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1

Quantum arithmetic with the Quantum Fourier Transform

The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.

Lidia Ruiz-Perez; Juan Carlos Garcia-Escartin

2014-11-21

2

Quantum fast Fourier transform using multilevel atoms

We propose an implementation of the quantum fast Fourier transform algorithm in an entangled system of multilevel atoms. The Fourier transform occurs naturally in the unitary time evolution of energy eigenstates and is used to define an alternate wave-packet basis for quantum information in the atom. A change of basis from energy levels to wave packets amounts to a discrete quantum Fourier transform within each atom. The algorithm then reduces to a series of conditional phase transforms between two entangled atoms in mixed energy and wave-packet bases. We show how to implement such transforms using wave-packet control of the internal states of the ions in the linear ion-trap scheme for quantum computing.

Ashok Muthukrishnan; C. R. Stroud Jr

2001-12-03

3

Quantum Fourier Transform Over Galois Rings

Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum algorithms and quantum error correction codes over Galois rings, we study the quantum Fourier transform (QFT) over Galois rings and prove it can be efficiently preformed on a quantum computer. The properties of the QFT over Galois rings lead to the quantum algorithm for hidden linear structures over Galois rings.

Yong Zhang

2009-04-16

4

Semiclassical Fourier Transform for Quantum Computation

It is shown that the Fourier transform preceding the final measurement in Shor's algorithm for factorization on a quantum computer can be carried out in a semiclassical way by using the ``classical'' (macroscopic) signal resulting from measuring one bit to determine the type of measurement carried out on the next bit, and so forth. In this way all the two-bit

Robert B. Griffiths; Chi-Sheng Niu

1996-01-01

5

Purple bacteria and quantum Fourier transform

The LH-II of purple bacteria Rhodospirillum (Rs.) molischianum and Rhodopseudomonas (Rps.) acidophila adopts a highly symmetrical ring shape, with a radius of about 7 nm. In the case of Rps. acidophila the ring has a ninefold symmetry axis, and in LH-II from Rs. molischianum the ring has an eightfold symmetry axis. These rings are found to exibit two bands of excitons. A simplified mathematical description of the exciton states is given in Hu, X. & Schulten, K. (1997) Physics Today 50, 28-34. Using this description, we will show, by suitable labeling of the lowest energy (Qy) excited states of individual BChls, that the resulting exciton states are the quantum Fourier transform of the BChls excited states. For Rs. molischianum ring exciton states will be modeled as the four qubit quantum Fourier transform and the explicit circuit will be derived. Exciton states for Rps. acidophila ring cannot be modeled with an integer number of qubits. Both quantum Fourier transforms are instances of the hidden subgroup problem and this opens up a possibility that both purple bacteria implement an efficient quantum circuit for light harvesting.

Samir Lipovaca

2007-02-22

6

Resource requirements for a fault-tolerant quantum Fourier transform

NASA Astrophysics Data System (ADS)

We investigate resource requirements for a fault-tolerant quantum Fourier transform. The quantum Fourier transform is a basic subroutine for quantum algorithms which provide an exponential speedup over known classical ones, such as Shor's algorithm for factoring. To implement single-qubit rotations required for a quantum Fourier transform in a fault-tolerant manner, we consider two types of approaches: gate synthesis and state distillation. While the gate synthesis approximates single-qubit rotations with basic quantum operations, the state distillation allows one to perform single-qubit rotations for a quantum Fourier transform exactly. It is unknown, however, which approach is better for a quantum Fourier transform. Here we develop a state-distillation method optimized for a quantum Fourier transform and compare this performance with those of state-of-the-art techniques for gate synthesis without and with ancillary states (ancillas). The performance is evaluated with the resource requirement for a quantum Fourier transform. The resource is measured by the total number of ? /8 gates denoted by T , which is called the T count. Contrary to the expectation, the T count for the state distillation is considerably larger than those for the ancilla-free and ancilla-assisted gate synthesis. Thus, we conclude that the ancilla-assisted gate synthesis is a better approach to a fault-tolerant quantum Fourier transform.

Goto, Hayato

2014-11-01

7

Structural stability of the quantum Fourier transform

NASA Astrophysics Data System (ADS)

While it is important to investigate the negative effects of decoherence on the performance of quantum information processors, Landauer was one of the first to point out that an equally basic problem, i.e., the effects of unavoidable hardware flaws in the real-world implementations of quantum gates, needs to be investigated as well. Following Landauer's suggestion, we investigated the structural stability of the quantum Fourier transform (QFT) via significantly changing the analytical form of its controlled rotation gates, thus modeling structural flaws in the Hamiltonian of the QFT. Three types of modified rotation gates were investigated, numerically and analytically, changing the exact QFT rotation angles ? /2^j to (1) ? /? ^j , (2) ? /2 j^{? } , and (3) ? /log _{? }(j+1) , where ? , ? , and ? are constants and j is the integer distance between QFT qubits. Surprisingly good performance is observed in all the three cases for a wide range of ? , ? , and ? . This demonstrates the structural stability of the QFT Hamiltonian. Our results also demonstrate that the precise implementation of QFT rotation angles is not critical as long as the angles (roughly) observe a monotonic decrease in j (hierarchy). This result is important since it indicates that stringent tolerances do not need to be imposed in the actual manufacturing process of quantum information hardware components.

Nam, Y. S.; Blümel, R.

2015-01-01

8

Quantum operation, quantum Fourier transform and semi-definite programming

We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier transform, is found for this class of operations. A more general class of operations on qudits is also considered and its completely positive condition is reduced to the well-known semi-definite programming problem.

Runyao Duan; Zhengfeng Ji; Yuan Feng; Mingsheng Ying

2003-12-25

9

From fractional Fourier transformation to quantum mechanical fractional squeezing transformation

NASA Astrophysics Data System (ADS)

By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function, i.e., tan ? ? tanh ?, sin ? ? sinh ?, we find the quantum mechanical fractional squeezing transformation (FrST) which satisfies additivity. By virtue of the integration technique within the ordered product of operators (IWOP) we derive the unitary operator responsible for the FrST, which is composite and is made of ei?a†a/2 and exp . The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches. Project supported by the National Natural Science Foundation of China (Grant No. 11304126), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20130532), the Natural Science Fund for Colleges and Universities in Jiangsu Province, China (Grant No. 13KJB140003), the Postdoctoral Science Foundation of China (Grant No. 2013M541608), and the Postdoctoral Science Foundation of Jiangsu Province, China (Grant No. 1202012B).

Lv, Cui-Hong; Fan, Hong-Yi; Li, Dong-Wei

2015-02-01

10

Efficient classical simulation of the approximate quantum Fourier transform

We present a method for classically simulating quantum circuits based on the tensor contraction model of Markov and Shi (quant-ph/0511069). Using this method we are able to classically simulate the approximate quantum Fourier transform in polynomial time. Moreover, our approach allows us to formulate a condition for the composability of simulable quantum circuits. We use this condition to show that any circuit composed of a constant number of approximate quantum Fourier transform circuits and log-depth circuits with limited interaction range can also be efficiently simulated.

Nadav Yoran; Anthony J. Short

2006-11-23

11

Scaling and better approximating quantum Fourier transform by higher radices

Quantum Fourier Transform (QFT) plays a principal role in the development of efficient quantum algorithms. Since the number of quantum bits that can currently built is limited, while many quantum technologies are inherently three- (or more) valued, we consider extending the reach of the realistic quantum systems by building a QFT over ternary quantum digits. Compared to traditional binary QFT, the q-valued transform improves approximation properties and increases the state space by a factor of (q/2)n. Further, we use non-binary QFT derivation to generalize and improve the approximation bounds for QFT.

Zeljko Zilic; Katarzyna Radecka

2007-02-20

12

Quantum computation of Fourier transforms over symmetric groups

Many algorithmic developments in quantum com- plexity theory, including Shor's celebrated algorithms for factoring and discrete logs, have made use of Fourier transforms over abelian groups. That is, at some point in the computation, the macline is in a superposition of states corresponding to elements of a finite abelian group G, and in quantum polynomial time (i.e., poly- nomial in

Robert Beals

1997-01-01

13

Efficient implementations of the Quantum Fourier Transform: an experimental perspective

The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the implementation. We focus here on an interesting decomposition of the QFT as a product of the non-selective Hadamard transformation followed by multiqubit gates corresponding to square- and higher-roots of controlled-NOT gates. This decomposition requires only O(n) operations and is thus linear in the number of qubits $n$. The schemes were implemented on a two-qubit NMR quantum information processor and the resultant density matrices reconstructed using standard quantum state tomography techniques. Their experimental fidelities have been measured and compared.

Kavita Dorai; Dieter Suter

2002-11-06

14

Uncertainty Principles for the Fourier Transforms in Quantum Calculus

Some properties of the $q$-Fourier-sine transform are studied and $q$-analogues of the Heisenberg uncertainty principle is derived for the $q$-Fourier-cosine transform studied in \\cite{FB} and for the $q$-Fourier-sine transform.

Neji Bettaibi; Ahmed Fitouhi; Wafa Binous

2006-02-28

15

Fast parallel circuits for the quantum Fourier transform

We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n + log log (1/epsilon)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2^n with error bounded by epsilon. Thus, even for exponentially small error, our circuits have depth O(log n). The best previous depth bound was O(n), even for approximations with constant error. Moreover, our circuits have size O(n log (n/epsilon)). We also give an upper bound of O(n (log n)^2 log log n) on the circuit size of the exact QFT modulo 2^n, for which the best previous bound was O(n^2). As an application of the above depth bound, we show that Shor's factoring algorithm may be based on quantum circuits with depth only O(log n) and polynomial-size, in combination with classical polynomial-time pre- and post-processing. In the language of computational complexity, this implies that factoring is in the complexity class ZPP^BQNC, where BQNC is the class of problems computable with bounded-error probability by quantum circuits with poly-logarithmic depth and polynomial size. Finally, we prove an Omega(log n) lower bound on the depth complexity of approximations of the QFT with constant error. This implies that the above upper bound is asymptotically optimal (for a reasonable range of values of epsilon).

Richard Cleve; John Watrous

2000-06-01

16

Obtaining the Quantum Fourier Transform from the Classical FFT with QR Decomposition

We present the detailed process of converting the classical Fourier Transform algorithm into the quantum one by using QR decomposition. This provides an example of a technique for building quantum algorithms using classical ones. The Quantum Fourier Transform is one of the most important quantum subroutines known at present, used in most algorithms that have exponential speed up compared to the classical ones. We briefly review Fast Fourier Transform and then make explicit all the steps that led to the quantum formulation of the algorithm, generalizing Coppersmith's work.

F. L. Marquezino; R. Portugal; F. D. Sasse

2010-05-20

17

Evolution of a human-competitive quantum fourier transform algorithm using genetic programming

In this paper, we show how genetic programming (GP) can be used to evolve system-size-independent quantum algorithms, and present a human-competitive Quantum Fourier Transform (QFT) algorithm evolved by GP.

Paul Massey; John A. Clark; Susan Stepney

2005-01-01

18

Fast parallel circuits for the quantum Fourier transform

We give new bounds on the circuit complexity of the quan- tum Fourier transform (QFT). We give an upper bound of on the circuit depth for comput- ing an approximation of the QFT with respect to the mod- ulus with error bounded by . Thus, even for exponen- tially small error, our circuits have depth . The best previous depth

Richard Cleve; John Watrous

2000-01-01

19

NASA Astrophysics Data System (ADS)

Knot and link invariants naturally arise from any braided Hopf algebra. We consider the computational complexity of the invariants arising from an elementary family of finite-dimensional Hopf algebras: quantum doubles of finite groups [denoted , for a group G]. These induce a rich family of knot invariants and, additionally, are directly related to topological quantum computation. Regarding algorithms for these invariants, we develop quantum circuits for the quantum Fourier transform over ; in general, we show that when one can uniformly and efficiently carry out the quantum Fourier transform over the centralizers Z( g) of the elements of G, one can efficiently carry out the quantum Fourier transform over . We apply these results to the symmetric groups to yield efficient circuits for the quantum Fourier transform over . With such a Fourier transform, it is straightforward to obtain additive approximation algorithms for the related link invariant. As for hardness results, first we note that in contrast to those concerning the Jones polynomial—where the images of the braid group representations are dense in the unitary group—the images of the representations arising from are finite. This important difference appears to be directly reflected in the complexity of these invariants. While additively approximating "dense" invariants is -complete and multiplicatively approximating them is -complete, we show that certain invariants (such as invariants) are -hard to additively approximate, -hard to multiplicatively approximate, and -hard to exactly evaluate. To show this, we prove that, for groups (such as A n ) which satisfy certain properties, the probability of success of any randomized computation can be approximated to within any by the plat closure. Finally, we make partial progress on the question of simulating anyonic computation in groups uniformly as a function of the group size. In this direction, we provide efficient quantum circuits for the Clebsch-Gordan transform over for "fluxon" irreps, i.e., irreps of characterized by a conjugacy class of G. For general irreps, i.e., those which are associated with a conjugacy class of G and an irrep of a centralizer, we present an efficient implementation under certain conditions, such as when there is an efficient Clebsch-Gordan transform over the centralizers (this could be a hard problem for some groups). We remark that this also provides a simulation of certain anyonic models of quantum computation, even in circumstances where the group may have size exponential in the size of the circuit.

Krovi, Hari; Russell, Alexander

2015-03-01

20

We perform Bell's measurement and perform quantum Fourier transform with the classical vortex beam. The violation of Bell's inequality for such a non-separable classical correlation has been demonstrated experimentally. Based on the classical vortex beam and nonquantum entanglement between the polarization and orbital angular momentum, the Hadamard gates and conditional phase gates have been designed. Furthermore, a quantum Fourier transform has been implemented experimentally, which is the crucial final step in Shor's algorithm

Song, Xinbing; Qin, Hongwei; Li, Pengyun; Zhang, Xiangdong

2015-01-01

21

We perform Bell's measurement and perform quantum Fourier transform with the classical vortex beam. The violation of Bell's inequality for such a non-separable classical correlation has been demonstrated experimentally. Based on the classical vortex beam and nonquantum entanglement between the polarization and orbital angular momentum, the Hadamard gates and conditional phase gates have been designed. Furthermore, a quantum Fourier transform has been implemented experimentally, which is the crucial final step in Shor's algorithm

Xinbing Song; Yifan Sun; Hongwei Qin; Pengyun Li; Xiangdong Zhang

2015-02-10

22

Evolution of a Human-Competitive Quantum Fourier Transform Algorithm Using Genetic Programming

programming (GP) can be used to evolve system-size-independent quantum algorithms, and present a human-competitive performance for quantum algorithm design? In this paper we show how GP has been used to evolve a humanEvolution of a Human-Competitive Quantum Fourier Transform Algorithm Using Genetic Programming Paul

Fernandez, Thomas

23

Random fractional Fourier transform.

We propose a novel random fractional Fourier transform by randomizing the transform kernel function of the conventional fractional Fourier transform. The random fractional Fourier transform inherits the excellent mathematical properties from the fractional Fourier transform and can be easily implemented in optics. As a primary application the random fractional Fourier transform can be directly used in optical image encryption and decryption. The double phase encoding image encryption schemes can thus be modeled with cascaded random fractional Fourier transformers. PMID:17671545

Liu, Zhengjun; Liu, Shutian

2007-08-01

24

Performance scaling of Shor's algorithm with a banded quantum Fourier transform

NASA Astrophysics Data System (ADS)

In excellent agreement with our numerical simulations of Shor's algorithm, equipped with a truncated quantum Fourier transform of bandwidth b, we find that its performance scales ˜2-?bn, where n is the number of qubits, ?b=1.1×2-2b, and the bandwidth b is the number of quantum states coupled by the quantum Fourier transform. Nonexponential behavior is observed for small n and explained analytically. The large-n exponential scaling implies that b=7 is sufficient to operate a 1000-qubit quantum computer running Shor's algorithm on the 95% performance level and implies hardware savings of the order of half a million rotation gates.

Nam, Y. S.; Blümel, R.

2012-10-01

25

Scale invariance and efficient classical simulation of the quantum Fourier transform

We provide numerical evidence that the quantum Fourier transform can be efficiently represented in a matrix product operator with a size growing relatively slowly with the number of qubits. Additionally, we numerically show that the tensors in the operator converge to a common tensor as the number of qubits in the transform increases. Together these results imply that the application of the quantum Fourier transform to a matrix product state with $n$ qubits of maximum Schmidt rank $\\chi$ can be simulated in $O(n (log(n))^2 \\chi^2)$ time. We perform such simulations and quantify the error involved in representing the transform as a matrix product operator and simulating the quantum Fourier transform of periodic states.

Kieran J. Woolfe; Charles D. Hill; Lloyd C. L. Hollenberg

2014-06-04

26

Large quantum Fourier transforms are never exactly realized by braiding conformal blocks

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set {l_brace}U(2), controlled-NOT{r_brace}, the discrete Fourier transforms F{sub N}=({omega}{sup ij}){sub NxN}, i,j=0,1,...,N-1, {omega}=e{sup 2{pi}}{sup i} at {sup {approx}}{sup sol{approx}} at {sup N}, can be realized exactly by quantum circuits of size O(n{sup 2}), n=ln N, and so can the discrete sine or cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms F{sub N} and the discrete sine or cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that an approximation is unavoidable in the implementation of Fourier transforms by braiding conformal blocks.

Freedman, Michael H. [Microsoft Project Q, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030 (United States); Wang, Zhenghan [Microsoft Project Q, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030 (United States); Department of Mathematics, Indiana University, Bloomington, Indiana 47405 (United States)

2007-03-15

27

A new method of quantum state tomography for quantum information processing is described. The method based on two-dimensional Fourier transform technique involves detection of all the off-diagonal elements of the density matrix in a two-dimensional experiment. All the diagonal elements are detected in another one-dimensional experiment. The method is efficient and applicable to a wide range of spin systems. The proposed method is explained using a 2 qubit system and demonstrated by tomographing arbitrary complex density matrices of 2 and 4 qubit systems using simulations.

Ranabir Das; T. S. Mahesh; Anil Kumar

2002-12-19

28

Novel image encryption/decryption based on quantum Fourier transform and double phase encoding

NASA Astrophysics Data System (ADS)

A novel gray-level image encryption/decryption scheme is proposed, which is based on quantum Fourier transform and double random-phase encoding technique. The biggest contribution of our work lies in that it is the first time that the double random-phase encoding technique is generalized to quantum scenarios. As the encryption keys, two phase coding operations are applied in the quantum image spatial domain and the Fourier transform domain respectively. Only applying the correct keys, the original image can be retrieved successfully. Because all operations in quantum computation must be invertible, decryption is the inverse of the encryption process. A detailed theoretical analysis is given to clarify its robustness, computational complexity and advantages over its classical counterparts. It paves the way for introducing more optical information processing techniques into quantum scenarios.

Yang, Yu-Guang; Xia, Juan; Jia, Xin; Zhang, Hua

2013-11-01

29

Fourier Transform Pairs The Fourier transform transforms a function of

Fourier Transform Pairs The Fourier transform transforms a function of time, f(t), into a function of frequency, F(s): F {f(t)}(s) = F(s) = Z - f(t)e- j2st dt. The inverse Fourier transform transforms a func. The inverse Fourier transform of the Fourier trans- form is the identity transform: f(t) = Z - Z - f()e- j2s

Masci, Frank

30

Analyzing Signals Fourier transform

Page 1 1 Analyzing Signals Fourier transform s frequency content s linear combination of sin frequency analysis s windowed Fourier transform 6 #12;Page 4 7 Gabor Transform function to analyze window Gabor Transform Spatial domain Gabor domain b #12;Page 5 9 Gabor Transform Problems s discrete version

Sweldens, Wim

31

Cavity QED implementation of the discrete quantum Fourier transform

scheme relies on the passage of a series of suitably chosen atoms through a sequence of classical fields and high- Q cavities. The QFT maps each state ua& into a superposition given by NQFTua&5 1A2q (c50 2q21 e2piac/2 quc&, ~1! where q... is the number of qubits. Our aim is the implemen- tation of this mapping using quantum logic gates. As quan- tum logic gates operate on qubits, we consider a representa- tion of state ua& in terms of qubits. Thus, for example, u9& [u1,0,0,1&. For 2q.a.2q21...

Scully, Marlan O.; Zubairy, M. Suhail

2002-01-01

32

Efficient classical simulation of the semi-classical Quantum Fourier Transform

A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability of the quantum Fourier transform (QFT). In this note, we show that one can demonstrate a number of simulability results for QFT circuits in a straightforward manner using Griffiths and Niu's semi-classical QFT construction [Phys. Rev. Lett. 76, 3228 (1996)]. We then discuss the consequences of these results in the context of Shor's factorisation algorithm.

Daniel E. Browne

2006-12-03

33

Unraveling quantum pathways using optical 3D Fourier-transform spectroscopy

Predicting and controlling quantum mechanical phenomena require knowledge of the system Hamiltonian. A detailed understanding of the quantum pathways used to construct the Hamiltonian is essential for deterministic control and improved performance of coherent control schemes. In complex systems, parameters characterizing the pathways, especially those associated with inter-particle interactions and coupling to the environment, can only be identified experimentally. Quantitative insight can be obtained provided the quantum pathways are isolated and independently analysed. Here we demonstrate this possibility in an atomic vapour using optical three-dimensional Fourier-transform spectroscopy. By unfolding the system’s nonlinear response onto three frequency dimensions, three-dimensional spectra unambiguously reveal transition energies, relaxation rates and dipole moments of each pathway. The results demonstrate the unique capacity of this technique as a powerful tool for resolving the complex nature of quantum systems. This experiment is a critical step in the pursuit of complete experimental characterization of a system’s Hamiltonian. PMID:23340430

Li, Hebin; Bristow, Alan D.; Siemens, Mark E.; Moody, Galan; Cundiff, Steven T.

2013-01-01

34

NASA Astrophysics Data System (ADS)

We demonstrate the use of a Fourier Transform Infrared microscope system to detect and measure electroreflectance (ER) from mid-infrared quantum cascade laser (QCL) device. To characterize intersubband transition (ISBT) energies in a functioning QCL device, a microscope is used to focus the probe on the QCL cleaved mirror. The measured ER spectra exhibit resonance features associated to ISBTs under applied electric field in agreement with the numerical calculations and comparable to observed photocurrent, and emission peaks. The method demonstrates the potential as a characterization tool for QCL devices.

Enobio, Eli Christopher I.; Ohtani, Keita; Ohno, Yuzo; Ohno, Hideo

2013-12-01

35

Fourier transform mass spectrometry.

This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802

Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

2011-07-01

36

Fourier Transforms, Fourier Series and the FFT

NSDL National Science Digital Library

The goal of this module is to give students an understanding of the one-dimensional Fourier Transform, both mathematically and computationally, with a focus on finding periodicity in data. To motivate the study of the Fourier Transform, the students will be presented with certain application areas, such as searching for periodic patterns in CO2 data and differentiating between two sound signals using their power spectra. Students will explore some computational issues and challenges of the Discrete and Fast Fourier Transforms.

Lisette de Pillis

37

NASA Astrophysics Data System (ADS)

Exciton dephasing and relaxation dynamics are studied in a GaAs quantum dot ensemble using optical twodimensional Fourier transform spectroscopy. We measure the temperature and excitation-density dependence of the exciton ground-state homogeneous lineshape of quantum dots within the ensemble and show that acoustic phonon sidebands are absent. The linewidth increases nonlinearly with temperature from 6 to 50 K and the behavior is well-described by an Arrhenius equation with an offset. The absence of a phonon-activation peak in the spectra reveals that elastic exciton-phonon scattering is the primary dephasing mechanism and the results can be explained qualitatively using an extension of the independent Boson model that includes quadratic coupling in the phonon displacement coordinates. At temperatures >= 35 K, spectral features associated with phonon-assisted population transfer of excitons out of the quantum dots and into quantum wells states begin to appear.

Moody, Galan; Siemens, Mark E.; Bristow, Alan D.; Dai, Xingcan; Karaiskaj, Denis; Bracker, Allan S.; Gammon, Daniel; Cundiff, Steven T.

2012-03-01

38

Fourier Transform Infrared (FTIR) Spectroscopy

Fourier Transform Infrared (FTIR) Spectroscopy Klaus Gerwert, Lehrstuhl fuÂ¨r Biophysik, Ruhr Transform IR by Johannes Orphal. Fourier transform infrared (FTIR) spectroscopy is an experimental technique information on molecular structure, chemical bondingandmolecularenvironment.Formanyyears,FTIR has been

Gerwert, Klaus

39

Scaling laws for Shor's algorithm with a banded quantum Fourier transform

NASA Astrophysics Data System (ADS)

We investigate the performance of a streamlined version of Shor's algorithm in which the quantum Fourier transform is replaced by a banded version that, for each qubit, retains only coupling to its b nearest neighbors. Defining the performance P(n,b) of the n-qubit algorithm for bandwidth b as the ratio of the success rates of Shor's algorithm equipped with the banded and the full-bandwidth (b=n-1) versions of the quantum Fourier transform, our numerical simulations show that P(n,b)?exp[-?max2(n,b)/100] for n

Nam, Y. S.; Blümel, R.

2013-03-01

40

Fourier Transform Mass Spectrometry.

ERIC Educational Resources Information Center

Discusses the nature of Fourier transform mass spectrometry and its unique combination of high mass resolution, high upper mass limit, and multichannel advantage. Examines its operation, capabilities and limitations, applications (ion storage, ion manipulation, ion chemistry), and future applications and developments. (JN)

Gross, Michael L.; Rempel, Don L.

1984-01-01

41

Imaging Fourier transform spectrometer

NASA Astrophysics Data System (ADS)

Design considerations and experimental measurements from an imaging Fourier transform spectrometer are presented. The system is based on the Bomem MB-series of Fourier transform interferometer and is capable of more than 8 frames/second at 4 cm(superscript -1 apodized spectral resolution. The interferometer features dual output beams, allowing for example, the coverage of two different spectral ranges using a short-wave array and a long- wave array. The present system uses a set of two 8 X 8 InSb detector arrays to cover the 2 to 5.3 micrometers spectral range on two coaligned fields of view of 4 mrad X 4 mrad and 1 mrad X 1 mrad. Predicted noise equivalent spectral radiance as well as instrument lineshape are compared to measurements on the actual system. Particular emphasis is devoted to the behavior of the instrument lineshape with respect to off-axis position in the focal plane.

Villemaire, Andre J.; Fortin, Serge; Giroux, Jean; Smithson, Tracy; Oermann, Raymond J.

1995-06-01

42

NASA Technical Reports Server (NTRS)

We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).

Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.

2012-01-01

43

Optical transformation from chirplet to fractional Fourier transformation kernel

We find a new integration transformation which can convert a chirplet function to fractional Fourier transformation kernel, this new transformation is invertible and obeys Parseval theorem. Under this transformation a new relationship between a phase space function and its Weyl-Wigner quantum correspondence operator is revealed.

Hong-yi Fan; Li-yun Hu

2009-02-11

44

NASA Astrophysics Data System (ADS)

In this letter, we have pointed out some problems existed in (Yang et al. in Quantum Inf Process 12(11):3477-3493,

Song, Xian-Hua; Niu, Xia-Mu

2014-06-01

45

Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a generalized Kronecker product is given. Applications include re-development of the networks for computing the Walsh-Hadamard and the quantum Fourier transform. New networks for two wavelet transforms are given. Quantum computation of Fourier transforms for non-Abelian groups is defined. A slightly relaxed definition is shown to simplify the analysis and the networks that computes the transforms. Efficient networks for computing such transforms for a class of metacyclic groups are introduced. A novel network for computing a Fourier transform for a group used in quantum error-correction is also given.

