not invariant under Cm-diffeomorphisms for any m.

Predicting detection performance with model observers: Fourier domain or spatial domain?

PubMed

Chen, Baiyu; Yu, Lifeng; Leng, Shuai; Kofler, James; Favazza, Christopher; Vrieze, Thomas; McCollough, Cynthia

2016-02-27

The use of Fourier domain model observer is challenged by iterative reconstruction (IR), because IR algorithms are nonlinear and IR images have noise texture different from that of FBP. A modified Fourier domain model observer, which incorporates nonlinear noise and resolution properties, has been proposed for IR and needs to be validated with human detection performance. On the other hand, the spatial domain model observer is theoretically applicable to IR, but more computationally intensive than the Fourier domain method. The purpose of this study is to compare the modified Fourier domain model observer to the spatial domain model observer with both FBP and IR images, using human detection performance as the gold standard. A phantom with inserts of various low contrast levels and sizes was repeatedly scanned 100 times on a third-generation, dual-source CT scanner at 5 dose levels and reconstructed using FBP and IR algorithms. The human detection performance of the inserts was measured via a 2-alternative-forced-choice (2AFC) test. In addition, two model observer performances were calculated, including a Fourier domain non-prewhitening model observer and a spatial domain channelized Hotelling observer. The performance of these two mode observers was compared in terms of how well they correlated with human observer performance. Our results demonstrated that the spatial domain model observer correlated well with human observers across various dose levels, object contrast levels, and object sizes. The Fourier domain observer correlated well with human observers using FBP images, but overestimated the detection performance using IR images.

Predicting detection performance with model observers: Fourier domain or spatial domain?

PubMed Central

Chen, Baiyu; Yu, Lifeng; Leng, Shuai; Kofler, James; Favazza, Christopher; Vrieze, Thomas; McCollough, Cynthia

2016-01-01

The use of Fourier domain model observer is challenged by iterative reconstruction (IR), because IR algorithms are nonlinear and IR images have noise texture different from that of FBP. A modified Fourier domain model observer, which incorporates nonlinear noise and resolution properties, has been proposed for IR and needs to be validated with human detection performance. On the other hand, the spatial domain model observer is theoretically applicable to IR, but more computationally intensive than the Fourier domain method. The purpose of this study is to compare the modified Fourier domain model observer to the spatial domain model observer with both FBP and IR images, using human detection performance as the gold standard. A phantom with inserts of various low contrast levels and sizes was repeatedly scanned 100 times on a third-generation, dual-source CT scanner at 5 dose levels and reconstructed using FBP and IR algorithms. The human detection performance of the inserts was measured via a 2-alternative-forced-choice (2AFC) test. In addition, two model observer performances were calculated, including a Fourier domain non-prewhitening model observer and a spatial domain channelized Hotelling observer. The performance of these two mode observers was compared in terms of how well they correlated with human observer performance. Our results demonstrated that the spatial domain model observer correlated well with human observers across various dose levels, object contrast levels, and object sizes. The Fourier domain observer correlated well with human observers using FBP images, but overestimated the detection performance using IR images. PMID:27239086

Feasibility of quantitative regional ventilation and perfusion mapping with phase-resolved functional lung (PREFUL) MRI in healthy volunteers and COPD, CTEPH, and CF patients.

PubMed

Voskrebenzev, Andreas; Gutberlet, Marcel; Klimeš, Filip; Kaireit, Till F; Schönfeld, Christian; Rotärmel, Alexander; Wacker, Frank; Vogel-Claussen, Jens

2018-04-01

In this feasibility study, a phase-resolved functional lung imaging postprocessing method for extraction of dynamic perfusion (Q) and ventilation (V) parameters using a conventional 1H lung MRI Fourier decomposition acquisition is introduced. Time series of coronal gradient-echo MR images with a temporal resolution of 288 to 324 ms of two healthy volunteers, one patient with chronic thromboembolic hypertension, one patient with cystic fibrosis, and one patient with chronic obstructive pulmonary disease were acquired at 1.5 T. Using a sine model to estimate cardiac and respiratory phases of each image, all images were sorted to reconstruct full cardiac and respiratory cycles. Time to peak (TTP), V/Q maps, and fractional ventilation flow-volume loops were calculated. For the volunteers, homogenous ventilation and perfusion TTP maps (V-TTP, Q-TTP) were obtained. The chronic thromboembolic hypertension patient showed increased perfusion TTP in hypoperfused regions in visual agreement with dynamic contrast-enhanced MRI, which improved postpulmonary endaterectomy surgery. Cystic fibrosis and chronic obstructive pulmonary disease patients showed a pattern of increased V-TTP and Q-TTP in regions of hypoventilation and decreased perfusion. Fractional ventilation flow-volume loops of the chronic obstructive pulmonary disease patient were smaller in comparison with the healthy volunteer, and showed regional differences in visual agreement with functional small airways disease and emphysema on CT. This study shows the feasibility of phase-resolved functional lung imaging to gain quantitative information regarding regional lung perfusion and ventilation without the need for ultrafast imaging, which will be advantageous for future clinical translation. Magn Reson Med 79:2306-2314, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Illumination Modulation for Improved Propagation-Based Phase Imaging

NASA Astrophysics Data System (ADS)

Chakraborty, Tonmoy

Propagation-based phase imaging enables the quantitative reconstruction of a light beam's phase from measurements of its intensity. Because the intensity depends on the time-averaged square of the field the relationship between intensity and phase is, in general, nonlinear. The transport of intensity equation (TIE), is a linear equation relating phase and propagated intensity that arises from restricting the propagation distance to be small. However, the TIE limits the spatial frequencies that can be reliably reconstructed to those below some cutoff, which limits the accuracy of reconstruction of fine features in phase. On the other hand, the low frequency components suffer from poor signal to noise ratio (SNR) unless the propagation distance is sufficiently large, which leads to low frequency artifacts that obscure the reconstruction. In this research, I will consider the use of incoherent primary sources of illumination, in a Kohler illumination setup, to enhance the low-frequency performance of the TIE. The necessary steps required to design and build a table-top imaging setup which is capable of capturing intensity at any defocused position while modulating the source will be explained. In addition, it will be shown how by employing such illumination, the steps required for computationally recovering the phase, i.e. Fourier transforms and frequency-domain filtering, may be performed in the optical system. While these methods can address the low-frequency performance of the TIE, they do not extend its high-frequency cutoff. To avoid this cutoff, for objects with slowly varying phase, the contrast transfer function (CTF) model, an alternative to the TIE, can be used to recover phase. By allowing the combination of longer propagation distances and incoherent sources, it will be shown how CTF can improve performance at both high and low frequencies.

[Evaluation of Image Quality of Readout Segmented EPI with Readout Partial Fourier Technique].

PubMed

Yoshimura, Yuuki; Suzuki, Daisuke; Miyahara, Kanae

Readout segmented EPI (readout segmentation of long variable echo-trains: RESOLVE) segmented k-space in the readout direction. By using the partial Fourier method in the readout direction, the imaging time was shortened. However, the influence on image quality due to insufficient data sampling is concerned. The setting of the partial Fourier method in the readout direction in each segment was changed. Then, we examined signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and distortion ratio for changes in image quality due to differences in data sampling. As the number of sampling segments decreased, SNR and CNR showed a low value. In addition, the distortion ratio did not change. The image quality of minimum sampling segments is greatly different from full data sampling, and caution is required when using it.

Wide-field FTIR microscopy using mid-IR pulse shaping

PubMed Central

Serrano, Arnaldo L.; Ghosh, Ayanjeet; Ostrander, Joshua S.; Zanni, Martin T.

2015-01-01

We have developed a new table-top technique for collecting wide-field Fourier transform infrared (FTIR) microscopic images by combining a femtosecond pulse shaper with a mid-IR focal plane array. The pulse shaper scans the delay between a pulse pair extremely rapidly for high signal-to-noise, while also enabling phase control of the individual pulses to under-sample the interferograms and subtract background. Infrared absorption images were collected for a mixture of W(CO)6 or Mn2(CO)10 absorbed polystyrene beads, demonstrating that this technique can spatially resolve chemically distinct species. The images are sub-diffraction limited, as measured with a USAF test target patterned on CaF2 and verified with scalar wave simulations. We also find that refractive, rather than reflective, objectives are preferable for imaging with coherent radiation. We discuss this method with respect to conventional FTIR microscopes. PMID:26191843

Quaternion-Based Texture Analysis of Multiband Satellite Images: Application to the Estimation of Aboveground Biomass in the East Region of Cameroon.

PubMed

Djiongo Kenfack, Cedrigue Boris; Monga, Olivier; Mpong, Serge Moto; Ndoundam, René

2018-03-01

Within the last decade, several approaches using quaternion numbers to handle and model multiband images in a holistic manner were introduced. The quaternion Fourier transform can be efficiently used to model texture in multidimensional data such as color images. For practical application, multispectral satellite data appear as a primary source for measuring past trends and monitoring changes in forest carbon stocks. In this work, we propose a texture-color descriptor based on the quaternion Fourier transform to extract relevant information from multiband satellite images. We propose a new multiband image texture model extraction, called FOTO++, in order to address biomass estimation issues. The first stage consists in removing noise from the multispectral data while preserving the edges of canopies. Afterward, color texture descriptors are extracted thanks to a discrete form of the quaternion Fourier transform, and finally the support vector regression method is used to deduce biomass estimation from texture indices. Our texture features are modeled using a vector composed with the radial spectrum coming from the amplitude of the quaternion Fourier transform. We conduct several experiments in order to study the sensitivity of our model to acquisition parameters. We also assess its performance both on synthetic images and on real multispectral images of Cameroonian forest. The results show that our model is more robust to acquisition parameters than the classical Fourier Texture Ordination model (FOTO). Our scheme is also more accurate for aboveground biomass estimation. We stress that a similar methodology could be implemented using quaternion wavelets. These results highlight the potential of the quaternion-based approach to study multispectral satellite images.

Logarithmic Laplacian Prior Based Bayesian Inverse Synthetic Aperture Radar Imaging.

PubMed

Zhang, Shuanghui; Liu, Yongxiang; Li, Xiang; Bi, Guoan

2016-04-28

This paper presents a novel Inverse Synthetic Aperture Radar Imaging (ISAR) algorithm based on a new sparse prior, known as the logarithmic Laplacian prior. The newly proposed logarithmic Laplacian prior has a narrower main lobe with higher tail values than the Laplacian prior, which helps to achieve performance improvement on sparse representation. The logarithmic Laplacian prior is used for ISAR imaging within the Bayesian framework to achieve better focused radar image. In the proposed method of ISAR imaging, the phase errors are jointly estimated based on the minimum entropy criterion to accomplish autofocusing. The maximum a posterior (MAP) estimation and the maximum likelihood estimation (MLE) are utilized to estimate the model parameters to avoid manually tuning process. Additionally, the fast Fourier Transform (FFT) and Hadamard product are used to minimize the required computational efficiency. Experimental results based on both simulated and measured data validate that the proposed algorithm outperforms the traditional sparse ISAR imaging algorithms in terms of resolution improvement and noise suppression.

Restoration algorithms for imaging through atmospheric turbulence

DTIC Science & Technology

2017-02-18

the Fourier spectrum of each frame. The reconstructed image is then obtained by taking the inverse Fourier transform of the average of all processed...with wipξq “ Gσp|Fpviqpξq|pq řM j“1Gσp|Fpvjqpξq|pq , where F denotes the Fourier transform (ξ are the frequencies) and Gσ is a Gaussian filter of...a combination of SIFT [26] and ORSA [14] algorithms) in order to remove affine transformations (translations, rotations and homothety). The authors

'Big Bang' tomography as a new route to atomic-resolution electron tomography.

PubMed

Van Dyck, Dirk; Jinschek, Joerg R; Chen, Fu-Rong

2012-06-13

Until now it has not been possible to image at atomic resolution using classical electron tomographic methods, except when the target is a perfectly crystalline nano-object imaged along a few zone axes. The main reasons are that mechanical tilting in an electron microscope with sub-ångström precision over a very large angular range is difficult, that many real-life objects such as dielectric layers in microelectronic devices impose geometrical constraints and that many radiation-sensitive objects such as proteins limit the total electron dose. Hence, there is a need for a new tomographic scheme that is able to deduce three-dimensional information from only one or a few projections. Here we present an electron tomographic method that can be used to determine, from only one viewing direction and with sub-ångström precision, both the position of individual atoms in the plane of observation and their vertical position. The concept is based on the fact that an experimentally reconstructed exit wave consists of the superposition of the spherical waves that have been scattered by the individual atoms of the object. Furthermore, the phase of a Fourier component of a spherical wave increases with the distance of propagation at a known 'phase speed'. If we assume that an atom is a point-like object, the relationship between the phase and the phase speed of each Fourier component is linear, and the distance between the atom and the plane of observation can therefore be determined by linear fitting. This picture has similarities with Big Bang cosmology, in which the Universe expands from a point-like origin such that the distance of any galaxy from the origin is linearly proportional to the speed at which it moves away from the origin (Hubble expansion). The proof of concept of the method has been demonstrated experimentally for graphene with a two-layer structure and it will work optimally for similar layered materials, such as boron nitride and molybdenum disulphide.

When holography meets coherent diffraction imaging.

PubMed

Latychevskaia, Tatiana; Longchamp, Jean-Nicolas; Fink, Hans-Werner

2012-12-17

The phase problem is inherent to crystallographic, astronomical and optical imaging where only the intensity of the scattered signal is detected and the phase information is lost and must somehow be recovered to reconstruct the object's structure. Modern imaging techniques at the molecular scale rely on utilizing novel coherent light sources like X-ray free electron lasers for the ultimate goal of visualizing such objects as individual biomolecules rather than crystals. Here, unlike in the case of crystals where structures can be solved by model building and phase refinement, the phase distribution of the wave scattered by an individual molecule must directly be recovered. There are two well-known solutions to the phase problem: holography and coherent diffraction imaging (CDI). Both techniques have their pros and cons. In holography, the reconstruction of the scattered complex-valued object wave is directly provided by a well-defined reference wave that must cover the entire detector area which often is an experimental challenge. CDI provides the highest possible, only wavelength limited, resolution, but the phase recovery is an iterative process which requires some pre-defined information about the object and whose outcome is not always uniquely-defined. Moreover, the diffraction patterns must be recorded under oversampling conditions, a pre-requisite to be able to solve the phase problem. Here, we report how holography and CDI can be merged into one superior technique: holographic coherent diffraction imaging (HCDI). An inline hologram can be recorded by employing a modified CDI experimental scheme. We demonstrate that the amplitude of the Fourier transform of an inline hologram is related to the complex-valued visibility, thus providing information on both, the amplitude and the phase of the scattered wave in the plane of the diffraction pattern. With the phase information available, the condition of oversampling the diffraction patterns can be relaxed, and the phase problem can be solved in a fast and unambiguous manner. We demonstrate the reconstruction of various diffraction patterns of objects recorded with visible light as well as with low-energy electrons. Although we have demonstrated our HCDI method using laser light and low-energy electrons, it can also be applied to any other coherent radiation such as X-rays or high-energy electrons.

Fourier-based automatic alignment for improved Visual Cryptography schemes.

PubMed

Machizaud, Jacques; Chavel, Pierre; Fournel, Thierry

2011-11-07

In Visual Cryptography, several images, called "shadow images", that separately contain no information, are overlapped to reveal a shared secret message. We develop a method to digitally register one printed shadow image acquired by a camera with a purely digital shadow image, stored in memory. Using Fourier techniques derived from Fourier Optics concepts, the idea is to enhance and exploit the quasi periodicity of the shadow images, composed by a random distribution of black and white patterns on a periodic sampling grid. The advantage is to speed up the security control or the access time to the message, in particular in the cases of a small pixel size or of large numbers of pixels. Furthermore, the interest of visual cryptography can be increased by embedding the initial message in two shadow images that do not have identical mathematical supports, making manual registration impractical. Experimental results demonstrate the successful operation of the method, including the possibility to directly project the result onto the printed shadow image.

Autofocus algorithm using one-dimensional Fourier transform and Pearson correlation

NASA Astrophysics Data System (ADS)

Bueno Mario, A.; Alvarez-Borrego, Josue; Acho, L.

2004-10-01

A new autofocus algorithm based on one-dimensional Fourier transform and Pearson correlation for Z automatized microscope is proposed. Our goal is to determine in fast response time and accuracy, the best focused plane through an algorithm. We capture in bright and dark field several images set at different Z distances from biological organism sample. The algorithm uses the one-dimensional Fourier transform to obtain the image frequency content of a vectors pattern previously defined comparing the Pearson correlation of these frequency vectors versus the reference image frequency vector, the most out of focus image, we find the best focusing. Experimental results showed the algorithm has fast response time and accuracy in getting the best focus plane from captured images. In conclusions, the algorithm can be implemented in real time systems due fast response time, accuracy and robustness. The algorithm can be used to get focused images in bright and dark field and it can be extended to include fusion techniques to construct multifocus final images beyond of this paper.

Research on effects of phase error in phase-shifting interferometer

NASA Astrophysics Data System (ADS)

Wang, Hongjun; Wang, Zhao; Zhao, Hong; Tian, Ailing; Liu, Bingcai

2007-12-01

Referring to phase-shifting interferometry technology, the phase shifting error from the phase shifter is the main factor that directly affects the measurement accuracy of the phase shifting interferometer. In this paper, the resources and sorts of phase shifting error were introduction, and some methods to eliminate errors were mentioned. Based on the theory of phase shifting interferometry, the effects of phase shifting error were analyzed in detail. The Liquid Crystal Display (LCD) as a new shifter has advantage as that the phase shifting can be controlled digitally without any mechanical moving and rotating element. By changing coded image displayed on LCD, the phase shifting in measuring system was induced. LCD's phase modulation characteristic was analyzed in theory and tested. Based on Fourier transform, the effect model of phase error coming from LCD was established in four-step phase shifting interferometry. And the error range was obtained. In order to reduce error, a new error compensation algorithm was put forward. With this method, the error can be obtained by process interferogram. The interferogram can be compensated, and the measurement results can be obtained by four-step phase shifting interferogram. Theoretical analysis and simulation results demonstrate the feasibility of this approach to improve measurement accuracy.

3D spectral imaging with synchrotron Fourier transform infrared spectro-microtomography

Treesearch

Michael C. Martin; Charlotte Dabat-Blondeau; Miriam Unger; Julia Sedlmair; Dilworth Y. Parkinson; Hans A. Bechtel; Barbara Illman; Jonathan M. Castro; Marco Keiluweit; David Buschke; Brenda Ogle; Michael J. Nasse; Carol J. Hirschmugl

2013-01-01

We report Fourier transform infrared spectro-microtomography, a nondestructive three-dimensional imaging approach that reveals the distribution of distinctive chemical compositions throughout an intact biological or materials sample. The method combines mid-infrared absorption contrast with computed tomographic data acquisition and reconstruction to enhance chemical...

Robust autofocus algorithm for ISAR imaging of moving targets

NASA Astrophysics Data System (ADS)

Li, Jian; Wu, Renbiao; Chen, Victor C.

2000-08-01

A robust autofocus approach, referred to as AUTOCLEAN (AUTOfocus via CLEAN), is proposed for the motion compensation in ISAR (inverse synthetic aperture radar) imaging of moving targets. It is a parametric algorithm based on a very flexible data model which takes into account arbitrary range migration and arbitrary phase errors across the synthetic aperture that may be induced by unwanted radial motion of the target as well as propagation or system instability. AUTOCLEAN can be classified as a multiple scatterer algorithm (MSA), but it differs considerably from other existing MSAs in several aspects: (1) dominant scatterers are selected automatically in the two-dimensional (2-D) image domain; (2) scatterers may not be well-isolated or very dominant; (3) phase and RCS (radar cross section) information from each selected scatterer are combined in an optimal way; (4) the troublesome phase unwrapping step is avoided. AUTOCLEAN is computationally efficient and involves only a sequence of FFTs (fast Fourier Transforms). Another good feature associated with AUTOCLEAN is that its performance can be progressively improved by assuming a larger number of dominant scatterers for the target. Hence it can be easily configured for real-time applications including, for example, ATR (automatic target recognition) of non-cooperative moving targets, and for some other applications where the image quality is of the major concern but not the computational time including, for example, for the development and maintenance of low observable aircrafts. Numerical and experimental results have shown that AUTOCLEAN is a very robust autofocus tool for ISAR imaging.