Peter Hoyer

1997-02-12

46

Multi-dimensional real Fourier transform

NASA Technical Reports Server (NTRS)

Four subroutines compute one-dimensional and multi-dimensional Fourier transforms for real data, multi-dimensional complex Fourier transforms, and multi-dimensional sine, cosine and sine-cosine transforms. Subroutines use Cooley-Tukey fast Fourier transform. In all but one-dimensional case, transforms are calculated in up to six dimensions.

Krogh, F. T.

1971-01-01

47

Discrete Fourier Transform on Multicores

This paper gives an overview on the techniques needed to implement the discrete Fourier transform (DFT) efficiently on current multicore systems. The focus is on Intel compatible multicores but we also discuss the IBM Cell, and briefly, graphics processing units (GPUs). The performance optimization is broken down into three key challenges: paral- lelization, vectorization, and memory hierarchy optimization. In each

Franz Franchetti; Markus P; Yevgen Voronenko; Srinivas Chellappa; Jos ´ e; M. F. Moura

2010-01-01

48

The Geostationary Fourier Transform Spectrometer

The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for an earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. The GeoFTS instrument is a half meter cube size instrument designed to operate in geostationary orbit as a secondary “hosted” payload on a commercial geostationary satellite mission. The

Richard Key; Stanley Sander; Annmarie Eldering; David Rider; Jean-Francois Blavier; Dmitriy Bekker; Yen-Hung Wu; Ken Manatt

2012-01-01

49

AIR POLLUTION MEASUREMENT BY FOURIER TRANSFORM SPECTROSCOPY

Fourier transform spectroscopy substantially reduces the limitations on infrared methods of pollution measurement. EPA has used long path cells and Fourier transform spectrometers for pollutant measurement both in the laboratory and in the field. Labile pollutants are best measur...

50

ERIC Educational Resources Information Center

This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…

Debnath, Lokenath

2012-01-01

51

Quantum Wavelet Transforms: Fast Algorithms and Complete Circuits

The quantum Fourier transform (QFT), a quantum analog of the classical Fourier transform, has been shown to be a powerful tool in developing quantum algorithms. However, in classical computing there is another class of unitary transforms, the wavelet transforms, which are every bit as useful as the Fourier transform. Wavelet transforms are used to expose the multi-scale structure of a

Amir Fijany; Colin P. Williams

1998-01-01

52

Fourier Transform Mass Spectrometry Lab

NSDL National Science Digital Library

This Web site discusses Boston University's Fourier Transform Mass Spectrometry (FTMS) Lab's devotion to the improvement of FTMS instrumentation and methods for its everyday biochemical functions. After discovering the importance of FTMS, visitors can find out about the lab's work in the enhancement of electrospray ion source and Cryogenic FTMS. Students can learn about the modern biochemistry's utilization of both traditional instrumentation such as gel electrophoresis and the latest devices including high performance chromatography, nuclear magnetic resonance, and X-ray crystallography. By downloading the Boston University Data Analysis (B.U.D.A.), researchers can participate in the development of analysis software for FTMS.

53

Tunable fractional-order Fourier transformer

A fractional two-dimensional Fourier transformer whose orders are tuned by means of optical quadrupoles is described. It is shown that in the optical scheme considered, the Fourier-transform order a element of [0,1] in one of the mutually orthogonal planes corresponds to the transform order (2-a) in another plane, i.e., to inversion and inverse Fourier transform of the order a. (laser modes and beams)

Malyutin, A A [A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow (Russian Federation)

2006-01-31

54

NASA Astrophysics Data System (ADS)

In this thesis we investigate two new Amplified Quantum Transforms. In particular we create and analyze the Amplified Quantum Fourier Transform (Amplified-QFT) and the Amplified-Haar Wavelet Transform. The Amplified-QFT algorithm is used to solve the Local Period Problem. We calculate the probabilities of success and compare this algorithm with the QFT and QHS algorithms. We also examine the Amplified-QFT algorithm for solving the Local Period Problem with Error Stream. We use the Amplified-Haar Wavelet Transform for solving the Local Constant or Balanced Signal Decision Problem which is a generalization of the Deutsch-Jozsa problem.

Cornwell, David J.

55

Laser Field Imaging Through Fourier Transform Heterodyne

The authors present a detection process capable of directly imaging the transverse amplitude, phase, and Doppler shift of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned RADAR/LADAR systems, Fourier Transform Heterodyne incorporates transverse spatial encoding of the reference local oscillator for image capture. Appropriate selection of spatial encoding functions allows image retrieval by way of classic Fourier manipulations. Of practical interest: (1) imaging may be accomplished with a single element detector/sensor requiring no additional scanning or moving components, (2) as detection is governed by heterodyne principles, near quantum limited performance is achievable, (3) a wide variety of appropriate spatial encoding functions exist that may be adaptively configured in real-time for applications requiring optimal detection, and (4) the concept is general with the applicable electromagnetic spectrum encompassing the RF through optical.

Cooke, B.J.; Laubscher, B.E.; Olivas, N.L.; Galbraith, A.E.; Strauss, C.E.; Grubler, A.C.

1999-04-05

56

Laser field imaging through Fourier transform heterodyne

NASA Astrophysics Data System (ADS)

We present a detection process capable of directly imaging the transverse amplitude, phase, and Doppler shift of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned RADAR/LADAR systems, Fourier Transform Heterodyne incorporates transverse spatial encoding of the reference local oscillator for image capture. Appropriate selection of spatial encoding functions allows image retrieval by way of classic Fourier manipulations. Of practical interest: (1) imaging may be accomplished with a single element detector/sensor requiring no additional scanning or moving components, (2) as detection is governed by heterodyne principles, near quantum limited performance is achievable, (3) a wide variety of appropriate spatial encoding functions exist that may be adaptively configured in real-time for applications requiring optimal detection, and (4) the concept is general with the applicable electromagnetic spectrum encompassing the RF through optical.

Cooke, Bradly J.; Galbraith, Amy E.; Laubscher, Bryan E.; Strauss, Charlie E. M.; Olivas, Nicholas L.; Grubler, Andrew C.

1999-05-01

57

FPGA FFT(Fast Fourier Transform) 1 FPGA FFT(Fast Fourier Transform)

FPGA FFT(Fast Fourier Transform) 1 FPGA FFT(Fast Fourier Transform) Gokul Govindu Viktor K. Prasanna FPGA (FFT) . FPGA FFT . , . . ,radix, Xilinx Virtex-2 . Xilinx 57% 78% . --(EAT) , Xilinx 3-13 . 1) : FFT

Jang, Ju-Wook

58

Molecular overlap-like quantum similarity measurements imply the evaluation of overlap integrals of two molecular electronic densities related by Dirac delta function. When the electronic densities are expanded over atomic orbitals using the usual LCAO-MO approach (linear combination of atomic orbitals), overlap-like quantum similarity integrals could be expressed in terms of four-center overlap integrals. It is shown that by introducing the Fourier transform of delta Dirac function in the integrals and using the Fourier transform approach combined with the so-called B functions, one can obtain analytic expressions of the integrals under consideration. These analytic expressions involve highly oscillatory semi-infinite spherical Bessel functions, which are the principal source of severe numerical and computational difficulties. In this work, we present a highly efficient algorithm for a fast and accurate numerical evaluation of these multicenter overlap-like quantum similarity integrals over Slater type functions. This algorithm is based on the SD-bar approach due to Safouhi. Recurrence formulae are used for a better control of the degree of accuracy and for a better stability of the algorithm. The numerical result section shows the efficiency of our algorithm, compared with the alternatives using the one-center two-range expansion method, which led to very complicated analytic expressions, the epsilon algorithm and the nonlinear D-bar transformation.

Safouhi, Hassan [Campus Saint-Jean, University of Alberta, 8406 Rue Marie-Anne Gaboury, 91 Street, Edmonton, Alta., T6C 4G9 (Canada)]. E-mail: hassan.safouhi@ualberta.ca; Berlu, Lilian [Laboratoire SEESIB, UMR 6504, Universite Blaise Pascal, 63177 Aubiere Cedex (France)

2006-07-20

59

Signal Processing Issues in Fourier Transform Spectrometers

There are a number of interesting and challenging signal processing problems related to the design of a Fourier Transform Spectrometer (FTS). In this project, we look at a few of these problems in two different types of spectrometers-the Geostationary Imaging Fourier Transform Spectrometer (GIFTS), and a Far Infrared (FIR) FTS. One of the si nal processing challenges in GIFTS is

Monson H. Hayes

2002-01-01

60

Fourier Transform Heterodyne Techniques Applied To Astronomy

Fourier Transform Heterodyne (FTH) is a detection process capable of directly imaging the transverse amplitude and phase of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned systems, Fourier Transform Heterodyne (FTH) incorporates transverse spatial encoding of the local oscillator for image capture. Appropriate selection of spatial encoding functions (basis set) allows image retrieval by way of classic

B. E. Laubscher; B. J. Cooke; B. C. Edwards

1998-01-01

61

Fourier Transform Heterodyne Techniques Applied To Astronomy

NASA Astrophysics Data System (ADS)

Fourier Transform Heterodyne (FTH) is a detection process capable of directly imaging the transverse amplitude and phase of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned systems, Fourier Transform Heterodyne (FTH) incorporates transverse spatial encoding of the local oscillator for image capture. Appropriate selection of spatial encoding functions (basis set) allows image retrieval by way of classic Fourier manipulations. Of practical interest: 1) Imaging is accomplished on a single element detector/sensor requiring no additional scanning or moving components. 2) Because detection is governed by heterodyne principles, near quantum limited performance is achievable. 3) The concept is general with the applicable electromagnetic spectrum encompassing the RF through optical. Although FTH is currently in its infancy, we believe this technique will provide new tools and concepts important to the development of future astronomical systems. For example: 1) An FTH-based optical or infrared interferometer (whether ground-based or space-based) can operate in direct analogy to VLBI radio astronomy systems. 2) FTH may be capable of measuring the atmospheric distortions of a target star to guide adaptive optical correction systems. 3) FTH may be used to determine the adjustments required to align a deployed structure in space and can remove aberrations from slight residual misalignments during operation. The work to be presented will include a brief introduction of the underlying principles governing FTH imaging, followed by cursory description of a simple proof-of-concept experiment carried out using a HeNe laser, a 69 element spatial phase modulator, and a 36 term Zernike basis set. Finally, astronomical applications will be discussed.

Laubscher, B. E.; Cooke, B. J.; Edwards, B. C.

1998-12-01

62

The Geostationary Fourier Transform Spectrometer

NASA Technical Reports Server (NTRS)

The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.

Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung

2012-01-01

63

The Geostationary Fourier Transform Spectrometer

NASA Technical Reports Server (NTRS)

The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for an earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. The GeoFTS instrument is a half meter cube size instrument designed to operate in geostationary orbit as a secondary "hosted" payload on a commercial geostationary satellite mission. The advantage of GEO is the ability to continuously stare at a region of the earth, enabling frequent sampling to capture the diurnal variability of biogenic fluxes and anthropogenic emissions from city to continental scales. The science goal is to obtain a process-based understanding of the carbon cycle from simultaneous high spatial resolution measurements of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) many times per day in the near infrared spectral region to capture their spatial and temporal variations on diurnal, synoptic, seasonal and interannual time scales. The GeoFTS instrument is based on a Michelson interferometer design with a number of advanced features incorporated. Two of the most important advanced features are the focal plane arrays and the optical path difference mechanism. A breadboard GeoFTS instrument has demonstrated functionality for simultaneous measurements in the visible and IR in the laboratory and subsequently in the field at the California Laboratory for Atmospheric Remote Sensing (CLARS) observatory on Mt. Wilson overlooking the Los Angeles basin. A GeoFTS engineering model instrument is being developed which will make simultaneous visible and IR measurements under space flight like environmental conditions (thermal-vacuum at 180 K). This will demonstrate critical instrument capabilities such as optical alignment stability, interferometer modulation efficiency, and high throughput FPA signal processing. This will reduce flight instrument development risk and show that the GeoFTS design is mature and flight ready.

Key, Richard; Sander, Stanley; Eldering, Annmarie; Miller, Charles; Frankenberg, Christian; Natra, Vijay; Rider, David; Blavier, Jean-Francois; Bekker, Dmitriy; Wu, Yen-Hung

2012-01-01

64

Demystification of the geometric Fourier transforms

NASA Astrophysics Data System (ADS)

As it will turn out in this paper, the recent hype about most of the Clifford Fourier transforms is not thoroughly worth the pain. Almost every one that has a real application is separable and these transforms can be decomposed into a sum of real valued transforms with constant multivecor factors. This fact makes their interpretation, their analysis, and their implementation almost trivial.

Bujack, Roxana; Scheuermann, Gerik; Hitzer, Eckhard

2013-10-01

65

Replica Fourier Transform: Properties and applications

NASA Astrophysics Data System (ADS)

The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically.

Crisanti, A.; De Dominicis, C.

2015-02-01

66

We show that the quantum Hamilton-Jacobi equation can be written in the classical form with the spatial derivative {partial_derivative}{sub q} replaced by {partial_derivative}{sub q} with dq = dq/{radical}1{minus}{beta}{sup 2}(q), where {beta}{sup 2}(q) is strictly related to the quantum potential. This can be seen as the opposite of the problem of finding the wave function representation of classical mechanics as formulated by Schiller and Rosen. The structure of the above {open_quotes}quantum transformation{close_quotes}, related to the recently formulated equivalence principle, indicates that the potential deforms space geometry. In particular, a result by Flanders implies that both W(q) = V(q) {minus} E and the quantum potential Q are proportional to the curvatures {kappa}{sub W} and {kappa}{sub Q} which arise as natural invariants in an equivalence problem for curves in the projective line. In this formulation the Schroedinger equation takes the geometrical form ({partial_derivative}{sub q}{sup 2} + {kappa}{sub W}){psi} = 0.

Faraggi, A.E. [Univ. of Florida, Gainesville, FL (United States). Institute for Fundamental Theory; Matone, M. [Univ. of Padova (Italy). Dept. of Physics G. Galilei

1998-01-09

67

The Relationship Between Two Fast Fourier Transforms

The purpose of this note is to show as clearly as possible the mathematical relationship between the two basic fast methods used for the calculation of discrete Fourier transforms and to generalize one of the methods a little further. This method applies to all those linear transformations whose matrices are expressible as direct products.

I. J. Good

1971-01-01

68

Parallel FFT & Isoefficiency 1 The Fast Fourier Transform in Parallel

Parallel FFT & Isoefficiency 1 The Fast Fourier Transform in Parallel the Fastest Fourier Transform February 2014 Introduction to Supercomputing (MCS 572) Parallel FFT & Isoefficiency L-14 14 February 2014 1 / 25 #12;Parallel FFT & Isoefficiency 1 The Fast Fourier Transform in Parallel the Fastest Fourier

Verschelde, Jan

69

Apodizing functions for Fourier transform spectroscopy

Apodizing functions for Fourier transform spectroscopy David A. Naylor* and Margaret K. Tahic; posted August 27, 2007 (Doc. ID 84862); published October 30, 2007 Apodizing functions are used interferogram. Three apodizing functions, which are considered optimal in the sense of produc- ing the smallest

Naylor, David A.

70

REMOTE FOURIER TRANSFORM INFRARED AIR POLLUTION STUDIES

A commercial Fourier transform infrared interferometer system has been installed in a van and used to make longpath absorption and single-ended emission measurements of gaseous pollutant concentrations at a variety of pollutant sources. The interferometer system is described and ...

71

Directional Uncertainty Principle for Quaternion Fourier Transform

This paper derives a new directional uncertainty principle for quaternion valued functions subject to the quaternion Fourier transformation. This can be generalized to establish directional uncertainty principles in Clifford geometric algebras with quaternion subalgebras. We demonstrate this with the example of a directional spacetime algebra function uncertainty principle related to multivector wave packets.

Eckhard Hitzer

2013-06-06

72

Discrete Fourier transforms of nonuniformly spaced data

NASA Technical Reports Server (NTRS)

Time series or spatial series of measurements taken with nonuniform spacings have failed to yield fully to analysis using the Discrete Fourier Transform (DFT). This is due to the fact that the formal DFT is the convolution of the transform of the signal with the transform of the nonuniform spacings. Two original methods are presented for deconvolving such transforms for signals containing significant noise. The first method solves a set of linear equations relating the observed data to values defined at uniform grid points, and then obtains the desired transform as the DFT of the uniform interpolates. The second method solves a set of linear equations relating the real and imaginary components of the formal DFT directly to those of the desired transform. The results of numerical experiments with noisy data are presented in order to demonstrate the capabilities and limitations of the methods.

Swan, P. R.

1982-01-01

73

Electro-optic imaging Fourier transform spectrometer

NASA Technical Reports Server (NTRS)

An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.

Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)

2009-01-01

74

Transforming quantum operations: quantum supermaps

We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.

G. Chiribella; G. M. D'Ariano; P. Perinotti

2008-10-22

75

Sigmund Selberg , DIFTA '06 Fourier transform restriction and estimates for

Sigmund Selberg , DIFTA '06 Fourier transform restriction and estimates for dispersive PDE Fourier Sigmund Selberg, Dept of Math Sciences #12;Sigmund Selberg , DIFTA '06 S Rn compact hypersurface Fourier restriction problem R f = f S Restriction mapping Fourier transform f () = Rn e-ix· f (x)dx #12;Sigmund

Selberg, Sigmund

76

Fourier transform analysis for periodic combinatorial arrays

NASA Astrophysics Data System (ADS)

Earlier we introduced a combinatorial synthetic method that employs one-dimensional supports ranging from cotton threads to optical fibres. This method affords parallel synthesis and availability of the complete library history ideally yielding identification of all library members. Moreover, the synthesized compound library will be arrayed periodically on the linear support, leading to assay data that also reflect this periodicity. This fact invites an analysis using the Fourier transform. Here we demonstrate how this approach presents n-dimensional data in a comprehensible manner and facilitates the identification of trends within the library. Carrying out an inverse Fourier transform on subsets of the data allows for the assignment of fitness profiles for each reactant and combination of reactants in the library. The tools should assist in drawing conclusions based on the diversity of library response as opposed to individual library members.

Schwabacher, Alan W.; Geissinger, Peter

2005-01-01

77

FFTC: Fastest Fourier Transform for the IBM Cell Broadband Engine

FFTC: Fastest Fourier Transform for the IBM Cell Broadband Engine David A. Bader and Virat Agarwal}@cc.gatech.edu Abstract. The Fast Fourier Transform (FFT) is of primary importance and a fundamental kernel in many design of an efficient parallel implementation of Fast Fourier Transform on the Cell Broadband Engine

Bader, David A.

78

Development of a multichannel Fourier transform spectrometer.

We devised a novel type of multichannel Fourier transform spectrometer (MCFTS) that incorporates a Wollaston prism, polarizing interferometer combined with two Savart plates and a phase-retarding plate. This original MCFTS produces a number of lines of folded interferograms recorded with a two-dimensional imaging detector such as a CCD detector. In the present type of MCFTS, the total incident light is available except for a small amount of reflection loss. It is possible to enhance the signal-to-noise ratio. The enhancement of the resolving power is also expected by the connection of the interferograms with a newly developed method. PMID:21068884

Ebizuka, N; Wakaki, M; Kobayashi, Y; Sato, S

1995-12-01

79

Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram

ERIC Educational Resources Information Center

Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…

Hanley, Quentin S.

2012-01-01

80

Two-dimensional fourier transform spectrometer

The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

DeFlores, Lauren; Tokmakoff, Andrei

2013-09-03

81

Fourier transform methods in local gravity modeling

NASA Technical Reports Server (NTRS)

New algorithms were derived for computing terrain corrections, all components of the attraction of the topography at the topographic surface and the gradients of these attractions. These algoriithms utilize fast Fourier transforms, but, in contrast to methods currently in use, all divergences of the integrals are removed during the analysis. Sequential methods employing a smooth intermediate reference surface were developed to avoid the very large transforms necessary when making computations at high resolution over a wide area. A new method for the numerical solution of Molodensky's problem was developed to mitigate the convergence difficulties that occur at short wavelengths with methods based on a Taylor series expansion. A trial field on a level surface is continued analytically to the topographic surface, and compared with that predicted from gravity observations. The difference is used to compute a correction to the trial field and the process iterated. Special techniques are employed to speed convergence and prevent oscillations. Three different spectral methods for fitting a point-mass set to a gravity field given on a regular grid at constant elevation are described. Two of the methods differ in the way that the spectrum of the point-mass set, which extends to infinite wave number, is matched to that of the gravity field which is band-limited. The third method is essentially a space-domain technique in which Fourier methods are used to solve a set of simultaneous equations.

Harrison, J. C.; Dickinson, M.

1989-01-01

82

Fourier Transforms for Chemists Part III. Fourier Transforms in Data Treatment.

ERIC Educational Resources Information Center

Discusses the factors affecting the behavior of a spectral function. Lists some important properties of Fourier transform (FT) pairs that are helpful when using the FT. Notes that these properties of the mathematical formulation have identical counterparts in the physical behavior of FT systems. (TW)

Glasser, L.

1987-01-01

83

Fast Fourier Transform in the Spiral Honeycomb Image Algebra

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 one such efficient implementation and discusses its implications to digital technology as well as biological vision. The significance of the fast Fourier transform (FFT) presented in

Phil Sheridan; David M. Alexander; Kelly S. Nunn-clark

2005-01-01

84

Optimal nonmonotonic convergence of the iterative Fourier-transform algorithm

NASA Astrophysics Data System (ADS)

The increase of the monotonic convergence rate is an important issue for iterative Fourier-transform algorithms. However, the steepest monotonic convergence of the iterative Fourier-transform algorithm does not always promise an optimal solution in the design of a diffractive optical element. The optimal nonmonotonic convergence of the iterative Fourier-transform algorithm is investigated by employing a microgenetic algorithm. The proposed hybrid scheme of the iterative Fourier-transform algorithm and the microgenetic algorithm show nonmonotonic convergence, and this results in a superior design.

Kim, Hwi; Lee, Byoungho

2005-02-01

85

Fourier transform spectrometer controller for partitioned architectures

NASA Astrophysics Data System (ADS)

The current trend in spacecraft computing is to integrate applications of different criticality levels on the same platform using no separation. This approach increases the complexity of the development, verification and integration processes, with an impact on the whole system life cycle. Researchers at ESA and NASA advocated for the use of partitioned architecture to reduce this complexity. Partitioned architectures rely on platform mechanisms to provide robust temporal and spatial separation between applications. Such architectures have been successfully implemented in several industries, such as avionics and automotive. In this paper we investigate the challenges of developing and the benefits of integrating a scientific instrument, namely a Fourier Transform Spectrometer, in such a partitioned architecture.

Tamas-Selicean, D.; Keymeulen, D.; Berisford, D.; Carlson, R.; Hand, K.; Pop, P.; Wadsworth, W.; Levy, R.

86

Fourier transform infrared spectroscopic study of truffles

NASA Astrophysics Data System (ADS)

Truffles are rare wild growing edible mushrooms belonging to Ascomycetes. In this paper, Fourier transform infrared (FTIR) spectroscopy was used to obtain vibrational spectra of truffles. The results show that the mushrooms exhibit characteristic spectra. The two strongest absorption bands appear at about 1077cm -1 and 1040 cm -1, which were described as C-O stretching in carbohydrate. The vibrational spectra indicate that the main compositions of the truffles are polysaccharide and protein. According to the characteristics bands and absorption ratios of spectra, different species of truffles can be discriminated. It is also found the great changes between moldy and healthy truffles, which the major differences are observed in the bands of protein. In addition, FTIR spectral differences are observed between the same species of truffles from different producing areas. It is showed that the FTIR spectroscopic method is valuable tool for rapid and nondestructive analysis of truffles prior to any extraction method used.

Zhao, Dezhang; Liu, Gang; Song, Dingshan; Liu, Jian-hong; Zhou, Yilan; Ou, Jiaming; Sun, Shizhong

2006-01-01

87

Surface Inspection using fourier transform infrared spectroscopy

The use of reflectance Fourier transform infrared (FTIR) spectroscopy as a tool for surface inspection is described. Laboratory instruments and portable instruments can support remote sensing probes that can map chemical contaminants on surfaces. Detection limits under the best of conditions are in the subnanometer range (i.e., near absolute cleanliness), excellent performance is obtained in the submicrometer range, and useful performance may exist for films tens of microns thick. Identifying and quantifying contamination such as mineral oils and greases, vegetable oils, and silicone oils on aluminum foil, galvanized sheet steel, smooth aluminum tubing, and gritblasted 7075 aluminum alloy and D6AC steel are described. The ability to map in time and space the distribution of oil stains on metals is demonstrated. Techniques for quantitatively applying oils to metals, subsequently verifying the application, and nonlinear relationships between reflectance and the quantity of oil are discussed.

Powell, G.L.; Smyrl, N.R.; Williams, D.M.; Meyers, H.M. III [Martin Marietta Energy Systems, Inc., TN (United States). Oak Ridge Y-12 Plant; Barber, T.E.; Marrero-Rivera, M. [Oak Ridge Institute for Science and Education, Oak Ridge, TN (United States)

1994-08-08

88

OPTI 512R-Linear Systems, Fourier Transforms Course Description

diffraction 16. Fresnel Diffraction, the Fresnel transform 17. Fresnel diffraction from circular apertures, convolution, the Fourier transform, linear filtering and sampling, two-dimensional operations, diffraction and Discrete Convolution Linear Systems applied to Electromagnetic Wave Propagation and Diffraction 13. Plane

Arizona, University of

89

Fingerprint classification using fast Fourier transform and nonlinear discriminant analysis

In this paper, we present a new approach for fingerprint class ification based on Discrete Fourier Transform (DFT) and nonlinear discriminant analysis. Utilizing the Discrete Fourier Transform and directional filters, a relia ble and efficient directional image is constructed from each fingerprint image, and then no nlinear discriminant analysis is applied to the constructed directional images, reducing the dimension dra-

Cheong Hee Park; Haesun Park

2005-01-01

90

The fractional Fourier transform and time-frequency representations

The functional Fourier transform (FRFT), which is a generalization of the classical Fourier transform, was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community, to which it may, however, be potentially useful. The FRFT depends on a parameter ? and can be interpreted as a rotation by

Luis B. Almeida

1994-01-01

91

Heisenberg Uncertainty Principle for the q-Bessel Fourier transform

Heisenberg Uncertainty Principle for the q-Bessel Fourier transform Lazhar Dhaouadi Abstract further variant of Heisen- bergs uncertainty principle. Let f be the Fourier transform of f defined by f is defined by V [g] = R x2 g(x)dx. The Heisenberg uncertainty principle can be stated as follows V [|f|2 ]V

Paris-Sud XI, Université de

92

Fourier transform spectroscopy to study planetary atmospheres.

NASA Astrophysics Data System (ADS)

Motivated by the selection of MATMOS for the ExoMars Trace Gas Orbiter (withdrawn), we have been working on algorithms for retrieving information about the Martian atmosphere using infrared spectroscopy.The Mars Atmospheric Trace Molecule Occultation Spectrometer (MATMOS) was a joint Canadian Space Agency (CSA) and Jet Propulsion Laboratory (JPL) mission to send a high-resolution Fourier transform spectrometer to Mars, similar to the CSA's Atmospheric Chemistry Experiment (ACE) FTS. The ACE-FTS, currently in Earth orbit, is a solar-occultation instrument measuring the solar spectrum between 750-4400 cm (-1) at a spectral resolution of 0.02 cm (-1) . We present an algorithm to retrieve temperatures and pressures from measured spectra, accurate knowledge of which is vital for inferring volume mixing ratios of trace gases. The effects of high dust quantities on spectra have been simulated using synthetic spectra of the Martian atmosphere and a method for mitigating these effects has been tested and will be presented. Work has been done to characterize the interferometer performance of the Engineering Demonstration Unit, constructed by ABB, with a focus on gaining a better understanding of the modulation efficiency of the interferometer.