Phase walk analysis of leptokurtic time series.

PubMed

Schreiber, Korbinian; Modest, Heike I; Räth, Christoph

2018-06-01

The Fourier phase information play a key role for the quantified description of nonlinear data. We present a novel tool for time series analysis that identifies nonlinearities by sensitively detecting correlations among the Fourier phases. The method, being called phase walk analysis, is based on well established measures from random walk analysis, which are now applied to the unwrapped Fourier phases of time series. We provide an analytical description of its functionality and demonstrate its capabilities on systematically controlled leptokurtic noise. Hereby, we investigate the properties of leptokurtic time series and their influence on the Fourier phases of time series. The phase walk analysis is applied to measured and simulated intermittent time series, whose probability density distribution is approximated by power laws. We use the day-to-day returns of the Dow-Jones industrial average, a synthetic time series with tailored nonlinearities mimicing the power law behavior of the Dow-Jones and the acceleration of the wind at an Atlantic offshore site. Testing for nonlinearities by means of surrogates shows that the new method yields strong significances for nonlinear behavior. Due to the drastically decreased computing time as compared to embedding space methods, the number of surrogate realizations can be increased by orders of magnitude. Thereby, the probability distribution of the test statistics can very accurately be derived and parameterized, which allows for much more precise tests on nonlinearities.

Hybrid-dual-fourier tomographic algorithm for a fast three-dimensionial optical image reconstruction in turbid media

NASA Technical Reports Server (NTRS)

Alfano, Robert R. (Inventor); Cai, Wei (Inventor)

2007-01-01

A reconstruction technique for reducing computation burden in the 3D image processes, wherein the reconstruction procedure comprises an inverse and a forward model. The inverse model uses a hybrid dual Fourier algorithm that combines a 2D Fourier inversion with a 1D matrix inversion to thereby provide high-speed inverse computations. The inverse algorithm uses a hybrid transfer to provide fast Fourier inversion for data of multiple sources and multiple detectors. The forward model is based on an analytical cumulant solution of a radiative transfer equation. The accurate analytical form of the solution to the radiative transfer equation provides an efficient formalism for fast computation of the forward model.

Fourier Plane Image Combination by Feathering

NASA Astrophysics Data System (ADS)

Cotton, W. D.

2017-09-01

Astronomical objects frequently exhibit structure over a wide range of scales whereas many telescopes, especially interferometer arrays, only sample a limited range of spatial scales. To properly image these objects, images from a set of instruments covering the range of scales may be needed. These images then must be combined in a manner to recover all spatial scales. This paper describes the feathering technique for image combination in the Fourier transform plane. Implementations in several packages are discussed and example combinations of single dish and interferometric observations of both simulated and celestial radio emission are given.

Improving the phase measurement by the apodization filter in the digital holography

NASA Astrophysics Data System (ADS)

Chang, Shifeng; Wang, Dayong; Wang, Yunxin; Zhao, Jie; Rong, Lu

2012-11-01

Due to the finite size of the hologram aperture in digital holography, high frequency intensity and phase fluctuations along the edges of the images, which reduce the precision of phase measurement. In this paper, the apodization filters are applied to improve the phase measurement in the digital holography. Firstly, the experimental setup of the lensless Fourier transform digital holography is built, where the sample is a standard phase grating with the grating constant of 300μm and the depth of 150nm. Then, apodization filters are applied to phase measurement of the sample with three kinds of the window functions: Tukey window, Hanning window and Blackman window, respectively. Finally, the results were compared to the detection data given by the commercial white-light interferometer. It is shown that aperture diffraction effects can be reduced by the digital apodization, and the phase measurement with the apodization is more accurate than in the unapodized case. Meanwhile, the Blackman window function produces better effect than the other two window functions in the measurement of the standard phase grating.

Computer synthesis of high resolution electron micrographs

NASA Technical Reports Server (NTRS)

Nathan, R.

1976-01-01

Specimen damage, spherical aberration, low contrast and noisy sensors combine to prevent direct atomic viewing in a conventional electron microscope. The paper describes two methods for obtaining ultra-high resolution in biological specimens under the electron microscope. The first method assumes the physical limits of the electron objective lens and uses a series of dark field images of biological crystals to obtain direct information on the phases of the Fourier diffraction maxima; this information is used in an appropriate computer to synthesize a large aperture lens for a 1-A resolution. The second method assumes there is sufficient amplitude scatter from images recorded in focus which can be utilized with a sensitive densitometer and computer contrast stretching to yield fine structure image details. Cancer virus characterization is discussed as an illustrative example. Numerous photographs supplement the text.

Fourier analysis: from cloaking to imaging

NASA Astrophysics Data System (ADS)

Wu, Kedi; Cheng, Qiluan; Wang, Guo Ping

2016-04-01

Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers.

A unified Fourier theory for time-of-flight PET data

PubMed Central

Li, Yusheng; Matej, Samuel; Metzler, Scott D

2016-01-01

Fully 3D time-of-flight (TOF) PET scanners offer the potential of previously unachievable image quality in clinical PET imaging. TOF measurements add another degree of redundancy for cylindrical PET scanners and make photon-limited TOF-PET imaging more robust than non-TOF PET imaging. The data space for 3D TOF-PET data is five-dimensional with two degrees of redundancy. Previously, consistency equations were used to characterize the redundancy of TOF-PET data. In this paper, we first derive two Fourier consistency equations and Fourier-John equation for 3D TOF PET based on the generalized projection-slice theorem; the three partial differential equations (PDEs) are the dual of the sinogram consistency equations and John's equation. We then solve the three PDEs using the method of characteristics. The two degrees of entangled redundancy of the TOF-PET data can be explicitly elicited and exploited by the solutions of the PDEs along the characteristic curves, which gives a complete understanding of the rich structure of the 3D X-ray transform with TOF measurement. Fourier rebinning equations and other mapping equations among different types of PET data are special cases of the general solutions. We also obtain new Fourier rebinning and consistency equations (FORCEs) from other special cases of the general solutions, and thus we obtain a complete scheme to convert among different types of PET data: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF data. The new FORCEs can be used as new Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. Further, we give a geometric interpretation of the general solutions—the two families of characteristic curves can be obtained by respectively changing the azimuthal and co-polar angles of the biorthogonal coordinates in Fourier space. We conclude the unified Fourier theory by showing that the Fourier consistency equations are necessary and sufficient for 3D X-ray transform with TOF measurement. Finally, we give numerical examples of inverse rebinning for a 3D TOF PET and Fourier-based rebinning for a 2D TOF PET using the FORCEs to show the efficacy of the unified Fourier solutions. PMID:26689836

A unified Fourier theory for time-of-flight PET data.

PubMed

Li, Yusheng; Matej, Samuel; Metzler, Scott D

2016-01-21

Fully 3D time-of-flight (TOF) PET scanners offer the potential of previously unachievable image quality in clinical PET imaging. TOF measurements add another degree of redundancy for cylindrical PET scanners and make photon-limited TOF-PET imaging more robust than non-TOF PET imaging. The data space for 3D TOF-PET data is five-dimensional with two degrees of redundancy. Previously, consistency equations were used to characterize the redundancy of TOF-PET data. In this paper, we first derive two Fourier consistency equations and Fourier-John equation for 3D TOF PET based on the generalized projection-slice theorem; the three partial differential equations (PDEs) are the dual of the sinogram consistency equations and John's equation. We then solve the three PDEs using the method of characteristics. The two degrees of entangled redundancy of the TOF-PET data can be explicitly elicited and exploited by the solutions of the PDEs along the characteristic curves, which gives a complete understanding of the rich structure of the 3D x-ray transform with TOF measurement. Fourier rebinning equations and other mapping equations among different types of PET data are special cases of the general solutions. We also obtain new Fourier rebinning and consistency equations (FORCEs) from other special cases of the general solutions, and thus we obtain a complete scheme to convert among different types of PET data: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF data. The new FORCEs can be used as new Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. Further, we give a geometric interpretation of the general solutions--the two families of characteristic curves can be obtained by respectively changing the azimuthal and co-polar angles of the biorthogonal coordinates in Fourier space. We conclude the unified Fourier theory by showing that the Fourier consistency equations are necessary and sufficient for 3D x-ray transform with TOF measurement. Finally, we give numerical examples of inverse rebinning for a 3D TOF PET and Fourier-based rebinning for a 2D TOF PET using the FORCEs to show the efficacy of the unified Fourier solutions.

Estimation of phase derivatives using discrete chirp-Fourier-transform-based method.

PubMed

Gorthi, Sai Siva; Rastogi, Pramod

2009-08-15

Estimation of phase derivatives is an important task in many interferometric measurements in optical metrology. This Letter introduces a method based on discrete chirp-Fourier transform for accurate and direct estimation of phase derivatives, even in the presence of noise. The method is introduced in the context of the analysis of reconstructed interference fields in digital holographic interferometry. We present simulation and experimental results demonstrating the utility of the proposed method.

Speckle correlation resolution enhancement of wide-field fluorescence imaging (Conference Presentation)

NASA Astrophysics Data System (ADS)

Yilmaz, Hasan

2016-03-01

Structured illumination enables high-resolution fluorescence imaging of nanostructures [1]. We demonstrate a new high-resolution fluorescence imaging method that uses a scattering layer with a high-index substrate as a solid immersion lens [2]. Random scattering of coherent light enables a speckle pattern with a very fine structure that illuminates the fluorescent nanospheres on the back surface of the high-index substrate. The speckle pattern is raster-scanned over the fluorescent nanospheres using a speckle correlation effect known as the optical memory effect. A series of standard-resolution fluorescence images per each speckle pattern displacement are recorded by an electron-multiplying CCD camera using a commercial microscope objective. We have developed a new phase-retrieval algorithm to reconstruct a high-resolution, wide-field image from several standard-resolution wide-field images. We have introduced phase information of Fourier components of standard-resolution images as a new constraint in our algorithm which discards ambiguities therefore ensures convergence to a unique solution. We demonstrate two-dimensional fluorescence images of a collection of nanospheres with a deconvolved Abbe resolution of 116 nm and a field of view of 10 µm × 10 µm. Our method is robust against optical aberrations and stage drifts, therefore excellent for imaging nanostructures under ambient conditions. [1] M. G. L. Gustafsson, J. Microsc. 198, 82-87 (2000). [2] H. Yilmaz, E. G. van Putten, J. Bertolotti, A. Lagendijk, W. L. Vos, and A. P. Mosk, Optica 2, 424-429 (2015).

Optical encryption of digital data in form of quick response code using spatially incoherent illumination

NASA Astrophysics Data System (ADS)

Cheremkhin, Pavel A.; Krasnov, Vitaly V.; Rodin, Vladislav G.; Starikov, Rostislav S.

2016-11-01

Applications of optical methods for encryption purposes have been attracting interest of researchers for decades. The most popular are coherent techniques such as double random phase encoding. Its main advantage is high security due to transformation of spectrum of image to be encrypted into white spectrum via use of first phase random mask which allows for encrypted images with white spectra. Downsides are necessity of using holographic registration scheme and speckle noise occurring due to coherent illumination. Elimination of these disadvantages is possible via usage of incoherent illumination. In this case, phase registration no longer matters, which means that there is no need for holographic setup, and speckle noise is gone. Recently, encryption of digital information in form of binary images has become quite popular. Advantages of using quick response (QR) code in capacity of data container for optical encryption include: 1) any data represented as QR code will have close to white (excluding zero spatial frequency) Fourier spectrum which have good overlapping with encryption key spectrum; 2) built-in algorithm for image scale and orientation correction which simplifies decoding of decrypted QR codes; 3) embedded error correction code allows for successful decryption of information even in case of partial corruption of decrypted image. Optical encryption of digital data in form QR codes using spatially incoherent illumination was experimentally implemented. Two liquid crystal spatial light modulators were used in experimental setup for QR code and encrypting kinoform imaging respectively. Decryption was conducted digitally. Successful decryption of encrypted QR codes is demonstrated.

Applications of Phase-Based Motion Processing

NASA Technical Reports Server (NTRS)

Branch, Nicholas A.; Stewart, Eric C.

2018-01-01

Image pyramids provide useful information in determining structural response at low cost using commercially available cameras. The current effort applies previous work on the complex steerable pyramid to analyze and identify imperceptible linear motions in video. Instead of implicitly computing motion spectra through phase analysis of the complex steerable pyramid and magnifying the associated motions, instead present a visual technique and the necessary software to display the phase changes of high frequency signals within video. The present technique quickly identifies regions of largest motion within a video with a single phase visualization and without the artifacts of motion magnification, but requires use of the computationally intensive Fourier transform. While Riesz pyramids present an alternative to the computationally intensive complex steerable pyramid for motion magnification, the Riesz formulation contains significant noise, and motion magnification still presents large amounts of data that cannot be quickly assessed by the human eye. Thus, user-friendly software is presented for quickly identifying structural response through optical flow and phase visualization in both Python and MATLAB.

Conceptual phase A design of a cryogenic shutter mechanism for the SAFARI flight instrument

NASA Astrophysics Data System (ADS)

Eigenmann, Max; Wehmeier, Udo J.; Vuilleumier, Aurèle; Messina, Gabriele; Meyer, Michael R.

2012-09-01

We present a conceptual design for a cryogenic optical mechanism for the SAFARI instrument. SAFARI is a long wavelength (34-210 micron) Imaging Fourier Transform Spectrometer (FTS) to fly as an ESA instrument on the JAXA SPICA mission projected to launch in 2021. SPICA is a large 3m class space telescope which will have an operating temperature of less than 7K. The SAFARI shutter is a single point of failure flight mechanism designed to operate in space at a temperature of 4K which meets redundancy and reliability requirements of this challenging mission. The conceptual design is part of a phase A study led by ETH Institute for Astronomy and conducted by RUAG Space AG.

Effect of microstructure on the elasto-viscoplastic deformation of dual phase titanium structures

NASA Astrophysics Data System (ADS)

Ozturk, Tugce; Rollett, Anthony D.

2018-02-01

The present study is devoted to the creation of a process-structure-property database for dual phase titanium alloys, through a synthetic microstructure generation method and a mesh-free fast Fourier transform based micromechanical model that operates on a discretized image of the microstructure. A sensitivity analysis is performed as a precursor to determine the statistically representative volume element size for creating 3D synthetic microstructures based on additively manufactured Ti-6Al-4V characteristics, which are further modified to expand the database for features of interest, e.g., lath thickness. Sets of titanium hardening parameters are extracted from literature, and The relative effect of the chosen microstructural features is quantified through comparisons of average and local field distributions.

Extracting and compensating dispersion mismatch in ultrahigh-resolution Fourier domain OCT imaging of the retina

PubMed Central

Choi, WooJhon; Baumann, Bernhard; Swanson, Eric A.; Fujimoto, James G.

2012-01-01

We present a numerical approach to extract the dispersion mismatch in ultrahigh-resolution Fourier domain optical coherence tomography (OCT) imaging of the retina. The method draws upon an analogy with a Shack-Hartmann wavefront sensor. By exploiting mathematical similarities between the expressions for aberration in optical imaging and dispersion mismatch in spectral / Fourier domain OCT, Shack-Hartmann principles can be extended from the two-dimensional paraxial wavevector space (or the x-y plane in the spatial domain) to the one-dimensional wavenumber space (or the z-axis in the spatial domain). For OCT imaging of the retina, different retinal layers, such as the retinal nerve fiber layer (RNFL), the photoreceptor inner and outer segment junction (IS/OS), or all the retinal layers near the retinal pigment epithelium (RPE) can be used as point source beacons in the axial direction, analogous to point source beacons used in conventional two-dimensional Shack-Hartman wavefront sensors for aberration characterization. Subtleties regarding speckle phenomena in optical imaging, which affect the Shack-Hartmann wavefront sensor used in adaptive optics, also occur analogously in this application. Using this approach and carefully suppressing speckle, the dispersion mismatch in spectral / Fourier domain OCT retinal imaging can be successfully extracted numerically and used for numerical dispersion compensation to generate sharper, ultrahigh-resolution OCT images. PMID:23187353

A color-corrected strategy for information multiplexed Fourier ptychographic imaging

NASA Astrophysics Data System (ADS)

Wang, Mingqun; Zhang, Yuzhen; Chen, Qian; Sun, Jiasong; Fan, Yao; Zuo, Chao

2017-12-01

Fourier ptychography (FP) is a novel computational imaging technique that provides both wide field of view (FoV) and high-resolution (HR) imaging capacity for biomedical imaging. Combined with information multiplexing technology, wavelength multiplexed (or color multiplexed) FP imaging can be implemented by lighting up R/G/B LED units simultaneously. Furthermore, a HR image can be recovered at each wavelength from the multiplexed dataset. This enhances the efficiency of data acquisition. However, since the same dataset of intensity measurement is used to recover the HR image at each wavelength, the mean value in each channel would converge to the same value. In this paper, a color correction strategy embedded in the multiplexing FP scheme is demonstrated, which is termed as color corrected wavelength multiplexed Fourier ptychography (CWMFP). Three images captured by turning on a LED array in R/G/B are required as priori knowledge to improve the accuracy of reconstruction in the recovery process. Using the reported technique, the redundancy requirement of information multiplexed FP is reduced. Moreover, the accuracy of reconstruction at each channel is improved with correct color reproduction of the specimen.

Electron holography—basics and applications

NASA Astrophysics Data System (ADS)

Lichte, Hannes; Lehmann, Michael

2008-01-01

Despite the huge progress achieved recently by means of the corrector for aberrations, allowing now a true atomic resolution of 0.1 nm, hence making it an unrivalled tool for nanoscience, transmission electron microscopy (TEM) suffers from a severe drawback: in a conventional electron micrograph only a poor phase contrast can be achieved, i.e. phase structures are virtually invisible. Therefore, conventional TEM is nearly blind for electric and magnetic fields, which are pure phase objects. Since such fields provoked by the atomic structure, e.g. of semiconductors and ferroelectrics, largely determine the solid state properties, hence the importance for high technology applications, substantial object information is missing. Electron holography in TEM offers the solution: by superposition with a coherent reference wave, a hologram is recorded, from which the image wave can be completely reconstructed by amplitude and phase. Now the object is displayed quantitatively in two separate images: one representing the amplitude, the other the phase. From the phase image, electric and magnetic fields can be determined quantitatively in the range from micrometre down to atomic dimensions by all wave optical methods that one can think of, both in real space and in Fourier space. Electron holography is pure wave optics. Therefore, we discuss the basics of coherence and interference, the implementation into a TEM, the path of rays for recording holograms as well as the limits in lateral and signal resolution. We outline the methods of reconstructing the wave by numerical image processing and procedures for extracting the object properties of interest. Furthermore, we present a broad spectrum of applications both at mesoscopic and atomic dimensions. This paper gives an overview of the state of the art pointing at the needs for further development. It is also meant as encouragement for those who refrain from holography, thinking that it can only be performed by specialists in highly specialized laboratories. In fact, a modern TEM built for atomic resolution and equipped with a field emitter or a Schottky emitter, well aligned by a skilled operator, can deliver good holograms. Running commercially available image processing software and mathematics programs on a laptop-computer is sufficient for reconstruction of the amplitude and phase images and extracting desirable object information.