Olsen, Kevin; Walker, Kaley; Strong, Kimberly; Hipkin, Victoria; Toon, Geoff; Conway, Stephanie; Berube, Philippe; Veilleux, James

93

A discrete Fourier transform for virtual memory machines

NASA Technical Reports Server (NTRS)

An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.

Galant, David C.

1992-01-01

94

In Fourier Transform Ion Cyclotron Resonance Mass Spectrometry (FT\\/ICR), one typically transforms the real time domain signal into the frequency domain (which is rescaled to yield a mass spectrum) using the Fourier transform (FT). Because the FT requires complex data as input, additional data manipulation is required to efficiently handle real data. The Hartley transform (HT) is better suited for

Christopher Paul Williams

1992-01-01

95

Signal Processing Issues in Fourier Transform Spectrometers

NASA Astrophysics Data System (ADS)

There are a number of interesting and challenging signal processing problems related to the design of a Fourier Transform Spectrometer (FTS). In this project, we look at a few of these problems in two different types of spectrometers-the Geostationary Imaging Fourier Transform Spectrometer (GIFTS), and a Far Infrared (FIR) FTS. One of the si nal processing challenges in GIFTS is the reduction of the massive data rate (2.4 x 109 bps) to an affordable telemetry rate of less than 60 Mbps. Since the GIFTS interferograms are heavily over-sampled, the first step is to decimate (down-sample) the interferograms with minimal distortion while keeping the signal processing algorithms simple enough to be implemented in the GIFTS hardware. Therefore, the first problem we looked at was the design of the decimation filters. Specifically, we performed a detailed analysis of two competing approaches that were being considered. The first, proposed by the Space Dynamics Lab (SDL), was to use a double sideband (real) band-pass filter. The second, proposed by Lincoln Laboratories (LL), was to use a single sideband (complex) band-pass filter. What the study showed was that a complex filter (LL approach) results in a savings of about 25% in the filtering requirements for the long-wave band, while in the mid-wave band the savings are approximately 50%. As a result, the decision was made to use a complex filter. Once the decision to use a complex filter had been made, we looked at some of the consequences of this decision. The most significant of these was the discovery that, with a complex filter, it is possible to extend the long-wave IR band beyond the folding frequency of 1174/cm and recover the SO2 line at 1176.5/cm. What this requires is the design of a band-pass decimation filter with a wider passband, and consequently of higher order. Specifically, it was shown that with about 25% more filter operations, the elusive SO2 line, believed to be irretrievable, could in fact be recovered. While working on the decimation filtering requirements, an issue arose with respect to how the 16-bit long-wave interferogram data should be processed by a 15-bit USES chip. There were two approaches being considered, and each one had at least one serious drawback. Therefore, given the nature of the data that is to be processed by the USES chip, we developed an efficient loss-less encoder that is robust to errors, and is easily decoded. Since the encoder eliminates the drawbacks of the other two approaches, and greatly simplifies the signal processing requirements, the downlink board is currently being redesigned to include this encoder. The last problem that was looked at involved an investigation into the optimum sampling strategy in the design of a far infrared FTS. The problem was to minimize the amount of spectral noise that is induced by non-uniform mirror velocity.

Hayes, Monson H.

2002-12-01

96

Cryogenic Scan Mechanism for Fourier Transform Spectrometer

NASA Technical Reports Server (NTRS)

A compact and lightweight mechanism has been developed to accurately move a Fourier transform spectrometer (FTS) scan mirror (a cube corner) in a near-linear fashion with near constant speed at cryogenic temperatures. This innovation includes a slide mechanism to restrict motion to one dimension, an actuator to drive the motion, and a linear velocity transducer (LVT) to measure the speed. The cube corner mirror is double-passed in one arm of the FTS; double-passing is required to compensate for optical beam shear resulting from tilting of the moving cube corner. The slide, actuator, and LVT are off-the-shelf components that are capable of cryogenic vacuum operation. The actuator drives the slide for the required travel of 2.5 cm. The LVT measures translation speed. A proportional feedback loop compares the LVT voltage with the set voltage (speed) to derive an error signal to drive the actuator and achieve near constant speed. When the end of the scan is reached, a personal computer reverses the set voltage. The actuator and LVT have no moving parts in contact, and have magnetic properties consistent with cryogenic operation. The unlubricated slide restricts motion to linear travel, using crossed roller bearings consistent with 100-million- stroke operation. The mechanism tilts several arc seconds during transport of the FTS mirror, which would compromise optical fringe efficiency when using a flat mirror. Consequently, a cube corner mirror is used, which converts a tilt into a shear. The sheared beam strikes (at normal incidence) a flat mirror at the end of the FTS arm with the moving mechanism, thereby returning upon itself and compensating for the shear

Brasunas, John C.; Francis, John L.

2011-01-01

97

Signal Approximation via the Gopher Fast Fourier Transform

NASA Astrophysics Data System (ADS)

We consider the problem of quickly estimating the best ?-term Fourier representation for a given frequency-sparse band-limited signal (i.e., function) f: [0,2?]?¢. In essence, this requires the identification of ? of the largest magnitude frequencies of \\vf?¢N, and the estimation their Fourier coefficients. Randomized sublinear-time Monte Carlo algorithms, which have a small probability of failing to output accurate answers for each input signal, have been developed for solving this problem [1, 2]. These methods were implemented as the Ann Arbor Fast Fourier Transform (AAFFT) and empirically evaluated in [3]. In this paper we present and evaluate the first implementation, called the Gopher Fast Fourier Transform (GFFT), of the more recently developed sparse Fourier transform techniques from [4]. Our experiments indicate that different variants of GFFT generally outperform AAFFT with respect to runtime and sample usage.

Ben Segal, I.; Iwen, M. A.

2010-11-01

98

A Reconfigurable Butterfly Architecture for Fourier and Fermat Transforms

A Reconfigurable Butterfly Architecture for Fourier and Fermat Transforms Ali Al Ghouwayel, Yves) used for the classical operations in the complex field. The second one is the Fermat Number Transform equal to Ft, where Ft = 22t + 1 is the Fermat number, the NTT is called the Fermat Number Transform (FNT

Boyer, Edmond

99

Pierre Jacquinot and the beginnings of Fourier transform spectrometry

NASA Astrophysics Data System (ADS)

Historical account of the early development of Fourier Transform Spectrometry at Laboratoire Aimé Cotton under Pierre Jacquinot's leadership, over the years 1954-1963. Compte rendu historique des premiers développements de la spectrométrie de Fourier au Laboratoire Aimé Cotton, sous la direction de Pierre Jacquinot, pendant les années 1954-1963.

Connes, Pierre

1992-04-01

100

THE UNCERTAINTY PRINCIPLE FOR FOURIER TRANSFORMS ON THE REAL LINE

THE UNCERTAINTY PRINCIPLE FOR FOURIER TRANSFORMS ON THE REAL LINE MITCH HILL Abstract. This paper inversion theorem and use this to prove the classical uncertainty principle which shows that the spread. Fourier Inversion 8 5. The Uncertainty Principle 13 6. The Amrein-Berthier Theorem 15 Acknowledgments 17

May, J. Peter

101

Matrix probing, skeleton decompositions, and sparse Fourier transform

In this thesis, we present three different randomized algorithms that help to solve matrices, compute low rank approximations and perform the Fast Fourier Transform. Matrix probing and its conditioning When a matrix A with ...

Chiu, Jiawei

2013-01-01

102

Fourier transform spectrometry at Laboratoire Aimé Cotton 1964-1974

NASA Astrophysics Data System (ADS)

An historical account of the development of high-resolution astronomical and laboratory Fourier transform spectrometry at Laboratoire Aimé Cotton under the leadership of P. Jacquinot, over the years 1964-1974.

Connes, Pierre

1995-07-01

103

FT Digital Filtering and Simulating Fourier transform Apodization via Excel

NSDL National Science Digital Library

This report presents an excel spreadsheet which simulates Fourier Transform apodization filtering on a noisy signal that contains either white or an environmental noise source. Users may download the report in PDF file format.

Overway, Ken

104

Fast Fourier transform on a 3D FPGA

Fast Fourier Transforms perform a vital role in many applications from astronomy to cellphones. The complexity of these algorithms results from the many computational steps, including multiplications, they require and, as ...

Basha, Elizabeth (Elizabeth Ann)

2005-01-01

105

Quasi-Fourier transform hologram format for data storage

For a recording medium such as dichromated gelatin, a quasi-Fourier transform holographic memory is preferred over the exact Fourier transform. We proceed here with angular multiplexing and consider undesired reconstructed waves such as cross-talk noise, and show that the signal-to-noise ratio is 33 dB for 20 angular multiplexed elements in 25 ?m thickness of the recording medium. We also study

H. Ramenah; P. Bertrand; E. H. Soubari; P. Meyrueis

1996-01-01

106

On localization properties of Fourier transforms of hyperfunctions

In [A.G. Smirnov, Fourier transformation of Sato's hyperfunctions, Adv. Math. 196 (2005) 310–345] the author introduced a new generalized function space U(Rk) which can be naturally interpreted as the Fourier transform of the space of Sato's hyperfunctions on Rk. It was shown that all Gelfand–Shilov spaces S??0(Rk) (?>1) of analytic functionals are canonically embedded in U(Rk). While the usual definition

A. G. Smirnov; I. E. Tamm; P. N. Lebedev

2009-01-01

107

On the accuracy of different Fourier transforms of VLSI designs

NASA Astrophysics Data System (ADS)

We evaluate the accuracy of the simulated aerial image computed using different types of Fourier transform: the Continuous Fourier transform (CFT), continuous Fourier series (CFS) and discrete Fourier transform (DFT), the transform currently used in practise. Lithography simulation necessitates efficient algorithms to accurately estimate the Fourier transform. The rectilinear mask structure can be used to compute the CFS efficiently, in most cases much faster than the DFT. We present a rigorous analysis and comparison of FFT-simulated aerial image and CFS-simulated aerial image. We also present the conditions under which the most accurate simulated aerial image for each type of Fourier transform can be obtained. We show that there are two main sources of inaccuracy in the computation of aerial image using the DFT. First, we establish that aliasing from the inherent discontinuity of rectilinear polygons is the main source of inaccuracy. We show the conditions under which this results in an over-estimate or underestimate of the Critical Dimension (CD). We thus describe how to perform aliasing-minimizing sampling. This adapts the sampling to the polygon pattern of the mask, by ensuring each discontinuity is exactly at the middle of two consecutive samples. Second, we show that sampling at twice the Nyquist rate of the filtered signal can in practise circumvent the inaccuracy due to the approximation of the integral by a discrete sum.

Nasser, Rajai; Hurley, Paul

2013-04-01

108

A Method to Perform a Fast Fourier Transform With Primitive Image Transformations

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).

Phil Sheridan

2007-01-01

109

Image Processing and the Arithmetic Fourier Trans-form

NASA Astrophysics Data System (ADS)

A new Fourier technique, the Arithmetic Fourier Transform (AFT) was recently developed for signal processing. This approach is based on the number-theoretic method of Mobius inversion. The AFT needs only additions except for a small amount of multiplications by prescribed scale factors. This new algorithm is also well suited to parallel processing. And there is no accumulation of rounding errors in the AFT algorithm. In this paper, the AFT is used to compute the discrete cosine transform and is also extended to 2-D cases for image processing. A 2-D Mobius inversion formula is proved. It is then applied to the computation of Fourier coefficients of a periodic 2-D function. It is shown that the output of an array of delay-line (or transversal) filters is the Mobius transform of the input harmonic terms. The 2-D Fourier coefficients can therefore be obtained through Mobius inversion of the output the filter array.

Tufts, Donald W.; Fan, Zhigang; Cao, Z.

1989-05-01

110

Dynamic measurement of deformation using Fourier transform digital holographic interferometry

NASA Astrophysics Data System (ADS)

Digital holographic interferometry (DHI) is a well-established optical technique for measurement of nano-scale deformations. It has become more and more important due to the rapid development of applications in aerospace engineering and biomedicine. Traditionally, phase shift technique is used to quantitatively measure the deformations in DHI. However, it cannot be applied in dynamic measurement. Fourier transform phase extraction method, which can determine the phase distribution from only a single hologram, becomes a promising method to extract transient phases in DHI. This paper introduces a digital holographic interferometric system based on 2D Fourier transform phase extraction method, with which deformations of objects can be measured quickly. In the optical setup, the object beam strikes a CCD via a lens and aperture, and the reference beam is projected on the CCD through a single-mode fiber. A small inclination angle between the diverging reference beam and optical axial is introduced in order to physically separate the Fourier components in frequency domain. Phase maps are then obtained by the utilization of Fourier transform and windowed inverse Fourier transform. The capability of the Fourier transform DHI is discussed by theoretical discussion as well as experiments.

Gao, Xinya; Wu, Sijin; Yang, Lianxiang

2013-10-01

111

We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to ``Hyperbolic phase space''. We show that this new unitary change of basis from the position x on the half line to the Hyperbolic momentum $p_\\eta$, transforms the wavefunction via a Mellin transform on to the critial line $s=1/2-ip_\\eta$. We utilise this new transform to find quantum wavefunctions whose Hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the Riemann Zeta function. We finally give possible physical realisations to perform an indirect measurement of the Hyperbolic momentum of a quantum system on the half-line.

J. Twamley; G. J. Milburn

2007-02-12

112

Advanced Hough transform using a multilayer fractional Fourier method.

The Hough transform (HT) is a commonly used technique for the identification of straight lines in an image. The Hough transform can be equivalently computed using the Radon transform (RT), by performing line detection in the frequency domain through use of central-slice theorem. In this research, an advanced Radon transform is developed using a multilayer fractional Fourier transform, a Cartesian-to-polar mapping, and 1-D inverse Fourier transforms, followed by peak detection in the sinogram. The multilayer fractional Fourier transform achieves a more accurate sampling in the frequency domain, and requires no zero padding at the stage of Cartesian-to-polar coordinate mapping. Our experiments were conducted on mix-shape images, noisy images, mixed-thickness lines and a large data set consisting of 751,000 handwritten Chinese characters. The experimental results have shown that our proposed method outperforms all known representative line detection methods based on the standard Hough transform or the Fourier transform. PMID:20144919

Shi, Daming; Zheng, Liying; Liu, Jigang

2010-06-01

113

NASA Astrophysics Data System (ADS)

Guided by theoretical predictions, the rotational spectrum of fluoroiodomethane, CH2FI, has been recorded and assigned. Accurate values are reported for the ground-state rotational constants, all quartic, sextic, and two octic centrifugal-distortion constants. The hyperfine structure of the rotational spectrum was thoroughly investigated using a Fourier-transform microwave spectrometer and the Lamb-dip technique in the millimeter-/submillimeter-wave region, thus allowing the accurate determination of the complete iodine quadrupole-coupling tensor and of the diagonal elements of the iodine spin-rotation tensor. Relativistic effects turned out to be essential for the accurate theoretical prediction of the dipole moment and quadrupole-coupling constants and were accounted for by direct perturbation theory and a spin-free four-component treatment based on the Dirac-Coulomb Hamiltonian. The relativistic corrections to the dipole moment amount to up to 34% and to the iodine quadrupole-coupling tensor to about 15-16% of the total values.

Puzzarini, Cristina; Cazzoli, Gabriele; López, Juan Carlos; Alonso, José Luis; Baldacci, Agostino; Baldan, Alessandro; Stopkowicz, Stella; Cheng, Lan; Gauss, Jürgen

2011-05-01

114

Eigenvectors and functions of the discrete Fourier transform

A method is presented for computing an orthonormal set of eigenvectors for the discrete Fourier transform (DFT). The technique is based on a detailed analysis of the eigenstructure of a special matrix which commutes with the DFT. It is also shown how fractional powers of the DFT can be efficiently computed, and possible applications to multiplexing and transform coding are

BRADLEY W. DICKINSON; KENNETH STEIGLITZ

1982-01-01

115

Practical Algorithm For Computing The 2-D Arithmetic Fourier Transform

NASA Astrophysics Data System (ADS)

Recently, Tufts and Sadasiv [10] exposed a method for computing the coefficients of a Fourier series of a periodic function using the Mobius inversion of series. They called this method of analysis the Arithmetic Fourier Transform(AFT). The advantage of the AFT over the FN 1' is that this method of Fourier analysis needs only addition operations except for multiplications by scale factors at one stage of the computation. The disadvantage of the AFT as they expressed it originally is that it could be used effectively only to compute finite Fourier coefficients of a real even function. To remedy this the AFT developed in [10] is extended in [11] to compute the Fourier coefficients of both the even and odd components of a periodic function. In this paper, the improved AFT [11] is extended to a two-dimensional(2-D) Arithmetic Fourier Transform for calculating the Fourier Transform of two-dimensional discrete signals. This new algorithm is based on both the number-theoretic method of Mobius inversion of double series and the complex conjugate property of Fourier coefficients. The advantage of this algorithm over the conventional 2-D FFT is that the corner-turning problem needed in a conventional 2-D Discrete Fourier Transform(DFT) can be avoided. Therefore, this new 2-D algorithm is readily suitable for VLSI implementation as a parallel architecture. Comparing the operations of 2-D AFT of a MxM 2-D data array with the conventional 2-D FFT, the number of multiplications is significantly reduced from (2log2M)M2 to (9/4)M2. Hence, this new algorithm is faster than the FFT algorithm. Finally, two simulation results of this new 2-D AFT algorithm for 2-D artificial and real images are given in this paper.

Reed, Irving S.; Choi, Y. Y.; Yu, Xiaoli

1989-05-01

116

CAT scan and Radon/X-ray transform Relations with the Fourier transform. Dual Radon

CAT scan and Radon/X-ray transform Relations with the Fourier transform. Dual Radon Radon transform over d dimensional planes. X-ray transform. Inversion formulas. Range Stability of inversion Incomplete geometric transforms A classification of tomographic procedures Electrical Impedance Tomography Optical

117

Computation of spectra with unequal resolution using the fast Fourier transform

The discrete Fourier transform of a sequence, which can be computed using the fast Fourier transform algorithm, represents samples of the z transform equally spaced around the unit circle. In this letter, a technique is discussed and illustrated for transforming a sequence to a new sequence whose discrete Fourier transform is equal to samples of the z transform of the

A. Oppenheim; D. Johnson; K. Steiglitz

1971-01-01

118

Electro-Optical Imaging Fourier-Transform Spectrometer

NASA Technical Reports Server (NTRS)

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.

Chao, Tien-Hsin; Zhou, Hanying

2006-01-01

119

Linear Response Theory 15.0.6 Fourier Transform

Chapter 15 Linear Response Theory 15.0.6 Fourier Transform A function of time f(t) which transform of f(t). Note that if f(t) = (t) such that (t)dt = 1, then F() = 1 2 , and (t) = 1 2 - eit d 85 #12;86 CHAPTER 15. LINEAR RESPONSE THEORY 15.0.7 Convolution Consider f(t) with transform F() and h

Palffy-Muhoray, Peter

120

Parallel fast Fourier transforms for non power of two data

This report deals with parallel algorithms for computing discrete Fourier transforms of real sequences of length N not equal to a power of two. The method described is an extension of existing power of two transforms to sequences with N a product of small primes. In particular, this implementation requires N = 2{sup p}3{sup q}5{sup r}. The communication required is the same as for a transform of length N = 2{sup p}. The algorithm presented is intended for use in the solution of partial differential equations, or in any situation in which a large number of forward and backward transforms must be performed and in which the Fourier Coefficients need not be ordered. This implementation is a one dimensional FFT but the techniques are applicable to multidimensional transforms as well. The algorithm has been implemented on a 128 node Intel Ipsc/860.

Semeraro, B.D.

1994-09-01

121

Modulated Fourier Transform Raman Fiber-Optic Spectroscopy

NASA Technical Reports Server (NTRS)

A modification to a commercial Fourier Transform (FT) Raman spectrometer is presented for the elimination of thermal backgrounds in the FT Raman spectra. The modification involves the use of a mechanical optical chopper to modulate the continuous wave laser, remote collection of the signal via fiber optics, and connection of a dual-phase digital-signal-processor (DSP) lock-in amplifier between the detector and the spectrometer's collection electronics to demodulate and filter the optical signals. The resulting Modulated Fourier Transform Raman Fiber-Optic Spectrometer is capable of completely eliminating thermal backgrounds at temperatures exceeding 300 C.

Jensen, Brian J. (Inventor); Cooper, John B. (Inventor); Wise, Kent L. (Inventor)

2000-01-01

122

Lensless Fourier-transform ghost imaging with classical incoherent light

The Fourier-transform ghost imaging of both amplitude-only and pure-phase objects was experimentally observed with classical incoherent light at Fresnel distance by a lensless scheme. The experimental results are in good agreement with the standard Fourier transform of the corresponding objects. This scheme provides a route toward aberration-free diffraction-limited three-dimensional images with classically incoherent thermal light (or neutrons), which have no resolution and depth-of-field limitations of lens-based tomographic systems.

Zhang, Minghui; Wei, Qing; Shen, Xia; Liu, Yongfeng; Liu, Honglin; Cheng, Jing; Han, Shensheng [Key Laboratory for Quantum Optics and Center for Cold Atom Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800 (China)

2007-02-15

123

Fourier-transform and global contrast interferometer alignment methods

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.

Goldberg, Kenneth A. (Berkeley, CA)

2001-01-01

124

NASA Astrophysics Data System (ADS)

Time-resolved infrared emission of CO2 and OCS was observed in reactions O(3P) + OCS and O(1D) + OCS with a step-scan Fourier transform spectrometer. The CO2 emission involves ??3 = -1 transitions from highly vibrationally excited states, whereas emission of OCS is mainly from the transition (0, 0°, 1) ? (0, 0°, 0); the latter derives its energy via near-resonant V-V energy transfer from highly excited CO2. Rotationally resolved emission lines of CO (v ? 4 and J ? 30) were also observed in the reaction O(1D) + OCS. For O(3P) + OCS, weak emission of CO2 diminishes when Ar is added, indicating that O(3P) is translationally hot to overcome the barrier for CO2 formation. The band contour of CO2 agrees with a band shape simulated on the basis of a Dunham expansion model of CO2; the average vibrational energy of CO2 in this channel is 49% of the available energy. This vibrational distribution fits with that estimated through a statistical partitioning of energy E* ? 18 000 ± 500 cm-1 into all vibrational modes of CO2. For the reaction of O(1D) + OCS, approximately 51% of the available energy is converted into vibrational energy of CO2, and a statistical prediction using E* ? 30 000 ± 500 cm-1 best fits the data. The mechanisms of these reactions are also investigated with the CCSD(T)/6-311+G(3df)//B3LYP/6-311+G(3df) method. The results indicate that the triplet O(3P) + OCS(X1?+) surface proceeds via direct abstraction and substitution channels with barriers of 27.6 and 36.4 kJ mol-1, respectively, to produce SO(X3?-) + CO(X1?+) and S(3P) + CO2(X1A1), whereas two intermediates, OSCO and SC(O)O, are formed from the singlet O(1D) + OCS(X1?+) surface without barrier, followed by decomposition to SO(a1?) + CO(X1?+) and S(1D) + CO2(X1A1), respectively. For the ground-state reaction O(3P) + OCS(X1?+), the singlet-triplet curve crossings play important roles in the observed kinetics and chemiluminescence.

Chiang, Hung-Chu; Wang, Niann-Shiah; Tsuchiya, Soji; Chen, Hsin-Tsung; Lee, Yuan-Pern; Lin, M. C.

2009-07-01

125

Cauchy transforms of measures viewed as some functionals of Fourier transforms

Cauchy transforms of measures viewed as some functionals of Fourier transforms Zbigniew J. Jurek Urbanik ABSTRACT. The Cauchy transform of a positive measure plays an impor- tant role in complex analysis and more recently in so-called free probability. We show here that the Cauchy transform restricted

Jurek, Zbigniew J.

126

Cauchy transforms of measures viewed as some functionals of Fourier transforms #

Cauchy transforms of measures viewed as some functionals of Fourier transforms # Zbigniew J. Jurek Urbanik ABSTRACT. The Cauchy transform of a positive measure plays an imporÂ tant role in complex analysis and more recently in soÂcalled free probability. We show here that the Cauchy transform restricted

Jurek, Zbigniew J.

127

Image encryption by using fractional Fourier transform and jigsaw transform in image bit planes

We propose a new method for image encryption and decryption in which the image is broken up into bit planes. Each bit plane undergoes a jigsaw transform. The transformed bit planes are combined together and then encrypted using random phase masks and fractional Fourier transforms. The different fractional parameters, the random phase codes, and the jigsaw transform index form the

Aloka Sinha; Kehar Singh

2005-01-01

128

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

NASA Technical Reports Server (NTRS)

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

Dean, Bruce H. (Inventor)

2012-01-01

129

Achieving Efficient Polynomial Multiplication in Fermat Fields Using the Fast Fourier Transform

Achieving Efficient Polynomial Multiplication in Fermat Fields Using the Fast Fourier Transform. Keywords Finite fields, polynomial multiplication, Fast Fourier Trans- form (FFT), Fermat numbers, Fermat

130

Discrete Fourier Transform Analysis in a Complex Vector Space

NASA Technical Reports Server (NTRS)

Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.

Dean, Bruce H.

2009-01-01

131

Fake Finger Detection Using the Fractional Fourier Transform

This paper introduces a new method for detecting fake finger using the fractional Fourier transform (FrFT). The advantage\\u000a of this method is to require one fingerprint image. The fingerprint is a texture with the interleaving of ridge and valley.\\u000a When the fingerprint is transformed into the spectral domain, we found energy of fingerprint. Generally, the energy of live\\u000a fingerprints is

Hyun-suk Lee; Hyun-ju Maeng; You-suk Bae

2009-01-01

132

APPLICATION OF FOURIER TRANSFORM SPECTROSCOPY TO AIR POLLUTION PROBLEMS

The nature of information that can be retrieved from spectra obtained with Fourier transform spectroscopy is discussed. Nonlinear, least-squares analysis of spectra is capable of retrieving information that is beyond the reach of conventional methods and has improved precision an...

133

Symmetrical factorization of the fast Fourier transform for efficient implementation

This paper shows a symmetrical decomposition of the Fast Fourier Transform (FFT) into stages such that butterflies of small radices can be applied efficiently. Due to symmetric, the bit reversal sorting is also symmetrical and allows semi in-place self-sorting to be carried out together with the butterfly processing at the middle stage. Furthermore, the mirroring effect due to the symmetry,

H. K. Sim

2004-01-01

134

Signal reconstruction from short-time Fourier transform magnitude

In this paper, a signal is shown to be uniquely represented by the magnitude of its short-time Fourier transform (STFT) under mild restrictions on the signal and the analysis window of the STFT. Furthermore, various algorithms are developed which reconstruct signal from appropriate samples of the STFT magnitude. Several of the algorithms can also be used to obtain signal estimates

S. Nawab; THOMAS F. QUATIERI; JAE S. LIM

1983-01-01

135

Transverse electric scattering widths for strips-Fourier transform technique

NASA Technical Reports Server (NTRS)

A technique which is based on Fourier transformations is introduced for predicting scattering widths. For a strip it is shown that explicit determination of the linear current density is not necessary for bistatic or monostatic scattering width calculations. Comparisons of the predictions of the technique are made with the integral equation technique predictions, which do not require explicit evaluations of linear current densities.

Cockrell, C. R.; Harrah, S. D.; Beck, F. B.

1991-01-01

136

Rainbow Fourier transform Mikhail D. Alexandrov a,b,n

Rainbow Fourier transform Mikhail D. Alexandrov a,b,n , Brian Cairns b , Michael I. Mishchenko b Rainbow Optical particle characterization Remote sensing a b s t r a c t We present a novel technique between 1351 and 1651 exhibit a sharply defined rainbow structure, the shape of which is determined mostly

137

Rainbow Fourier transform Mikhail D. Alexandrov a,b,n

71 73 75 77 79 81 Rainbow Fourier transform Mikhail D. Alexandrov a,b,n , Brian Cairns b , Michael I, USAQ3 a r t i c l e i n f o Keywords: ElectromagneticQ4 scattering Polarization Mie theory Rainbow angle range between 1351 and 1651 exhibit a sharply defined rainbow structure, the shape of which

138

The q-Fourier transformation of q-generalized functions

A study is made of functions on the lattice generated by the integer powers of q{sup 2}, 0Fourier transformation is constructed based on the Jackson integral in the space of generalized functions on the lattice.

Ol'shanetskii, M A [Russian Federation State Scientific Center 'A.I. Alikhanov Institute for Theoretical and Experimental Physics', Moscow (Russian Federation); Rogov, V-B K [Moscow State University of Railway Engineering, Moscow (Russian Federation)

1999-06-30

139

Helium speech enhancement using the short-time Fourier transform

Speech produced in a hyperbaric helium-oxygen atmosphere suffers a variety of distortions which render it virtually unintelligible. This paper describes a new system for helium speech enhancement based on a short-time Fourier transform signal representation. The algorithm is robust, allows nonlinear warping of the spectral envelope, and includes provisions for generating the enhanced speech at a reduced sampling rate. Noise

M. Richards

1982-01-01

140

Fourier transform spectroscopy of cotton and cotton trash

Technology Transfer Automated Retrieval System (TEKTRAN)

Fourier Transform techniques have been shown to have higher signal-to-noise capabilities, higher throughput, negligible stray light, continuous spectra, and higher resolution. In addition, FT spectroscopy affords for frequencies in spectra to be measured all at once and more precise wavelength calib...

141

Spatial Fourier Transform Analysis of Polishing Pad Surface Topography

NASA Astrophysics Data System (ADS)

The spatial Fourier transform analysis is proposed to quantitatively evaluate the irregular topography of the conditioned chemical mechanical polishing (CMP) pad surface. We discuss the power spectrum in the spatial wavelengths of the surface topographies corresponding to polishing time. We conclude that the spatial wavelength of less than 5 µm in the topography yielded high material removal rates.

Khajornrungruang, Panart; Kimura, Keiichi; Okuzono, Takahisa; Suzuki, Keisuke; Kushida, Takashi

2012-05-01

142

Ultrafast ranging lidar based on real-time Fourier transformation.

Real-time Fourier-transformation-based ranging lidar using a mode-locked femtosecond fiber laser is demonstrated. The object signal and the reference signal are guided from a fiber Mach-Zehnder interferometer into a dispersive element. The two optical pulses extend and overlap with each other temporally, which yields a microwave pulse on the photodetector with its frequency proportional to the time delay between the two signals. The temporal interferograms are transformed from the time domain into the frequency domain using a time-to-frequency conversion function obtained in the calibration process. The Fourier transform is used in the data processing. A range resolution of 334 nm at a sampling rate of 48.6 MHz over a distance of 16 cm is demonstrated in the laboratory. PMID:19823517

Xia, Haiyun; Zhang, Chunxi

2009-07-15

143

Recovering missing slices of the discrete Fourier transform using Ghosts.

The discrete Fourier transform (DFT) underpins the solution to many inverse problems commonly possessing missing or unmeasured frequency information. This incomplete coverage of the Fourier space always produces systematic artifacts called Ghosts. In this paper, a fast and exact method for deconvolving cyclic artifacts caused by missing slices of the DFT using redundant image regions is presented. The slices discussed here originate from the exact partitioning of the Discrete Fourier Transform (DFT) space, under the projective Discrete Radon Transform, called the discrete Fourier slice theorem. The method has a computational complexity of O(n log(2) n) (for an n=N×N image) and is constructed from a new cyclic theory of Ghosts. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. This paper concludes with an application to fast, exact, non-iterative image reconstruction from a highly asymmetric set of rational angle projections that give rise to sets of sparse slices within the DFT. PMID:22752128

Chandra, Shekhar S; Svalbe, Imants D; Guédon, Jeanpierre; Kingston, Andrew M; Normand, Nicolas

2012-10-01

144

Compression imaging based on Fourier transform optical system

NASA Astrophysics Data System (ADS)

Shannon / Nyquist sampling theorem indicates that during the sampling process the minimum sample rate must be more than the double of the band of the signal so that we can achieve images without distortion. High-frequency sampling leads to mass data and results in high cost of storage and transmission procedure. Compressed sensing indicates that we can sample data at far below the Nyquist frequency when the signals are sparse or can be represented as sparse on some orthogonal basis, and the signals can be recovered without distortion after some certain recovery algorithms. By this means the cost of storage and transmission can be reduced significantly. Unlike conventional optical imaging process, this paper presents a new imaging method using a Fourier transform lens system, which enables single-exposure and single-aperture compressed imaging. First, the Fourier transformation of image signals is accomplished after they pass through a Fourier transform optical system. Second, sparse sample data can be obtained after the spectrum signals pass the sensor array. The process mentioned above can be interpreted as that using a Fourier matrix and a sparse matrix to complete the measurement of the image signals. Third, we make use of fast iterative threshold recovery algorithm to compute the sampling values and obtain the target image signals. Compared with the conventional imaging methods, in the case of ensuring the image quality, our method can significantly reduce the number of samples, thus greatly reduce the data redundancy. Simulation results indicate that the imaging method proposed can be prospective.

Lv, Jinfeng; Zhao, Huaici; Zhao, Chunyang

2014-11-01

145

A VLSI architecture for simplified arithmetic Fourier transform algorithm

NASA Technical Reports Server (NTRS)

The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical FFT in terms of accuracy, complexity, and speed. Theorems developed in a previous paper for the AFT algorithm are used here to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A VLSI architecture is suggested for this simplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25 percent of that used in the direct method.

Reed, Irving S.; Shih, Ming-Tang; Truong, T. K.; Hendon, E.; Tufts, D. W.

1992-01-01

146

Novel fringe scanning/Fourier transform method of synthetic imaging

We have developed a one-dimensional theory and a computer model for synthetically imaging scenes using a novel fringe scanning/Fourier transform technique. Our method probes a scene using two interfering beams of slightly different frequency. These beams form a moving fringe pattern which scans the scene and resonates with any spatial frequency components having the same spatial frequency as the scanning fringe pattern. A simple, non-imaging detector above the scene observes any scattered radiation from the scene falling onto it. If a resonance occurs between the scanning fringe pattern and the scene, then the scattered radiation will be modulated at the difference frequency between the two probing beams. By changing the spatial period of the fringe pattern and then measuring the amplitude and phase of the modulated radiation that is scattered from the scene, the Fourier amplitudes and phases of the different spatial frequency components making up the scene can be measured. A synthetic image of the scene being probed can be generated from this Fourier amplitude and phase data by taking the inverse Fourier transform of this information. This technique could be used to image objects using light, ultrasonic, or other electromagnetic or acoustic waves.

Crawford, T.M.; Albano, R.K.

1993-08-01

147

Fourier transform digital holographic adaptive optics imaging system

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

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

2013-01-01

148

Optical OFDM based on the fractional Fourier transform

NASA Astrophysics Data System (ADS)

We describe a innovative OFDM scheme based on orthogonal chirped subcarriers, that corresponds to the fractional Fourier transform (FrFT) of the input signal. The FrFT can be electronically implemented with a complexity equivalent to the conventional fast Fourier transform (FFT); on the other hand, the planar device that implements the FrFT in the optical domain is similar to the passive arrayed waveguide grating (AWG) device that performs the FFT. We analyze the spectral efficiency, the peak-to-average power ratio (PAPR) and the frequency offset sensitivity of a FrFT-based optical OFDM system, and make an accurate comparison with the standard FFT-based implementation.

Cincotti, Gabriella

2012-01-01

149

Perfect vortex beam: Fourier transformation of a Bessel beam.

We derive a mathematical description of a perfect vortex beam as the Fourier transformation of a Bessel beam. Building on this development, we experimentally generate Bessel-Gauss beams of different orders and Fourier transform them to form perfect vortex beams. By controlling the radial wave vector of a Bessel-Gauss beam, we can control the ring radius of the generated beam. Our theoretical predictions match with the experimental results and also provide an explanation for previous published works. We find the perfect vortex resembles that of an orbital angular momentum (OAM) mode supported in annular profiled waveguides. Our prefect vortex beam generation method can be used to excite OAM modes in an annular core fiber. PMID:25680159

Vaity, Pravin; Rusch, Leslie

2015-02-15

150

Fourier-Transformed Inelastic STM Tunneling into High-Temperature

NASA Astrophysics Data System (ADS)

There are heightened interest in relating the STM observations with other spectroscopy measurements with momentum resolution in high-Tc cuprates. We have proposed earlier that STM can be used to detect the 41;meV (,) mode as observed in neutron scattering experiments. Recent ARPES on optimally doped Bi2Sr2Ca0.92Y0.08Cu2O8+? suggests an anisotropic electron-phonon coupling. Here we address the role of these phonons (O B1g mode and in-plane Cu-O breathing mode) and the Fourier-transformed STM features they might generate in the local density of states. We also look into the effect of a distributed random potential on these features. The Fourier-transformed inelastic electron tunneling spectrocopy STM would allow one to extract the Eliashberg function in both frequency and momentum space, if successful.

Zhu, Jian-Xin

2005-03-01

151

Target Image Enhancement in Radar Imaging Using Fractional Fourier Transform

NASA Astrophysics Data System (ADS)

This paper presents a new Range-Doppler Algorithm based on Fractional Fourier Transform (RDA-FrFT) to obtain High-Resolution (HR) images for targets in radar imaging. The performance of the proposed RDA-FrFT is compared with the classical RDA algorithm, which is based on the Fast Fourier Transform (FFT). A closed-form expression for the range and azimuth compression of the proposed RDA-FrFT is mathematically derived and analyzed from the HR Synthetic Aperture Radar (SAR) imaging point of view. The proposed RDA-FrFT takes its advantage of the property of the FrFT to resolve chirp signals with high precision. Results show that the proposed RDA-FrFT gives low Peak Side-Lobe (PSL) and Integrated Side-Lobe (ISL) levels in range and azimuth directions for detected targets. HR images are obtained using the proposed RDA-FrFT algorithm.

El-Mashed, M. G.; Dessouky, M. I.; El-Kordy, M.; Zahran, O.; Abd El-Samie, F. E.

2012-03-01

152

Fourier spectroscopy with a one-million-point transformation

NASA Technical Reports Server (NTRS)

A new type of interferometer for use in Fourier spectroscopy has been devised at the Aime Cotton Laboratory of the National Center for Scientific Research (CNRS), Orsay, France. With this interferometer and newly developed computational techniques, interferograms comprising as many as one million samples can now be transformed. The techniques are described, and examples of spectra of thorium and holmium, derived from one million-point interferograms, are presented.

Connes, J.; Delouis, H.; Connes, P.; Guelachvili, G.; Maillard, J.; Michel, G.

1972-01-01

153

Fourier transform profilometry by using digital dc subtraction

NASA Astrophysics Data System (ADS)

A new method for eliminating unwanted background of Fourier transform profilometry (FTP) by using simple dc bias and background eliminations from the deformed grating images is proposed. The proposed method has an advantage over a conventional FTP in that the 3-D object profile can be accurately measured although original fundamental spectra are corrupted by a zeroth-order spectrum. Experimental verifications of the proposed method are presented.

Wongjarern, J.; Widjaja, J.; Sangpech, W.; Thongdee, N.; Santisoonthornwat, P.; Traisak, O.; Chuamchaitrakool, P.; Meemon, P.

2014-06-01

154

Fourier transform microwave spectrum of CO-dimethyl ether

Two sets of 32 rotational transitions were observed for the carbon monoxide-dimethyl ether (CO-DME) complex and two sets of 30 transitions for both 13CO-DME and C18O-DME, in the frequency region from 3.5 to 25.2 GHz, with J ranging from 1<--0 up to 7<--6, by using a Fourier transform microwave spectrometer. The splittings between the two sets of the same transition

Yoshiyuki Kawashima; Yasumasa Morita; Yoshio Tatamitani; Nobuyuki Ohashi; Eizi Hirota

2007-01-01

155

IR spectral depth profiling using Fourier transform photothermal beam deflection

Fourier transform IR photothermal beam-deflection spectroscopy (PBDS) was used to make spectral depth-profiling measurements with synthetic bilayer samples of polyethylene\\/nitrocellulose, with a commercial plastic having surface printing and with a single human hair. An interferometer modified to operate at several scan speeds was used to record the spectra, without the cell-resonance problems found with photoacoustic spectroscopy (PAS). The utility of

P. G. Varlashkin; M. J. D. Low

1986-01-01

156

Cryogenic Fourier transform infrared spectrometer from 4 to 20 micrometers

We describe the design and performance of a cryogenic Fourier transform spectrometer (Cryo-FTS) operating at a temperature of approximately 15 K. The instrument is based on a porch-swing scanning mirror design with active alignment stabilization using a fiber-optic coupled diode laser and voice-coil actuator mechanism. It has a KBr beamsplitter and has been integrated into an infrared radiometer containing a

Simon G. Kaplan; Solomon I. Woods; Timothy M. Jung; Adriaan C. Carter

2010-01-01

157

An Orthogonally Multiplexed QAM System Using the Discrete Fourier Transform

An orthogonally multiplexed QAM (O-QAM) system is a multichannel system with a baud rate spacing between adjacent carrier frequencies; this property is desirable to digitally implement the system using the discrete Fourier transformation (DFT). This paper provides a novel digital signal processing method based on anN\\/2-point DFT processing in the O-QAM system. A complexity comparison between a digital O-QAM system

BOTARO HIROSAKI

1981-01-01

158

Apparatus and methods for continuous beam fourier transform mass spectrometry

A continuous beam Fourier transform mass spectrometer in which a sample of ions to be analyzed is trapped in a trapping field, and the ions in the range of the mass-to-charge ratios to be analyzed are excited at their characteristic frequencies of motion by a continuous excitation signal. The excited ions in resonant motions generate real or image currents continuously which can be detected and processed to provide a mass spectrum.

McLuckey, Scott A. (Oak Ridge, TN); Goeringer, Douglas E. (Oak Ridge, TN)

2002-01-01

159

Fourier transform techniques for mode separation in piezocomposites

One and two dimensional real and complex fast fourier transform (FFT) algorithms were applied to the results of displacement phase and magnitude maps obtained from interferometric studies on a type 1-3 piezocomposite specimen electrically driven at a number of frequencies between 6 kHz and 1.0 MHz. Analysis was performed on experimental results for materials consisting of square cross section piezoelectric

Dianne M. Granata; William R. Scott; Martin J. Ryan

1993-01-01

160

Seafood freshness determination through vapour phase Fourier transform infrared spectroscopy

A new vapour-phase manifold has been developed to determine trimethylamine (TMA) in fish and cephalopod samples by Fourier transform infrared (FT-IR) spectroscopy. Samples were treated off-line for 1h with trichloroacetic acid (TCA), filtered and washed. The obtained extracts were aspirated and alkalinized with NaOH 2.0M, in an on-line system. TMA was separated from the solution in a gas phase separator

S. Armenta; N. M. M. Coelho; R. Roda; S. Garrigues; M. de la Guardia

2006-01-01

161

The determination of peroxide value by fourier transform infrared spectroscopy

A rapid method for the quantitative determination of peroxide value (PV) of vegetable oils by Fourier transform infrared (FTIR)\\u000a transmission spectroscopy is described. Calibration standards were prepared by the addition oft-butyl hydroperoxide to a series of vegetable oils, along with random amounts of oleic acid and water. Additional standards\\u000a were derived through the addition of mono- and diglyceride spectral contributions,

F. R. van de Voort; A. A. Ismail; J. Sedman; J. Dubois; T. Nicodemo

1994-01-01

162

Pulsed Nozzle Fourier Transform Microwave Spectrometer: Advances and Applications

The pulsed nozzle Fourier transform microwave (PNFTMW) spectrometer was developed by Balle and Flygare [A new method for observing the rotational spectra of weak molecular complexes: KrHCl. J. Chem. Phys. 1979, 71 (6), 2723–2724 and 1980, 72 (2), 922–932] in 1979. The design, fabrication, and operation of this spectrometer are complicated and it has largely remained a research laboratory tool

E. Arunan; Sagarika Dev; Pankaj K. Mandal

2004-01-01

163

Differential operators on toric varieties and Fourier transform

. We show that Fourier transforms on the Weyl algebras have a geometric counterpart in the framework of toric varieties, namely\\u000a they induce isomorphisms between twisted rings of differential operators on regular toric varieties, whose fans are related\\u000a to each other by reflections of one-dimensional cones. The simplest class of examples is provided by the toric varieties related\\u000a by such reflections

Giovanni Felder; Carlo A. Rossi

2008-01-01

164

Wavelength-encoded tomography based on optical temporal Fourier transform

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?-?m (ideally 36??m) resolution is achieved based on a 7.5-nm bandwidth swept-pump, 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.

Zhang, Chi; Wong, Kenneth K. Y., E-mail: kywong@eee.hku.hk [Photonic Systems Research Laboratory, Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road (Hong Kong)

2014-09-01

165

Mass Spectral Peak Distortion Due to Fourier Transform Signal Processing

NASA Astrophysics Data System (ADS)

Distortions of peaks can occur when one uses the standard method of signal processing of data from the Orbitrap and other FT-based methods of mass spectrometry. These distortions arise because the standard method of signal processing is not a linear process. If one adds two or more functions, such as time-dependent signals from a Fourier transform mass spectrometer and performs a linear operation on the sum, the result is the same as if the operation was performed on separate functions and the results added. If this relationship is not valid, the operation is non-linear and can produce unexpected and/or distorted results. Although the Fourier transform itself is a linear operator, the standard algorithm for processing spectra in Fourier transform-based methods include non-linear mathematical operators such that spectra processed by the standard algorithm may become distorted. The most serious consequence is that apparent abundances of the peaks in the spectrum may be incorrect. In light of these considerations, we performed theoretical modeling studies to illustrate several distortion effects that can be observed, including abundance distortions. In addition, we discuss experimental systems where these effects may manifest, including suggested systems for study that should demonstrate these peak distortions. Finally, we point to several examples in the literature where peak distortions may be rationalized by the phenomena presented here.

Rockwood, Alan L.; Erve, John C. L.

2014-12-01

166

Wavelength-encoded tomography based on optical temporal Fourier transform

NASA Astrophysics Data System (ADS)

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 -?m (ideally 36 ?m) resolution is achieved based on a 7.5-nm bandwidth swept-pump, 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.

Zhang, Chi; Wong, Kenneth K. Y.

2014-09-01

167

Scanning tunneling spectroscopy is used to study the real-space local density of states of a two-dimensional electron system in a magnetic field, in particular within higher Landau levels. By Fourier transforming the local density of states, we find a set of n radial minima at fixed momenta for the nth Landau levels. The momenta of the minima depend only on the inverse magnetic length. By comparison with analytical theory and numerical simulations, we attribute the minima to the nodes of the quantum cyclotron orbits, which decouple in a Fourier representation from the random guiding center motion due to disorder. Adequate Fourier filtering reveals the nodal structure in real space in some areas of the sample with relatively smooth potential disorder. PMID:23005665

Hashimoto, K; Champel, T; Florens, S; Sohrmann, C; Wiebe, J; Hirayama, Y; Römer, R A; Wiesendanger, R; Morgenstern, M

2012-09-14

168

Improved digital filters for evaluating Fourier and Hankel transform integrals

New algorithms are described for evaluating Fourier (cosine, sine) and Hankel (J0,J1) transform integrals by means of digital filters. The filters have been designed with extended lengths so that a variable convolution operation can be applied to a large class of integral transforms having the same system transfer function. A f' lagged-convolution method is also presented to significantly decrease the computation time when computing a series of like-transforms over a parameter set spaced the same as the filters. Accuracy of the new filters is comparable to Gaussian integration, provided moderate parameter ranges and well-behaved kernel functions are used. A collection of Fortran IV subprograms is included for both real and complex functions for each filter type. The algorithms have been successfully used in geophysical applications containing a wide variety of integral transforms

Anderson, Walter L.

1975-01-01

169

NASA Astrophysics Data System (ADS)

IR Fourier spectra of two enaminoketones with general formula F3Csbnd COsbnd CRdbnd CHsbnd N(CH3)2, R = F (DMTFBN); R = CH3, (DMTMBN) were studied in various pure solvents. For comparison results of earlier investigated enaminoketone R = H (DMTBN) was also presented. On the basis of NMR and IR spectra it was shown that enaminoketones DMTBN, DMTFBN and DMTMBN presented in solutions as equilibrium of two conformers, (E-s-Z) ? (E-s-E) (for DMTFBN these conformers are denoted as (Z-s-Z) and (Z-s-E), respectively). DFT calculations were carried out to evaluate relative energy and dipole moment of each spatial form. It was shown that ‘closed-ring' complex formation between (E-s-Z) and (E-s-E) conformers of DMTBN accounts for discrepancies between DFT calculations of conformer relative energies and experimentally evaluated enthalpies of (E-s-Z) ? (E-s-E) equilibrium. In ?-substituted DMTFBN and DMTMBN, where formation of ‘closed-ring' complex was impossible we did not observe such discrepancies. For both (E-s-Z) and (E-s-E) conformers of the DMTBN and DMTMBN the main influence on the ?˜(Cdbnd O) vibrations has the solvent's hydrogen bond donor (HBD) acidity, whereas for the DMTFBN an influence of the solvent's polarity/polarizability dominated.

Vdovenko, Sergey I.; Gerus, Igor I.; Zhuk, Yuri I.; Kukhar, Valery P.; Röschenthaler, Gerd-Volker

2014-10-01

170

Partial differential equation transform — Variational formulation and Fourier analysis

Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systematically provide intrinsic mode functions (IMFs) of signals and images. Due to their tunable time-frequency localization and perfect reconstruction, the operation of MoDEEs is called a PDE transform. By appropriate selection of PDE transform parameters, we can tune IMFs into trends, edges, textures, noise etc., which can be further utilized in the secondary processing for various purposes. This work introduces the variational formulation, performs the Fourier analysis, and conducts biomedical and biological applications of the proposed PDE transform. The variational formulation offers an algorithm to incorporate two image functions and two sets of low-pass PDE operators in the total energy functional. Two low-pass PDE operators have different signs, leading to energy disparity, while a coupling term, acting as a relative fidelity of two image functions, is introduced to reduce the disparity of two energy components. We construct variational PDE transforms by using Euler-Lagrange equation and artificial time propagation. Fourier analysis of a simplified PDE transform is presented to shed light on the filter properties of high order PDE transforms. Such an analysis also offers insight on the parameter selection of the PDE transform. The proposed PDE transform algorithm is validated by numerous benchmark tests. In one selected challenging example, we illustrate the ability of PDE transform to separate two adjacent frequencies of sin(x) and sin(1.1x). Such an ability is due to PDE transform’s controllable frequency localization obtained by adjusting the order of PDEs. The frequency selection is achieved either by diffusion coefficients or by propagation time. Finally, we explore a large number of practical applications to further demonstrate the utility of proposed PDE transform. PMID:22207904

Wang, Yang; Wei, Guo-Wei; Yang, Siyang

2011-01-01

171

Two-Dimensional Fourier Transform Analysis of Helicopter Flyover Noise

NASA Technical Reports Server (NTRS)

A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to separate main rotor and tail rotor noise. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.

SantaMaria, Odilyn L.; Farassat, F.; Morris, Philip J.

1999-01-01

172

The Quantum Schur Transform: I. Efficient Qudit Circuits

We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d-dimensional quantum systems is a transform between a standard computational basis to a labelling related to the representation theory of the symmetric and unitary groups. If we desire to implement the Schur transform to an accuracy of epsilon, then our circuit construction uses a number of gates which is polynomial in n, d and log(1/epsilon). The important insights we use to perform this construction are the selection of the appropriate subgroup adapted basis and the Wigner-Eckart theorem. Our efficient circuit construction renders numerous protocols in quantum information theory computationally tractable and is an important new efficient quantum circuit family which goes significantly beyond the standard paradigm of the quantum Fourier transform.

Dave Bacon; Isaac L. Chuang; Aram W. Harrow

2005-12-30

173

SCUBA-2 Fourier transform spectrometer (FTS-2) commissioning results

NASA Astrophysics Data System (ADS)

We present the latest commissioning results and instrument performance for the SCUBA-2 imaging Fourier Transform Spectrometer (FTS-2) installed at the James Clerk Maxwell Telescope (JCMT). This ancillary instrument provides intermediate spectral resolution (R ~10 to 5000) across both the 450 and 850 ?m atmospheric transmission windows with a FOV of ~5 arcmin2. The superconducting TES sensors and SQUID readout of SCUBA-2 present unique challenges for operation of an FTS; the sensitivity requirements demand high detector linearity and stability in addition to control of systematic atmospheric and optical spillover effects. We discuss the challenges encountered during commissioning and ongoing efforts to mitigate their effects.

Gom, Brad G.; Naylor, David A.; Friberg, Per; Bell, Graham S.; Bintley, Daniel; Abdelazim, Sherif; Sherwood, Matt

2014-07-01

174

IR spectral depth profiling using Fourier transform photothermal beam deflection

NASA Astrophysics Data System (ADS)

Fourier transform IR photothermal beam-deflection spectroscopy (PBDS) was used to make spectral depth-profiling measurements with synthetic bilayer samples of polyethylene/nitrocellulose, with a commercial plastic having surface printing and with a single human hair. An interferometer modified to operate at several scan speeds was used to record the spectra, without the cell-resonance problems found with photoacoustic spectroscopy (PAS). The utility of spectral depth profiling is discussed; significant S/N improvements seem to be needed and, with either PBDS or PAS, a wider range of modulation frequencies is required for the methods to be useful.

Varlashkin, P. G.; Low, M. J. D.

1986-05-01

175

Beam profile for the Herschel-SPIRE Fourier transform spectrometer

NASA Astrophysics Data System (ADS)

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.

Makiwa, Gibion; Naylor, David A.; Ferlet, Marc; Salji, Carl; Swinyard, Bruce; Polehampton, Edward; van der Wiel, Matthijs H. D.

2013-06-01

176

Fourier transform spectrum of the second torsional band of hydrazine

NASA Astrophysics Data System (ADS)

The far-infrared v = 2 ? 0 torsional overtone band has been studied by Fourier transform spectroscopy with an apodized resolution of 0.006 cm -1. About 800 pPK, pQK, rQK, and rRK transitions of 15 subbands with ? K· K? from -8 to 6 were assigned. A global fitting was made with the use of Hougen's group-theoretical formalism to determine 34 molecular parameters in the second torsional state and to obtain a standard deviation 0.001 04 cm -1. Pure torsionalwagging levels in the second torsional state are derived from the tunneling parameters obtained.

Ohashi, Nobukimi; Olson, W. Bruce

1991-02-01

177

Retrievals for the atmospheric chemistry experiment Fourier-transform spectrometer.