Grating-based x-ray differential phase contrast imaging with twin peaks in phase-stepping curves—phase retrieval and dewrapping

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Yi; Xie, Huiqiao; Tang, Xiangyang, E-mail: xiangyang.tang@emory.edu

Purpose: X-ray differential phase contrast CT implemented with Talbot interferometry employs phase-stepping to extract information of x-ray attenuation, phase shift, and small-angle scattering. Since inaccuracy may exist in the absorption grating G{sub 2} due to an imperfect fabrication, the effective period of G{sub 2} can be as large as twice the nominal period, leading to a phenomenon of twin peaks that differ remarkably in their heights. In this work, the authors investigate how to retrieve and dewrap the phase signal from the phase-stepping curve (PSC) with the feature of twin peaks for x-ray phase contrast imaging. Methods: Based on themore » paraxial Fresnel–Kirchhoff theory, the analytical formulae to characterize the phenomenon of twin peaks in the PSC are derived. Then an approach to dewrap the retrieved phase signal by jointly using the phases of the first- and second-order Fourier components is proposed. Through an experimental investigation using a prototype x-ray phase contrast imaging system implemented with Talbot interferometry, the authors evaluate and verify the derived analytic formulae and the proposed approach for phase retrieval and dewrapping. Results: According to theoretical analysis, the twin-peak phenomenon in PSC is a consequence of combined effects, including the inaccuracy in absorption grating G{sub 2}, mismatch between phase grating and x-ray source spectrum, and finite size of x-ray tube’s focal spot. The proposed approach is experimentally evaluated by scanning a phantom consisting of organic materials and a lab mouse. The preliminary data show that compared to scanning G{sub 2} over only one single nominal period and correcting the measured phase signal with an intuitive phase dewrapping method that is being used in the field, stepping G{sub 2} over twice its nominal period and dewrapping the measured phase signal with the proposed approach can significantly improve the quality of x-ray differential phase contrast imaging in both radiograph and CT. Conclusions: Using the phase retrieval and dewrapping methods proposed to deal with the phenomenon of twin peaks in PSCs and phase wrapping, the performance of grating-based x-ray differential phase contrast radiography and CT can be significantly improved.« less

Spatially Fourier-encoded photoacoustic microscopy using a digital micromirror device.

PubMed

Liang, Jinyang; Gao, Liang; Li, Chiye; Wang, Lihong V

2014-02-01

We have developed spatially Fourier-encoded photoacoustic (PA) microscopy using a digital micromirror device. The spatial intensity distribution of laser pulses is Fourier-encoded, and a series of such encoded PA measurements allows one to decode the spatial distribution of optical absorption. The throughput and Fellgett advantages were demonstrated by imaging a chromium target. By using 63 spatial elements, the signal-to-noise ratio in the recovered PA signal was enhanced by ∼4×. The system was used to image two biological targets, a monolayer of red blood cells and melanoma cells.

Spatially Fourier-encoded photoacoustic microscopy using a digital micromirror device

PubMed Central

Liang, Jinyang; Gao, Liang; Li, Chiye; Wang, Lihong V.

2014-01-01

We have developed spatially Fourier-encoded photoacoustic microscopy using a digital micromirror device. The spatial intensity distribution of laser pulses is Fourier-encoded, and a series of such encoded photoacoustic measurements allows one to decode the spatial distribution of optical absorption. The throughput and Fellgett advantages were demonstrated by imaging a chromium target. By using 63 spatial elements, the signal-to-noise ratio in the recovered photoacoustic signal was enhanced by ~4×. The system was used to image two biological targets, a monolayer of red blood cells and melanoma cells. PMID:24487832

Correcting sample drift using Fourier harmonics.

PubMed

Bárcena-González, G; Guerrero-Lebrero, M P; Guerrero, E; Reyes, D F; Braza, V; Yañez, A; Nuñez-Moraleda, B; González, D; Galindo, P L

2018-07-01

During image acquisition of crystalline materials by high-resolution scanning transmission electron microscopy, the sample drift could lead to distortions and shears that hinder their quantitative analysis and characterization. In order to measure and correct this effect, several authors have proposed different methodologies making use of series of images. In this work, we introduce a methodology to determine the drift angle via Fourier analysis by using a single image based on the measurements between the angles of the second Fourier harmonics in different quadrants. Two different approaches, that are independent of the angle of acquisition of the image, are evaluated. In addition, our results demonstrate that the determination of the drift angle is more accurate by using the measurements of non-consecutive quadrants when the angle of acquisition is an odd multiple of 45°. Copyright © 2018 Elsevier Ltd. All rights reserved.

Tumor or abnormality identification from magnetic resonance images using statistical region fusion based segmentation.

PubMed

Subudhi, Badri Narayan; Thangaraj, Veerakumar; Sankaralingam, Esakkirajan; Ghosh, Ashish

2016-11-01

In this article, a statistical fusion based segmentation technique is proposed to identify different abnormality in magnetic resonance images (MRI). The proposed scheme follows seed selection, region growing-merging and fusion of multiple image segments. In this process initially, an image is divided into a number of blocks and for each block we compute the phase component of the Fourier transform. The phase component of each block reflects the gray level variation among the block but contains a large correlation among them. Hence a singular value decomposition (SVD) technique is adhered to generate a singular value of each block. Then a thresholding procedure is applied on these singular values to identify edgy and smooth regions and some seed points are selected for segmentation. By considering each seed point we perform a binary segmentation of the complete MRI and hence with all seed points we get an equal number of binary images. A parcel based statistical fusion process is used to fuse all the binary images into multiple segments. Effectiveness of the proposed scheme is tested on identifying different abnormalities: prostatic carcinoma detection, tuberculous granulomas identification and intracranial neoplasm or brain tumor detection. The proposed technique is established by comparing its results against seven state-of-the-art techniques with six performance evaluation measures. Copyright © 2016 Elsevier Inc. All rights reserved.

Multichannel High Resolution Wide Swath SAR Imaging for Hypersonic Air Vehicle with Curved Trajectory.

PubMed

Zhou, Rui; Sun, Jinping; Hu, Yuxin; Qi, Yaolong

2018-01-31

Synthetic aperture radar (SAR) equipped on the hypersonic air vehicle in near space has many advantages over the conventional airborne SAR. However, its high-speed maneuvering characteristics with curved trajectory result in serious range migration, and exacerbate the contradiction between the high resolution and wide swath. To solve this problem, this paper establishes the imaging geometrical model matched with the flight trajectory of the hypersonic platform and the multichannel azimuth sampling model based on the displaced phase center antenna (DPCA) technology. Furthermore, based on the multichannel signal reconstruction theory, a more efficient spectrum reconstruction model using discrete Fourier transform is proposed to obtain the azimuth uniform sampling data. Due to the high complexity of the slant range model, it is difficult to deduce the processing algorithm for SAR imaging. Thus, an approximate range model is derived based on the minimax criterion, and the optimal second-order approximate coefficients of cosine function are obtained using the two-population coevolutionary algorithm. On this basis, aiming at the problem that the traditional Omega-K algorithm cannot compensate the residual phase with the difficulty of Stolt mapping along the range frequency axis, this paper proposes an Exact Transfer Function (ETF) algorithm for SAR imaging, and presents a method of range division to achieve wide swath imaging. Simulation results verify the effectiveness of the ETF imaging algorithm.

Multichannel High Resolution Wide Swath SAR Imaging for Hypersonic Air Vehicle with Curved Trajectory

PubMed Central

Zhou, Rui; Hu, Yuxin; Qi, Yaolong

2018-01-01

Synthetic aperture radar (SAR) equipped on the hypersonic air vehicle in near space has many advantages over the conventional airborne SAR. However, its high-speed maneuvering characteristics with curved trajectory result in serious range migration, and exacerbate the contradiction between the high resolution and wide swath. To solve this problem, this paper establishes the imaging geometrical model matched with the flight trajectory of the hypersonic platform and the multichannel azimuth sampling model based on the displaced phase center antenna (DPCA) technology. Furthermore, based on the multichannel signal reconstruction theory, a more efficient spectrum reconstruction model using discrete Fourier transform is proposed to obtain the azimuth uniform sampling data. Due to the high complexity of the slant range model, it is difficult to deduce the processing algorithm for SAR imaging. Thus, an approximate range model is derived based on the minimax criterion, and the optimal second-order approximate coefficients of cosine function are obtained using the two-population coevolutionary algorithm. On this basis, aiming at the problem that the traditional Omega-K algorithm cannot compensate the residual phase with the difficulty of Stolt mapping along the range frequency axis, this paper proposes an Exact Transfer Function (ETF) algorithm for SAR imaging, and presents a method of range division to achieve wide swath imaging. Simulation results verify the effectiveness of the ETF imaging algorithm. PMID:29385059

Evaluation of partial k-space strategies to speed up time-domain EPR imaging.

PubMed

Subramanian, Sankaran; Chandramouli, Gadisetti V R; McMillan, Alan; Gullapalli, Rao P; Devasahayam, Nallathamby; Mitchell, James B; Matsumoto, Shingo; Krishna, Murali C

2013-09-01

Narrow-line spin probes derived from the trityl radical have led to the development of fast in vivo time-domain EPR imaging. Pure phase-encoding imaging modalities based on the single-point imaging scheme have demonstrated the feasibility of three-dimensional oximetric images with functional information in minutes. In this article, we explore techniques to improve the temporal resolution and circumvent the relatively short biological half-lives of trityl probes using partial k-space strategies. There are two main approaches: one involves the use of the Hermitian character of the k-space by which only part of the k-space is measured and the unmeasured part is generated using the Hermitian symmetry. This approach is limited in success by the accuracy of numerical estimate of the phase roll in the k-space that corrupts the Hermiticy. The other approach is to measure only a judicially chosen reduced region of k-space (a centrosymmetric ellipsoid region) that more or less accounts for >70% of the k-space energy. Both of these aspects were explored in Fourier transform-EPR imaging with a doubling of scan speed demonstrated by considering ellipsoid geometry of the k-space. Partial k-space strategies help improve the temporal resolution in studying fast dynamics of functional aspects in vivo with infused spin probes. Copyright © 2012 Wiley Periodicals, Inc.

Quantification of susceptibility change at high-concentrated SPIO-labeled target by characteristic phase gradient recognition.

PubMed

Zhu, Haitao; Nie, Binbin; Liu, Hua; Guo, Hua; Demachi, Kazuyuki; Sekino, Masaki; Shan, Baoci

2016-05-01

Phase map cross-correlation detection and quantification may produce highlighted signal at superparamagnetic iron oxide nanoparticles, and distinguish them from other hypointensities. The method may quantify susceptibility change by performing least squares analysis between a theoretically generated magnetic field template and an experimentally scanned phase image. Because characteristic phase recognition requires the removal of phase wrap and phase background, additional steps of phase unwrapping and filtering may increase the chance of computing error and enlarge the inconsistence among algorithms. To solve problem, phase gradient cross-correlation and quantification method is developed by recognizing characteristic phase gradient pattern instead of phase image because phase gradient operation inherently includes unwrapping and filtering functions. However, few studies have mentioned the detectable limit of currently used phase gradient calculation algorithms. The limit may lead to an underestimation of large magnetic susceptibility change caused by high-concentrated iron accumulation. In this study, mathematical derivation points out the value of maximum detectable phase gradient calculated by differential chain algorithm in both spatial and Fourier domain. To break through the limit, a modified quantification method is proposed by using unwrapped forward differentiation for phase gradient generation. The method enlarges the detectable range of phase gradient measurement and avoids the underestimation of magnetic susceptibility. Simulation and phantom experiments were used to quantitatively compare different methods. In vivo application performs MRI scanning on nude mice implanted by iron-labeled human cancer cells. Results validate the limit of detectable phase gradient and the consequent susceptibility underestimation. Results also demonstrate the advantage of unwrapped forward differentiation compared with differential chain algorithms for susceptibility quantification at high-concentrated iron accumulation. Copyright © 2015 Elsevier Inc. All rights reserved.

Wavelength modulation spectroscopy--digital detection of gas absorption harmonics based on Fourier analysis.

PubMed

Mei, Liang; Svanberg, Sune

2015-03-20

This work presents a detailed study of the theoretical aspects of the Fourier analysis method, which has been utilized for gas absorption harmonic detection in wavelength modulation spectroscopy (WMS). The lock-in detection of the harmonic signal is accomplished by studying the phase term of the inverse Fourier transform of the Fourier spectrum that corresponds to the harmonic signal. The mathematics and the corresponding simulation results are given for each procedure when applying the Fourier analysis method. The present work provides a detailed view of the WMS technique when applying the Fourier analysis method.

Wave Propagation, Scattering and Imaging Using Dual-domain One-way and One-return Propagators

NASA Astrophysics Data System (ADS)

Wu, R.-S.

- Dual-domain one-way propagators implement wave propagation in heterogeneous media in mixed domains (space-wavenumber domains). One-way propagators neglect wave reverberations between heterogeneities but correctly handle the forward multiple-scattering including focusing/defocusing, diffraction, refraction and interference of waves. The algorithm shuttles between space-domain and wavenumber-domain using FFT, and the operations in the two domains are self-adaptive to the complexity of the media. The method makes the best use of the operations in each domain, resulting in efficient and accurate propagators. Due to recent progress, new versions of dual-domain methods overcame some limitations of the classical dual-domain methods (phase-screen or split-step Fourier methods) and can propagate large-angle waves quite accurately in media with strong velocity contrasts. These methods can deliver superior image quality (high resolution/high fidelity) for complex subsurface structures. One-way and one-return (De Wolf approximation) propagators can be also applied to wave-field modeling and simulations for some geophysical problems. In the article, a historical review and theoretical analysis of the Born, Rytov, and De Wolf approximations are given. A review on classical phase-screen or split-step Fourier methods is also given, followed by a summary and analysis of the new dual-domain propagators. The applications of the new propagators to seismic imaging and modeling are reviewed with several examples. For seismic imaging, the advantages and limitations of the traditional Kirchhoff migration and time-space domain finite-difference migration, when applied to 3-D complicated structures, are first analyzed. Then the special features, and applications of the new dual-domain methods are presented. Three versions of GSP (generalized screen propagators), the hybrid pseudo-screen, the wide-angle Padé-screen, and the higher-order generalized screen propagators are discussed. Recent progress also makes it possible to use the dual-domain propagators for modeling elastic reflections for complex structures and long-range propagations of crustal guided waves. Examples of 2-D and 3-D imaging and modeling using GSP methods are given.

Quantification of fibre polymerization through Fourier space image analysis

PubMed Central

Nekouzadeh, Ali; Genin, Guy M.

2011-01-01

Quantification of changes in the total length of randomly oriented and possibly curved lines appearing in an image is a necessity in a wide variety of biological applications. Here, we present an automated approach based upon Fourier space analysis. Scaled, band-pass filtered power spectral densities of greyscale images are integrated to provide a quantitative measurement of the total length of lines of a particular range of thicknesses appearing in an image. A procedure is presented to correct for changes in image intensity. The method is most accurate for two-dimensional processes with fibres that do not occlude one another. PMID:24959096

Quantum Image Steganography and Steganalysis Based On LSQu-Blocks Image Information Concealing Algorithm

NASA Astrophysics Data System (ADS)

A. AL-Salhi, Yahya E.; Lu, Songfeng

2016-08-01

Quantum steganography can solve some problems that are considered inefficient in image information concealing. It researches on Quantum image information concealing to have been widely exploited in recent years. Quantum image information concealing can be categorized into quantum image digital blocking, quantum image stereography, anonymity and other branches. Least significant bit (LSB) information concealing plays vital roles in the classical world because many image information concealing algorithms are designed based on it. Firstly, based on the novel enhanced quantum representation (NEQR), image uniform blocks clustering around the concrete the least significant Qu-block (LSQB) information concealing algorithm for quantum image steganography is presented. Secondly, a clustering algorithm is proposed to optimize the concealment of important data. Finally, we used Con-Steg algorithm to conceal the clustered image blocks. Information concealing located on the Fourier domain of an image can achieve the security of image information, thus we further discuss the Fourier domain LSQu-block information concealing algorithm for quantum image based on Quantum Fourier Transforms. In our algorithms, the corresponding unitary Transformations are designed to realize the aim of concealing the secret information to the least significant Qu-block representing color of the quantum cover image. Finally, the procedures of extracting the secret information are illustrated. Quantum image LSQu-block image information concealing algorithm can be applied in many fields according to different needs.

GIFTS SM EDU Data Processing and Algorithms

NASA Technical Reports Server (NTRS)

Tian, Jialin; Johnson, David G.; Reisse, Robert A.; Gazarik, Michael J.

2007-01-01

The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) Sensor Module (SM) Engineering Demonstration Unit (EDU) is a high resolution spectral imager designed to measure infrared (IR) radiances using a Fourier transform spectrometer (FTS). The GIFTS instrument employs three Focal Plane Arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The raw interferogram measurements are radiometrically and spectrally calibrated to produce radiance spectra, which are further processed to obtain atmospheric profiles via retrieval algorithms. This paper describes the processing algorithms involved in the calibration stage. The calibration procedures can be subdivided into three stages. In the pre-calibration stage, a phase correction algorithm is applied to the decimated and filtered complex interferogram. The resulting imaginary part of the spectrum contains only the noise component of the uncorrected spectrum. Additional random noise reduction can be accomplished by applying a spectral smoothing routine to the phase-corrected blackbody reference spectra. In the radiometric calibration stage, we first compute the spectral responsivity based on the previous results, from which, the calibrated ambient blackbody (ABB), hot blackbody (HBB), and scene spectra can be obtained. During the post-processing stage, we estimate the noise equivalent spectral radiance (NESR) from the calibrated ABB and HBB spectra. We then implement a correction scheme that compensates for the effect of fore-optics offsets. Finally, for off-axis pixels, the FPA off-axis effects correction is performed. To estimate the performance of the entire FPA, we developed an efficient method of generating pixel performance assessments. In addition, a random pixel selection scheme is designed based on the pixel performance evaluation.

Phase unwrapping with a virtual Hartmann-Shack wavefront sensor.

PubMed

Akondi, Vyas; Falldorf, Claas; Marcos, Susana; Vohnsen, Brian

2015-10-05

The use of a spatial light modulator for implementing a digital phase-shifting (PS) point diffraction interferometer (PDI) allows tunability in fringe spacing and in achieving PS without the need for mechanically moving parts. However, a small amount of detector or scatter noise could affect the accuracy of wavefront sensing. Here, a novel method of wavefront reconstruction incorporating a virtual Hartmann-Shack (HS) wavefront sensor is proposed that allows easy tuning of several wavefront sensor parameters. The proposed method was tested and compared with a Fourier unwrapping method implemented on a digital PS PDI. The rewrapping of the Fourier reconstructed wavefronts resulted in phase maps that matched well the original wrapped phase and the performance was found to be more stable and accurate than conventional methods. Through simulation studies, the superiority of the proposed virtual HS phase unwrapping method is shown in comparison with the Fourier unwrapping method in the presence of noise. Further, combining the two methods could improve accuracy when the signal-to-noise ratio is sufficiently high.

Fourier Domain Optical Coherence Tomography With 3D and En Face Imaging of the Punctum and Vertical Canaliculus: A Step Toward Establishing a Normative Database.

PubMed

Kamal, Saurabh; Ali, Mohammad Javed; Ali, Mohammad Hasnat; Naik, Milind N

2016-01-01

To report the features of Fourier domain optical coherence tomography imaging of the normal punctum and vertical canaliculus. Prospective, interventional series of consecutive healthy and asymptomatic adults, who volunteered for optical coherence tomography imaging, were included in the study. Fourier domain optical coherence tomography images of the punctum and vertical canaliculus along with 3D and En face images were captured using the RTVue scanner with a corneal adaptor module and a wide-angled lens. Maximum punctal diameter, mid-canalicular diameter, and vertical canalicular height were calculated. Statistical analysis was performed using Pearson correlation test, and scatter plot matrices were analyzed. A total of 103 puncta of 52 healthy subjects were studied. Although all the images could depict the punctum and vertical canaliculus and all the desired measurements could be obtained, occasional tear debris within the canaliculus was found to be interfering with the imaging. The mean maximum punctal diameter, mid-canalicular diameter, and vertical canalicular height were recorded as 214.71 ± 73 μm, 125.04 ± 60.69 μm, and 890.41 ± 154.76 μm, respectively, with an insignificant correlation between them. The maximum recorded vertical canalicular height in all the cases was far less than the widely reported depth of 2 mm. High-resolution 3D and En face images provided a detailed topography of punctal surface and overview of vertical canaliculus. Fourier domain optical coherence tomography with 3D and En face imaging is a useful noninvasive modality to image the proximal lacrimal system with consistently reproducible high-resolution images. This is likely to help clinicians in the management of proximal lacrimal disorders.