SCISAT-1, also known as the Atmospheric Chemistry Experiment, is a satellite mission for remote sensing of the Earth's atmosphere, launched on 12 August 2003. The primary instrument on the satellite is a 0.02 cm(-1) resolution Fourier-transform spectrometer operating in the mid-IR (750-4400 cm(-1)). We describe the approach developed for the retrieval of atmospheric temperature and pressure from the troposphere to the lower thermosphere as well as the strategy for the retrievals of volume-mixing ratio profiles of atmospheric species. PMID:16318195

Boone, Chris D; Nassar, Ray; Walker, Kaley A; Rochon, Yves; McLeod, Sean D; Rinsland, Curtis P; Bernath, Peter F

2005-11-20

178

Fiber-optic thermometer using Fourier transform spectroscopy

NASA Technical Reports Server (NTRS)

An integrated-optic Mach-Zender interferometer is used as a Fourier transform spectrometer to analyze the input and output spectra of a temperature-sensing thin-film etalon. This configuration provides a high degree of immunity to the effects of changes in the source spectrum, and it readily permits the interrogation of a number of different sensors using a single spectrometer. In addition, this system has a potentially low cost because it uses optical communications hardware that may in the future be manufactured in large quantities.

Beheim, Glenn; Sotomayor, Jorge L.; Flatico, Joseph M.; Azar, Massood T.

1991-01-01

179

Fourier transform vibrational circular dichroism of small pharmaceutical molecules

NASA Astrophysics Data System (ADS)

Fourier transform vibrational circular dichroism (FT-VCD) spectra of the small pharmaceutical molecules propanolol, ibuprofen and naproxen have been measured in the hydrogen stretching and mid-infrared regions to obtain information on solution conformation and to identify markers for absolute configuration determination. Ab initio molecular orbital calculations of low energy conformations, vibrational frequencies and VCD intensities for fragments of the drugs were utilized in interpreting the spectra. Features characteristic of five conformers of propranolol were identified. The weak positive CH stretching VCD signal in ibuprofen and naproxen is characteristic of the S-configuration of the chiral center common to these two analgesics.

Long, Fujin; Freedman, Teresa B.; Nafie, Laurence A.

1998-06-01

180

Data Transmission by Frequency-Division Multiplexing Using the Discrete Fourier Transform

The Fourier transform data communication system is a realization of frequency-division multiplexing (FDM) in which discrete Fourier transforms are computed as part of the modulation and demodulation processes. In addition to eliminating the bunks of subcarrier oscillators and coherent demodulators usually required in FDM systems, a completely digital implementation can be built around a special-purpose computer performing the fast Fourier

S. B. WEINSTEIN; PAUL M. EBERT

1971-01-01

181

2D discrete Fourier transform on sliding windows.

Discrete Fourier transform (DFT) is the most widely used method for determining the frequency spectra of digital signals. In this paper, a 2D sliding DFT (2D SDFT) algorithm is proposed for fast implementation of the DFT on 2D sliding windows. The proposed 2D SDFT algorithm directly computes the DFT bins of the current window using the precalculated bins of the previous window. Since the proposed algorithm is designed to accelerate the sliding transform process of a 2D input signal, it can be directly applied to computer vision and image processing applications. The theoretical analysis shows that the computational requirement of the proposed 2D SDFT algorithm is the lowest among existing 2D DFT algorithms. Moreover, the output of the 2D SDFT is mathematically equivalent to that of the traditional DFT at all pixel positions. PMID:25585421

Park, Chun-Su

2015-03-01

182

Fourier Transform for Fermionic Systems and the Spectral Tensor Network

NASA Astrophysics Data System (ADS)

Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law. Translationally invariant systems of free fermions in arbitrary dimensions as well as 1D systems solved by the Jordan-Wigner transformation are shown to be exactly represented in this class. Further, it is proposed that these tensor networks be used as generic structures to variationally describe more complicated systems, such as interacting fermions. This class shares some similarities with the Evenbly-Vidal branching multiscale entanglement renormalization ansatz, but with some important differences and greatly reduced computational demands.

Ferris, Andrew J.

2014-07-01

183

Voigt line infrared atmospheric transmittance calculations by Fourier transform

NASA Astrophysics Data System (ADS)

The absorption coefficient space of an IR atmospheric path contains the linear superposition of many Voigt spectral lines. This paper discusses the practical application of Karp's method to the simulation of satellite transmittance and radiance observations by using fast Fourier transforms on the recursively generated Voigt transforms. Although the procedure is physically straightforward, it is nonetheless computationally demanding and suited primarily to narrow isolated Q-branch regions. Performing the calculation on a 2.4/cm wide 15-micron CO2 Q-branch region demonstrates that 4% of the total absorption takes place above 0.1 mb. This absorption is in the cold mesopause and results in a 1-2% radiation deficit with its inclusion in a satellite radiation calculation.

Neuendorffer, A. C.

1980-04-01

184

Fast Fourier Transform Co-processor (FFTC), towards embedded GFLOPs

NASA Astrophysics Data System (ADS)

Many signal processing applications and algorithms perform their operations on the data in the transform domain to gain efficiency. The Fourier Transform Co-Processor has been developed with the aim to offload General Purpose Processors from performing these transformations and therefore to boast the overall performance of a processing module. The IP of the commercial PowerFFT processor has been selected and adapted to meet the constraints of the space environment. In frame of the ESA activity "Fast Fourier Transform DSP Co-processor (FFTC)" (ESTEC/Contract No. 15314/07/NL/LvH/ma) the objectives were the following: • Production of prototypes of a space qualified version of the commercial PowerFFT chip called FFTC based on the PowerFFT IP. • The development of a stand-alone FFTC Accelerator Board (FTAB) based on the FFTC including the Controller FPGA and SpaceWire Interfaces to verify the FFTC function and performance. The FFTC chip performs its calculations with floating point precision. Stand alone it is capable computing FFTs of up to 1K complex samples in length in only 10?sec. This corresponds to an equivalent processing performance of 4.7 GFlops. In this mode the maximum sustained data throughput reaches 6.4Gbit/s. When connected to up to 4 EDAC protected SDRAM memory banks the FFTC can perform long FFTs with up to 1M complex samples in length or multidimensional FFT-based processing tasks. A Controller FPGA on the FTAB takes care of the SDRAM addressing. The instructions commanded via the Controller FPGA are used to set up the data flow and generate the memory addresses. The paper will give an overview on the project, including the results of the validation of the FFTC ASIC prototypes.

Kuehl, Christopher; Liebstueckel, Uwe; Tejerina, Isaac; Uemminghaus, Michael; Witte, Felix; Kolb, Michael; Suess, Martin; Weigand, Roland; Kopp, Nicholas

2012-10-01

185

Soft x-ray microscope using Fourier transform holography

A Fourier transform holographic microscope with an anticipated resolution of better than 100 nm has been built. Extensive testing of the apparatus has begun. Preliminary results include the recording of interference fringes using 3.6 nm x-rays. The microscope employs a charge-coupled device (CCD) detector array of 576 {times} 384 elements. The system is illuminated by soft x-rays from a high brightness undulator. The reference point source is formed by a Fresnel zone plate with a finest outer zone width of 50 nm. Sufficient temporal coherence for hologram formation is obtained by a spherical grating monochromator. The x-ray hologram intensities at the recording plane are to be collected, digitized and reconstructed by computer. Data acquisition is under CAMAC control, while image display and off-line processing takes place on a VAX graphics workstation. Computational models of Fourier transform hologram synthesis, and reconstruction in the presence of noise, have demonstrated the feasibility of numerical methods in two dimensions, and that three-dimensional information is potentially recoverable. 13 refs., 3 figs.

McNulty, I.; Kirz, J.; Jacobsen, C.; Anderson, E.; Howells, M.R.; Rarback, H. (State Univ. of New York, Stony Brook, NY (USA). Dept. of Physics; Lawrence Berkeley Lab., CA (USA); Brookhaven National Lab., Upton, NY (USA))

1989-01-01

186

Ultrafast and versatile spectroscopy by temporal Fourier transform.

One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges. PMID:24939667

Zhang, Chi; Wei, Xiaoming; Marhic, Michel E; Wong, Kenneth K Y

2014-01-01

187

Ultrafast and versatile spectroscopy by temporal Fourier transform

NASA Astrophysics Data System (ADS)

One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges.

Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.

2014-06-01

188

Fourier transform spectrometer processing: Data reduction and processor design

NASA Astrophysics Data System (ADS)

A laboratory model of a flexible processing and data handling module for the Imaging Fourier Transform Spectrometer (IFTS) is described. The IFTS is one of the instruments under the Solar Interferometeric Mission for Ultrahigh Resolution Imaging Spectroscopy (SIMURIS) mission. The purpose of the data handling module is to do data compression and to select the data to be transmitted for each observation program. The interferogram time-series-out from the optical filter and the IFTS is selected by demodulation and filtered by a set of multirate filters. The bandwidths of the compressed interferograms is close to the optical bandwidths, and they can be transmitted with reduced bit rates. The short Fourier transformation of these bands is left for ground based preprocessing. The data handling module consists of standard 6U VME boards. Each board has a TMS320C30 signal processor and a special purpose input processor. A complete data handling module would consist of between 5 and 10 boards for a 400 by 400 array with 0.05 arcsec pixels. The model consists of two boards, of which one functions as an input data generator.

Andreassen, K.; Armbruster, P. A.

1992-05-01

189

Radial Hilbert Transform in terms of the Fourier Transform applied to Image Encryption

NASA Astrophysics Data System (ADS)

In the present investigation, a mathematical algorithm under Matlab platform using Radial Hilbert Transform and Random Phase Mask for encrypting digital images is implemented. The algorithm is based on the use of the conventional Fourier transform and two random phase masks, which provide security and robustness to the system implemented. Random phase masks used during encryption and decryption are the keys to improve security and make the system immune to attacks by program generation phase masks.

Morales, Y.; Díaz, L.; Torres, C.

2015-01-01

190

Quantum Canonical Transformations: Physical Equivalence of Quantum Theories

Two quantum theories are physically equivalent if they are related, not by a unitary transformation, but by an isometric transformation. The conditions under which a quantum canonical transformation is an isometric transformation are given.

Arlen Anderson

1993-02-15

191

The Empirical Mode Decomposition algorithm via Fast Fourier Transform

NASA Astrophysics Data System (ADS)

In this paper we consider a problem of implementing a fast algorithm for the Empirical Mode Decomposition (EMD). EMD is one of the newest methods for decomposition of non-linear and non-stationary signals. A basis of EMD is formed "on-the-fly", i.e. it depends from a distribution of the signal and not given a priori in contrast on cases Fourier Transform (FT) or Wavelet Transform (WT). The EMD requires interpolating of local extrema sets of signal to find upper and lower envelopes. The data interpolation on an irregular lattice is a very low-performance procedure. A classical description of EMD by Huang suggests doing this through splines, i.e. through solving of a system of equations. Existence of a fast algorithm is the main advantage of the FT. A simple description of an algorithm in terms of Fast Fourier Transform (FFT) is a standard practice to reduce operation's count. We offer a fast implementation of EMD (FEMD) through FFT and some other cost-efficient algorithms. Basic two-stage interpolation algorithm for EMD is composed of a Upscale procedure through FFT and Downscale procedure through a selection procedure for signal's points. First we consider the local maxima (or minima) set without reference to the axis OX, i.e. on a regular lattice. The Upscale through the FFT change the signal's length to the Least Common Multiple (LCM) value of all distances between neighboring extremes on the axis OX. If the LCM value is too large then it is necessary to limit local set of extrema. In this case it is an analog of the spline interpolation. A demo for FEMD in noise reduction task for OCT has been shown.

Myakinin, Oleg O.; Zakharov, Valery P.; Bratchenko, Ivan A.; Kornilin, Dmitry V.; Artemyev, Dmitry N.; Khramov, Alexander G.

2014-09-01

192

Bivariate raising and lowering differential operators for eigenfunctions of a 2D Fourier transform

NASA Astrophysics Data System (ADS)

We define a two-dimensional (2D) Fourier transform that self-reproduces a one-parameter family of bivariate Hermite functions; these are eigenfunctions of a Hamiltonian differential operator of second order, whose exponential is that transform. We find explicit forms of the bivariate raising and lowering partial differential operators of first degree for the eigenfunctions of this 2D Fourier transform.

Area, Iván; Atakishiyev, Natig; Godoy, Eduardo; Wolf, Kurt Bernardo

2015-02-01

193

The Radon Transform on SO(3): A Fourier Slice Theorem and Numerical

The Radon Transform on SO(3): A Fourier Slice Theorem and Numerical Inversion Ralf Hielscherdimensional Radon transform on the rotation group SO(3) is an ill posed inverse problem which applies to X inversion of the onedimensional Radon transform on SO(3). Based on a Fourier slice theorem the discrete

194

NASA Astrophysics Data System (ADS)

We propose a generalization of the encryption system based on double random phase encoding (DRPE) and a joint transform correlator (JTC), from the Fourier domain to the fractional Fourier domain (FrFD) by using the fractional Fourier operators, such as the fractional Fourier transform (FrFT), fractional traslation, fractional convolution and fractional correlation. Image encryption systems based on a JTC architecture in the FrFD usually produce low quality decrypted images. In this work, we present two approaches to improve the quality of the decrypted images, which are based on nonlinear processing applied to the encrypted function (that contains the joint fractional power spectrum, JFPS) and the nonzero-order JTC in the FrFD. When the two approaches are combined, the quality of the decrypted image is higher. In addition to the advantages introduced by the implementation of the DRPE using a JTC, we demonstrate that the proposed encryption system in the FrFD preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of both the key random mask in the decryption process and the retrieval of the primary image. The feasibility of this encryption system is verified and analyzed by computer simulations.

Vilardy, Juan M.; Torres, Yezid; Millán, María S.; Pérez-Cabré, Elisabet

2014-12-01

195

Optical image encryption based on the multiple-parameter fractional Fourier transform.

A novel image encryption algorithm is proposed based on the multiple-parameter fractional Fourier transform, which is a generalized fractional Fourier transform, without the use of phase keys. The image is encrypted simply by performing a multiple-parameter fractional Fourier transform with four keys. Optical implementation is suggested. The method has been compared with existing methods and shows superior robustness to blind decryption. PMID:18347716

Tao, Ran; Lang, Jun; Wang, Yue

2008-03-15

196

Multiresolution graph Fourier transform for compression of piecewise smooth images.

Piecewise smooth (PWS) images (e.g., depth maps or animation images) contain unique signal characteristics such as sharp object boundaries and slowly varying interior surfaces. Leveraging on recent advances in graph signal processing, in this paper, we propose to compress the PWS images using suitable graph Fourier transforms (GFTs) to minimize the total signal representation cost of each pixel block, considering both the sparsity of the signal's transform coefficients and the compactness of transform description. Unlike fixed transforms, such as the discrete cosine transform, we can adapt GFT to a particular class of pixel blocks. In particular, we select one among a defined search space of GFTs to minimize total representation cost via our proposed algorithms, leveraging on graph optimization techniques, such as spectral clustering and minimum graph cuts. Furthermore, for practical implementation of GFT, we introduce two techniques to reduce computation complexity. First, at the encoder, we low-pass filter and downsample a high-resolution (HR) pixel block to obtain a low-resolution (LR) one, so that a LR-GFT can be employed. At the decoder, upsampling and interpolation are performed adaptively along HR boundaries coded using arithmetic edge coding, so that sharp object boundaries can be well preserved. Second, instead of computing GFT from a graph in real-time via eigen-decomposition, the most popular LR-GFTs are pre-computed and stored in a table for lookup during encoding and decoding. Using depth maps and computer-graphics images as examples of the PWS images, experimental results show that our proposed multiresolution-GFT scheme outperforms H.264 intra by 6.8 dB on average in peak signal-to-noise ratio at the same bit rate. PMID:25494508

Hu, Wei; Cheung, Gene; Ortega, Antonio; Au, Oscar C

2015-01-01

197

Quantum Optical Version of Classical Optical Transformations and Beyond

By the newly developed technique of integration within an ordered product (IWOP) of operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel-Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We can not only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. We derive GFO's normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area to finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the IWOP technique are fully used. All these confirms Dirac's assertion: " ... for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory".

Hong-yi Fan; Li-yun Hu

2010-10-03

198

Initial Results from the USNO Dispersed Fourier Transform Spectrograph

We have designed and constructed a ``dispersed Fourier Transform Spectrometer'' (dFTS), consisting of a conventional FTS followed by a grating spectrometer. By combining these two devices, we negate a substantial fraction of the sensitivity disadvantage of a conventional FTS for high resolution, broadband, optical spectroscopy, while preserving many of the advantages inherent to interferometric spectrometers. In addition, we have implemented a simple and inexpensive laser metrology system, which enables very precise calibration of the interferometer wavelength scale. The fusion of interferometric and dispersive technologies with a laser metrology system yields an instrument well-suited to stellar spectroscopy, velocimetry, and extrasolar planet detection, which is competitive with existing high-resolution, high accuracy stellar spectrometers. In this paper, we describe the design of our prototype dFTS, explain the algorithm we use to efficiently reconstruct a broadband spectrum from a sequence of narrowband interferograms, and present initial observations and resulting velocimetry of stellar targets.

Arsen R. Hajian; Bradford B. Behr; Andrew T. Cenko; Robert P. Olling; David Mozurkewich; J. Thomas Armstrong; Brian Pohl; Sevan Petrossian; Kevin H. Knuth; Robert B. Hindsley; Marc Murison; Michael Efroimsky; Ronald Dantowitz; Marek Kozubal; Douglas G. Currie; Tyler E. Nordgren; Christopher Tycner; Robert S. McMillan

2007-02-05

199

Gas emission analysis based on Fourier transformed infrared spectroscopy

NASA Astrophysics Data System (ADS)

Solar occultation flux (SOF), a new optical technology to detect the gas based on the traditional Fourier transformed infrared spectroscopy (FTIR) developed quickly recently. In this paper, the system and the data analysis is investigated. First a multilayer transmission model of solar radiation is simulated. Then the retrieval process is illustrated. In the proceeding of the data analysis, the Levenberg-Marquardt non-linear square fitting is used to obtain the gas column concentration and the related emission ratio. After the theory certification, the built up system is conducted in a fertilizer plant in Hefei city .The results show SOF is available in the practice and the retrieved gas column concentration can give important information about the pollution emission and dispersion

Shu, Xiaowen; Zhang, Xiaofu; Lian, Xu; Jin, Hui

2014-12-01

200

Fourier transform microwave spectroscopy of CH(2)CFO.

Rotational spectra of the CH(2)CFO radical in the (2)A(") ground state with resolved fine and hyperfine structures have been observed for the first time by Fourier transform microwave spectroscopy. Rotational transitions are analyzed using the ordinary rigid asymmetric top Hamiltonian for doublet species with three nuclear spins. Seventeen molecular constants including the fine and hyperfine coupling constants have been determined. The CH(2)CFO radical is confirmed to be a planer molecule in the ground electronic state since it has a small positive inertial defect. From the hyperfine coupling constants of protons, the unpaired electron density on the CH(2) carbon atom is estimated to be about 85%. Thus, the formylmethyl-type resonance form (CH(2)CF=O) is a dominant structure in the ground electronic state, and fluorine substitution has negligible effect on the C-C-O pi conjugate system. PMID:19530765

Watanabe, Akihiro; Sumiyoshi, Yoshihiro; Endo, Yasuki

2009-06-14

201

Instrument concept of the imaging Fourier transform spectrometer GLORIA

NASA Astrophysics Data System (ADS)

The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) is an imaging limb emission sounder operating in the thermal infrared region. It is designed to provide measurements of the Upper Troposphere/Lower Stratosphere with high spatial and high spectral resolution. The instrument consists of an imaging Fourier transform spectrometer integrated in a gimbal. The assembly can be mounted in the belly pod of the German high altitude and long range research aircraft HALO and in instrument bays of the Russian M55 Geophysica. Measurements are made predominantly in two distinct modes: the chemistry mode emphasises chemical analysis with high spectral resolution, the dynamics mode focuses on dynamical processes of the atmosphere with very high spatial resolution. In addition the instrument allows tomographic analyses of air volumes. The first measurement campaigns have shown compliance with key performance and operational requirements.

Friedl-Vallon, F.; Gulde, T.; Hase, F.; Kleinert, A.; Kulessa, T.; Maucher, G.; Neubert, T.; Olschewski, F.; Piesch, C.; Preusse, P.; Rongen, H.; Sartorius, C.; Schneider, H.; Schönfeld, A.; Tan, V.; Bayer, N.; Blank, J.; Dapp, R.; Ebersoldt, A.; Fischer, H.; Graf, F.; Guggenmoser, T.; Höpfner, M.; Kaufmann, M.; Kretschmer, E.; Latzko, T.; Nordmeyer, H.; Oelhaf, H.; Orphal, J.; Riese, M.; Schardt, G.; Schillings, J.; Sha, M. K.; Suminska-Ebersoldt, O.; Ungermann, J.

2014-03-01

202

Instrument concept of the imaging Fourier transform spectrometer GLORIA

NASA Astrophysics Data System (ADS)

The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) is an imaging limb emission sounder operating in the thermal infrared region. It is designed to provide measurements of the upper troposphere/lower stratosphere with high spatial and high spectral resolution. The instrument consists of an imaging Fourier transform spectrometer integrated into a gimbal. The assembly can be mounted in the belly pod of the German High Altitude and Long Range research aircraft (HALO) and in instrument bays of the Russian M55 Geophysica. Measurements are made in two distinct modes: the chemistry mode emphasises chemical analysis with high spectral resolution, and the dynamics mode focuses on dynamical processes of the atmosphere with very high spatial resolution. In addition, the instrument allows tomographic analyses of air volumes. The first measurement campaigns have shown compliance with key performance and operational requirements.

Friedl-Vallon, F.; Gulde, T.; Hase, F.; Kleinert, A.; Kulessa, T.; Maucher, G.; Neubert, T.; Olschewski, F.; Piesch, C.; Preusse, P.; Rongen, H.; Sartorius, C.; Schneider, H.; Schönfeld, A.; Tan, V.; Bayer, N.; Blank, J.; Dapp, R.; Ebersoldt, A.; Fischer, H.; Graf, F.; Guggenmoser, T.; Höpfner, M.; Kaufmann, M.; Kretschmer, E.; Latzko, T.; Nordmeyer, H.; Oelhaf, H.; Orphal, J.; Riese, M.; Schardt, G.; Schillings, J.; Sha, M. K.; Suminska-Ebersoldt, O.; Ungermann, J.

2014-10-01

203

Surface analysis by Fourier-transform infrared (FTIR) spectroscopy

A diffuse-reflectance capability for the Fourier transform infrared spectrometer at the Y-12 Plant Laboratory has been implemented. A sample cell with a 25 to 400/sup 0/C temperature-controlled sample stage and an ultrahigh-vacuum-to-atmospheric pressure gas-handling capability has been developed. Absorbance of light from the spectrometer beam, resulting from the beam being scattered from a powder sample, can be measured. This capability of detecting molecular species on and in powders is to be used to study chemisorption on actinide and rare-earth metals, alloys, and compounds. Cell design is described along with experiments demonstrating its performance in detecting moisture absorption on uranium oxide, moisture and carbon dioxide absorption on the lithium hydride/hydroxide system, and carbon dioxide absorption on potassium borohydride. 13 figures.

Powell, G.L.; Smyrl, N.R.; Fuller, E.L.

1981-08-12

204

Discrimination of different Chrysanthemums with Fourier transform infrared spectroscopy

NASA Astrophysics Data System (ADS)

Use Fourier transform infrared spectroscopy (FT-IR) to analyze simultaneously the main chemical constituents in different solvent extracts of seven kinds of Chrysanthemum samples of different regions. The findings indicate that different Chrysanthemum samples have dissimilar fingerprint characters in FT-IR spectra. Such spectral technique can provide substance structural information of the complicated test samples. According to these spectral fingerprint features, we cannot only identify the main components of different extracts, but also distinguish the origins of the Chrysanthemum samples from different regions easily, which is a troublesome work by existing analytical methods. FT-IR, with the characters of speediness, good repeatability and easy operation, can be used as an effective analytical means to study the complicated system, in our research, the tradition Chinese medicines.

Liu, Hong-xia; Zhou, Qun; Sun, Su-qin; Bao, Hong-juan

2008-07-01

205

Identification of Amanita mushrooms by fourier transform infrared spectroscopy

NASA Astrophysics Data System (ADS)

Amanita is one of cosmopolitan genera of basidiomycetes. This genus contains some of the most poisonous toadstools, as well as several species of the most favorite edible mushrooms. In this paper, Fourier transform infrared spectroscopy was used for obtaining vibrational spectra of the fruiting bodies of wild growing Amanita mushrooms. The results show that the mushrooms exhibit characteristic spectra, whose strong absorption bands appear at about 1655, 1076, and 1040 cm -1. The vibrational spectra indicate that the main compositions of the Amanita mushrooms are proteins and polysaccharides. The observed spectral differences might be used to discriminate different species of Amanita. It is showed that FTIR spectroscopic method is a valuable tool for rapid and nondestructive identification of Amanita mushrooms.

Zhao, Dezhang; Liu, Gang; Song, Dingshan; Liu, Jian-hong; Zhou, Yilan; Ou, Jiaming; Sun, Shizhong

2006-09-01

206

Generation of Fourier-transform-limited heralded single photons

In this paper we study the spectral (temporal) properties of heralded single photon wave packets, triggered by the detection of an idler photon in the process of parametric down conversion. The generated single photons are studied within the framework of the chronocyclic Wigner function, from which the single photon spectral width and temporal duration can be computed. We derive specific conditions on the two-photon joint spectral amplitude which result in both pure and Fourier-transform-limited heralded single photons. Likewise, we present specific source geometries which lead to the fulfillment of these conditions and show that one of these geometries leads, for a given pump bandwidth, to the temporally shortest possible heralded single photon wave packets.

U'Ren, Alfred B.; Jeronimo-Moreno, Yasser [Division de Fisica Aplicada, Centro de Investigacion Cientifica y Educacion Superior de Ensenada (CICESE), Baja California, 22860 (Mexico); Garcia-Gracia, Hipolito [Photonics and Mathematical Optics Group, Tecnologico de Monterrey, Nuevo Leon, 64849 (Mexico)

2007-02-15

207

[Identification of edible mushrooms by Fourier transform infrared spectroscopy].

In this paper, Fourier transform infrared spectroscopy (FTIR) was used to identify edible mushrooms belonging to Auriculariales, Aphyllophorales, and Agaricales of Basidiomycotina. Vibrational spectra of fruiting bodies of ten species belonging to nine different genera of mushrooms (one is cultivated, and the others are wild growing) were recorded. The spectra were divided into five regions, i.e. 3 050 to 2 800 cm(-1), 1 750 to 1 500 cm(-1), 1 500 to 1 200 cm(-1), 1 200 to 950 cm(-1), and 950 to 700 cm(-1). These regions contain characteristic bands among different mushrooms. According to the characteristic bands in the five regions, different species of mushrooms can be identified. Vibrational spectra in the interval between 950 and 700 cm(-1) could serve as fingerprints to discriminate different genera of mushrooms. PMID:15766114

Liu, Gang; Liu, Jian-Hong; Yang, Ai-Ming; Dong, Qin; Song, Ding-Shan

2004-08-01

208

Process control using fiber optics and Fourier transform infrared spectroscopy

NASA Astrophysics Data System (ADS)

A process control system has been constructed using optical fibers interfaced to a Fourier transform infrared (FT-IR) spectrometer, to achieve remote spectroscopic analysis of food samples during processing. The multichannel interface accommodates six fibers, allowing the sequential observation of up to six samples. Novel fiber-optic sampling cells have been constructed, including transmission and attenuated total reflectance (ATR) designs. Different fiber types have been evaluated; in particular, plastic clad silica (PCS) and zirconium fluoride fibers. Processes investigated have included the dilution of fruit juice concentrate, and the addition of alcohol to fruit syrup. Suitable algorithms have been written which use the results of spectroscopic measurements to control and monitor the course of each process, by actuating devices such as valves and switches.

Kemsley, E. K.; Wilson, Reginald H.

1992-03-01

209

Detecting hypovolemia in postoperative patients using a discrete Fourier transform.

In the present paper, an attempt was made to find waveform-derived variables that would be useful for a more precise diagnosis of hypovolemia. In attempting this, arterial blood pressure graphs of 18 hypovolemic postoperative patients were analysed using a discrete Fourier transform. Using a paired samples t-test, the amplitude of the first harmonic (A1) is shown to be significantly higher in normovolemic cases than in hypovolemic ones (p<0.001). Based on the values of A1, a preliminary study was performed in which an additional group of 14 hypovolemic and 14 normovolemic patients were categorized into hypovolemic and normovolemic groups using logistic regression. The method proved to be successful in identifying hypovolemic patients: the prediction was correct in 80% and wrong only in 20%, indicating that A1 is potentially a useful parameter in detecting hypovolemia. PMID:25665937

Szabó, Viktor; Halász, Gábor; Gondos, Tibor

2015-04-01

210

Data processing in Fourier transform ion cyclotron resonance mass spectrometry.

The Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer intricately couples advanced physics, instrumentation, and electronics with chemical and particularly biochemical research. However, general understanding of the data processing methodologies used lags instrumentation, and most data processing algorithms we are familiar with in FT-ICR are not well studied; thus, professional skill and training in FT-ICR operation and data analysis is still the key to achieve high performance in FT-ICR. This review article is focused on FT-ICR data processing, and explains the procedures step-by-step for users with the goal of maximizing spectral features, such as mass accuracy, resolving power, dynamic range, and detection limits. PMID:24403247

Qi, Yulin; O'Connor, Peter B

2014-01-01

211

Structural Characterization of Carbohydrates by Fourier Transform Tandem Mass Spectrometry

Fourier transform tandem mass spectrometry (MS/MS) provides high mass accuracy, high sensitivity, and analytical versatility and has therefore emerged as an indispensable tool for structural elucidation of biomolecules. Glycosylation is one of the most common posttranslational modifications, occurring in ~50% of proteins. However, due to the structural diversity of carbohydrates, arising from non-template driven biosynthesis, achievement of detailed structural insight is highly challenging. This review briefly discusses carbohydrate sample preparation and ionization methods, and highlights recent developments in alternative high-resolution MS/MS strategies, including infrared multiphoton dissociation (IRMPD), electron capture dissociation (ECD), and electron detachment dissociation (EDD), for carbohydrates with a focus on glycans and proteoglycans from mammalian glycoproteins. PMID:22389641

Zhou, Wen; Håkansson, Kristina

2012-01-01

212

A compact hot-nozzle Fourier-transform microwave spectrometer

NASA Astrophysics Data System (ADS)

A newly constructed pulsed nozzle, Fourier-transform microwave spectrometer utilizes a Fabry-Perot cavity consisting of spherical resonators having diameters of only 10 cm. Tests of this very compact-cavity system show that its sensitivity is only slightly lower than that of a comparably configured system of the Balle-Flygare design having resonators with diameters of 36 cm. With a volume 50 times smaller than in conventional systems, the compact cavity also requires a much smaller vacuum chamber which can be pumped by a relatively small 6 in. diffusion pump. The system includes an integral ceramic nozzle which can be heated to temperatures above 1000 °C. Spectrometer characteristics have been demonstrated by means of experiments on OCS isotopomers in ground and excited vibrational states, ArOCS complexes, and chloroketene, a reactive intermediate formed by pyrolysis of chloroacetylchloride.

Harmony, Marlin D.; Beran, Kyle A.; Angst, Deanna M.; Ratzlaff, Kenneth L.

1995-11-01

213

A rheumatoid arthritis study by Fourier transform infrared spectroscopy

NASA Astrophysics Data System (ADS)

Rheumatoid arthritis is a systemic inflammatory disease of unknown causes and a new methods to identify it in early stages are needed. The main purpose of this work is the biochemical differentiation of sera between normal and RA patients, through the establishment of a statistical method that can be appropriately used for serological analysis. The human sera from 39 healthy donors and 39 rheumatics donors were collected and analyzed by Fourier Transform Infrared Spectroscopy. The results show significant spectral variations with p<0.05 in regions corresponding to protein, lipids and immunoglobulins. The technique of latex particles, coated with human IgG and monoclonal anti-CRP by indirect agglutination known as FR and CRP, was performed to confirm possible false-negative results within the groups, facilitating the statistical interpretation and validation of the technique.

Carvalho, Carolina S.; Silva, Ana Carla A.; Santos, Tatiano J. P. S.; Martin, Airton A.; dos Santos Fernandes, Ana Célia; Andrade, Luís E.; Raniero, Leandro

2012-01-01

214

Vector power multiple-parameter fractional Fourier transform of image encryption algorithm

NASA Astrophysics Data System (ADS)

In this paper, we propose a multiple-parameter fractional Fourier transform with its transform order being a real vector, based on which a high-security image encryption scheme is also given. This novel fractional Fourier transform has removed the restriction on the dimension of transform order and highly enhances the security of image encryption scheme proposed in this paper without increasing the computational complexity and hardware cost. The numerical results verify the efficacy and security of this image encryption method. The vector power multi-parameter fractional Fourier transform is a generalized form of the classical fractional Fourier transform with all the previous fractional Fourier transform as its special cases and has theoretical significance in information processing and information security.

Ran, Qiwen; Zhao, Tieyu; Yuan, Lin; Wang, Jian; Xu, Lei

2014-11-01

215

COMPARISON OF METHOD OF MOMENTS, LAPLACE TRANSFORMS, AND FOURIER TRANSFORMS IN PARAMETER ESTIMATION FROM TAYLOR DISPERSION DATA A Thesis by DAVID ALAN BALISTER Submitted to the Graduate College of Texas ASSAM University in partial... Fulfillment of the requirement for the degree of MASTER OF SCIENCE December 1986 Major Subject: Chemical Engineering COMPARISON OF METHOD OF MOMENTS, LAPLACE TRANSFORMS, AND FOURIER TRANSFORMS IN PARAMETER ESTIMATION FROM TAYLOR DISPERSION DATA A Thesis...

Balister, David Alan

1986-01-01

216

Quantization maps, algebra representation, and non-commutative Fourier transform for Lie groups

The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a generalized notion of (non-commutative) Fourier transform, different from standard harmonic analysis, has been recently developed, and found several applications, especially in the quantum gravity literature. We show that this algebra representation can be defined on the sole basis of a quantization map of the classical Poisson algebra, and identify the conditions for its existence. In particular, the corresponding non-commutative star-product carried by this representation is obtained directly from the quantization map via deformation quantization. We then clarify under which conditions a unitary intertwiner between such algebra representation and the usual group representation can be constructed giving rise to the non-commutative plane waves and consequently, the non-commutative Fourier transform. The compact groups U(1) and SU(2) are considered for different choices of quantization maps, such as the symmetric and the Duflo map, and we exhibit the corresponding star-products, algebra representations, and non-commutative plane waves.

Guedes, Carlos; Oriti, Daniele [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam (Germany)] [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam (Germany); Raasakka, Matti [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam (Germany) [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam (Germany); LIPN, Institut Galilée, Université Paris-Nord, 99, av. Clement, 93430 Villetaneuse (France)

2013-08-15

217

A rapid and non-destructive method was used to discriminate between calligraphies by means of Fourier transform infrared (FTIR) and FT-Raman spectroscopy in this paper. In order to discriminate two real calligraphies of Ouyang Zhong-shi from two counterfeit ones, the authors investigated the inkpad and the rice paper of the calligraphies by means of FT-Raman spectroscopy and tested the inkpad and the ink mark of the calligraphies by means of FTIR spectroscopy. It could be seen that the tiny, delicated varied chemical components of the real and the counterfeit calligraphies lead to different characters in vibration frequencies of IR and Raman functional groups and also the real calligraphies have the perfect reiteration. So the authors can discriminate between the real and the counterfeit calligraphies. It is proved that FTIR and FT-Raman are useful in the non-destructive identification of calligraphies and more precise and quicker than traditional approaches. PMID:15762467

Na, Na; Ouyang, Qi-ming; Qiao, Yu-qing; Ouyang, Jin; Wang, Ya-hui

2004-11-01

218

Quantum transition probabilities and classical Fourier harmonics

NASA Astrophysics Data System (ADS)

A quantum dot is an atomic-like system consisting of a semiconductor nanoparticle surrounded by an insulator. When an electron in the valence band of the semiconductor becomes excited, the electron-hole pair that is created (called an exiton) acts much like a hydrogen atom. Investigations have demonstrated the potential application of quantum dots for optical switching and optical memory. A model of a truncated pyramidal InAs quantum dot in an InP matrix will be presented and described. The model uses a single band envelope theory that accurately describes the truncated pyramidal shape of the dot. The matrix representation of the Hamiltonian is calculated in a basis consisting of kinetic energy eigenfunctions that vanish on the surface of a cube containing the dot. The eigenvalues of this matrix are the energy levels. These results will then be compared with photoluminescence measurements of energy levels conducted at the Microelectronics-Photonics Center at the University of Arkansas - Fayetteville

Fedak, William

2002-03-01

219

Transmission line distance relaying using a variable window short-time Fourier transform

This paper presents a new approach for transmission line protection using a variable window short-time Fourier transform known as S-transform. The S-transform (ST) is a time–frequency spectral localization method, similar to short-time Fourier transform (STFT), but with a Gaussian window whose width scales inversely, and whose height scales linearly with the frequency. The change in spectral energy of the ST

S. R. Samantaray; P. K. Dash

2008-01-01

220

X-ray refractive optics as a Fourier transformer for high resolution diffraction

NASA Astrophysics Data System (ADS)

Refractive optics is proposed as a Fourier transformer for high resolution X-ray crystal diffraction. Employing refractive lenses the wave transmitted through the object transforms into spatial intensity distribution at its back focal plane according to the Fourier relations. A theoretical consideration of the Fourier transform technique is presented. Two types of samples were studied in Bragg reflection geometry: a grating made of strips of a thin SiO2 film on Si substrate and a grating made by profiling a Si crystal. Rocking curves of Si(111) Bragg reflection and corresponding Fourier patterns were analyzed.

Ershov, P.; Kuznetsov, S.; Snigireva, I.; Yunkin, V.; Goikhman, A.; Snigirev, A.

2013-05-01

221

The use of Fourier reverse transforms in crystallographic phase refinement

Often a crystallographer obtains an electron density map which shows only part of the structure. In such cases, the phasing of the trial model is poor enough that the electron density map may show peaks in some of the atomic positions, but other atomic positions are not visible. There may also be extraneous peaks present which are not due to atomic positions. A method for determination of crystal structures that have resisted solution through normal crystallographic methods has been developed. PHASER is a series of FORTRAN programs which aids in the structure solution of poorly phased electron density maps by refining the crystallographic phases. It facilitates the refinement of such poorly phased electron density maps for difficult structures which might otherwise not be solvable. The trial model, which serves as the starting point for the phase refinement, may be acquired by several routes such as direct methods or Patterson methods. Modifications are made to the reverse transform process based on several assumptions. First, the starting electron density map is modified based on the fact that physically the electron density map must be non-negative at all points. In practice a small positive cutoff is used. A reverse Fourier transform is computed based on the modified electron density map. Secondly, the authors assume that a better electron density map will result by using the observed magnitudes of the structure factors combined with the phases calculated in the reverse transform. After convergence has been reached, more atomic positions and less extraneous peaks are observed in the refined electron density map. The starting model need not be very large to achieve success with PHASER; successful phase refinement has been achieved with a starting model that consists of only 5% of the total scattering power of the full molecule. The second part of the thesis discusses three crystal structure determinations.

Ringrose, S.

1997-10-08

222

Transformative effects of higher magnetic field in Fourier transform ion cyclotron mass spectrometry

The relationship of magnetic field strength and Fourier transform ion cyclotron resonance mass spectrometry performance was tested using three instruments with the same designs but different fields of 4.7, 7 and 9.4 tesla. We found that the theoretically predicted “transformative” effects of magnetic field are indeed observed experimentally. The most striking effects were that mass accuracy demonstrated approximately 2nd–3rd-order improvement with the magnetic field, depending upon the charge state of the analyte, and that peak splitting, which prohibited automated data analysis at 4.7 T, was not observed at 9.4 T. PMID:20444622

Karabacak, N. Murat; Easterling, Michael L.; Agar, N.Y.R.; Agar, Jeffrey N.

2010-01-01

223

Optimization of Fast Fourier Transforms on the Blue Gene\\/L Supercomputer

Fast Fourier Transform is a class of efficient algorithms usedto compute Discrete Fourier Transforms, widely used in many scientific and technical applications. In this paper, we analyze the bottlenecks in the parallel FFT algorithm and describe opti- mizations carried out for the algorithm on the Blue Gene\\/L Supercomputer. There were three avenues for improving the performance of the algorithm -

Yogish Sabharwal; Saurabh K. Garg; Rahul Garg; John A. Gunnels; Ramendra K. Sahoo

2008-01-01

224

An Incremental Algorithm for Signal Reconstruction from Short-Time Fourier Transform Magnitude

An Incremental Algorithm for Signal Reconstruction from Short-Time Fourier Transform Magnitude Jake@mit.edu Abstract We present an algorithm for reconstructing a time-domain signal from the magnitude of a short-domain signal from only the magnitude of the short-time Fourier transform (STFT) is a common prob- lem in speech

Poggio, Tomaso

225

mass spectrum, like 2D NMR spec- troscopy. Because of limitations of electronics and com- puters, fewREVIEW Towards analytically useful two-dimensional Fourier transform ion cyclotron resonance mass # Springer-Verlag Berlin Heidelberg 2012 Abstract Fourier transform ion cyclotron resonance (FT- ICR) mass

226

Contributed article Fractional Fourier transform pre-processing for neural networks

Contributed article Fractional Fourier transform pre-processing for neural networks and its This study investigates fractional Fourier transform pre-processing of input signals to neural networks. Judicious choice of this parameter can lead to overall improvement of the neural network performance

Barshan, Billur

227

359. LE FILTRAGE MATHÉMATIQUE DANS LA SPECTROSCOPIE PAR TRANSFORMATION DE FOURIER Par J. CONNES (*) et V. NOZAL, Laboratoire Aimé-Cotton, Bellevue. Résumé. 2014 On est conduit pour obtenir le rapport the Fourier transform of the new interferogram with a smaller number of points ; the computing time is thus

Paris-Sud XI, Université de

228

NASA Astrophysics Data System (ADS)

This paper first reviews some basic properties of the discrete chirp-Fourier transform and then present an adaptive chirp- Fourier transform, a generalization of the amplitude and phase estimation of sinusoids (APES) algorithm proposed by Li and Stoica for sinusoidal signals. We finally applied it to the ISAR imaging of maneuvering targets.

Xia, Xiang-Gen; Wang, Genyuan; Chen, Victor C.

2001-03-01

229

The rapid differentiation of Streptomyces isolates using Fourier transform infrared spectroscopy

The rapid differentiation of Streptomyces isolates using Fourier transform infrared spectroscopy putative Streptomyces spp. isolated from soil were selected to be analysed using Fourier transform infrared be used for preliminary differentiation of Streptomyces spp. at sub-species or strain level. # 2005

Griffith, Gareth

230

Practical aspects of Fourier transform and correlation based processing of spectrochemical data

NASA Astrophysics Data System (ADS)

Fourier transform based signal processing methods are beginning to be widely used for the treatment of spectrochemical data. The most common approach to Fourier transformation is through the utilization of the so called Fast Fourier Transform algorithm or FFT as it is usually designated. However, several versions of the FFT abound in the literature and in program libraries and many subtleties exist with respect to data pre-treatment, data post-treatment, inverse Fourier transformation and manipulation of real and imaginary arrays that can cause considerable grief to the uninitiated. In this presentation numerous examples will be presented illustrating several practical aspects of implementing FFT's and cross-correlations (Fourier transform route) on spectrochemical data sets. Particular attention is paid to the manipulation to the input and output real and imaginary arrays.

Ng, R. C. L.; Horlick, Gary

231

Physical transformations between quantum states

Given two sets of quantum states {A_1, ..., A_k} and {B_1, ..., B_k}, represented as sets of density matrices, necessary and sufficient conditions are obtained for the existence of a physical transformation T, represented as a trace-preserving completely positive map, such that T(A_i) = B_i for i = 1, ..., k. General completely positive maps without the trace-preserving requirement, and unital completely positive maps transforming the states are also considered.

Zejun Huang; Chi-Kwong Li; Edward Poon; Nung-Sing Sze

2012-10-26

232

Fourier transform infrared spectroscopy for Kona coffee authentication.

Kona coffee, the variety of "Kona typica" grown in the north and south districts of Kona-Island, carries a unique stamp of the region of Big Island of Hawaii, U.S.A. The excellent quality of Kona coffee makes it among the best coffee products in the world. Fourier transform infrared (FTIR) spectroscopy integrated with an attenuated total reflectance (ATR) accessory and multivariate analysis was used for qualitative and quantitative analysis of ground and brewed Kona coffee and blends made with Kona coffee. The calibration set of Kona coffee consisted of 10 different blends of Kona-grown original coffee mixture from 14 different farms in Hawaii and a non-Kona-grown original coffee mixture from 3 different sampling sites in Hawaii. Derivative transformations (1st and 2nd), mathematical enhancements such as mean centering and variance scaling, multivariate regressions by partial least square (PLS), and principal components regression (PCR) were implemented to develop and enhance the calibration model. The calibration model was successfully validated using 9 synthetic blend sets of 100% Kona coffee mixture and its adulterant, 100% non-Kona coffee mixture. There were distinct peak variations of ground and brewed coffee blends in the spectral "fingerprint" region between 800 and 1900 cm(-1). The PLS-2nd derivative calibration model based on brewed Kona coffee with mean centering data processing showed the highest degree of accuracy with the lowest standard error of calibration value of 0.81 and the highest R(2) value of 0.999. The model was further validated by quantitative analysis of commercial Kona coffee blends. Results demonstrate that FTIR can be a rapid alternative to authenticate Kona coffee, which only needs very quick and simple sample preparations. PMID:19646032

Wang, Jun; Jun, Soojin; Bittenbender, H C; Gautz, Loren; Li, Qing X

2009-06-01

233

Vehicle Recognition Based on Fourier, Wavelet and Curvelet Transforms - a Comparative Study

Summary This paper proposes the application of 3 different kinds of feature extractors to recognize & classify 5 models of vehicles. These feature extractors are Fast Fourier transform, discrete wavelet transform & discrete curvelet transform. To justify the correct amount of each feature extractor, we perform each of the mentioned transforms to input images, precisely. The classifier used in this

Farhad Mohamad Kazemi; Saeed Samadi; Hamid Reza Pourreza; Mohammad R. Akbarzadeh-totonchi

2007-01-01

234

Fourier transform infrared difference spectroscopy of bacteriorhodopsin and its photoproducts.

Fourier transform infrared difference spectroscopy has been used to obtain the vibrational modes in the chromophore and apoprotein that change in intensity or position between light-adapted bacteriorhodopsin and the K and M intermediates in its photocycle and between dark-adapted and light-adapted bacteriorhodopsin. Our infrared measurements provide independent verification of resonance Raman results that in light-adapted bacteriorhodopsin the protein-chromophore linkage is a protonated Schiff base and in the M state the Schiff base is unprotonated. Although we cannot unambiguously identify the Schiff base stretching frequency in the K state, the most likely interpretation of deuterium shifts of the chromophore hydrogen out-of-plane vibrations is that the Schiff base in K is protonated. The intensity of the hydrogen out-of-plane vibrations in the K state compared with the intensities of those in light-adapted and dark-adapted bacteriorhodopsin shows that the conformation of the chromophore in K is considerably distorted. In addition, we find evidence that the conformation of the protein changes during the photocycle. PMID:6956906

Bagley, K; Dollinger, G; Eisenstein, L; Singh, A K; Zimányi, L

1982-01-01

235

Single beam Fourier transform digital holographic quantitative phase microscopy

NASA Astrophysics Data System (ADS)

Quantitative phase contrast microscopy reveals thickness or height information of a biological or technical micro-object under investigation. The information obtained from this process provides a means to study their dynamics. Digital holographic (DH) microscopy is one of the most used, state of the art single-shot quantitative techniques for three dimensional imaging of living cells. Conventional off axis DH microscopy directly provides phase contrast images of the objects. However, this process requires two separate beams and their ratio adjustment for high contrast interference fringes. Also the use of two separate beams may make the system more vulnerable to vibrations. Single beam techniques can overcome these hurdles while remaining compact as well. Here, we describe the development of a single beam DH microscope providing whole field imaging of micro-objects. A hologram of the magnified object projected on to a diffuser co-located with a pinhole is recorded with the use of a commercially available diode laser and an arrayed sensor. A Fourier transform of the recorded hologram directly yields the complex amplitude at the image plane. The method proposed was investigated using various phase objects. It was also used to image the dynamics of human red blood cells in which sub-micrometer level thickness variation were measurable.

Anand, A.; Faridian, A.; Chhaniwal, V. K.; Mahajan, S.; Trivedi, V.; Dubey, S. K.; Pedrini, G.; Osten, W.; Javidi, B.

2014-03-01

236

Fourier transform methods applied to an optical heterodyne profilometer

NASA Astrophysics Data System (ADS)

In this work, theory and experiment describe the performance of a surface profile measurement device based on optical heterodyne interferometry are presented. The object and reference beams propagating through the interferometer are obtained by single-pass through an acousto-optic modulator. The diffraction orders 0 and the Doppler-shifted +1 (object and reference beams, respectively) are manipulated to propagate collinearly towards the interferometer output where a fast photodetector is placed to collect the irradiance. The modulated optical signal is Fourier transformed using a data acquisition card and RF communications software. The peak centered at the acousto-optic frequency in the power spectrum is filtered and averaged. The irregularities on the surface of the reflective sample are proportional to the height of this peak. The profile of a reflective blazed grating has been sketched by translating laterally the sample using a nanopositioning system. Experimental results are compared to the measurement done with a scanning electron microscope. There has been found a good agreement between both methods.

Beltrán-González, A.; García-Torales, G.; Martínez-Ponce, G.

2013-11-01

237

Picolinic and isonicotinic acids: a Fourier transform microwave spectroscopy study.

The rotational spectra of laser ablated picolinic and isonicotinic acids have been studied using broadband chirped pulse (CP-FTMW) and narrowband molecular beam (MB-FTMW) Fourier transform microwave spectroscopies. Two conformers of picolinic acid, s-cis-I and s-cis-II, and one conformer of isonicotinic acid have been identified through the analysis of their rotational spectra. The values of the inertial defect and the quadrupole coupling constants obtained for the most stable s-cis-I conformer of picolinic acid, evidence the formation of an O-H···N hydrogen bond between the acid group and the endocyclic N atom. The stabilization provided by this hydrogen bond compensates the destabilization energy due to the adoption of a -COOH trans configuration in this conformer. Its rs structure has been derived from the rotational spectra of several (13)C, (15)N, and (18)O species observed in their natural abundances. Mesomeric effects have been revealed by comparing the experimental values of the (14)N nuclear quadrupole coupling constants in the isomeric series of picolinic, isonicotinic, and nicotinic acids. PMID:25382020

Peña, Isabel; Varela, Marcelino; Franco, Vanina G; López, Juan C; Cabezas, Carlos; Alonso, José L

2014-12-01

238

Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS): Imaging and Tracking Capability

NASA Technical Reports Server (NTRS)

The geosynchronous-imaging Fourier transform spectrometer (GIFTS) engineering demonstration unit (EDU) is an imaging infrared spectrometer designed for atmospheric soundings. It measures the infrared spectrum in two spectral bands (14.6 to 8.8 microns, 6.0 to 4.4 microns) using two 128 128 detector arrays with a spectral resolution of 0.57/cm with a scan duration of approx. 11 seconds. From a geosynchronous orbit, the instrument will have the capability of taking successive measurements of such data to scan desired regions of the globe, from which atmospheric status, cloud parameters, wind field profiles, and other derived products can be retrieved. The GIFTS EDU provides a flexible and accurate testbed for the new challenges of the emerging hyperspectral era. The EDU ground-based measurement experiment, held in Logan, Utah during September 2006, demonstrated its extensive capabilities and potential for geosynchronous and other applications (e.g., Earth observing environmental measurements). This paper addresses the experiment objectives and overall performance of the sensor system with a focus on the GIFTS EDU imaging capability and proof of the GIFTS measurement concept.

Zhou, D. K.; Larar, A. M.; Liu, Xu; Reisse, R. A.; Smith, W. L.; Revercomb, H. E.; Bingham, G. E.; Zollinger, L. J.; Tansock, J. J.; Huppi, Ronald J.

2007-01-01

239

Diagnostic ultrasound tooth imaging using fractional Fourier transform.

An ultrasound contact imaging method is proposed to measure the enamel thickness in the human tooth. A delay-line transducer with a working frequency of 15 MHz is chosen to achieve a minimum resolvable distance of 400 ?m in human enamel. To confirm the contact between the tooth and the transducer, a verification technique based on the phase shift upon reflection is used. Because of the high attenuation in human teeth, linear frequency-modulated chirp excitation and pulse compression are exploited to increase the penetration depth and improve the SNR. Preliminary measurements show that the enamel-dentin boundary creates numerous internal reflections, which cause the applied chirp signals to interfere arbitrarily. In this work, the fractional Fourier transform (FrFT) is employed for the first time in dental imaging to separate chirp signals overlapping in both time and frequency domains. The overlapped chirps are compressed using the FrFT and matched filter techniques. Micro-computed tomography is used for validation of the ultrasound measurements for both techniques. For a human molar, the thickness of the enamel layer is measured with an average error of 5.5% after compressing with the FrFT and 13.4% after compressing with the matched filter based on the average speed of sound in human teeth. PMID:21989873

Harput, Sevan; Evans, Tony; Bubb, Nigel; Freear, Steven

2011-10-01

240

Fourier transform infrared spectroscopy (FTIR) of laser-irradiated cementum

NASA Astrophysics Data System (ADS)

Utilizing Fourier Transform Infrared Spectroscopy (FTIR) in specular reflectance mode chemical changes of root cement surfaces due to laser radiation were investigated. A total of 18 samples of root cement were analyzed, six served as controls. In this study laser energies were set to those known for removal of calculus or for disinfection of periodontal pockets. Major changes in organic as well as inorganic components of the cementum were observed following Nd:YAG laser irradiation (wavelength 1064 nm, pulse duration 250 ?s, free running, pulse repetition rate 20 Hz, fiber diameter 320 ?m, contact mode; Iskra Twinlight, Fontona, Slovenia). Er:YAG laser irradiation (wavelength 2.94 ?m, pulse duration 250 ?s, free running, pulse repetition rate 6 Hz, focus diameter 620 ?m, air water cooling 30 ml/min; Iskra Twinlight, Fontona, Slovenia) significantly reduced the Amid bands due to changes in the organic components. After irradiation with a frequency doubled Alexandrite laser (wavelength 377 nm, pulse duration 200 ns, q-switched, pulse repetition rate 20 Hz, beam diameter 800 ?m, contact mode, water cooling 30 ml/min; laboratory prototype) only minimal reductions in the peak intensity of the Amide-II band were detected.