Unconventional methods of imaging: computational microscopy and compact implementations

NASA Astrophysics Data System (ADS)

McLeod, Euan; Ozcan, Aydogan

2016-07-01

In the past two decades or so, there has been a renaissance of optical microscopy research and development. Much work has been done in an effort to improve the resolution and sensitivity of microscopes, while at the same time to introduce new imaging modalities, and make existing imaging systems more efficient and more accessible. In this review, we look at two particular aspects of this renaissance: computational imaging techniques and compact imaging platforms. In many cases, these aspects go hand-in-hand because the use of computational techniques can simplify the demands placed on optical hardware in obtaining a desired imaging performance. In the first main section, we cover lens-based computational imaging, in particular, light-field microscopy, structured illumination, synthetic aperture, Fourier ptychography, and compressive imaging. In the second main section, we review lensfree holographic on-chip imaging, including how images are reconstructed, phase recovery techniques, and integration with smart substrates for more advanced imaging tasks. In the third main section we describe how these and other microscopy modalities have been implemented in compact and field-portable devices, often based around smartphones. Finally, we conclude with some comments about opportunities and demand for better results, and where we believe the field is heading.

Analytical Bistatic k Space Images Compared to Experimental Swept Frequency EAR Images

NASA Technical Reports Server (NTRS)

Shaeffer, John; Cooper, Brett; Hom, Kam

2004-01-01

A case study of flat plate scattering images obtained by the analytical bistatic k space and experimental swept frequency ISAR methods is presented. The key advantage of the bistatic k space image is that a single excitation is required, i.e., one frequency I one angle. This means that prediction approaches such as MOM only need to compute one solution at a single frequency. Bistatic image Fourier transform data are obtained by computing the scattered field at various bistatic positions about the body in k space. Experimental image Fourier transform data are obtained from the measured response to a bandwidth of frequencies over a target rotation range.

Application of the fractional Fourier transform to image reconstruction in MRI.

PubMed

Parot, Vicente; Sing-Long, Carlos; Lizama, Carlos; Tejos, Cristian; Uribe, Sergio; Irarrazaval, Pablo

2012-07-01

The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding. Copyright © 2011 Wiley Periodicals, Inc.

Fully automated corneal endothelial morphometry of images captured by clinical specular microscopy

NASA Astrophysics Data System (ADS)

Bucht, Curry; Söderberg, Per; Manneberg, Göran

2010-02-01

The corneal endothelium serves as the posterior barrier of the cornea. Factors such as clarity and refractive properties of the cornea are in direct relationship to the quality of the endothelium. The endothelial cell density is considered the most important morphological factor of the corneal endothelium. Pathological conditions and physical trauma may threaten the endothelial cell density to such an extent that the optical property of the cornea and thus clear eyesight is threatened. Diagnosis of the corneal endothelium through morphometry is an important part of several clinical applications. Morphometry of the corneal endothelium is presently carried out by semi automated analysis of pictures captured by a Clinical Specular Microscope (CSM). Because of the occasional need of operator involvement, this process can be tedious, having a negative impact on sampling size. This study was dedicated to the development and use of fully automated analysis of a very large range of images of the corneal endothelium, captured by CSM, using Fourier analysis. Software was developed in the mathematical programming language Matlab. Pictures of the corneal endothelium, captured by CSM, were read into the analysis software. The software automatically performed digital enhancement of the images, normalizing lights and contrasts. The digitally enhanced images of the corneal endothelium were Fourier transformed, using the fast Fourier transform (FFT) and stored as new images. Tools were developed and applied for identification and analysis of relevant characteristics of the Fourier transformed images. The data obtained from each Fourier transformed image was used to calculate the mean cell density of its corresponding corneal endothelium. The calculation was based on well known diffraction theory. Results in form of estimated cell density of the corneal endothelium were obtained, using fully automated analysis software on 292 images captured by CSM. The cell density obtained by the fully automated analysis was compared to the cell density obtained from classical, semi-automated analysis and a relatively large correlation was found.

Two-dimensional Kerr-Fourier imaging of translucent phantoms in thick turbid media

NASA Astrophysics Data System (ADS)

Liang, X.; Wang, L.; Ho, P. P.; Alfano, R. R.

1995-06-01

Translucent scattering phantoms hidden inside a 5.5-cm-thick Intralipid solution were imaged as a function of phantom scattering coefficients by the use of a picosecond time-and space-gated Kerr-Fourier imaging system. A 2-mm-thick translucent phantom with a 0.1% concentration (scattering coefficient) difference from the 55-mm-thick surrounding scattering host can be distinguished at a signal level of approximately 10-10 of the incidence illumination intensity.

FIBER AND INTEGRATED OPTICS, LASER APPLICATIONS, AND OTHER PROBLEMS IN QUANTUM ELECTRONICS: Numerical simulation of an unstable ring resonator with a Fourier phase corrector

NASA Astrophysics Data System (ADS)

Kliment'ev, S. I.; Kuprenyuk, V. I.; Lyubimov, V. V.; Sherstobitov, V. E.

1989-04-01

The results are given of calculations of the parameters of an unstable ring resonator with an internal angular selector based on a Fourier phase corrector. It is shown that the use of such a selector makes it possible to compensate partly for the effects of small-scale phase inhomogeneities and to reduce also the influence of the edge diffraction on the structure of the field in a resonator.

A Space Object Detection Algorithm using Fourier Domain Likelihood Ratio Test

NASA Astrophysics Data System (ADS)

Becker, D.; Cain, S.

Space object detection is of great importance in the highly dependent yet competitive and congested space domain. Detection algorithms employed play a crucial role in fulfilling the detection component in the situational awareness mission to detect, track, characterize and catalog unknown space objects. Many current space detection algorithms use a matched filter or a spatial correlator to make a detection decision at a single pixel point of a spatial image based on the assumption that the data follows a Gaussian distribution. This paper explores the potential for detection performance advantages when operating in the Fourier domain of long exposure images of small and/or dim space objects from ground based telescopes. A binary hypothesis test is developed based on the joint probability distribution function of the image under the hypothesis that an object is present and under the hypothesis that the image only contains background noise. The detection algorithm tests each pixel point of the Fourier transformed images to make the determination if an object is present based on the criteria threshold found in the likelihood ratio test. Using simulated data, the performance of the Fourier domain detection algorithm is compared to the current algorithm used in space situational awareness applications to evaluate its value.

Method and apparatus for wavefront sensing

DOEpatents

Bahk, Seung-Whan

2016-08-23

A method of measuring characteristics of a wavefront of an incident beam includes obtaining an interferogram associated with the incident beam passing through a transmission mask and Fourier transforming the interferogram to provide a frequency domain interferogram. The method also includes selecting a subset of harmonics from the frequency domain interferogram, individually inverse Fourier transforming each of the subset of harmonics to provide a set of spatial domain harmonics, and extracting a phase profile from each of the set of spatial domain harmonics. The method further includes removing phase discontinuities in the phase profile, rotating the phase profile, and reconstructing a phase front of the wavefront of the incident beam.

Non-invasive quantitative pulmonary V/Q imaging using Fourier decomposition MRI at 1.5T.

PubMed

Kjørstad, Åsmund; Corteville, Dominique M R; Henzler, Thomas; Schmid-Bindert, Gerald; Zöllner, Frank G; Schad, Lothar R

2015-12-01

Techniques for quantitative pulmonary perfusion and ventilation using the Fourier Decomposition method were recently demonstrated. We combine these two techniques and show that ventilation-perfusion (V/Q) imaging is possible using only a single MR acquisition of less than thirty seconds. The Fourier Decomposition method is used in combination with two quantification techniques, which extract baselines from within the images themselves and thus allows quantification. For the perfusion, a region assumed to consist of 100% blood is utilized, while for the ventilation the zero-frequency component is used. V/Q-imaging is then done by dividing the quantified ventilation map with the quantified perfusion map. The techniques were used on ten healthy volunteers and fifteen patients diagnosed with lung cancer. A mean V/Q-ratio of 1.15 ± 0.22 was found for the healthy volunteers and a mean V/Q-ratio of 1.93 ± 0.83 for the non-afflicted lung in the patients. Mean V/Q-ratio in the afflicted (tumor-bearing) lung was found to be 1.61 ± 1.06. Functional defects were clearly visible in many of the patient images, but 5 of 15 patient images had to be excluded due to artifacts or low SNR, indicating a lack of robustness. Non-invasive, quantitative V/Q-imaging is possible using Fourier Decomposition MRI. The method requires only a single acquisition of less than 30 seconds, but robustness in patients remains an issue. Copyright © 2015. Published by Elsevier GmbH.

Single-shot full resolution region-of-interest (ROI) reconstruction in image plane digital holographic microscopy

NASA Astrophysics Data System (ADS)

Singh, Mandeep; Khare, Kedar

2018-05-01

We describe a numerical processing technique that allows single-shot region-of-interest (ROI) reconstruction in image plane digital holographic microscopy with full pixel resolution. The ROI reconstruction is modelled as an optimization problem where the cost function to be minimized consists of an L2-norm squared data fitting term and a modified Huber penalty term that are minimized alternately in an adaptive fashion. The technique can provide full pixel resolution complex-valued images of the selected ROI which is not possible to achieve with the commonly used Fourier transform method. The technique can facilitate holographic reconstruction of individual cells of interest from a large field-of-view digital holographic microscopy data. The complementary phase information in addition to the usual absorption information already available in the form of bright field microscopy can make the methodology attractive to the biomedical user community.

Shape measurement and vibration analysis of moving speaker cone

NASA Astrophysics Data System (ADS)

Zhang, Qican; Liu, Yuankun; Lehtonen, Petri

2014-06-01

Surface three-dimensional (3-D) shape information is needed for many fast processes such as structural testing of material, standing waves on loudspeaker cone, etc. Usually measurement is done from limited number of points using electrical sensors or laser distance meters. Fourier Transform Profilometry (FTP) enables fast shape measurement of the whole surface. Method is based on angled sinusoidal fringe pattern projection and image capturing. FTP requires only one image of the deformed fringe pattern to restore the 3-D shape of the measured object, which makes real-time or dynamic data processing possible. In our experiment the method was used for loudspeaker cone distortion measurement in dynamic conditions. For sound quality issues it is important that the whole cone moves in same phase and there are no partial waves. Our imaging resolution was 1280x1024 pixels and frame rate was 200 fps. Using our setup we found unwanted spatial waves in our sample cone.

Identification of arteries and veins in cerebral angiography fluoroscopic images

NASA Astrophysics Data System (ADS)

Andra Tache, Irina

2017-11-01

In the present study a new method for pixels tagging into arteries and veins classes from temporal cerebral angiography is presented. This need comes from the neurosurgeon who is evaluating the fluoroscopic angiography and the magnetic resonance images from the brain in order to locate the fistula of the patients who suffer from arterio-venous malformation. The method includes the elimination of the background pixels from a previous segmentation and the generation of the time intensity curves for each remaining pixel. The later undergo signal processing in order to extract the characteristic parameters needed for applying the k-means clustering algorithm. Some of the parameters are: the phase and the maximum amplitude extracted from the Fourier transform, the standard deviation and the mean value. The tagged classes are represented into images which then are re-classified by an expert into artery and vein pixels.

Deficiencies of the cryptography based on multiple-parameter fractional Fourier transform.

PubMed

Ran, Qiwen; Zhang, Haiying; Zhang, Jin; Tan, Liying; Ma, Jing

2009-06-01

Methods of image encryption based on fractional Fourier transform have an incipient flaw in security. We show that the schemes have the deficiency that one group of encryption keys has many groups of keys to decrypt the encrypted image correctly for several reasons. In some schemes, many factors result in the deficiencies, such as the encryption scheme based on multiple-parameter fractional Fourier transform [Opt. Lett.33, 581 (2008)]. A modified method is proposed to avoid all the deficiencies. Security and reliability are greatly improved without increasing the complexity of the encryption process. (c) 2009 Optical Society of America.

Characterization of Mechanical Properties of Tissue Scaffolds by Phase Contrast Imaging and Finite Element Modeling.

PubMed

Bawolin, Nahshon K; Dolovich, Allan T; Chen, Daniel X B; Zhang, Chris W J

2015-08-01

In tissue engineering, the cell and scaffold approach has shown promise as a treatment to regenerate diseased and/or damaged tissue. In this treatment, an artificial construct (scaffold) is seeded with cells, which organize and proliferate into new tissue. The scaffold itself biodegrades with time, leaving behind only newly formed tissue. The degradation qualities of the scaffold are critical during the treatment period, since the change in the mechanical properties of the scaffold with time can influence cell behavior. To observe in time the scaffold's mechanical properties, a straightforward method is to deform the scaffold and then characterize scaffold deflection accordingly. However, experimentally observing the scaffold deflection is challenging. This paper presents a novel study on characterization of mechanical properties of scaffolds by phase contrast imaging and finite element modeling, which specifically includes scaffold fabrication, scaffold imaging, image analysis, and finite elements (FEs) modeling of the scaffold mechanical properties. The innovation of the work rests on the use of in-line phase contrast X-ray imaging at 20 KeV to characterize tissue scaffold deformation caused by ultrasound radiation forces and the use of the Fourier transform to identify movement. Once deformation has been determined experimentally, it is then compared with the predictions given by the forward solution of a finite element model. A consideration of the number of separate loading conditions necessary to uniquely identify the material properties of transversely isotropic and fully orthotropic scaffolds is also presented, along with the use of an FE as a form of regularization.

TH-EF-BRA-05: A Method of Near Real-Time 4D MRI Using Volumetric Dynamic Keyhole (VDK) in the Presence of Respiratory Motion for MR-Guided Radiotherapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lewis, B; Kim, S; Kim, T

Purpose: To develop a novel method that enables 4D MR imaging in near real-time for continuous monitoring of tumor motion in MR-guided radiotherapy. Methods: This method is mainly based on an idea of expanding dynamic keyhole to full volumetric imaging acquisition. In the VDK approach introduced in this study, a library of peripheral volumetric k-space data is generated in given number of phases (5 and 10 in this study) in advance. For 4D MRI at any given time, only volumetric central k-space data are acquired in real-time and combined with pre-acquired peripheral volumetric k-space data in the library corresponding tomore » the respiratory phase (or amplitude). The combined k-space data are Fourier-transformed to MR images. For simulation study, an MRXCAT program was used to generate synthetic MR images of the thorax with desired respiratory motion, contrast levels, and spatial and temporal resolution. 20 phases of volumetric MR images, with 200 ms temporal resolution in 4 s respiratory period, were generated using balanced steady-state free precession MR pulse sequence. The total acquisition time was 21.5s/phase with a voxel size of 3×3×5 mm{sup 3} and an image matrix of 128×128×56. Image similarity was evaluated with difference maps between the reference and reconstructed images. The VDK, conventional keyhole, and zero filling methods were compared for this simulation study. Results: Using 80% of the ky data and 70% of the kz data from the library resulted in 12.20% average intensity difference from the reference, and 21.60% and 28.45% difference in threshold pixel difference for conventional keyhole and zero filling, respectively. The imaging time will be reduced from 21.5s to 1.3s per volume using the VDK method. Conclusion: Near real-time 4D MR imaging can be achieved using the volumetric dynamic keyhole method. That makes the possibility of utilizing 4D MRI during MR-guided radiotherapy.« less

Phase shifts in the Fourier spectra of phase gratings and phase grids: an application for one-shot phase-shifting interferometry.

PubMed

Toto-Arellano, Noel-Ivan; Rodriguez-Zurita, Gustavo; Meneses-Fabian, Cruz; Vazquez-Castillo, Jose F

2008-11-10

Among several techniques, phase shifting interferometry can be implemented with a grating used as a beam divider to attain several interference patterns around each diffraction order. Because each pattern has to show a different phase-shift, a suitable shifting technique must be employed. Phase gratings are attractive to perform the former task due to their higher diffraction efficiencies. But as is very well known, the Fourier coefficients of only-phase gratings are integer order Bessel functions of the first kind. The values of these real-valued functions oscillate around zero, so they can adopt negative values, thereby introducing phase shifts of pi at certain diffraction orders. Because this almost trivial fact seems to have been overlooked in the literature regarding its practical implications, in this communication such phase shifts are stressed in the description of interference patterns obtained with grating interferometers. These patterns are obtained by placing two windows in the object plane of a 4f system with a sinusoidal grating/grid in the Fourier plane. It is shown that the corresponding experimental observations of the fringe modulation, as well as the corresponding phase measurements, are all in agreement with the proposed description. A one-shot phase shifting interferometer is finally proposed taking into account these properties after proper incorporation of modulation of polarization.

Digital watermarking algorithm research of color images based on quaternion Fourier transform

NASA Astrophysics Data System (ADS)

An, Mali; Wang, Weijiang; Zhao, Zhen

2013-10-01

A watermarking algorithm of color images based on the quaternion Fourier Transform (QFFT) and improved quantization index algorithm (QIM) is proposed in this paper. The original image is transformed by QFFT, the watermark image is processed by compression and quantization coding, and then the processed watermark image is embedded into the components of the transformed original image. It achieves embedding and blind extraction of the watermark image. The experimental results show that the watermarking algorithm based on the improved QIM algorithm with distortion compensation achieves a good tradeoff between invisibility and robustness, and better robustness for the attacks of Gaussian noises, salt and pepper noises, JPEG compression, cropping, filtering and image enhancement than the traditional QIM algorithm.

Quantum Color Image Encryption Algorithm Based on A Hyper-Chaotic System and Quantum Fourier Transform

NASA Astrophysics Data System (ADS)

Tan, Ru-Chao; Lei, Tong; Zhao, Qing-Min; Gong, Li-Hua; Zhou, Zhi-Hong

2016-12-01

To improve the slow processing speed of the classical image encryption algorithms and enhance the security of the private color images, a new quantum color image encryption algorithm based on a hyper-chaotic system is proposed, in which the sequences generated by the Chen's hyper-chaotic system are scrambled and diffused with three components of the original color image. Sequentially, the quantum Fourier transform is exploited to fulfill the encryption. Numerical simulations show that the presented quantum color image encryption algorithm possesses large key space to resist illegal attacks, sensitive dependence on initial keys, uniform distribution of gray values for the encrypted image and weak correlation between two adjacent pixels in the cipher-image.

Image Reconstruction from Under sampled Fourier Data Using the Polynomial Annihilation Transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Archibald, Richard K.; Gelb, Anne; Platte, Rodrigo

Fourier samples are collected in a variety of applications including magnetic resonance imaging and synthetic aperture radar. The data are typically under-sampled and noisy. In recent years, l 1 regularization has received considerable attention in designing image reconstruction algorithms from under-sampled and noisy Fourier data. The underlying image is assumed to have some sparsity features, that is, some measurable features of the image have sparse representation. The reconstruction algorithm is typically designed to solve a convex optimization problem, which consists of a fidelity term penalized by one or more l 1 regularization terms. The Split Bregman Algorithm provides a fastmore » explicit solution for the case when TV is used for the l1l1 regularization terms. Due to its numerical efficiency, it has been widely adopted for a variety of applications. A well known drawback in using TV as an l 1 regularization term is that the reconstructed image will tend to default to a piecewise constant image. This issue has been addressed in several ways. Recently, the polynomial annihilation edge detection method was used to generate a higher order sparsifying transform, and was coined the “polynomial annihilation (PA) transform.” This paper adapts the Split Bregman Algorithm for the case when the PA transform is used as the l 1 regularization term. In so doing, we achieve a more accurate image reconstruction method from under-sampled and noisy Fourier data. Our new method compares favorably to the TV Split Bregman Algorithm, as well as to the popular TGV combined with shearlet approach.« less

High speed CMOS acquisition system based on FPGA embedded image processing for electro-optical measurements

NASA Astrophysics Data System (ADS)

Rosu-Hamzescu, Mihnea; Polonschii, Cristina; Oprea, Sergiu; Popescu, Dragos; David, Sorin; Bratu, Dumitru; Gheorghiu, Eugen

2018-06-01

Electro-optical measurements, i.e., optical waveguides and plasmonic based electrochemical impedance spectroscopy (P-EIS), are based on the sensitive dependence of refractive index of electro-optical sensors on surface charge density, modulated by an AC electrical field applied to the sensor surface. Recently, P-EIS has emerged as a new analytical tool that can resolve local impedance with high, optical spatial resolution, without using microelectrodes. This study describes a high speed image acquisition and processing system for electro-optical measurements, based on a high speed complementary metal-oxide semiconductor (CMOS) sensor and a field-programmable gate array (FPGA) board. The FPGA is used to configure CMOS parameters, as well as to receive and locally process the acquired images by performing Fourier analysis for each pixel, deriving the real and imaginary parts of the Fourier coefficients for the AC field frequencies. An AC field generator, for single or multi-sine signals, is synchronized with the high speed acquisition system for phase measurements. The system was successfully used for real-time angle-resolved electro-plasmonic measurements from 30 Hz up to 10 kHz, providing results consistent to ones obtained by a conventional electrical impedance approach. The system was able to detect amplitude variations with a relative variation of ±1%, even for rather low sampling rates per period (i.e., 8 samples per period). The PC (personal computer) acquisition and control software allows synchronized acquisition for multiple FPGA boards, making it also suitable for simultaneous angle-resolved P-EIS imaging.

Dark-field optical coherence microscopy

NASA Astrophysics Data System (ADS)

Pache, C.; Villiger, M. L.; Lasser, T.

2010-02-01

Many solutions have been proposed to produce phase quantitative images of biological cell samples. Among these, Spectral Domain Phase Microscopy combines the fast imaging speed and high sensitivity of Optical Coherence Microscopy (OCM) in the Fourier domain with the high phase stability of common-path interferometry. We report on a new illumination scheme for OCM that enhances the sensitivity for backscattered light and detects the weak sample signal, otherwise buried by the signal from specular reflection. With the use of a Bessel-like beam, a dark-field configuration was realized. Sensitivity measurements for three different illumination configurations were performed to compare our method to standard OCM and extended focus OCM. Using a well-defined scattering and reflecting object, we demonstrated an attenuation of -40 dB of the DC-component and a relative gain of 30 dB for scattered light, compared to standard OCM. In a second step, we applied this technique, referred to as dark-field Optical Coherence Microscopy (dfOCM), to living cells. Chinese hamster ovarian cells were applied in a drop of medium on a coverslide. The cells of ~15 μm in diameter and even internal cell structures were visualized in the acquired tomograms.

A Fast Variant of 1H Spectroscopic U-FLARE Imaging Using Adjusted Chemical Shift Phase Encoding

NASA Astrophysics Data System (ADS)

Ebel, Andreas; Dreher, Wolfgang; Leibfritz, Dieter

2000-02-01

So far, fast spectroscopic imaging (SI) using the U-FLARE sequence has provided metabolic maps indirectly via Fourier transformation (FT) along the chemical shift (CS) dimension and subsequent peak integration. However, a large number of CS encoding steps Nω is needed to cover the spectral bandwidth and to achieve sufficient spectral resolution for peak integration even if the number of resonance lines is small compared to Nω and even if only metabolic images are of interest and not the spectra in each voxel. Other reconstruction algorithms require extensive prior knowledge, starting values, and/or model functions. An adjusted CS phase encoding scheme (APE) can be used to overcome these drawbacks. It incorporates prior knowledge only about the resonance frequencies present in the sample. Thus, Nω can be reduced by a factor of 4 for many 1H in vivo studies while no spectra have to be reconstructed, and no additional user interaction, prior knowledge, starting values, or model function are required. Phantom measurements and in vivo experiments on rat brain have been performed at 4.7 T to test the feasibility of the method for proton SI.

Cosmological Constraints from Fourier Phase Statistics

NASA Astrophysics Data System (ADS)

Ali, Kamran; Obreschkow, Danail; Howlett, Cullan; Bonvin, Camille; Llinares, Claudio; Oliveira Franco, Felipe; Power, Chris

2018-06-01

Most statistical inference from cosmic large-scale structure relies on two-point statistics, i.e. on the galaxy-galaxy correlation function (2PCF) or the power spectrum. These statistics capture the full information encoded in the Fourier amplitudes of the galaxy density field but do not describe the Fourier phases of the field. Here, we quantify the information contained in the line correlation function (LCF), a three-point Fourier phase correlation function. Using cosmological simulations, we estimate the Fisher information (at redshift z = 0) of the 2PCF, LCF and their combination, regarding the cosmological parameters of the standard ΛCDM model, as well as a Warm Dark Matter (WDM) model and the f(R) and Symmetron modified gravity models. The galaxy bias is accounted for at the level of a linear bias. The relative information of the 2PCF and the LCF depends on the survey volume, sampling density (shot noise) and the bias uncertainty. For a volume of 1h^{-3}Gpc^3, sampled with points of mean density \\bar{n} = 2× 10^{-3} h3 Mpc^{-3} and a bias uncertainty of 13%, the LCF improves the parameter constraints by about 20% in the ΛCDM cosmology and potentially even more in alternative models. Finally, since a linear bias only affects the Fourier amplitudes (2PCF), but not the phases (LCF), the combination of the 2PCF and the LCF can be used to break the degeneracy between the linear bias and σ8, present in 2-point statistics.

A technique for phase correction in Fourier transform spectroscopy

NASA Astrophysics Data System (ADS)

Artsang, P.; Pongchalee, P.; Palawong, K.; Buisset, C.; Meemon, P.

2018-03-01

Fourier transform spectroscopy (FTS) is a type of spectroscopy that can be used to analyze components in the sample. The basic setup that is commonly used in this technique is "Michelson interferometer". The interference signal obtained from interferometer can be Fourier transformed into the spectral pattern of the illuminating light source. To experimentally study the concept of the Fourier transform spectroscopy, the project started by setup the Michelson interferometer in the laboratory. The implemented system used a broadband light source in near infrared region (0.81-0.89 μm) and controlled the movable mirror by using computer controlled motorized translation stage. In the early study, there is no sample the interference path. Therefore, the theoretical spectral results after the Fourier transformation of the captured interferogram must be the spectral shape of the light source. One main challenge of the FTS is to retrieve the correct phase information of the inferferogram that relates with the correct spectral shape of the light source. One main source of the phase distortion in FTS that we observed from our system is the non-linear movement of the movable reference mirror of the Michelson interferometer. Therefore, to improve the result, we coupled a monochromatic light source to the implemented interferometer. We simultaneously measured the interferograms of the monochromatic and broadband light sources. The interferogram of the monochromatic light source was used to correct the phase of the interferogram of the broadband light source. The result shows significant improvement in the computed spectral shape.

Quantitative Susceptibility Mapping of Human Brain Reflects Spatial Variation in Tissue Composition

PubMed Central

Li, Wei; Wu, Bing; Liu, Chunlei

2011-01-01

Image phase from gradient echo MRI provides a unique contrast that reflects brain tissue composition variations, such as iron and myelin distribution. Phase imaging is emerging as a powerful tool for the investigation of functional brain anatomy and disease diagnosis. However, the quantitative value of phase is compromised by its nonlocal and orientation dependent properties. There is an increasing need for reliable quantification of magnetic susceptibility, the intrinsic property of tissue. In this study, we developed a novel and accurate susceptibility mapping method that is also phase-wrap insensitive. The proposed susceptibility mapping method utilized two complementary equations: (1) the Fourier relationship of phase and magnetic susceptibility; and (2) the first-order partial derivative of the first equation in the spatial frequency domain. In numerical simulation, this method reconstructed the susceptibility map almost free of streaking artifact. Further, the iterative implementation of this method allowed for high quality reconstruction of susceptibility maps of human brain in vivo. The reconstructed susceptibility map provided excellent contrast of iron-rich deep nuclei and white matter bundles from surrounding tissues. Further, it also revealed anisotropic magnetic susceptibility in brain white matter. Hence, the proposed susceptibility mapping method may provide a powerful tool for the study of brain physiology and pathophysiology. Further elucidation of anisotropic magnetic susceptibility in vivo may allow us to gain more insight into the white matter microarchitectures. PMID:21224002

Variable-temperature Fourier transform near-infrared imaging spectroscopy of the deuterium/hydrogen exchange in liquid D₂O.

PubMed

Unger, Miriam; Ozaki, Yukihiro; Siesler, Heinz W

2014-01-01

In the present publication, the deuterium/hydrogen (D/H) exchange of liquid D2O exposed to water vapor of the surrounding atmosphere has been studied by variable-temperature Fourier transform near-infrared (FT-NIR) imaging spectroscopy. Apart from the visualization of the exchange process in the time-resolved FT-NIR images, kinetic parameters and the activation energy for this D/H exchange reaction have been derived from the Arrhenius plot of the variable-temperature spectroscopic data.

Beam profile for the Herschel-SPIRE Fourier transform spectrometer.

PubMed

Makiwa, Gibion; Naylor, David A; Ferlet, Marc; Salji, Carl; Swinyard, Bruce; Polehampton, Edward; van der Wiel, Matthijs H D

2013-06-01

One of the instruments on board the Herschel Space Observatory is the Spectral and Photometric Imaging Receiver (SPIRE). SPIRE employs a Fourier transform spectrometer with feed-horn-coupled bolometers to provide imaging spectroscopy. To interpret the resultant spectral images requires knowledge of the wavelength-dependent beam, which in the case of SPIRE is complicated by the use of multimoded feed horns. In this paper we describe a series of observations and the analysis conducted to determine the wavelength dependence of the SPIRE spectrometer beam profile.

High-resolution retinal imaging using adaptive optics and Fourier-domain optical coherence tomography

DOEpatents

Olivier, Scot S.; Werner, John S.; Zawadzki, Robert J.; Laut, Sophie P.; Jones, Steven M.

2010-09-07

This invention permits retinal images to be acquired at high speed and with unprecedented resolution in three dimensions (4.times.4.times.6 .mu.m). The instrument achieves high lateral resolution by using adaptive optics to correct optical aberrations of the human eye in real time. High axial resolution and high speed are made possible by the use of Fourier-domain optical coherence tomography. Using this system, we have demonstrated the ability to image microscopic blood vessels and the cone photoreceptor mosaic.

Fizeau Fourier transform imaging spectroscopy: missing data reconstruction.

PubMed

Thurman, Samuel T; Fienup, James R

2008-04-28

Fizeau Fourier transform imaging spectroscopy yields both spatial and spectral information about an object. Spectral information, however, is not obtained for a finite area of low spatial frequencies. A nonlinear reconstruction algorithm based on a gray-world approximation is presented. Reconstruction results from simulated data agree well with ideal Michelson interferometer-based spectral imagery. This result implies that segmented-aperture telescopes and multiple telescope arrays designed for conventional imaging can be used to gather useful spectral data through Fizeau FTIS without the need for additional hardware.

T1 and susceptibility contrast at high fields

NASA Astrophysics Data System (ADS)

Neelavalli, Jaladhar

Clinical imaging at high magnetic field strengths (≥ 3Tesla) is sought after primarily due to the increased signal strength available at these fields. This increased SNR can be used to perform: (a) high resolution imaging in the same time as at lower field strengths; (b) the same resolution imaging with much faster acquisition; and (c) functional MR imaging (fMRI), dynamic perfusion and diffusion imaging with increased sensitivity. However they are also associated with increased power deposition (SAR) due to increase in imaging frequency and longer T1 relaxation times. Longer T1s mean longer imaging times for generating good T1 contrast images. On the other hand for faster imaging, at high fields fast spin echo or magnetization prepared sequences are conventionally proposed which are, however, associated with high SAR values. Imaging with low SAR is more and more important as we move towards high fields and particularly for patients with metallic implants like pacemakers or deep brain stimulator. The SAR limit acceptable for these patients is much less than the limit acceptable for normal subjects. A new method is proposed for imaging at high fields with good contrast with simultaneous reduction in power deposition. Further, T1 based contrast optimization problem in FLASH imaging is considered for tissues with different T1s but same spin densities. The solution providing optimal imaging parameters is simplified for quick and easy computation in a clinical setting. The efficacy of the simplification is evaluated and practical limits under which the simplification can be applied are worked out. The phase difference due to variation in magnetic susceptibility property among biological tissues is another unique source of contrast which is different from the conventional T1, T2 and T2* contrast. This susceptibility based phase contrast has become more and more important at high fields, partly due to contrast generation issues due to longer T 1s and shorter T2s and partly because of the invariance of most tissue susceptibilities with field strength. This essentially ensures a constant available phase contrast between tissues across field strengths. In fact, with the increased SNR at high fields, the phase CNR actually increases with field strength which is even better. Susceptibility weighted imaging, which uniquely combines this phase and magnitude information to generate enhanced susceptibility contrast magnitude images, has proven to be an important tool in the study of various neurological conditions like, Alzheimer's, Parkinson's, Huntington's disease and multiple sclerosis even at conventional field strength of 1.5T and should have more applicability at high fields. A major issue in using phase images for susceptibility contrast, directly or as processed SWI magnitude images, is the large scale background phase variations that obscure the local susceptibility based contrast. A novel method is proposed for removing such geometrically induced large scale phase variations using a Fourier Transform based field calculation method. It is shown that the new method is capable of successfully removing the background field effects. It is shown that the new method is not only capable of successfully removing the background field effects but also helps in preserving more local phase information.

Optical Scatter Imaging with a digital micromirror device.

PubMed

Zheng, Jing-Yi; Pasternack, Robert M; Boustany, Nada N

2009-10-26

We had developed Optical Scatter Imaging (OSI) as a method which combines light scattering spectroscopy with microscopic imaging to probe local particle size in situ. Using a variable diameter iris as a Fourier spatial filter, the technique consisted of collecting images that encoded the intensity ratio of wide-to-narrow angle scatter at each pixel in the full field of view. In this paper, we replace the variable diameter Fourier filter with a digital micromirror device (DMD) to extend our assessment of morphology to the characterization of particle shape and orientation. We describe our setup in detail and demonstrate how to eliminate aberrations associated with the placement of the DMD in a conjugate Fourier plane of our microscopic imaging system. Using bacteria and polystyrene spheres, we show how this system can be used to assess particle aspect ratio even when imaged at low resolution. We also show the feasibility of detecting alterations in organelle aspect ratio in situ within living cells. This improved OSI system could be further developed to automate morphological quantification and sorting of non-spherical particles in situ.

Panoramic optical-servoing for industrial inspection and repair

NASA Astrophysics Data System (ADS)

Sallinger, Christian; O'Leary, Paul; Retschnig, Alexander; Kammerhofer, Martin

2004-05-01

Recently specialized robots were introduced to perform the task of inspection and repair in large cylindrical structures such as ladles, melting furnaces and converters. This paper reports on the image processing system and optical servoing for one such a robot. A panoramic image of the vessels inner surface is produced by performing a coordinated robot motion and image acquisition. The level of projective distortion is minimized by acquiring a high density of images. Normalized phase correlation calculated via the 2D Fourier transform is used to calculate the shift between the single images. The narrow strips from the dense image map are then stitched together to build the panorama. The mapping between the panoramic image and the positioning of the robot is established during the stitching of the images. This enables optical feedback. The robots operator can locate a defect on the surface by selecting the area of the image. Calculation of the forward and inverse kinematics enable the robot to automatically move to the location on the surface requiring repair. Experimental results using a standard 6R industrial robot have shown the full functionality of the system concept. Finally, were test measurements carried out successfully, in a ladle at a temperature of 1100° C.

Fusion of infrared and visible images based on saliency scale-space in frequency domain

NASA Astrophysics Data System (ADS)

Chen, Yanfei; Sang, Nong; Dan, Zhiping

2015-12-01

A fusion algorithm of infrared and visible images based on saliency scale-space in the frequency domain was proposed. Focus of human attention is directed towards the salient targets which interpret the most important information in the image. For the given registered infrared and visible images, firstly, visual features are extracted to obtain the input hypercomplex matrix. Secondly, the Hypercomplex Fourier Transform (HFT) is used to obtain the salient regions of the infrared and visible images respectively, the convolution of the input hypercomplex matrix amplitude spectrum with a low-pass Gaussian kernel of an appropriate scale which is equivalent to an image saliency detector are done. The saliency maps are obtained by reconstructing the 2D signal using the original phase and the amplitude spectrum, filtered at a scale selected by minimizing saliency map entropy. Thirdly, the salient regions are fused with the adoptive weighting fusion rules, and the nonsalient regions are fused with the rule based on region energy (RE) and region sharpness (RS), then the fused image is obtained. Experimental results show that the presented algorithm can hold high spectrum information of the visual image, and effectively get the thermal targets information at different scales of the infrared image.

Fast and robust estimation of ophthalmic wavefront aberrations

NASA Astrophysics Data System (ADS)

Dillon, Keith

2016-12-01

Rapidly rising levels of myopia, particularly in the developing world, have led to an increased need for inexpensive and automated approaches to optometry. A simple and robust technique is provided for estimating major ophthalmic aberrations using a gradient-based wavefront sensor. The approach is based on the use of numerical calculations to produce diverse combinations of phase components, followed by Fourier transforms to calculate the coefficients. The approach does not utilize phase unwrapping nor iterative solution of inverse problems. This makes the method very fast and tolerant to image artifacts, which do not need to be detected and masked or interpolated as is needed in other techniques. These features make it a promising algorithm on which to base low-cost devices for applications that may have limited access to expert maintenance and operation.

High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform

PubMed Central

Chan, Kenny K. H.; Tang, Shuo

2010-01-01

The useful imaging range in spectral domain optical coherence tomography (SD-OCT) is often limited by the depth dependent sensitivity fall-off. Processing SD-OCT data with the non-uniform fast Fourier transform (NFFT) can improve the sensitivity fall-off at maximum depth by greater than 5dB concurrently with a 30 fold decrease in processing time compared to the fast Fourier transform with cubic spline interpolation method. NFFT can also improve local signal to noise ratio (SNR) and reduce image artifacts introduced in post-processing. Combined with parallel processing, NFFT is shown to have the ability to process up to 90k A-lines per second. High-speed SD-OCT imaging is demonstrated at camera-limited 100 frames per second on an ex-vivo squid eye. PMID:21258551

High-resolution noise substitution to measure overfitting and validate resolution in 3D structure determination by single particle electron cryomicroscopy.

PubMed

Chen, Shaoxia; McMullan, Greg; Faruqi, Abdul R; Murshudov, Garib N; Short, Judith M; Scheres, Sjors H W; Henderson, Richard

2013-12-01

Three-dimensional (3D) structure determination by single particle electron cryomicroscopy (cryoEM) involves the calculation of an initial 3D model, followed by extensive iterative improvement of the orientation determination of the individual particle images and the resulting 3D map. Because there is much more noise than signal at high resolution in the images, this creates the possibility of noise reinforcement in the 3D map, which can give a false impression of the resolution attained. The balance between signal and noise in the final map at its limiting resolution depends on the image processing procedure and is not easily predicted. There is a growing awareness in the cryoEM community of how to avoid such over-fitting and over-estimation of resolution. Equally, there has been a reluctance to use the two principal methods of avoidance because they give lower resolution estimates, which some people believe are too pessimistic. Here we describe a simple test that is compatible with any image processing protocol. The test allows measurement of the amount of signal and the amount of noise from overfitting that is present in the final 3D map. We have applied the method to two different sets of cryoEM images of the enzyme beta-galactosidase using several image processing packages. Our procedure involves substituting the Fourier components of the initial particle image stack beyond a chosen resolution by either the Fourier components from an adjacent area of background, or by simple randomisation of the phases of the particle structure factors. This substituted noise thus has the same spectral power distribution as the original data. Comparison of the Fourier Shell Correlation (FSC) plots from the 3D map obtained using the experimental data with that from the same data with high-resolution noise (HR-noise) substituted allows an unambiguous measurement of the amount of overfitting and an accompanying resolution assessment. A simple formula can be used to calculate an unbiased FSC from the two curves, even when a substantial amount of overfitting is present. The approach is software independent. The user is therefore completely free to use any established method or novel combination of methods, provided the HR-noise test is carried out in parallel. Applying this procedure to cryoEM images of beta-galactosidase shows how overfitting varies greatly depending on the procedure, but in the best case shows no overfitting and a resolution of ~6 Å. (382 words). © 2013 The Authors. Published by Elsevier B.V. All rights reserved.