Rechmann, Peter; White, Joel M.; Cecchini, Silvia C. M.; Hennig, Thomas

2003-06-01

241

Fourier transform infrared spectroscopic analysis of cell differentiation

NASA Astrophysics Data System (ADS)

Stem cells and its differentiations have got a lot of attentions in regenerative medicine. The process of differentiations, the formation of tissues, has become better understood by the study using a lot of cell types progressively. These studies of cells and tissue dynamics at molecular levels are carried out through various approaches like histochemical methods, application of molecular biology and immunology. However, in case of using regenerative sources (cells, tissues and biomaterials etc.) clinically, they are measured and quality-controlled by non-invasive methods from the view point of safety. Recently, the use of Fourier Transform Infrared spectroscopy (FT-IR) has been used to monitor biochemical changes in cells, and has gained considerable importance. The objective of this study is to establish the infrared spectroscopy of cell differentiation as a quality control of cell sources for regenerative medicine. In the present study, as a basic study, we examined the adipose differentiation kinetics of preadipocyte (3T3-L1) and the osteoblast differentiation kinetics of bone marrow mesenchymal stem cells (Kusa-A1) to analyze the infrared absorption spectra. As a result, we achieved to analyze the adipose differentiation kinetics using the infrared absorption peak at 1739 cm-1 derived from ester bonds of triglyceride and osteoblast differentiation kinetics using the infrared absorption peak at 1030 cm-1 derived from phosphate groups of calcium phosphate.

Ishii, Katsunori; Kimura, Akinori; Kushibiki, Toshihiro; Awazu, Kunio

2007-02-01

242

Ribosomal DNA nanoprobes studied by Fourier transform infrared spectroscopy.

Paracoccidioides brasiliensis (P. brasiliensis) is a thermo-dimorphic fungus that causes paracoccidioidomycosis. Brazil epidemiological data shows that endemic areas are the subtropical regions, especially where agricultural activities predominate such as the Southeast, South, and Midwest. There are several tests to diagnose paracoccidioidomycosis, but they have many limitations such as low sensitivity, high cost, and a cross-reacting problem. In this work, gold nanoprobes were used to identify P. brasiliensis as an alternative diagnostic technique, which is easier to apply, costs less, and has great potential for application. The specific Ribosomal sequence of P. brasiliensis DNA was amplified and used to design the nanoprobes using a thiol-modified oligonucleotide. The results of positive and negative tests were done by UV-visible and Fourier Transform Infrared (FT-IR) measurements. The deconvolution of FT-IR sample spectra showed differences in the vibrational modes from the hydrogen bridge NHN and NHO bands that form the double helix DNA for samples matching the DNA sequence of nanoprobes that could be used to classify the samples. PMID:24036304

Fagundes, Jaciara; Castilho, Maiara L; Téllez Soto, Claudio A; Vieira, Laís de Souza; Canevari, Renata A; Fávero, Priscila P; Martin, Airton A; Raniero, Leandro

2014-01-24

243

Single beam Fourier transform digital holographic quantitative phase microscopy

Quantitative phase contrast microscopy reveals thickness or height information of a biological or technical micro-object under investigation. The information obtained from this process provides a means to study their dynamics. Digital holographic (DH) microscopy is one of the most used, state of the art single-shot quantitative techniques for three dimensional imaging of living cells. Conventional off axis DH microscopy directly provides phase contrast images of the objects. However, this process requires two separate beams and their ratio adjustment for high contrast interference fringes. Also the use of two separate beams may make the system more vulnerable to vibrations. Single beam techniques can overcome these hurdles while remaining compact as well. Here, we describe the development of a single beam DH microscope providing whole field imaging of micro-objects. A hologram of the magnified object projected on to a diffuser co-located with a pinhole is recorded with the use of a commercially available diode laser and an arrayed sensor. A Fourier transform of the recorded hologram directly yields the complex amplitude at the image plane. The method proposed was investigated using various phase objects. It was also used to image the dynamics of human red blood cells in which sub-micrometer level thickness variation were measurable.

Anand, A., E-mail: arun-nair-in@yahoo.com; Chhaniwal, V. K.; Mahajan, S.; Trivedi, V. [Optics Laboratory, Applied Physics Department, Faculty of Technology and Engineering, M.S. University of Baroda, Vadodara 390001 (India)] [Optics Laboratory, Applied Physics Department, Faculty of Technology and Engineering, M.S. University of Baroda, Vadodara 390001 (India); Faridian, A.; Pedrini, G.; Osten, W. [Institut für Technische Optik, Universität Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart (Germany)] [Institut für Technische Optik, Universität Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart (Germany); Dubey, S. K. [Siemens Technology and Services Pvt. Ltd, Corporate Technology—Research and Technology Centre, Bangalore 560100 (India)] [Siemens Technology and Services Pvt. Ltd, Corporate Technology—Research and Technology Centre, Bangalore 560100 (India); Javidi, B. [Department of Electrical and Computer Engineering, U-4157, University of Connecticut, Storrs, Connecticut 06269-2157 (United States)] [Department of Electrical and Computer Engineering, U-4157, University of Connecticut, Storrs, Connecticut 06269-2157 (United States)

2014-03-10

244

Ribosomal DNA Nanoprobes studied by Fourier Transform Infrared spectroscopy

NASA Astrophysics Data System (ADS)

Paracoccidioides brasiliensis (P. brasiliensis) is a thermo-dimorphic fungus that causes paracoccidioidomycosis. Brazil epidemiological data shows that endemic areas are the subtropical regions, especially where agricultural activities predominate such as the Southeast, South, and Midwest. There are several tests to diagnose paracoccidioidomycosis, but they have many limitations such as low sensitivity, high cost, and a cross-reacting problem. In this work, gold nanoprobes were used to identify P. brasiliensis as an alternative diagnostic technique, which is easier to apply, costs less, and has great potential for application. The specific Ribosomal sequence of P. brasiliensis DNA was amplified and used to design the nanoprobes using a thiol-modified oligonucleotide. The results of positive and negative tests were done by UV-visible and Fourier Transform Infrared (FT-IR) measurements. The deconvolution of FT-IR sample spectra showed differences in the vibrational modes from the hydrogen bridge NHN and NHO bands that form the double helix DNA for samples matching the DNA sequence of nanoprobes that could be used to classify the samples.

Fagundes, Jaciara; Castilho, Maiara L.; Téllez Soto, Claudio A.; Vieira, Laís de Souza; Canevari, Renata A.; Fávero, Priscila P.; Martin, Airton A.; Raniero, Leandro

2014-01-01

245

Fourier transform infrared and physicochemical analyses of roasted coffee.

In this study, Brazilian coffee beans processed to different stages of roast at 210, 220, 230, and 240 °C were analyzed for pH value, titratable acidity, moisture content, and color lightness. Fourier transform infrared (FTIR) spectroscopy, in conjunction with principal component analysis, was conducted to study the effects of process time and temperature on the IR-active components of the acetyl acetate extract of the roasted coffee. The results showed that high-temperature-short-time resulted in higher moisture content, higher pH value, and higher titratable acidity when the beans were roasted beyond the start-of-second-crack stage, as compare to low-temperature-long-time process (LTLT). The LTLT process also resulted in greater IR absorbance for aldehydes, ketones, aliphatic acids, aromatic acids, and caffeine carbonyl bands on the FTIR spectra. Clusters for principal component score plots were well separated, indicating that the changes IR-active components in the coffee extracts, due to the different roasting treatments, can be discriminated by the FTIR technique. On the basis of the loading plots of principal components, changes of IR-active compounds in the coffee extract at various stages of roasting were discussed. PMID:22563854

Wang, Niya; Lim, Loong-Tak

2012-05-30

246

Spectroscopic Stokes polarimetry based on Fourier transform spectrometer

NASA Astrophysics Data System (ADS)

Two methods are proposed for measuring the spectroscopic Stokes parameters using a Fourier transform spectrometer. In the first method, it is designed for single point measurement. The parameters are extracted using an optical setup comprising a white light source, a polarizer set to 0°, a quarter-wave plate and a scanning Michelson interferometer. In the proposed approach, the parameters are extracted from the intensity distributions of the interferograms produced with the quarter-wave plate rotated to 0°, 22.5°, 45° and -45°, respectively. For the second approach, the full-field and dynamic measurement can be designed based upon the first method with special angle design in a polarizer and a quarter-wave plate. Hence, the interferograms of two-dimensional detection also can be simultaneously extracted via a pixelated phase-retarder and polarizer array on a high-speed CCD camera and a parallel read-out circuit with a multi-channel analog to digital converter. Thus, a full-field and dynamic spectroscopic Stokes polarimetry without any rotating components could be developed. The validity of the proposed methods is demonstrated both numerically and experimentally. To the authors' knowledge, this could be the simplest optical arrangement in extracting the spectral Stokes parameters. Importantly, the latter one method avoids the need for rotating components within the optical system and therefore provides an experimentally straightforward means of extracting the dynamic spectral Stokes parameters.

Liu, Yeng-Cheng; Lo, Yu-Lung; Li, Chang-Ye; Liao, Chia-Chi

2015-02-01

247

Remote detection of organics using Fourier transform infrared spectroscopy

Fourier transform infrared (FTIR) spectroscopy is an ideal technique for remote detection of organic emissions. There is an atmospheric window in the 1200 to 800 cm{sup {minus}1} region, which corresponds to the fingerprint'' region for organic molecules. Virtually all organic molecules have a unique absorption/emission pattern in the fingerprint region. A remote-passive FTIR relies on ambient emission of infrared energy from organics to obtain spectra. The instrumentation consists of inlet optics, and interferometer, a mercury cadmium telluride (MCT) detector, and an on-board computer. The transportable unit measures 40 cm by 50 cm and has been used to collect data while mounted on a helicopter or ground vehicle. Through the use of this FTIR combined with least squares software, it is possible to analyze qualitatively and quantitatively for organic vapors from either the air or ground. The data presented will include quantitative releases of common organics present in incinerator stacks, hazardous wastes, and illegal laboratories. Data will be presented for pure compounds, mixtures, and target analytes in the presence of interfering compounds. The sensitivity, reproducibility, and the potential of the technique will be discussed. 1 ref., 8 figs., 6 tabs.

Demirgian, J.C.; Spurgash, S.M.

1990-01-01

248

Liquid chromatography/Fourier transform IR spectrometry interface flow cell

A zero dead volume (ZDV) microbore high performance liquid chromatography (.mu.HPLC)/Fourier transform infrared (FTIR) interface flow cell includes an IR transparent crystal having a small diameter bore therein through which a sample liquid is passed. The interface flow cell further includes a metal holder in combination with a pair of inner, compressible seals for directly coupling the thus configured spectrometric flow cell to the outlet of a .mu.HPLC column end fitting to minimize the transfer volume of the effluents exiting the .mu.HPLC column which exhibit excellent flow characteristics due to the essentially unencumbered, open-flow design. The IR beam passes transverse to the sample flow through the circular bore within the IR transparent crystal, which is preferably comprised of potassium bromide (KBr) or calcium fluoride (CaF.sub.2), so as to minimize interference patterns and vignetting encountered in conventional parallel-plate IR cells. The long IR beam pathlength and lensing effect of the circular cross-section of the sample volume in combination with the refractive index differences between the solvent and the transparent crystal serve to focus the IR beam in enhancing sample detection sensitivity by an order of magnitude.

Johnson, Charles C. (Fairfield, OH); Taylor, Larry T. (Blacksburg, VA)

1986-01-01

249

Liquid chromatography/Fourier transform IR spectrometry interface flow cell

A zero dead volume (ZDV) microbore high performance liquid chromatography (..mu.. HPLC)/Fourier transform infrared (FTIR) interface flow cell includes an IR transparent crystal having a small diameter bore therein through which a sample liquid is passed. The interface flow cell further includes a metal holder in combination with a pair of inner, compressible seals for directly coupling the thus configured spectrometric flow cell to the outlet of a ..mu.. HPLC column end fitting to minimize the transfer volume of the effluents exiting the ..mu.. HPLC column which exhibit excellent flow characteristics due to the essentially unencumbered, open-flow design. The IR beam passes transverse to the sample flow through the circular bore within the IR transparent crystal, which is preferably comprised of potassium bromide (KBr) or calcium fluoride (CaF/sub 2/), so as to minimize interference patterns and vignetting encountered in conventional parallel-plate IR cells. The long IR beam pathlength and lensing effect of the circular cross-section of the sample volume in combination with the refractive index differences between the solvent and the transparent crystal serve to focus the IR beam in enhancing sample detection sensitivity by an order of magnitude.

Johnson, C.C.; Taylor, L.T.

1985-01-04

250

The use of fast Fourier transform techniques in blasting analysis

The US Bureau of Mines has developed computer software which uses fast Fourier transform (FFT) techniques to evaluate blasting data. The software is useful because it allows blasters to evaluate (1) the frequency content of ground vibration time history data; (2) the effects of initiator scatter on the frequency spectra of ground vibrations; and (3) the fragmentation distribution of rock muckpiles from photographs. A one-dimensional version of the software was used in the first two cases. Monte Carlo techniques were used to simulate the scatter of initiators. The results are shown in computer generated three-dimensional color contour plots. To determine the fragment size distribution using photographic and digital image processing techniques a two-dimensional FFT routine was written. The FFT of the digitized muckpile images are filtered to remove lower spatial frequencies. The higher spatial frequencies, which are associated with rock particle edges, are subsequently enhanced. The inverse two-dimensional FFT was used to reconstruct the digital image. Photographic images taken of rock muckpiles resulting from full scale blasts at a limestone quarry were digitized and evaluated using the new FFT techniques. The fragment size distributions determined from the photographs agree with the distributions determined by partial screening.

Rholl, S.A.; Stagg, M.S. [Bureau of Mines, Minneapolis, MN (United States). Twin Cities Research Center

1995-12-31

251

Continued Development of a Planetary Imaging Fourier Transform Spectrometer (PIFTS)

NASA Technical Reports Server (NTRS)

This report describes continued efforts to evaluate a breadboard of a Planetary Imaging Fourier Transform Spectrometer (PIFTS). The PIFTS breadboard was developed under prior PIDDP funding. That effort is described in the final report for NASA Grant NAG5-6248 and in two conference papers (Sromovsky et al. 2000; Revercomb et al. 2000). The PIFTS breadboard was designed for near-IR (1-5.2 micrometer imaging of planetary targets with spectral resolving powers of several hundred to several thousand, using an InSb detector array providing at least 64x64 pixels imaging detail. The major focus of the development effort was to combine existing technologies to produce a small and low power design compatible with a very low mass flyable instrument. The objective of this grant (NAG5-10729) was further characterization of the breadboard performance, including intercomparisons with the highly accurate non-imaging Advanced Emitted Radiance Interferometer (AERI) (Revercomb et al. 1994; Best et al. 1997).

Sromovsky, L. A.

2002-01-01

252

Optimal Padding for the Two-Dimensional Fast Fourier Transform

NASA Technical Reports Server (NTRS)

One-dimensional Fast Fourier Transform (FFT) operations work fastest on grids whose size is divisible by a power of two. Because of this, padding grids (that are not already sized to a power of two) so that their size is the next highest power of two can speed up operations. While this works well for one-dimensional grids, it does not work well for two-dimensional grids. For a two-dimensional grid, there are certain pad sizes that work better than others. Therefore, the need exists to generalize a strategy for determining optimal pad sizes. There are three steps in the FFT algorithm. The first is to perform a one-dimensional transform on each row in the grid. The second step is to transpose the resulting matrix. The third step is to perform a one-dimensional transform on each row in the resulting grid. Steps one and three both benefit from padding the row to the next highest power of two, but the second step needs a novel approach. An algorithm was developed that struck a balance between optimizing the grid pad size with prime factors that are small (which are optimal for one-dimensional operations), and with prime factors that are large (which are optimal for two-dimensional operations). This algorithm optimizes based on average run times, and is not fine-tuned for any specific application. It increases the amount of times that processor-requested data is found in the set-associative processor cache. Cache retrievals are 4-10 times faster than conventional memory retrievals. The tested implementation of the algorithm resulted in faster execution times on all platforms tested, but with varying sized grids. This is because various computer architectures process commands differently. The test grid was 512 512. Using a 540 540 grid on a Pentium V processor, the code ran 30 percent faster. On a PowerPC, a 256x256 grid worked best. A Core2Duo computer preferred either a 1040x1040 (15 percent faster) or a 1008x1008 (30 percent faster) grid. There are many industries that can benefit from this algorithm, including optics, image-processing, signal-processing, and engineering applications.

Dean, Bruce H.; Aronstein, David L.; Smith, Jeffrey S.

2011-01-01

253

Far-field radiation patterns of aperture antennas by the Winograd Fourier transform algorithm

NASA Technical Reports Server (NTRS)

A more time-efficient algorithm for computing the discrete Fourier transform, the Winograd Fourier transform (WFT), is described. The WFT algorithm is compared with other transform algorithms. Results indicate that the WFT algorithm in antenna analysis appears to be a very successful application. Significant savings in cpu time will improve the computer turn around time and circumvent the need to resort to weekend runs.

Heisler, R.

1978-01-01

254

Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms

The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient (size poly(n,d,log(1/\\epsilon)) for accuracy \\epsilon) quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. These circuits are based on efficient circuits for the Clebsch-Gordan transformation. We also present an efficient circuit for a limited version of the Schur transform in which one needs only to project onto different Schur subspaces. This second circuit is based on a generalization of phase estimation to any nonabelian finite group for which there exists a fast quantum Fourier transform.

Dave Bacon; Isaac Chuang; Aram Harrow

2004-08-05

255

NASA Technical Reports Server (NTRS)

By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.

2012-01-01

256

NASA Astrophysics Data System (ADS)

The pure rotational spectrum of ?-propiolactone (c-C 2H 4COO) has been recorded between 7 and 21 GHz using a pulsed jet Fourier transform microwave spectrometer. The resulting ground state spectroscopic constants guided the analysis of the rotationally-resolved infrared spectra of two bands that were collected using the far infrared beamline at the Canadian Light Source synchrotron. The observed modes correspond to motions best described as ring deformation ( ?12) at 747.2 cm -1 and CO ring stretching ( ?8) at 1095.4 cm -1. A global fit of 4430 a- and b-type transitions from the microwave spectrum and the two infrared bands provided an accurate set of ground state and excited state spectroscopic parameters. To complement the experimental results, the harmonic and anharmonic vibrational frequencies of all 21 infrared active modes of ?-propiolactone have been calculated using the DFT B3LYP method (6-311+G(d,p), 6-311++G(2d,3p) basis sets).

Chen, Ziqiu; van Wijngaarden, Jennifer

2009-10-01

257

Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy.

The dephasing of the Fermi edge singularity excitations in two modulation doped single quantum wells of 12 nm and 18 nm thickness and in-well carrier concentration of ?4 × 10(11) cm(-2) was carefully measured using spectrally resolved four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. Although the absorption at the Fermi edge is broad at this doping level, the spectrally resolved FWM shows narrow resonances. Two peaks are observed separated by the heavy hole/light hole energy splitting. Temperature dependent "rephasing" (S1) 2DFT spectra show a rapid linear increase of the homogeneous linewidth with temperature. The dephasing rate increases faster with temperature in the narrower 12 nm quantum well, likely due to an increased carrier-phonon scattering rate. The S1 2DFT spectra were measured using co-linear, cross-linear, and co-circular polarizations. Distinct 2DFT lineshapes were observed for co-linear and cross-linear polarizations, suggesting the existence of polarization dependent contributions. The "two-quantum coherence" (S3) 2DFT spectra for the 12 nm quantum well show a single peak for both co-linear and co-circular polarizations. PMID:25296819

Paul, J; Dey, P; Tokumoto, T; Reno, J L; Hilton, D J; Karaiskaj, D

2014-10-01

258

Continuously tunable optical multidimensional Fourier-transform spectrometer

NASA Astrophysics Data System (ADS)

A multidimensional optical nonlinear spectrometer (MONSTR) is a robust, ultrastable platform consisting of nested and folded Michelson interferometers that can be actively phase stabilized. The MONSTR provides output pulses for nonlinear excitation of materials and phase-stabilized reference pulses for heterodyne detection of the induced signal. This platform generates a square of identical laser pulses that can be adjusted to have arbitrary time delays between them while maintaining phase stability. This arrangement is ideal for performing coherent optical experiments, such as multidimensional Fourier-transform spectroscopy. The present work reports on overcoming some important limitations on the original design of the MONSTR apparatus. One important advantage of the MONSTR is the fact that it is a closed platform, which provides the high stability. Once the optical alignment is performed, it is desirable to maintain the alignment over long periods of time. The previous design of the MONSTR was limited to a narrow spectral range defined by the optical coating of the beam splitters. In order to achieve tunability over a broad spectral range the internal optics needed to be changed. By using broadband coated and wedged beam splitters and compensator plates, combined with modifications of the beam paths, continuous tunability can be achieved from 520 nm to 1100 nm without changing any optics or performing alignment of the internal components of the MONSTR. Furthermore, in order to achieve continuous tunability in the spectral region between 520 nm and 720 nm, crucially important for studies on numerous biological molecules, a single longitudinal mode laser at 488.5 nm was identified and used as a metrology laser. The shorter wavelength of the metrology laser as compared to the usual HeNe laser has also increased the phase stability of the system. Finally, in order to perform experiments in the reflection geometry, a simple method to achieve active phase stabilization between the signal and the reference beams has been developed.

Dey, P.; Paul, J.; Bylsma, J.; Deminico, S.; Karaiskaj, D.

2013-02-01

259

SPICA/SAFARI Fourier transform spectrometer mechanism evolutionary design

NASA Astrophysics Data System (ADS)

TNO, together with its partners, have designed a cryogenic scanning mechanism for use in the SAFARI1 Fourier Transform Spectrometer (FTS) on board of the SPICA mission. SPICA is one of the M-class missions competing to be launched in ESA's Cosmic Vision Programme2 in 2022. JAXA3 leads the development of the SPICA satellite and SRON is the prime investigator of the Safari instrument. The FTS scanning mechanism (FTSM) has to meet a 35 mm stroke requirement with an Optical Path Difference resolution of less then 15 nm and must fit in a small volume. It consists of two back-to-back roof-top mirrors mounted on a small carriage, which is moved using a magnetic bearing linear guiding system in combination with a magnetic linear motor serving as the OPD actuator. The FTSM will be used at cryogenic temperatures of 4 Kelvin inducing challenging requirements on the thermal power dissipation and heat leak. The magnetic bearing enables movements over a scanning stroke of 35.5 mm in a small volume. It supports the optics in a free-floating way with no friction, or other non-linearities, with sub-nanometer accuracy. This solution is based on the design of the breadboard ODL (Optical Delay Line) developed for the ESA Darwin mission4 and the MABE mechanism developed by Micromega Dynamics. During the last couple of years the initial design of the SAFARI instrument, as described in an earlier SPIE 2010 paper5, was adapted by the SAFARI team in an evolutionary way to meet the changing requirements of the SPICA payload module. This presentation will focus on the evolution of the FTSM to meet these changing requirements. This work is supported by the Netherlands Space Office (NSO).

van den Dool, Teun C.; Kruizinga, Bob; Braam, Ben C.; Hamelinck, Roger F. M. M.; Loix, Nicolas; Van Loon, Dennis; Dams, Johan

2012-09-01

260

Libyan Desert Glass: New field and Fourier transform infrared data

NASA Astrophysics Data System (ADS)

Results are presented of new geological observations and laboratory analyses on Libyan Desert Glass (LDG), a unique kind of impact glass found in Egypt, probably 28.5-29.4 million years in age. A new LDG occurrence has been discovered some 50 km southward of the main LDG occurrences in the Great Sand Sea. From Fourier transform infrared (FTIR) analysis, the molecular structure of LDG is refined and significant differences are shown between LDG specimens and other pure silica glasses (fulgurite, industrial fused quartz, and amorphous biogenic silica) that are related to differences in their structures. The slight variations observed here for the mean Si-O-Si angle between the different glasses are attributed to their thermal histories. With regard to the other glasses analyzed, the LDG infrared spectral parameters point to a higher ratio of discontinuities and defects in the tetrahedral (SiO4) network. The quantitative mineralogical constitutions of sandstones and quartzites from the LDG geological setting were analyzed by FTIR. Cretaceous sandstones have a specific composition (about 90 wt% quartz, 10% dickite), clearly different from the Paleozoic ones (about 90 wt% quartz, but ?7% kaolinite). It is shown that the reddish silts bearing the LDG are constituted mainly of microquartz enriched with dickite, whose particle size distribution is characteristic of fluvio-lacustrine deposits, probably Oligocene to Miocene in age. The target rocks, most probably quartz sand, resulted from the weathering (loss of the cementing microquartz) of the Cretaceous sandstones from the Gilf Khebir Plateau with deposition in a high-energy environment.

Fröhlich, F.; Poupeau, G.; Badou, A.; Le Bourdonnec, F. X.; Sacquin, Y.; Dubernet, S.; Bardintzeff, J. M.; Véran, M.; Smith, D. C.; Diemer, E.

2013-12-01

261

Calibration of the Herschel SPIRE Fourier Transform Spectrometer

NASA Astrophysics Data System (ADS)

The Herschel Spectral and Photometric REceiver (SPIRE) instrument consists of an imaging photometric camera and an imaging Fourier Transform Spectrometer (FTS), both operating over a frequency range of ˜450-1550 GHz. In this paper, we briefly review the FTS design, operation, and data reduction, and describe in detail the approach taken to relative calibration (removal of instrument signatures) and absolute calibration against standard astronomical sources. The calibration scheme assumes a spatially extended source and uses the Herschel telescope as primary calibrator. Conversion from extended to point-source calibration is carried out using observations of the planet Uranus. The model of the telescope emission is shown to be accurate to within 6 per cent and repeatable to better than 0.06 per cent and, by comparison with models of Mars and Neptune, the Uranus model is shown to be accurate to within 3 per cent. Multiple observations of a number of point-like sources show that the repeatability of the calibration is better than 1 per cent, if the effects of the satellite absolute pointing error (APE) are corrected. The satellite APE leads to a decrement in the derived flux, which can be up to ˜10 per cent (1 ?) at the high-frequency end of the SPIRE range in the first part of the mission, and ˜4 per cent after Herschel operational day 1011. The lower frequency range of the SPIRE band is unaffected by this pointing error due to the larger beam size. Overall, for well-pointed, point-like sources, the absolute flux calibration is better than 6 per cent, and for extended sources where mapping is required it is better than 7 per cent.

Swinyard, B. M.; Polehampton, E. T.; Hopwood, R.; Valtchanov, I.; Lu, N.; Fulton, T.; Benielli, D.; Imhof, P.; Marchili, N.; Baluteau, J.-P.; Bendo, G. J.; Ferlet, M.; Griffin, M. J.; Lim, T. L.; Makiwa, G.; Naylor, D. A.; Orton, G. S.; Papageorgiou, A.; Pearson, C. P.; Schulz, B.; Sidher, S. D.; Spencer, L. D.; van der Wiel, M. H. D.; Wu, R.

2014-06-01

262

A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers

NASA Technical Reports Server (NTRS)

A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.