Mosaicking Techniques for Deep Submergence Vehicle Video Imagery - Applications to Ridge2000 Science

NASA Astrophysics Data System (ADS)

Mayer, L.; Rzhanov, Y.; Fornari, D. J.; Soule, A.; Shank, T. M.; Beaulieu, S. E.; Schouten, H.; Tivey, M.

2004-12-01

Severe attenuation of visible light and limited power capabilities of many submersible vehicles require acquisition of imagery from short ranges, rarely exceeding 8-10 meters. Although modern video- and photo-equipment makes high-resolution video surveying possible, the field of view of each image remains relatively narrow. To compensate for the deficiencies in light and field of view researchers have been developing techniques allowing for combining images into larger composite images i.e., mosaicking. A properly constructed, accurate mosaic has a number of well-known advantages in comparison with the original sequence of images, the most notable being improved situational awareness. We have developed software strategies for PC-based computers that permit conversion of video imagery acquired from any underwater vehicle, operated within both absolute (e.g. LBL or USBL) or relative (e.g. Doppler Velocity Log-DVL) navigation networks, to quickly produce a set of geo-referenced photomosaics which can then be directly incorporated into a Geographic Information System (GIS) data base. The timescale of processing is rapid enough to permit analysis of the resulting mosaics between submersible dives thus enhancing the efficiency of deep-sea research. Commercial imaging processing packages usually handle cases where there is no or little parallax - an unlikely situation for undersea world where terrain has pronounced 3D content and imagery is acquired from moving platforms. The approach we have taken is optimized for situations in which there is significant relief and thus parallax in the imagery (e.g. seafloor fault scarps or constructional volcanic escarpments and flow fronts). The basis of all mosaicking techniques is a pair-wise image registration method that finds a transformation relating pixels of two consecutive image frames. We utilize a "rigid affine model" with four degrees of freedom for image registration that allows for camera translation in all directions and camera rotation about its optical axis. The coefficients of the transformation can be determined robustly using the well-established and powerful "featureless Fourier domain-based technique" (FFDT), which is an extension of the FFT-based correlation approach. While calculation of cross-correlation allows the recovery of only two parameters of the transformation (translation in 2D), FFDT uses the "Phase shift" theorem of the Fourier Transform as well as a log-polar transform of the Fourier magnitude spectrum to recover all four transformation coefficients required for the rigid affine model. Examples of results of our video mosaicking data processing for the East Pacific Rise ISS will be presented.

Image Display and Manipulation System (IDAMS) program documentation, Appendixes A-D. [including routines, convolution filtering, image expansion, and fast Fourier transformation

NASA Technical Reports Server (NTRS)

Cecil, R. W.; White, R. A.; Szczur, M. R.

1972-01-01

The IDAMS Processor is a package of task routines and support software that performs convolution filtering, image expansion, fast Fourier transformation, and other operations on a digital image tape. A unique task control card for that program, together with any necessary parameter cards, selects each processing technique to be applied to the input image. A variable number of tasks can be selected for execution by including the proper task and parameter cards in the input deck. An executive maintains control of the run; it initiates execution of each task in turn and handles any necessary error processing.

Method and apparatus for Delta Kappa synthetic aperture radar measurement of ocean current

NASA Technical Reports Server (NTRS)

Jain, A. (Inventor)

1985-01-01

A synthetic aperture radar (SAR) employed for delta k measurement of ocean current from a spacecraft without the need for a narrow beam and long observation times. The SAR signal is compressed to provide image data for different sections of the chirp band width, equivalent to frequencies and a common area for the separate image fields is selected. The image for the selected area at each frequency is deconvolved to obtain the image signals for the different frequencies and the same area. A product of pairs of signals is formed, Fourier transformed and squared. The spectrum thus obtained from different areas for the same pair of frequencies are added to provide an improved signal to noise ratio. The shift of the peak from the center of the spectrum is measured and compared to the expected shift due to the phase velocity of the Bragg scattering wave. Any difference is a measure of current velocity v sub o (delta k).

Cryptanalysis and Improvement of an Image Encryption Scheme Using Fourier Series

NASA Astrophysics Data System (ADS)

Ahmad, Musheer; Doja, M. N.; Beg, M. M. Sufyan

2017-12-01

This paper proposes cryptanalysis of an image encryption scheme reported in (Khan, J Vib Control 21(16):3450-3455, 2015). The encryption scheme synthesized nonlinear substitution-box using Fourier series to accomplish encryption of color images. Security investigation unveils that the scheme has inherent flaws which can be exploited by an attacker to reveal the plain-image information. We show that the encryption scheme is breakable under chosen-plaintext attack without owning secret key. The simulation analyses bring to notice that Khan's scheme is insecure for encryption of images during secure communication. Besides, an improved image encryption scheme is proposed which is backed up by better statistical results and performance.

Compact OAM microscope for edge enhancement of biomedical and object samples

NASA Astrophysics Data System (ADS)

Gozali, Richard; Nguyen, Thien-An; Bendau, Ethan; Alfano, Robert R.

2017-09-01

The production of orbital angular momentum (OAM) by using a q-plate, which functions as an electrically tunable spatial frequency filter, provides a simple and efficient method of edge contrast in biological and medical sample imaging for histological evaluation of tissue, smears, and PAP smears. An instrument producing OAM, such as a q-plate, situated at the Fourier plane of a 4f lens system, similar to the use of a high-pass spatial filter, allows the passage of high spatial frequencies and enables the production of an image with highly illuminated edges contrasted against a dark background for both opaque and transparent objects. Compared with ordinary spiral phase plates and spatial light modulators, the q-plate has the added advantage of electric control and tunability.

Study on the algorithm of computational ghost imaging based on discrete fourier transform measurement matrix

NASA Astrophysics Data System (ADS)

Zhang, Leihong; Liang, Dong; Li, Bei; Kang, Yi; Pan, Zilan; Zhang, Dawei; Gao, Xiumin; Ma, Xiuhua

2016-07-01

On the basis of analyzing the cosine light field with determined analytic expression and the pseudo-inverse method, the object is illuminated by a presetting light field with a determined discrete Fourier transform measurement matrix, and the object image is reconstructed by the pseudo-inverse method. The analytic expression of the algorithm of computational ghost imaging based on discrete Fourier transform measurement matrix is deduced theoretically, and compared with the algorithm of compressive computational ghost imaging based on random measurement matrix. The reconstruction process and the reconstruction error are analyzed. On this basis, the simulation is done to verify the theoretical analysis. When the sampling measurement number is similar to the number of object pixel, the rank of discrete Fourier transform matrix is the same as the one of the random measurement matrix, the PSNR of the reconstruction image of FGI algorithm and PGI algorithm are similar, the reconstruction error of the traditional CGI algorithm is lower than that of reconstruction image based on FGI algorithm and PGI algorithm. As the decreasing of the number of sampling measurement, the PSNR of reconstruction image based on FGI algorithm decreases slowly, and the PSNR of reconstruction image based on PGI algorithm and CGI algorithm decreases sharply. The reconstruction time of FGI algorithm is lower than that of other algorithms and is not affected by the number of sampling measurement. The FGI algorithm can effectively filter out the random white noise through a low-pass filter and realize the reconstruction denoising which has a higher denoising capability than that of the CGI algorithm. The FGI algorithm can improve the reconstruction accuracy and the reconstruction speed of computational ghost imaging.

Fourier transform profilometry (FTP) using an innovative band-pass filter for accurate 3-D surface reconstruction

NASA Astrophysics Data System (ADS)

Chen, Liang-Chia; Ho, Hsuan-Wei; Nguyen, Xuan-Loc

2010-02-01

This article presents a novel band-pass filter for Fourier transform profilometry (FTP) for accurate 3-D surface reconstruction. FTP can be employed to obtain 3-D surface profiles by one-shot images to achieve high-speed measurement. However, its measurement accuracy has been significantly influenced by the spectrum filtering process required to extract the phase information representing various surface heights. Using the commonly applied 2-D Hanning filter, the measurement errors could be up to 5-10% of the overall measuring height and it is unacceptable to various industrial application. To resolve this issue, the article proposes an elliptical band-pass filter for extracting the spectral region possessing essential phase information for reconstructing accurate 3-D surface profiles. The elliptical band-pass filter was developed and optimized to reconstruct 3-D surface models with improved measurement accuracy. Some experimental results verify that the accuracy can be effectively enhanced by using the elliptical filter. The accuracy improvement of 44.1% and 30.4% can be achieved in 3-D and sphericity measurement, respectively, when the elliptical filter replaces the traditional filter as the band-pass filtering method. Employing the developed method, the maximum measured error can be kept within 3.3% of the overall measuring range.

Modified Polar-Format Software for Processing SAR Data

NASA Technical Reports Server (NTRS)

Chen, Curtis

2003-01-01

HMPF is a computer program that implements a modified polar-format algorithm for processing data from spaceborne synthetic-aperture radar (SAR) systems. Unlike prior polar-format processing algorithms, this algorithm is based on the assumption that the radar signal wavefronts are spherical rather than planar. The algorithm provides for resampling of SAR pulse data from slant range to radial distance from the center of a reference sphere that is nominally the local Earth surface. Then, invoking the projection-slice theorem, the resampled pulse data are Fourier-transformed over radial distance, arranged in the wavenumber domain according to the acquisition geometry, resampled to a Cartesian grid, and inverse-Fourier-transformed. The result of this process is the focused SAR image. HMPF, and perhaps other programs that implement variants of the algorithm, may give better accuracy than do prior algorithms for processing strip-map SAR data from high altitudes and may give better phase preservation relative to prior polar-format algorithms for processing spotlight-mode SAR data.

High resolution wavenumber analysis for investigation of arterial pulse wave propagation

NASA Astrophysics Data System (ADS)

Hasegawa, Hideyuki; Sato, Masakazu; Irie, Takasuke

2016-07-01

The propagation of the pulse wave along the artery is relatively fast (several m/s), and a high-temporal resolution is required to measure pulse wave velocity (PWV) in a regional segment of the artery. High-frame-rate ultrasound enables the measurement of the regional PWV. In analyses of wave propagation phenomena, the direction and propagation speed are generally identified in the frequency-wavenumber space using the two-dimensional Fourier transform. However, the wavelength of the pulse wave is very long (1 m at a propagation velocity of 10 m/s and a temporal frequency of 10 Hz) compared with a typical lateral field of view of 40 mm in ultrasound imaging. Therefore, PWV cannot be identified in the frequency-wavenumber space owing to the low resolution of the two-dimensional Fourier transform. In the present study, PWV was visualized in the wavenumber domain using phases of arterial wall acceleration waveforms measured by high-frame-rate ultrasound.

An epistemology on the nature of polymers.

PubMed

Laridjani, Mortéza; Leboucher, Pierre

2014-01-01

Liquids have neither a periodic structure nor the completely random character of gases therefore the detailed study of their x-ray scattering diagram encounters many difficulties. The idea of periodic regularity in molecules of liquid polymers has been an attractive proposition for the simple interpretation of liquid polymer x-ray diagrams. The categorisation of polymer substances as being between a crystal phase with a perfect order and an amorphous disordered state is an over simplification of the complex reality. For obtaining structural information, during the early stages of the application of x-ray diffraction, a near crystalline model of the molecular arrangements in liquids was utilised. However, the results from these investigations led to just an approximation of the crystalline state. Our studies have analysed the real image of Fourier space of liquid polymers, for the first time, using anomalous diffractometry. The findings show the precise atomic structure of liquid polymers when transformed, by cooling, to solid polymers. We demonstrate that there is an intermediate ordered structure, characterised by the real full image of Fourier space. This prominent state of matter, an intermediate ordered structure, is defined by a regular unit cell with a five-fold symmetry. These structural atomic studies contribute to a more detailed understanding of the properties of polymers than the traditional studies of the degree of crystallinity.

An Epistemology on the Nature of Polymers

PubMed Central

Laridjani, Mortéza; Leboucher, Pierre

2014-01-01

Liquids have neither a periodic structure nor the completely random character of gases therefore the detailed study of their x-ray scattering diagram encounters many difficulties. The idea of periodic regularity in molecules of liquid polymers has been an attractive proposition for the simple interpretation of liquid polymer x-ray diagrams. The categorisation of polymer substances as being between a crystal phase with a perfect order and an amorphous disordered state is an over simplification of the complex reality. For obtaining structural information, during the early stages of the application of x-ray diffraction, a near crystalline model of the molecular arrangements in liquids was utilised. However, the results from these investigations led to just an approximation of the crystalline state. Our studies have analysed the real image of Fourier space of liquid polymers, for the first time, using anomalous diffractometry. The findings show the precise atomic structure of liquid polymers when transformed, by cooling, to solid polymers. We demonstrate that there is an intermediate ordered structure, characterised by the real full image of Fourier space. This prominent state of matter, an intermediate ordered structure, is defined by a regular unit cell with a five-fold symmetry. These structural atomic studies contribute to a more detailed understanding of the properties of polymers than the traditional studies of the degree of crystallinity. PMID:25329440

New formulation for interferometric synthetic aperture radar for terrain mapping

NASA Astrophysics Data System (ADS)

Jakowatz, Charles V., Jr.; Wahl, Daniel E.; Eichel, Paul H.; Thompson, Paul A.

1994-06-01

The subject of interferometric synthetic aperture radar (IFSAR) for high-accuracy terrain elevation mapping continues to gain importance in the arena of radar signal processing. Applications to problems in precision terrain-aided guidance and automatic target recognition, as well as a variety of civil applications, are being studied by a number of researchers. Not unlike many other areas of SAR processing, the subject of IFSAR can, at first glance, appear to be somewhat mysterious. In this paper we show how the mathematics of IFSAR for terrain elevation mapping using a pair of spotlight mode SAR collections can be derived in a very straightforward manner. Here, we employ an approach that relies entirely on Fourier transforms, and utilizes no reference to range equations or Doppler concepts. The result is a simplified explanation of the fundamentals of interferometry, including an easily-seen link between image domain phase difference and terrain elevation height. The derivation builds upon previous work by the authors in which a framework for spotlight mode SAR image formation based on an analogy to 3D computerized axial tomography (CAT) was developed. After outlining the major steps in the mathematics, we show how a computer simulator which utilizes 3D Fourier transforms can be constructed that demonstrates all of the major aspects of IFSAR from spotlight mode collections.

Microvascular anastomosis in rodent model evaluated by Fourier domain Doppler optical coherence tomography

NASA Astrophysics Data System (ADS)

Huang, Yong; Tong, Dedi; Zhu, Shan; Wu, Lehao; Ibrahim, Zuhaib; Lee, WP Andrew; Brandacher, Gerald; Kang, Jin U.

2014-03-01

Vascular and microvascular anastomosis are critical components of reconstructive microsurgery, vascular surgery and transplant surgery. Imaging modality that provides immediate, real-time in-depth view and 3D structure and flow information of the surgical site can be a great valuable tool for the surgeon to evaluate surgical outcome following both conventional and innovative anastomosis techniques, thus potentially increase the surgical success rate. Microvascular anastomosis for vessels with outer diameter smaller than 1.0 mm is extremely challenging and effective evaluation of the outcome is very difficult if not impossible using computed tomography (CT) angiograms, magnetic resonance (MR) angiograms and ultrasound Doppler. Optical coherence tomography (OCT) is a non-invasive high-resolution (micron level), high-speed, 3D imaging modality that has been adopted widely in biomedical and clinical applications. Phaseresolved Doppler OCT that explores the phase information of OCT signals has been shown to be capable of characterizing dynamic blood flow clinically. In this work, we explore the capability of Fourier domain Doppler OCT as an evaluation tool to detect commonly encountered post-operative complications that will cause surgical failure and to confirm positive result with surgeon's observation. Both suture and cuff based techniques were evaluated on the femoral artery and vein in the rodent model.

Quadratic Frequency Modulation Signals Parameter Estimation Based on Two-Dimensional Product Modified Parameterized Chirp Rate-Quadratic Chirp Rate Distribution.

PubMed

Qu, Zhiyu; Qu, Fuxin; Hou, Changbo; Jing, Fulong

2018-05-19

In an inverse synthetic aperture radar (ISAR) imaging system for targets with complex motion, the azimuth echo signals of the target are always modeled as multicomponent quadratic frequency modulation (QFM) signals. The chirp rate (CR) and quadratic chirp rate (QCR) estimation of QFM signals is very important to solve the ISAR image defocus problem. For multicomponent QFM (multi-QFM) signals, the conventional QR and QCR estimation algorithms suffer from the cross-term and poor anti-noise ability. This paper proposes a novel estimation algorithm called a two-dimensional product modified parameterized chirp rate-quadratic chirp rate distribution (2D-PMPCRD) for QFM signals parameter estimation. The 2D-PMPCRD employs a multi-scale parametric symmetric self-correlation function and modified nonuniform fast Fourier transform-Fast Fourier transform to transform the signals into the chirp rate-quadratic chirp rate (CR-QCR) domains. It can greatly suppress the cross-terms while strengthening the auto-terms by multiplying different CR-QCR domains with different scale factors. Compared with high order ambiguity function-integrated cubic phase function and modified Lv's distribution, the simulation results verify that the 2D-PMPCRD acquires higher anti-noise performance and obtains better cross-terms suppression performance for multi-QFM signals with reasonable computation cost.

Sinc or Sine? The Band Excitation Method and Energy Dissipation Measurements by SPM

NASA Astrophysics Data System (ADS)

Jesse, Stephen; Kalinin, Sergei

2007-03-01

Quantitative energy dissipation measurements in force-based SPM is the key to understanding fundamental mechanisms of energy transformations on the nanoscale, molecular, and atomic levels. To date, these measurements are invariably based on either phase and amplitude detection in constant frequency mode, or as amplitude detection in frequency-tracking mode. The analysis in both cases implicitly assumes that amplitude is inversely proportional to the Q-factor and is not applicable when the driving force is position dependent, as is the case for virtually all SPM measurements. All current SPM methods sample only a single frequency in the Fourier domain of the system. Thus, only two out of three parameters (amplitude, resonance, and Q) can be determined independently. Here, we developed and implemented a new approach for SPM detection based on the excitation and detection of a signal having a finite amplitude over a selected region in the Fourier domain and allows simultaneous determination of all three parameters. This band excitation method allows acquisition of the local spectral response at a 10ms/pixel rate, compatible with fast imaging, and is illustrated for electromechanical and mechanical imaging and force-distance spectroscopy. The BE method thus represents a new paradigm in SPM, beyond traditional single-frequency excitation.

Pulsation Detection from Noisy Ultrasound-Echo Moving Images of Newborn Baby Head Using Fourier Transform

NASA Astrophysics Data System (ADS)

Yamada, Masayoshi; Fukuzawa, Masayuki; Kitsunezuka, Yoshiki; Kishida, Jun; Nakamori, Nobuyuki; Kanamori, Hitoshi; Sakurai, Takashi; Kodama, Souichi

1995-05-01

In order to detect pulsation from a series of noisy ultrasound-echo moving images of a newborn baby's head for pediatric diagnosis, a digital image processing system capable of recording at the video rate and processing the recorded series of images was constructed. The time-sequence variations of each pixel value in a series of moving images were analyzed and then an algorithm based on Fourier transform was developed for the pulsation detection, noting that the pulsation associated with blood flow was periodically changed by heartbeat. Pulsation detection for pediatric diagnosis was successfully made from a series of noisy ultrasound-echo moving images of newborn baby's head by using the image processing system and the pulsation detection algorithm developed here.

Astronomical imaging Fourier spectroscopy at far-infrared wavelengths

NASA Astrophysics Data System (ADS)

Naylor, David A.; Gom, Brad G.; van der Wiel, Matthijs H. D.; Makiwa, Gibion

2013-11-01

The principles and practice of astronomical imaging Fourier transform spectroscopy (FTS) at far-infrared wavelengths are described. The Mach–Zehnder (MZ) interferometer design has been widely adopted for current and future imaging FTS instruments; we compare this design with two other common interferometer formats. Examples of three instruments based on the MZ design are presented. The techniques for retrieving astrophysical parameters from the measured spectra are discussed using calibration data obtained with the Herschel–SPIRE instrument. The paper concludes with an example of imaging spectroscopy obtained with the SPIRE FTS instrument.

SU-E-I-90: Characterizing Small Animal Lung Properties Using Speckle Observed with An In-Line X-Ray Phase Contrast Benchtop System

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garson, A; Gunsten, S; Guan, H

Purpose: We demonstrate a novel X-ray phase-contrast (XPC) method for lung imaging representing a paradigm shift in the way small animal functional imaging is performed. In our method, information regarding airway microstructure that is encoded within speckle texture of a single XPC radiograph is decoded to produce 2D parametric images that will spatially resolve changes in lung properties such as microstructure sizes and air volumes. Such information cannot be derived from conventional lung radiography or any other 2D imaging modality. By computing these images at different points within a breathing cycle, dynamic functional imaging will be readily achieved without themore » need for tomography. Methods: XPC mouse lung radiographs acquired in situ with an in-line X-ray phase contrast benchtop system. The lung air volume is varied and controlled with a small animal ventilator. XPC radiographs will be acquired for various lung air volume levels representing different phases of the respiratory cycle. Similar data will be acquired of microsphere-based lung phantoms containing hollow glass spheres with known distributions of diameters. Image texture analysis is applied to the data to investigate relationships between texture characteristics and airspace/microsphere physical properties. Results: Correlations between Fourier-based texture descriptors (FBTDs) and regional lung air volume indicate that the texture features in 2D radiographs reveal information on 3D properties of the lungs. For example, we find for a 350 × 350 πm2 lung ROI a linear relationship between injected air volume and FBTD value with slope and intercept of 8.9×10{sup 5} and 7.5, respectively. Conclusion: We demonstrate specific image texture measures related to lung speckle features are correlated with physical characteristics of refracting elements (i.e. lung air spaces). Furthermore, we present results indicating the feasibility of implementing the technique with a simple imaging system design, short exposures, and low dose which provides potential for widespread use in laboratory settings for in vivo studies. This research was supported in part by NSF Award CBET1263988.« less

Fringe pattern demodulation with a two-frame digital phase-locked loop algorithm.

PubMed

Gdeisat, Munther A; Burton, David R; Lalor, Michael J

2002-09-10

A novel technique called a two-frame digital phase-locked loop for fringe pattern demodulation is presented. In this scheme, two fringe patterns with different spatial carrier frequencies are grabbed for an object. A digital phase-locked loop algorithm tracks and demodulates the phase difference between both fringe patterns by employing the wrapped phase components of one of the fringe patterns as a reference to demodulate the second fringe pattern. The desired phase information can be extracted from the demodulated phase difference. We tested the algorithm experimentally using real fringe patterns. The technique is shown to be suitable for noncontact measurement of objects with rapid surface variations, and it outperforms the Fourier fringe analysis technique in this aspect. Phase maps produced withthis algorithm are noisy in comparison with phase maps generated with the Fourier fringe analysis technique.

Motion-induced error reduction by combining Fourier transform profilometry with phase-shifting profilometry.

PubMed

Li, Beiwen; Liu, Ziping; Zhang, Song

2016-10-03

We propose a hybrid computational framework to reduce motion-induced measurement error by combining the Fourier transform profilometry (FTP) and phase-shifting profilometry (PSP). The proposed method is composed of three major steps: Step 1 is to extract continuous relative phase maps for each isolated object with single-shot FTP method and spatial phase unwrapping; Step 2 is to obtain an absolute phase map of the entire scene using PSP method, albeit motion-induced errors exist on the extracted absolute phase map; and Step 3 is to shift the continuous relative phase maps from Step 1 to generate final absolute phase maps for each isolated object by referring to the absolute phase map with error from Step 2. Experiments demonstrate the success of the proposed computational framework for measuring multiple isolated rapidly moving objects.

GIFTS SM EDU Level 1B Algorithms

NASA Technical Reports Server (NTRS)

Tian, Jialin; Gazarik, Michael J.; Reisse, Robert A.; Johnson, David G.

2007-01-01

The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) SensorModule (SM) Engineering Demonstration Unit (EDU) is a high resolution spectral imager designed to measure infrared (IR) radiances using a Fourier transform spectrometer (FTS). The GIFTS instrument employs three focal plane arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The raw interferogram measurements are radiometrically and spectrally calibrated to produce radiance spectra, which are further processed to obtain atmospheric profiles via retrieval algorithms. This paper describes the GIFTS SM EDU Level 1B algorithms involved in the calibration. The GIFTS Level 1B calibration procedures can be subdivided into four blocks. In the first block, the measured raw interferograms are first corrected for the detector nonlinearity distortion, followed by the complex filtering and decimation procedure. In the second block, a phase correction algorithm is applied to the filtered and decimated complex interferograms. The resulting imaginary part of the spectrum contains only the noise component of the uncorrected spectrum. Additional random noise reduction can be accomplished by applying a spectral smoothing routine to the phase-corrected spectrum. The phase correction and spectral smoothing operations are performed on a set of interferogram scans for both ambient and hot blackbody references. To continue with the calibration, we compute the spectral responsivity based on the previous results, from which, the calibrated ambient blackbody (ABB), hot blackbody (HBB), and scene spectra can be obtained. We now can estimate the noise equivalent spectral radiance (NESR) from the calibrated ABB and HBB spectra. The correction schemes that compensate for the fore-optics offsets and off-axis effects are also implemented. In the third block, we developed an efficient method of generating pixel performance assessments. In addition, a random pixel selection scheme is designed based on the pixel performance evaluation. Finally, in the fourth block, the single pixel algorithms are applied to the entire FPA.

Signal-to-noise ratio comparison of encoding methods for hyperpolarized noble gas MRI

NASA Technical Reports Server (NTRS)

Zhao, L.; Venkatesh, A. K.; Albert, M. S.; Panych, L. P.

2001-01-01

Some non-Fourier encoding methods such as wavelet and direct encoding use spatially localized bases. The spatial localization feature of these methods enables optimized encoding for improved spatial and temporal resolution during dynamically adaptive MR imaging. These spatially localized bases, however, have inherently reduced image signal-to-noise ratio compared with Fourier or Hadamad encoding for proton imaging. Hyperpolarized noble gases, on the other hand, have quite different MR properties compared to proton, primarily the nonrenewability of the signal. It could be expected, therefore, that the characteristics of image SNR with respect to encoding method will also be very different from hyperpolarized noble gas MRI compared to proton MRI. In this article, hyperpolarized noble gas image SNRs of different encoding methods are compared theoretically using a matrix description of the encoding process. It is shown that image SNR for hyperpolarized noble gas imaging is maximized for any orthonormal encoding method. Methods are then proposed for designing RF pulses to achieve normalized encoding profiles using Fourier, Hadamard, wavelet, and direct encoding methods for hyperpolarized noble gases. Theoretical results are confirmed with hyperpolarized noble gas MRI experiments. Copyright 2001 Academic Press.

Miniaturized Fourier-plane fiber scanner for OCT endoscopy

NASA Astrophysics Data System (ADS)

Vilches, Sergio; Kretschmer, Simon; Ataman, Çağlar; Zappe, Hans

2017-10-01

A forward-looking endoscopic optical coherence tomography (OCT) probe featuring a Fourier-plane fiber scanner is designed, manufactured and characterized. In contrast to common image-plane fiber scanners, the Fourier-plane scanner is a telecentric arrangement that eliminates vignetting and spatial resolution variations across the image plane. To scan the OCT beam in a spiral pattern, a tubular piezoelectric actuator is used to resonate an optical fiber bearing a collimating GRIN lens at its tip. The free-end of the GRIN lens sits at the back focal plane of an objective lens, such that its rotation replicates the beam angles in the collimated region of a classical telecentric 4f optical system. Such an optical arrangement inherently has a low numerical aperture combined with a relatively large field-of-view, rendering it particularly useful for endoscopic OCT imaging. Furthermore, the optical train of the Fourier-plane scanner is shorter than that of a comparable image-plane scanner by one focal length of the objective lens, significantly shortening the final arrangement. As a result, enclosed within a 3D printed housing of 2.5 mm outer diameter and 15 mm total length, the developed probe is the most compact forward-looking endoscopic OCT imager to date. Due to its compact form factor and compatibility with real-time OCT imaging, the developed probe is also ideal for use in the working channel of flexible endoscopes as a potential optical biopsy tool.

Accurate determination of the diffusion coefficient of proteins by Fourier analysis with whole column imaging detection.

PubMed

Zarabadi, Atefeh S; Pawliszyn, Janusz

2015-02-17

Analysis in the frequency domain is considered a powerful tool to elicit precise information from spectroscopic signals. In this study, the Fourier transformation technique is employed to determine the diffusion coefficient (D) of a number of proteins in the frequency domain. Analytical approaches are investigated for determination of D from both experimental and data treatment viewpoints. The diffusion process is modeled to calculate diffusion coefficients based on the Fourier transformation solution to Fick's law equation, and its results are compared to time domain results. The simulations characterize optimum spatial and temporal conditions and demonstrate the noise tolerance of the method. The proposed model is validated by its application for the electropherograms from the diffusion path of a set of proteins. Real-time dynamic scanning is conducted to monitor dispersion by employing whole column imaging detection technology in combination with capillary isoelectric focusing (CIEF) and the imaging plug flow (iPF) experiment. These experimental techniques provide different peak shapes, which are utilized to demonstrate the Fourier transformation ability in extracting diffusion coefficients out of irregular shape signals. Experimental results confirmed that the Fourier transformation procedure substantially enhanced the accuracy of the determined values compared to those obtained in the time domain.

A comprehensive numerical analysis of background phase correction with V-SHARP.

PubMed

Özbay, Pinar Senay; Deistung, Andreas; Feng, Xiang; Nanz, Daniel; Reichenbach, Jürgen Rainer; Schweser, Ferdinand

2017-04-01

Sophisticated harmonic artifact reduction for phase data (SHARP) is a method to remove background field contributions in MRI phase images, which is an essential processing step for quantitative susceptibility mapping (QSM). To perform SHARP, a spherical kernel radius and a regularization parameter need to be defined. In this study, we carried out an extensive analysis of the effect of these two parameters on the corrected phase images and on the reconstructed susceptibility maps. As a result of the dependence of the parameters on acquisition and processing characteristics, we propose a new SHARP scheme with generalized parameters. The new SHARP scheme uses a high-pass filtering approach to define the regularization parameter. We employed the variable-kernel SHARP (V-SHARP) approach, using different maximum radii (R m ) between 1 and 15 mm and varying regularization parameters (f) in a numerical brain model. The local root-mean-square error (RMSE) between the ground-truth, background-corrected field map and the results from SHARP decreased towards the center of the brain. RMSE of susceptibility maps calculated with a spatial domain algorithm was smallest for R m between 6 and 10 mm and f between 0 and 0.01 mm -1 , and for maps calculated with a Fourier domain algorithm for R m between 10 and 15 mm and f between 0 and 0.0091 mm -1 . We demonstrated and confirmed the new parameter scheme in vivo. The novel regularization scheme allows the use of the same regularization parameter irrespective of other imaging parameters, such as image resolution. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

A Robust Wrap Reduction Algorithm for Fringe Projection Profilometry and Applications in Magnetic Resonance Imaging.

PubMed

Arevalillo-Herraez, Miguel; Cobos, Maximo; Garcia-Pineda, Miguel

2017-03-01

In this paper, we present an effective algorithm to reduce the number of wraps in a 2D phase signal provided as input. The technique is based on an accurate estimate of the fundamental frequency of a 2D complex signal with the phase given by the input, and the removal of a dependent additive term from the phase map. Unlike existing methods based on the discrete Fourier transform (DFT), the frequency is computed by using noise-robust estimates that are not restricted to integer values. Then, to deal with the problem of a non-integer shift in the frequency domain, an equivalent operation is carried out on the original phase signal. This consists of the subtraction of a tilted plane whose slope is computed from the frequency, followed by a re-wrapping operation. The technique has been exhaustively tested on fringe projection profilometry (FPP) and magnetic resonance imaging (MRI) signals. In addition, the performance of several frequency estimation methods has been compared. The proposed methodology is particularly effective on FPP signals, showing a higher performance than the state-of-the-art wrap reduction approaches. In this context, it contributes to canceling the carrier effect at the same time as it eliminates any potential slope that affects the entire signal. Its effectiveness on other carrier-free phase signals, e.g., MRI, is limited to the case that inherent slopes are present in the phase data.

Generation of dark hollow beam by use of phase-only filtering

NASA Astrophysics Data System (ADS)

Liu, Zhengjun; Dai, Jingmin; Zhao, Xiaoyi; Sun, Xiaogang; Liu, Shutian; Ashfaq Ahmad, Muhammad

2009-11-01

A simple but effective scheme to generate dark hollow beams is proposed by use of phase-only filtering and optical Fourier transform. A Gaussian beam of fundamental mode is modulated by a pre-designed phase mask, which is a piecewise modification of an axicon lens, and followed by a Fourier transform to generate an ideal dark hollow beam at the focal plane. This method has an advantage that the total energy of the beam is conserved under paraxial approximation. Numerical calculations are provided to show the validity of the proposed scheme.

Optical joint transform correlation on the DMD. [deformable mirror device

NASA Technical Reports Server (NTRS)

Knopp, Jerome; Juday, Richard D.

1989-01-01

Initial experimental investigation of the deformable mirror device (DMD) in a joint optical transform correlation is reported. The inverted cloverleaf version of the DMD, in which form the DMD is phase-mostly but of limited phase range, is used. Binarized joint Fourier transforms were calculated for similar and dissimilar objects and written onto the DMD. Inverse Fourier transform was done in a diffraction order for which the DMD shows phase-mostly modulation. Matched test objects produced sharp correlation, distinct objects did not. Further studies are warranted and they are outlined.

Partial Fourier techniques in single-shot cross-term spatiotemporal encoded MRI.

PubMed

Zhang, Zhiyong; Frydman, Lucio

2018-03-01

Cross-term spatiotemporal encoding (xSPEN) is a single-shot approach with exceptional immunity to field heterogeneities, the images of which faithfully deliver 2D spatial distributions without requiring a priori information or using postacquisition corrections. xSPEN, however, suffers from signal-to-noise ratio penalties due to its non-Fourier nature and due to diffusion losses-especially when seeking high resolution. This study explores partial Fourier transform approaches that, acting along either the readout or the spatiotemporally encoded dimensions, reduce these penalties. xSPEN uses an orthogonal (e.g., z) gradient to read, in direct space, the low-bandwidth (e.g., y) dimension. This substantially changes the nature of partial Fourier acquisitions vis-à-vis conventional imaging counterparts. A suitable theoretical analysis is derived to implement these procedures, along either the spatiotemporally or readout axes. Partial Fourier single-shot xSPEN images were recorded on preclinical and human scanners. Owing to their reduction in the experiments' acquisition times, this approach provided substantial sensitivity gains vis-à-vis previous implementations for a given targeted in-plane resolution. The physical origins of these gains are explained. Partial Fourier approaches, particularly when implemented along the low-bandwidth spatiotemporal dimension, provide several-fold sensitivity advantages at minimal costs to the execution and processing of the single-shot experiments. Magn Reson Med 79:1506-1514, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Recording multiple spatially-heterodyned direct to digital holograms in one digital image

DOEpatents

Hanson, Gregory R [Clinton, TN; Bingham, Philip R [Knoxville, TN

2008-03-25

Systems and methods are described for recording multiple spatially-heterodyned direct to digital holograms in one digital image. A method includes digitally recording, at a first reference beam-object beam angle, a first spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; Fourier analyzing the recorded first spatially-heterodyned hologram by shifting a first original origin of the recorded first spatially-heterodyned hologram to sit on top of a first spatial-heterodyne carrier frequency defined by the first reference beam-object beam angle; digitally recording, at a second reference beam-object beam angle, a second spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; Fourier analyzing the recorded second spatially-heterodyned hologram by shifting a second original origin of the recorded second spatially-heterodyned hologram to sit on top of a second spatial-heterodyne carrier frequency defined by the second reference beam-object beam angle; applying a first digital filter to cut off signals around the first original origin and define a first result; performing a first inverse Fourier transform on the first result; applying a second digital filter to cut off signals around the second original origin and define a second result; and performing a second inverse Fourier transform on the second result, wherein the first reference beam-object beam angle is not equal to the second reference beam-object beam angle and a single digital image includes both the first spatially-heterodyned hologram and the second spatially-heterodyned hologram.

Screening retinal transplants with Fourier-domain OCT

NASA Astrophysics Data System (ADS)

Rao, Bin

2009-02-01

Transplant technologies have been studied for the recovery of vision loss from retinitis pigmentosa (RP) and age-related macular degeneration (AMD). In several rodent retinal degeneration models and in patients, retinal progenitor cells transplanted as layers to the subretinal space have been shown to restore or preserve vision. The methods for evaluation of transplants are expensive considering the large amount of animals. Alternatively, time-domain Stratus OCT was previously shown to be able to image the morphological structure of transplants to some extent, but could not clearly identify laminated transplants. The efficacy of screening retinal transplants with Fourier-domain OCT was studied on 37 S334ter line 3 rats with retinal degeneration 6-67 days after transplant surgery. The transplants were morphologically categorized as no transplant, detachment, rosettes, small laminated area and larger laminated area with both Fourier-domain OCT and histology. The efficacy of Fourier-domain OCT in screening retinal transplants was evaluated by comparing the categorization results with OCT and histology. Additionally, 4 rats were randomly selected for multiple OCT examinations (1, 5, 9, 14 and 21days post surgery) in order to determine the earliest image time of OCT examination since the transplanted tissue may need some time to show its tendency of growing. Finally, we demonstrated the efficacy of Fourier-domain OCT in screening retinal transplants in early stages and determined the earliest imaging time for OCT. Fourier-domain OCT makes itself valuable in saving resource spent on animals with unsuccessful transplants.

Fully automated corneal endothelial morphometry of images captured by clinical specular microscopy

NASA Astrophysics Data System (ADS)

Bucht, Curry; Söderberg, Per; Manneberg, Göran

2009-02-01

The corneal endothelium serves as the posterior barrier of the cornea. Factors such as clarity and refractive properties of the cornea are in direct relationship to the quality of the endothelium. The endothelial cell density is considered the most important morphological factor. Morphometry of the corneal endothelium is presently done by semi-automated analysis of pictures captured by a Clinical Specular Microscope (CSM). Because of the occasional need of operator involvement, this process can be tedious, having a negative impact on sampling size. This study was dedicated to the development of fully automated analysis of images of the corneal endothelium, captured by CSM, using Fourier analysis. Software was developed in the mathematical programming language Matlab. Pictures of the corneal endothelium, captured by CSM, were read into the analysis software. The software automatically performed digital enhancement of the images. The digitally enhanced images of the corneal endothelium were transformed, using the fast Fourier transform (FFT). Tools were developed and applied for identification and analysis of relevant characteristics of the Fourier transformed images. The data obtained from each Fourier transformed image was used to calculate the mean cell density of its corresponding corneal endothelium. The calculation was based on well known diffraction theory. Results in form of estimated cell density of the corneal endothelium were obtained, using fully automated analysis software on images captured by CSM. The cell density obtained by the fully automated analysis was compared to the cell density obtained from classical, semi-automated analysis and a relatively large correlation was found.

Atmospheric convective velocities and the Fourier phase spectrum

NASA Technical Reports Server (NTRS)

Cliff, W. C.

1974-01-01

The relationship between convective velocity and the Fourier phase spectrum of the cross correlation is developed. By examining the convective velocity as a function of frequency, one may determine if Taylor's conversion from time statistics to space statistics is valid. It is felt that the high shear regions of the atmospheric boundary layer need to be explored to determine the validity of the use of Taylor's hypothesis for this region.

The derivative-free Fourier shell identity for photoacoustics.

PubMed

Baddour, Natalie

2016-01-01

In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the 'Fourier shell identity' has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions.

Tutorial on Fourier space coverage for scattering experiments, with application to SAR

NASA Astrophysics Data System (ADS)

Deming, Ross W.

2010-04-01

The Fourier Diffraction Theorem relates the data measured during electromagnetic, optical, or acoustic scattering experiments to the spatial Fourier transform of the object under test. The theorem is well-known, but since it is based on integral equations and complicated mathematical expansions, the typical derivation may be difficult for the non-specialist. In this paper, the theorem is derived and presented using simple geometry, plus undergraduatelevel physics and mathematics. For practitioners of synthetic aperture radar (SAR) imaging, the theorem is important to understand because it leads to a simple geometric and graphical understanding of image resolution and sampling requirements, and how they are affected by radar system parameters and experimental geometry. Also, the theorem can be used as a starting point for imaging algorithms and motion compensation methods. Several examples are given in this paper for realistic scenarios.

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization

NASA Astrophysics Data System (ADS)

Zhao, Jin; Han-Ming, Zhang; Bin, Yan; Lei, Li; Lin-Yuan, Wang; Ai-Long, Cai

2016-03-01

Sparse-view x-ray computed tomography (CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform (NUFFT) is presented in this work along with advanced total variation (TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively. Projected supported by the National High Technology Research and Development Program of China (Grant No. 2012AA011603) and the National Natural Science Foundation of China (Grant No. 61372172).

Fast Fourier transform-based Retinex and alpha-rooting color image enhancement

NASA Astrophysics Data System (ADS)

Grigoryan, Artyom M.; Agaian, Sos S.; Gonzales, Analysa M.

2015-05-01

Efficiency in terms of both accuracy and speed is highly important in any system, especially when it comes to image processing. The purpose of this paper is to improve an existing implementation of multi-scale retinex (MSR) by utilizing the fast Fourier transforms (FFT) within the illumination estimation step of the algorithm to improve the speed at which Gaussian blurring filters were applied to the original input image. In addition, alpha-rooting can be used as a separate technique to achieve a sharper image in order to fuse its results with those of the retinex algorithm for the sake of achieving the best image possible as shown by the values of the considered color image enhancement measure (EMEC).

Microvascular anastomosis guidance and evaluation using real-time three-dimensional Fourier-domain Doppler optical coherence tomography

PubMed Central

Ibrahim, Zuhaib; Tong, Dedi; Zhu, Shan; Mao, Qi; Pang, John; Andrew Lee, Wei Ping; Brandacher, Gerald; Kang, Jin U.

2013-01-01

Abstract. Vascular and microvascular anastomoses are critical components of reconstructive microsurgery, vascular surgery, and transplant surgery. Intraoperative surgical guidance using a surgical imaging modality that provides an in-depth view and three-dimensional (3-D) imaging can potentially improve outcome following both conventional and innovative anastomosis techniques. Objective postoperative imaging of the anastomosed vessel can potentially improve the salvage rate when combined with other clinical assessment tools, such as capillary refill, temperature, blanching, and skin turgor. Compared to other contemporary postoperative monitoring modalities—computed tomography angiograms, magnetic resonance (MR) angiograms, and ultrasound Doppler—optical coherence tomography (OCT) is a noninvasive high-resolution (micron-level), high-speed, 3-D imaging modality that has been adopted widely in biomedical and clinical applications. For the first time, to the best of our knowledge, the feasibility of real-time 3-D phase-resolved Doppler OCT (PRDOCT) as an assisted intra- and postoperative imaging modality for microvascular anastomosis of rodent femoral vessels is demonstrated, which will provide new insights and a potential breakthrough to microvascular and supermicrovascular surgery. PMID:23856833

Imaging of human finger nail-fold with MHz A-scan rate swept source optical coherence tomography

NASA Astrophysics Data System (ADS)

Poddar, Raju; Mondal, Indranil

2018-07-01

We present a non-invasive three-dimensional depth-resolved micro-structure and micro-vasculature imaging of a human fingernail-fold with a swept-source optical coherence tomography (ssOCT) system at a 1064 nm center wavelength. A phase variance OCT angiography (OCTA) method was implemented for motion contrast OCT imaging. A Fourier-domain mode-locked light source with an A-scan rate of 1.7 MHz (1 700 000 A-scans s‑1) was utilized for imaging. The experimental setup demonstrates OCT and OCTA imaging with an area of ~5 mm  ×  5 mm (within the Nyquist limit). Details of the ssOCTA system such as system parameters, scanning protocols, acquisition time, challenges, and scanning density are discussed. The selected features of the nail-fold structure and vascular networks are also deliberated. The system has potential for real-time monitoring of transdermal drug delivery, and the management and diagnosis of various diseases such as connective tissue diseases and Raynaud’s phenomenon.

The Fourier Imaging X-ray Spectrometer (FIXS) for the Argentinian, Scout-launched satelite de Aplicaciones Cienficas-1 (SAC-1)

NASA Technical Reports Server (NTRS)

Dennis, Brian R.; Crannell, Carol JO; Desai, Upendra D.; Orwig, Larry E.; Kiplinger, Alan L.; Schwartz, Richard A.; Hurford, Gordon J.; Emslie, A. Gordon; Machado, Marcos; Wood, Kent

1988-01-01

The Fourier Imaging X-ray Spectrometer (FIXS) is one of four instruments on SAC-1, the Argentinian satellite being proposed for launch by NASA on a Scout rocket in 1992/3. The FIXS is designed to provide solar flare images at X-ray energies between 5 and 35 keV. Observations will be made on arcsecond size scales and subsecond time scales of the processes that modify the electron spectrum and the thermal distribution in flaring magnetic structures.

Acceleration of integral imaging based incoherent Fourier hologram capture using graphic processing unit.

PubMed

Jeong, Kyeong-Min; Kim, Hee-Seung; Hong, Sung-In; Lee, Sung-Keun; Jo, Na-Young; Kim, Yong-Soo; Lim, Hong-Gi; Park, Jae-Hyeung

2012-10-08

Speed enhancement of integral imaging based incoherent Fourier hologram capture using a graphic processing unit is reported. Integral imaging based method enables exact hologram capture of real-existing three-dimensional objects under regular incoherent illumination. In our implementation, we apply parallel computation scheme using the graphic processing unit, accelerating the processing speed. Using enhanced speed of hologram capture, we also implement a pseudo real-time hologram capture and optical reconstruction system. The overall operation speed is measured to be 1 frame per second.

A Fourier-based textural feature extraction procedure

NASA Technical Reports Server (NTRS)

Stromberg, W. D.; Farr, T. G.

1986-01-01

A procedure is presented to discriminate and characterize regions of uniform image texture. The procedure utilizes textural features consisting of pixel-by-pixel estimates of the relative emphases of annular regions of the Fourier transform. The utility and derivation of the features are described through presentation of a theoretical justification of the concept followed by a heuristic extension to a real environment. Two examples are provided that validate the technique on synthetic images and demonstrate its applicability to the discrimination of geologic texture in a radar image of a tropical vegetated area.

Artifacts in Radar Imaging of Moving Targets

DTIC Science & Technology

2012-09-01

CA, USA, 2007. [11] B. Borden, Radar imaging of airborne targets: A primer for Applied mathematicians and Physicists . New York, NY: Taylor and... Project (0704–0188) Washington DC 20503. 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 21 September 2012 3. REPORT TYPE AND DATES COVERED...CW Continuous Wave DAC Digital to Analog Convertor DFT Discrete Fourier Transform FBP Filtered Back Projection FFT Fast Fourier Transform GPS

Determination of grain size distribution function using two-dimensional Fourier transforms of tone pulse encoded images

NASA Technical Reports Server (NTRS)

Generazio, E. R.

1986-01-01

Microstructural images may be tone pulse encoded and subsequently Fourier transformed to determine the two-dimensional density of frequency components. A theory is developed relating the density of frequency components to the density of length components. The density of length components corresponds directly to the actual grain size distribution function from which the mean grain shape, size, and orientation can be obtained.

Parameter Estimation for the Blind Restoration of Blurred Imagery.

DTIC Science & Technology

1986-09-01

17 Noise Process .... ............. 23 Restoration Methods .... .......... 26 Inverse Filter .... ........... 26 Wiener Filter...of Eq. (155) ....... .................... ... 64 Table 2 Restored Pictures and Noise Variances ........ . 69 v 5𔃼 5- viq °,. r -’ .’S’ .N’% N...restoration system. g(x,y) Degraded image. G(u,v) Discrete Fourier Transform of the degraded image. n(x,y) Noise . N(u,v) Discrete Fourier transform of n

Rapid estimation of 4DCT motion-artifact severity based on 1D breathing-surrogate periodicity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Guang, E-mail: lig2@mskcc.org; Caraveo, Marshall; Wei, Jie

2014-11-01

Purpose: Motion artifacts are common in patient four-dimensional computed tomography (4DCT) images, leading to an ill-defined tumor volume with large variations for radiotherapy treatment and a poor foundation with low imaging fidelity for studying respiratory motion. The authors developed a method to estimate 4DCT image quality by establishing a correlation between the severity of motion artifacts in 4DCT images and the periodicity of the corresponding 1D respiratory waveform (1DRW) used for phase binning in 4DCT reconstruction. Methods: Discrete Fourier transformation (DFT) was applied to analyze 1DRW periodicity. The breathing periodicity index (BPI) was defined as the sum of the largestmore » five Fourier coefficients, ranging from 0 to 1. Distortional motion artifacts (excluding blurring) of cine-scan 4DCT at the junctions of adjacent couch positions around the diaphragm were classified in three categories: incomplete, overlapping, and duplicate anatomies. To quantify these artifacts, discontinuity of the diaphragm at the junctions was measured in distance and averaged along six directions in three orthogonal views. Artifacts per junction (APJ) across the entire diaphragm were calculated in each breathing phase and phase-averaged APJ{sup ¯}, defined as motion-artifact severity (MAS), was obtained for each patient. To make MAS independent of patient-specific motion amplitude, two new MAS quantities were defined: MAS{sup D} is normalized to the maximum diaphragmatic displacement and MAS{sup V} is normalized to the mean diaphragmatic velocity (the breathing period was obtained from DFT analysis of 1DRW). Twenty-six patients’ free-breathing 4DCT images and corresponding 1DRW data were studied. Results: Higher APJ values were found around midventilation and full inhalation while the lowest APJ values were around full exhalation. The distribution of MAS is close to Poisson distribution with a mean of 2.2 mm. The BPI among the 26 patients was calculated with a value ranging from 0.25 to 0.93. The DFT calculation was within 3 s per 1DRW. Correlations were found between 1DRW periodicity and 4DCT artifact severity: −0.71 for MAS{sup D} and −0.73 for MAS{sup V}. A BPI greater than 0.85 in a 1DRW suggests minimal motion artifacts in the corresponding 4DCT images. Conclusions: The breathing periodicity index and motion-artifact severity index are introduced to assess the relationship between 1DRW and 4DCT. A correlation between 1DRW periodicity and 4DCT artifact severity has been established. The 1DRW periodicity provides a rapid means to estimate 4DCT image quality. The rapid 1DRW analysis and the correlative relationship can be applied prospectively to identify irregular breathers as candidates for breath coaching prior to 4DCT scan and retrospectively to select high-quality 4DCT images for clinical motion-management research.« less

Rapid estimation of 4DCT motion-artifact severity based on 1D breathing-surrogate periodicity

PubMed Central

Li, Guang; Caraveo, Marshall; Wei, Jie; Rimner, Andreas; Wu, Abraham J.; Goodman, Karyn A.; Yorke, Ellen

2014-01-01

Purpose: Motion artifacts are common in patient four-dimensional computed tomography (4DCT) images, leading to an ill-defined tumor volume with large variations for radiotherapy treatment and a poor foundation with low imaging fidelity for studying respiratory motion. The authors developed a method to estimate 4DCT image quality by establishing a correlation between the severity of motion artifacts in 4DCT images and the periodicity of the corresponding 1D respiratory waveform (1DRW) used for phase binning in 4DCT reconstruction. Methods: Discrete Fourier transformation (DFT) was applied to analyze 1DRW periodicity. The breathing periodicity index (BPI) was defined as the sum of the largest five Fourier coefficients, ranging from 0 to 1. Distortional motion artifacts (excluding blurring) of cine-scan 4DCT at the junctions of adjacent couch positions around the diaphragm were classified in three categories: incomplete, overlapping, and duplicate anatomies. To quantify these artifacts, discontinuity of the diaphragm at the junctions was measured in distance and averaged along six directions in three orthogonal views. Artifacts per junction (APJ) across the entire diaphragm were calculated in each breathing phase and phase-averaged APJ¯, defined as motion-artifact severity (MAS), was obtained for each patient. To make MAS independent of patient-specific motion amplitude, two new MAS quantities were defined: MASD is normalized to the maximum diaphragmatic displacement and MASV is normalized to the mean diaphragmatic velocity (the breathing period was obtained from DFT analysis of 1DRW). Twenty-six patients’ free-breathing 4DCT images and corresponding 1DRW data were studied. Results: Higher APJ values were found around midventilation and full inhalation while the lowest APJ values were around full exhalation. The distribution of MAS is close to Poisson distribution with a mean of 2.2 mm. The BPI among the 26 patients was calculated with a value ranging from 0.25 to 0.93. The DFT calculation was within 3 s per 1DRW. Correlations were found between 1DRW periodicity and 4DCT artifact severity: −0.71 for MASD and −0.73 for MASV. A BPI greater than 0.85 in a 1DRW suggests minimal motion artifacts in the corresponding 4DCT images. Conclusions: The breathing periodicity index and motion-artifact severity index are introduced to assess the relationship between 1DRW and 4DCT. A correlation between 1DRW periodicity and 4DCT artifact severity has been established. The 1DRW periodicity provides a rapid means to estimate 4DCT image quality. The rapid 1DRW analysis and the correlative relationship can be applied prospectively to identify irregular breathers as candidates for breath coaching prior to 4DCT scan and retrospectively to select high-quality 4DCT images for clinical motion-management research. PMID:25370631

Hyper-spectral imaging of aircraft exhaust plumes

NASA Astrophysics Data System (ADS)

Bowen, Spencer; Bradley, Kenneth; Gross, Kevin; Perram, Glen; Marciniak, Michael

2008-10-01

An imaging Fourier-transform spectrometer has been used to determine low spatial resolution temperature and chemical species concentration distributions of aircraft jet engine exhaust plumes. An overview of the imaging Fourier transform spectrometer and the methodology of the project is presented. Results to date are shared and future work is discussed. Exhaust plume data from a Turbine Technologies, LTD, SR-30 turbojet engine at three engine settings was collected using a Telops Field-portable Imaging Radiometric Spectrometer Technology Mid-Wave Extended (FIRST-MWE). Although the plume exhibited high temporal frequency fluctuations, temporal averaging of hyper-spectral data-cubes produced steady-state distributions, which, when co-added and Fourier transformed, produced workable spectra. These spectra were then reduced using a simplified gaseous effluent model to fit forward-modeled spectra obtained from the Line-By-Line Radiative Transfer Model (LBLRTM) and the high-resolution transmission (HITRAN) molecular absorption database to determine approximate temperature and concentration distributions. It is theorized that further development of the physical model will produce better agreement between measured and modeled data.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Foxley, Sean, E-mail: sean.foxley@ndcn.ox.ac.uk; Karczmar, Gregory S.; Domowicz, Miriam

Purpose: Widely used MRI methods show brain morphology both in vivo and ex vivo at very high resolution. Many of these methods (e.g., T{sub 2}{sup *}-weighted imaging, phase-sensitive imaging, or susceptibility-weighted imaging) are sensitive to local magnetic susceptibility gradients produced by subtle variations in tissue composition. However, the spectral resolution of commonly used methods is limited to maintain reasonable run-time combined with very high spatial resolution. Here, the authors report on data acquisition at increased spectral resolution, with 3-dimensional high spectral and spatial resolution MRI, in order to analyze subtle variations in water proton resonance frequency and lineshape that reflectmore » local anatomy. The resulting information compliments previous studies based on T{sub 2}{sup *} and resonance frequency. Methods: The proton free induction decay was sampled at high resolution and Fourier transformed to produce a high-resolution water spectrum for each image voxel in a 3D volume. Data were acquired using a multigradient echo pulse sequence (i.e., echo-planar spectroscopic imaging) with a spatial resolution of 50 × 50 × 70 μm{sup 3} and spectral resolution of 3.5 Hz. Data were analyzed in the spectral domain, and images were produced from the various Fourier components of the water resonance. This allowed precise measurement of local variations in water resonance frequency and lineshape, at the expense of significantly increased run time (16–24 h). Results: High contrast T{sub 2}{sup *}-weighted images were produced from the peak of the water resonance (peak height image), revealing a high degree of anatomical detail, specifically in the hippocampus and cerebellum. In images produced from Fourier components of the water resonance at −7.0 Hz from the peak, the contrast between deep white matter tracts and the surrounding tissue is the reverse of the contrast in water peak height images. This indicates the presence of a shoulder in the water resonance that is not present at +7.0 Hz and may be specific to white matter anatomy. Moreover, a frequency shift of 6.76 ± 0.55 Hz was measured between the molecular and granular layers of the cerebellum. This shift is demonstrated in corresponding spectra; water peaks from voxels in the molecular and granular layers are consistently 2 bins apart (7.0 Hz, as dictated by the spectral resolution) from one another. Conclusions: High spectral and spatial resolution MR imaging has the potential to accurately measure the changes in the water resonance in small voxels. This information can guide optimization and interpretation of more commonly used, more rapid imaging methods that depend on image contrast produced by local susceptibility gradients. In addition, with improved sampling methods, high spectral and spatial resolution data could be acquired in reasonable run times, and used for in vivo scans to increase sensitivity to variations in local susceptibility.« less

Quantitative holographic interferometry applied to combustion and compressible flow research

NASA Astrophysics Data System (ADS)

Bryanston-Cross, Peter J.; Towers, D. P.

1993-03-01

The application of holographic interferometry to phase object analysis is described. Emphasis has been given to a method of extracting quantitative information automatically from the interferometric fringe data. To achieve this a carrier frequency has been added to the holographic data. This has made it possible, firstly to form a phase map using a fast Fourier transform (FFT) algorithm. Then to `solve,' or unwrap, this image to give a contiguous density map using a minimum weight spanning tree (MST) noise immune algorithm, known as fringe analysis (FRAN). Applications of this work to a burner flame and a compressible flow are presented. In both cases the spatial frequency of the fringes exceed the resolvable limit of conventional digital framestores. Therefore, a flatbed scanner with a resolution of 3200 X 2400 pixels has been used to produce very high resolution digital images from photographs. This approach has allowed the processing of data despite the presence of caustics, generated by strong thermal gradients at the edge of the combustion field. A similar example is presented from the analysis of a compressible transonic flow in the shock wave and trailing edge regions.