Campbell, Joel

2008-01-01

263

Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl 3,0

. First, the basic concept of the vector derivative in geometric algebra is introduced. Second, beginning with the Fourier transform\\u000a on a scalar function we generalize to a real Fourier transform on Clifford multivector-valued functions\\u000a \\u000a $$ (f:\\\\user2{\\\\mathbb{R}}^3 \\\\to Cl_{3,0} ). $$\\u000a Third, we show a set of important properties of the Clifford Fourier transform on Cl3,0 such as differentiation properties, and

Bahri Mawardi

2006-01-01

264

Complexation of chitosan with acetic acid according to Fourier transform Raman spectroscopy data

NASA Astrophysics Data System (ADS)

The results of the interaction between the protonated chitosan (CHI) macromolecule and the acetate ion in dilute acetic acid solutions were studied by Fourier transform Raman spectroscopy and quantum-chemical modeling. The complexation of CHI with the acetate ion showed itself as the 934 cm-1 band in the Raman spectrum, which suggests the formation of [CHI+ · CH3COO-] type ion pairs. It was concluded that a comparative analysis of the integrated intensities of the Raman bands in the range 880-940 cm-1 makes it possible to judge about the relative content of hydrated acetate ions, CHI macromolecules of the [CHI+ · CH3COO-] complex, and acetic acid molecules not involved in CHI protonation.

Mikhailov, G. P.; Tuchkov, S. V.; Lazarev, V. V.; Kulish, E. I.

2014-06-01

265

Absolute iodine (I2) standards measured by means of Fourier transform spectroscopy

791 Absolute iodine (I2) standards measured by means of Fourier transform spectroscopy S the absorption spectrum of the iodine mole- cule recorded in the visible by means of Fourier spectroscopy. The result is that the wavenumbers previously published in the iodine-atlas extending from 14 800 to 20 000

Paris-Sud XI, UniversitÃ© de

266

Motion detection, the Wigner distribution function, and the optical fractional Fourier transform

NASA Astrophysics Data System (ADS)

It is shown that both surface tilting and translational motion can be independently estimated by use of the speckle photographic technique by capturing consecutive images in two different fractional Fourier domains. A geometric interpretation, based on use of the Wigner distribution function, is presented to describe this application of the optical fractional Fourier transform when little prior information is known about the motion.

Sheridan, John T.; Hennelly, Bryan; Kelly, Damien

2003-06-01

267

Momentum-space Lippmann-Schwinger-Equation, Fourier-transform with Gauss-Expansion-Method

In these notes we construct the momentum-space potentials from configuration-space using for the Fourier-transformation the Gaussian-Expansion-Method (GEM). This has the advantage that the Fourier-Bessel integrals can be performed analytically, avoiding possible problems with the oscillations in the Bessel functions for large r, in particular for $p_f \

Th. A. Rijken

2014-09-19

268

Calcium floride, magnesium fluoride, sulfur, silver bromide, silver chloride, and five different particle sizes of diamond powder were studied for use as matrix materials for diffuse reflectance Fourier transform infrared spectrometry. Potassium chloride was used as a reference b...

269

Data processing pipeline for a time-sampled imaging Fourier transform spectrometer

plants, growth of illegal crops, etc.), earth observations from air/space (crop management, mineral, to study such things as a galaxy's red shift, a cell's DNA or a counterfeit currency. Fourier transform

Naylor, David A.

270

SPECIATION OF HAZARDOUS INORGANIC COMPOUNDS BY FOURIER TRANSFORM INFRARED (FTIR) SPECTROSCOPY

The report describes an extension of the application of infrared methodology to characterize hazardous inorganic compounds in solid inorganic emissions, based on recent advances in instrumentation for Fourier transform infrared (FTIR) spectroscopy. The improved instrumentation, c...

271

This project explored the feasibility of developing new techniques for evaluation of the effects of environmental toxic materials on complex biopolymer systems using high sensitivity Fourier transform nuclear magnetic resonance (nmr) spectroscopy. Commercial instrumentation avail...

272

The Fourier Transform in Chemistry. Part 1. Nuclear Magnetic Resonance: Introduction.

ERIC Educational Resources Information Center

Using fourier transformation methods in nuclear magnetic resonance has made possible increased sensitivity in chemical analysis. This article describes these methods as they relate to magnetization, the RF magnetic field, nuclear relaxation, the RF pulse, and free induction decay. (CW)

King, Roy W.; Williams, Kathryn R.

1989-01-01

273

Fourier transform spectroscopy of BaO: New ground-state constants from the A 1

¿ chemiluminescence Hongzhi Li, Cristian Focsa,a) Bernard Pinchemel,a) Robert J. Le Roy,b) and P. F. Bernathc) Guelph in a Broida-type oven was revisited using a Fourier transform spectrometer. Chemiluminescence was observed

Le Roy, Robert J.

274

Infrared (IR) spectroscopy has been widely used for the structural investigation of humic substances. Although Fourier Transform Infrared (FTIR) instrumentation has been available for sometime, relatively little work with these instruments has been reported for humic substances,...

275

NASA Technical Reports Server (NTRS)

Spectra measured by off-axis detectors in a high-resolution Fourier transform spectrometer (FTS) are characterized by frequency scaling, asymmetry and broadening of their line shape, and self-apodization in the corresponding interferogram.

Bowman, K.; Worden, H.; Beer, R.

1999-01-01

276

Fourier Transform Raman Spectroscopy of Photoactive Proteins with Near-Infrared Excitation

The Fourier transform (FT) Raman spectroscopic treatment of the photoactive proteins bacteriorhodopsin and the photosynthetic reaction center is reported, with excitation at 1.06 ?m. Excitation at this wavelength circumvents the limitations...

Johnson, Carey K.; Rubinovitz, Ronald

1990-07-01

277

CHARACTERIZING MODERN AND FOSSIL GYMNOSPERM EXUDATES USING MICRO-FOURIER TRANSFORM INFRARED spectroscopy have direct implications for the assessment of the fossil potential and the chemotaxonomic interpretation of modern and fossil gymnosperm exudates. Keywords: chemotaxonomy, plant resin, gum, conifers

Wolfe, Alexander P.

278

Tandem quadrupole Fourier-transform mass spectrometry of oligopeptides and small proteins.

Modifications to the newly developed tandem quadrupole Fourier-transform mass spectrometer have made it possible to record mass spectra on oligopeptides and small proteins in the mass range between 2 and 13 kDa. PMID:3468502

Hunt, D F; Shabanowitz, J; Yates, J R; Zhu, N Z; Russell, D H; Castro, M E

1987-01-01

279

Forecasting performance of denoising signal by Wavelet and Fourier Transforms using SARIMA model

NASA Astrophysics Data System (ADS)

The goal of this research is to determine the forecasting performance of denoising signal. Monthly rainfall and monthly number of raindays with duration of 20 years (1990-2009) from Bayan Lepas station are utilized as the case study. The Fast Fourier Transform (FFT) and Wavelet Transform (WT) are used in this research to find the denoise signal. The denoise data obtained by Fast Fourier Transform and Wavelet Transform are being analyze by seasonal ARIMA model. The best fitted model is determined by the minimum value of MSE. The result indicates that Wavelet Transform is an effective method in denoising the monthly rainfall and number of rain days signals compared to Fast Fourier Transform.

Ismail, Mohd Tahir; Mamat, Siti Salwana; Hamzah, Firdaus Mohamad; Karim, Samsul Ariffin Abdul

2014-07-01

280

Broadband Mid-Infrared Comb-Resolved Fourier Transform Spectroscopy

NASA Astrophysics Data System (ADS)

We report on a comb-resolved, broadband, direct-comb spectroscopy system in the mid-IR and its application to the detection of trace gases and molecular line shape analysis. By coupling an optical parametric oscillator (OPO), a 100 m multipass cell, and a high-resolution Fourier transform spectrometer (FTS), sensitive, comb-resolved broadband spectroscopy of dilute gases is possible. The OPO has radiation output at 3.1-3.7 and 4.5-5.5 ?m. The laser repetition rate is scanned to arbitrary values with 1 Hz accuracy around 417 MHz. The comb-resolved spectrum is produced with an absolute frequency axis depending only on the RF reference (in this case a GPS disciplined oscillator), stable to 1 part in 10^9. The minimum detectable absorption is 1.6x10-6 wn Hz-1/2. The operating range of the experimental setup enables access to strong fundamental transitions of numerous molecular species for applications based on trace gas detection such as environmental monitoring, industrial gas calibration or medical application of human breath analysis. In addition to these capabilities, we show the application for careful line shape analysis of argon-broadened CO band spectra around 4.7 ?m. Fits of the obtained spectra clearly illustrate the discrepancy between the measured spectra and the Voigt profile (VP), indicating the need to include effects such as Dicke narrowing and the speed-dependence of the collisional width and shift in the line shape model, as was shown in previous cw-laser studies. In contrast to cw-laser based experiments, in this case the entire spectrum (˜ 250 wn) covering the whole P and R branches can be measured in 16 s with 417 MHz resolution, decreasing the acquisition time by orders of magnitude. The parallel acquisition allows collection of multiple lines simultaneously, removing the correlation of possible temperature and pressure drifts. While cw-systems are capable of measuring spectra with higher precision, this demonstration opens the door for fast, massively parallel line shape parameters retrieval combined with analysis reaching beyond the VP and with absolute frequency calibration delivered by frequency combs. R. Wehr et al. J. Mol. Spec. 235 54-68 (2003) A. Cygan, et al. Eur. Phys. J. Special Topics 222 2119-2142 (2013)

Lee, Kevin; Mills, Andrew; Mohr, Christian; Jiang, Jie; Fermann, Martin; Maslowski, Piotr

2014-06-01

281

Rapid Bacterial Identification Using Fourier Transform Infrared Spectroscopy

Recent studies at Pacific Northwest National Laboratory (PNNL) using infrared spectroscopy combined with statistical analysis have shown the ability to identify and discriminate vegetative bacteria, bacterial spores and background interferents from one another. Since the anthrax releases in 2001, rapid identification of unknown powders has become a necessity. Bacterial endospores are formed by some Bacillus species as a result of the vegetative bacteria undergoing environmental stress, e.g. a lack of nutrients. Endospores are formed as a survival mechanism and are extremely resistant to heat, cold, sunlight and some chemicals. They become airborne easily and are thus readily dispersed which was demonstrated in the Hart building. Fourier Transform Infrared (FTIR) spectroscopy is one of several rapid analytical methods used for bacterial endospore identification. The most common means of bacterial identification is culturing, but this is a time-consuming process, taking hours to days. It is difficult to rapidly identify potentially harmful bacterial agents in a highly reproducible way. Various analytical methods, including FTIR, Raman, photoacoustic FTIR and Matrix Assisted Laser Desorption/Ionization (MALDI) have been used to identify vegetative bacteria and bacterial endospores. Each has shown certain areas of promise, but each has shortcomings in terms of sensitivity, measurement time or portability. IR spectroscopy has been successfully used to distinguish between the sporulated and vegetative state. [1,2] It has also shown its utility at distinguishing between the spores of different species. [2-4] There are several Bacillus species that occur commonly in nature, so it is important to be able to distinguish between the many different species versus those that present an imminent health threat. The spectra of the different sporulated species are all quite similar, though there are some subtle yet reproducible spectroscopic differences. Thus, a more robust and reliable method is needed for differentiation. Using chemometrics, a classification scheme was developed and performed on samples sporulated in glucose broth. PNNL has demonstrated that vegetative bacteria and endospores have unique infrared (IR) signatures that can be used to identify to the species-, and in some cases, even to the strain-level. We have shown that the IR spectra of spores of different species tend to be quite similar, yet the small but reproducible differences in the spectra allow for a certain degree of differentiation. Further studies have shown that the culture medium can also have an effect on the spectra. For the distinction between vegetative and endospores, we have consistently observed a series of four peaks at 766, 725, 702, and a fairly sharp peak (FWHM 7 cm-1) at 660 cm-1, present only in the endospore spectra.

Valentine, Nancy B.; Johnson, Timothy J.; Su, Yin-Fong; Forrester, Joel B.

2007-02-01

282

An uncertainty principle for real signals in the fractional Fourier transform domain

The fractional Fourier transform (FrFT) can be thought of as a generalization of the Fourier transform to rotate a signal representation by an arbitrary angle ? in the time-frequency plane. A lower bound on the uncertainty product of signal representations in two FrFT domains for real signals is obtained, and it is shown that a Gaussian signal achieves the lower

Sudarshan Shinde; Vikram M. Gadre

2001-01-01

283

FAST FOURIER TRANSFORMS: A TUTORIAL REVIEW AND A STATE OF THE ART

The publication of the Cooley-Tukey fast Fourier transform (FIT) algorithm in 1965 has opened a new area in digital signal processing by reducing the order of complexity of some crucial computational tasks like Fourier transform and convolution from N 2 to N log2 N, where N is the problem size. The development of the major algorithms (Cooley-Tukey and split-radix FFT,

P. DUHAMEL; M. VETTERLI

1990-01-01

284

Alternative path to the boundary: The CFT as the Fourier transform in AdS space

In this paper we shed new light on the AdS/CFT duality by interpreting the CFT as the Fourier transform in AdS space. We make use of well-known integral geometry techniques to derive the Fourier transformation of a function defined on the AdS hyperboloid. We show that the Fourier transformation of a function on the hyperboloid is a function defined on the boundary. We find that the Green's functions from the literature are actually the Fourier weights (i.e. plane wave solutions) of the transformation and that the boundary values of fields appearing in the correspondence are the Fourier components of the transformation. One is thus left to interpret the CFT as the quantized version of a classical theory in AdS and the dual operator as the Fourier coefficients. Group theoretic considerations are discussed in relation to the transformation and its potential use in constructing QCD-like theories. In addition, we consider possible implications involving understanding the dual of AdS black holes.

Tolfree, Ian M. [Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218 (United States)

2008-11-15

285

The performance characteristics of the wavelet transform and the short-time Fourier transform (STFT) for transient detection are examined by means of computer simulation. The STFT uses a power-of-two decimation-in-time FFT with various frame sizes...

Pilgrim, Richard Allen

1994-01-01

286

Quantum algorithms using the curvelet transform

The curvelet transform is a directional wavelet transform over Rn, which is used to analyze functions that have singularities along smooth surfaces (Candes and Donoho, 2002). I demon- strate how this can lead to new quantum algorithms. I give an efficient implementation of a quantum curvelet transform, together with two applications: a single-shot measurement proce- dure for approximately finding the

Yi-kai Liu

2009-01-01

287

Fourier-Transform Raman Spectroscopy Of Biological Assemblies

NASA Astrophysics Data System (ADS)

Although the successful coupling of Raman scattered near-infrared radiation to a Michelson interferometer has recently created an outburst of intense interest in Fourier-transform (FT) Raman spectrometry," extended applications of the technique to macromolecular assemblies of biochemical and biophysical relevance have not progressed as rapidly as studies directed primarily at more conventional chemical characterizations. Since biological materials sampled with visible laser excitation sources typically emit a dominant fluorescence signal originating either from the intrinsic fluorescence of the molecular scatterer or from unrelenting contaminants, the use of near-infrared Nd:YAG laser excitation offers a convenient approach for avoiding this frequently overwhelming effect. In addition, the FT-Raman instrumentation provides a means of eliminating the deleterious resonance and decomposition effects often observed with the more accessible green and blue laser emissions. However, in choosing the incident near-infrared wavelength at, for example, 1064nm, the Raman scattered intensity decreases by factors of eighteen to forty from the Raman emissions induced by the shorter, visible excitations. Depending upon the experiment, this disadvantage is offset by the throughput and multiplex advantages afforded by the interferometric design. Thus, for most chemical systems, near-infrared FT-Raman spectroscopy, clearly provides a means for obtaining vibrational Raman spectra from samples intractable to the use of visible laser sources. In particular, for neat liquids, dilute solutions or polycrystalline materials, the ability to achieve high quality, reproducible spectra is, with moderate experience and perhaps relatively high laser powers, as straightforward as the conventional methods used to obtain Raman spectra with visible excitation and dispersive monochromators. In using near-infrared FT techniques to determine the Raman spectra of biological samples, one encounters new sets of experimental problems that may entail an initial, relatively steep learning curve. These difficulties originate particularly from the fragility of the weakly scattering aggregate paired with the dilute nature of the biochemical or cellular dispersion. Often, the Raman scattered intensity from these samples can be increased by carefully peileting the biological suspension using ultracentrifugation techniques. Since the overtone region of water, the usual medium for biological samples, absorbs radiation from both the Rayleigh signal at the exciting wavelength of the Nd:YAG laser and the longer wavelength Raman scattering from the sample, reproducible temperature measurements and temperature control become significant concerns. In these cases one appeals to internal temperature calibrations, use of deuterium oxide (D20) as a solvent (since absorptions of the laser exciting wavelength and Raman scattered photons are minimized), manipulation of incident laser spot size and the use of fiber optic bundles to carry the exciting and scattered radiation. In the present discussion we briefly cite some of the experimental approaches we have developed and experiences we have encountered in adapting near-infrared FT-Raman spectroscopy to the more challenging biophysical and biochemical systems amenable to vibrational analysis. We emphasize here the determination of the spectra of membrane assemblies and membrane related materials; in particular, we elucidate the interaction of several polyene antibiotics, including amphotericin A, amphotericin B and nystatin, with a model membrane system composed of dipalmitoylphosphatidylcholine bilayers.

Levin, Ira W.; Lewis, E. Neil

1989-12-01

288

Super-high-efficiency approximate calculation of series sum and discrete Fourier transform

We present a super-high-efficiency approximate computing scheme for series sum and discrete Fourier transform. The summation of a series sum or a discrete Fourier transform is approximated by summing over part of the terms multiplied by corresponding weights. The calculation is valid for the function under the transform being piecewise smooth in the continuum variable. The scheme reduces significantly the requirement for computer memory storage and enhances the numerical computation efficiency without losing accuracy. By comparing with the known results of examples, we show the accuracy and the efficiency of the scheme. The efficiency can be higher than $10^6$ for the examples.

Xin-Zhong Yan

2013-11-18

289

Optical movie encryption based on a discrete multiple-parameter fractional Fourier transform

NASA Astrophysics Data System (ADS)

A movie encryption scheme is proposed using a discrete multiple-parameter fractional Fourier transform and theta modulation. After being modulated by sinusoidal amplitude grating, each frame of the movie is transformed by a filtering procedure and then multiplexed into a complex signal. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted by a discrete multiple-parameter fractional Fourier transform. The movie can be retrieved by using the correct keys, such as a random phase mask, a pixel scrambling operation, the parameters in a discrete multiple-parameter fractional Fourier transform and a time sequence. Numerical simulations have been performed to demonstrate the validity and the security of the proposed method.

Zhong, Zhi; Zhang, Yujie; Shan, Mingguang; Wang, Ying; Zhang, Yabin; Xie, Hong

2014-12-01

290

The analysis of cetacean vocalizations is considered using Fourier-based techniques that employ chirp functions in their decomposition. In particular, the paper considers a short-time methods based on the fractional Fourier transform for detecting frequency modulated narrow-band signals, such as dolphin whistles, and compares this to the classical short-time Fourier methods. The fractional Fourier technique explored computes transforms associated with a range of chirp rates and automatically selects the rate for the final analysis. This avoids the need for prior knowledge of signal's chirp rate. An analysis is presented that details the performance of both methods as signal detectors and allows one to determine their detection thresholds. These thresholds are then used to measure the detectability of synthetic signals. This principle is then extended to measure performance on a set of recordings of narrow-band vocalizations from a range of cetacean species. PMID:21973352

Locke, Jonathan; White, Paul R

2011-10-01

291

Scaled diffraction calculation between tilted planes using nonuniform fast Fourier transform.

A method of diffraction calculation between tilted planes with variable sampling rates is proposed. The proposed method is based on the Fourier spectrum rotation from a tilted plane to a parallel plane. The nonuniform fast Fourier transformation (NUFFT) is used to calculate the nonuniform sampled Fourier spectrum on the tilted plane with variable sampling rates, which overcomes the sampling restriction of FFT in the conventional method. Both of the computer simulation and the optical experiment shows the feasibility of our method in calculating the hologram of polygon-based object with scalable size, which can be considered as an important application in the holographic three-dimensional display. PMID:25090546

Chang, Chenliang; Xia, Jun; Wu, Jun; Lei, Wei; Xie, Yi; Kang, Mingwu; Zhang, Qiuzhi

2014-07-14

292

NASA Technical Reports Server (NTRS)

An input analog signal to be frequency analyzed is separated into N number of simultaneous analog signal components each identical to the original but delayed relative to the original by a successively larger time delay. The separated and delayed analog components are combined together in a suitable number of adders and attenuators in accordance with at least one component product of the continuous Fourier transform and analog signal matrices to separate the analog input signal into at least one of its continuous analog frequency components of bandwidth 1/N times the bandwidth of the original input signal. The original analog input signal can be reconstituted by combining the separate analog frequency components in accordance with the component products of the continuous Fourier transform and analog frequency component matrices. The continuous Fourier transformation is useful for spectrum analysis, filtering, transfer function synthesis, and communications.

Munoz, R. M. (inventor)

1974-01-01

293

Reduction and coding of synthetic aperture radar data with Fourier transforms

NASA Technical Reports Server (NTRS)

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.

Tilley, David G.

1995-01-01

294

NASA Astrophysics Data System (ADS)

Series of thermodiffusion experiments using optical digital interferometry (ODI) have been conducted onboard the International Space Station. Conventionally, the two-dimensional (2D) fast Fourier transform (FFT) fringe analysis technique has been applied as a fast and reliable technique to extract data. In this study, for the first time, the windowed Fourier transform (WFT) method is used to analyze the same experiments. In this method, a Fourier transformation is applied on the fringes at two different stages: initially, during the filtration of the non-zero peaks and then on the wrapped phase image. We provide a detailed comparison between FFT and WFT results of binary and ternary mixtures for ODI thermodiffusion experiments. The substantial enhancements of this method are presented and discussed for different experiments conducted for both binary and ternary mixtures. We show that while disturbances in the phase fringe pattern can cause significant error in FFT techniques, if the windowed Fourier filtration (WFF) parameters are properly chosen this type of noise can be eliminated during WFF analysis. The importance of replacing the FFT method becomes more pronounced for the ternary system, as this method fails to reconcile reliable concentration profiles. The results of this work can show that the application of the windowed Fourier transform in optical digital interferometry investigations show improved results over the same experiments analyzed using FFT methods, especially for experiments involving very small heat and mass fluxes such as the Soret effect in multicomponent mixtures.

Ahadi, Amirhossein; Khoshnevis, Ahmad; Saghir, M. Ziad

2014-04-01

295

NASA Astrophysics Data System (ADS)

As the impact of the instrument internal error, external interference and other factors, the interferogram measured by Fourier transform spectrometer is asymmetric, result in the complex outcome after Fourier transform. Currently, most radiometric calibration method used for Fourier transform spectrometer is usually based on real spectrums, which is converted from the above complex spectrum by calculating magnitude value or make the phase correction first. Proceed from error sources and mechanisms of the Fourier transform spectrometer, we propose a multi-point radiometric calibration method based on complex spectral data to improve the processing efficiency and accuracy, which is obtained by the original interferogram via Fourier transform. We solving the instrument response function include linear gain and offset by complex spectrum above to calculate complex spectral radiance. Compared with the traditional method based on real spectrum, the present efficient method does not limited to real spectrum and the phase correction is not required. In this paper, we use BOMEM's MR304 Fourier transform infrared spectrometer and the DCN1000N3 blackbody made by HGH Infrared Systems to carry out the radiation calibration experiment in laboratory. The results show that, the amplitude of complex radiance spectrum obtained by this method has a high consistency with the theoretical value, while the extra imaginary spectrum is similar with the difference between results and theoretical value in absolute value and trends. It proved that, this multi-point radiometric calibration method by using the amplitude of complex spectral data is highly reliable; meanwhile, the imaginary spectrum can reflect the calibration error very well and offer a new technical approach for accuracy evaluation research.

He, Qian; Wang, Guangping; Wu, Jingli; Li, Junwei

2014-11-01

296

Simple examples of finding tracks by Fourier transform with filter or correlation function are presented. Possibilities for using this method in more complicated real situations and the processing times which might be achieved are discussed. The method imitates the simplest examples in the literature on optical pattern recognition and optical processing. The possible benefits of the method are in speed of processing in the optical Fourier transform wherein an entire picture is processed simultaneously. The speed of a computer vector processor may be competitive with present electro-optical devices. 2 refs., 6 figs.

Underwood, D.

1986-09-05

297

Dispersive Fourier transformation is a powerful technique in which the spectrum of an optical pulse is mapped into a time-domain waveform using chromatic dispersion. It replaces a diffraction grating and detector array with a dispersive fiber and single photodetector. This simplifies the system and, more importantly, enables fast real-time measurements. Here we describe a novel ultrafast barcode reader and displacement sensor that employs internally-amplified dispersive Fourier transformation. This technique amplifies and simultaneously maps the spectrally encoded barcode into a temporal waveform. It achieves a record acquisition speed of 25 MHz -- four orders of magnitude faster than the current state-of-the-art.

Goda, Keisuke; Jalali, Bahram

2008-01-01

298

Three-dimensional radiative transfer using a Fourier-transform matrix-operator method

NASA Technical Reports Server (NTRS)

The three-dimensional equation of transfer for a scattering medium with planar geometry is solved by using a spatial Fourier transform and extending matrix-operator techniques developed previously for the one-dimensional equation. Doubling and adding algorithms were derived by means of an interaction principle for computing the Fourier-transformed radiation field. The resulting expressions fully describe the radiative transfer process in a scattering medium, inhomogeneous in the x-, y- and z-directions, illuminated from above by an arbitrarily general intensity field and bounded from below by a surface with completely general reflection properties.

Martonchik, J. V.; Diner, D. J.

1985-01-01

299

Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage

NASA Astrophysics Data System (ADS)

Magneto-Hydrodynamic (MHD) flow over an accelerated plate is investigated with partial slip conditions. Generalized Fourier Transform is used to get the exact solution not only for uniform acceleration but also for variable acceleration. The numerical solution is obtained by using linear finite element method in space and One-Step-?-scheme in time. The resulting discretized algebraic systems are solved by applying geometric-multigrid approach. Numerical solutions are compared with the obtained Fourier transform results. Many interesting results related with slippage and MHD effects are discussed in detail through graphical sketches and tables. Application of Dirac-Delta function is one of the main features of present work.

Ahmad, Salman; Hussain, Shafqat; Siddiqui, Abuzar Abid; Ali, Asad; Aqeel, Muhammad

2014-06-01

300

NASA Astrophysics Data System (ADS)

Dispersive Fourier transformation is a powerful technique in which the spectrum of an optical pulse is mapped into a time-domain waveform using chromatic dispersion. It replaces a diffraction grating and detector array with a dispersive fiber and single photodetector. This simplifies the system and, more importantly, enables fast real-time measurements. Here we describe a novel ultrafast barcode reader and displacement sensor that employs internally amplified dispersive Fourier transformation. This technique amplifies and simultaneously maps the spectrally encoded barcode into a temporal waveform. It achieves a record acquisition speed of 25MHz—four orders of magnitude faster than the current state of the art.

Goda, Keisuke; Tsia, Kevin K.; Jalali, Bahram

2008-09-01

301

Quantum Algorithms using the Curvelet Transform

The curvelet transform is a directional wavelet transform over R^n, originally due to Candes and Donoho (2002). It is used to analyze functions that have singularities along smooth surfaces. I demonstrate how this can lead to new quantum algorithms. I give an efficient implementation of a quantum curvelet transform, together with two applications: a single-shot measurement procedure for approximately finding the center of a ball in R^n, given quantum-samples over the ball; and, a quantum algorithm for finding the center of a radial function over R^n, given oracle access to the function. I conjecture that these algorithms only require a constant number of quantum-samples or oracle queries, independent of the dimension n -- this can be interpreted as a quantum speed-up. Finally, I prove some rigorous bounds on the distribution of probability mass for the continuous curvelet transform. This almost proves my conjecture, except for issues of discretization.

Liu, Yi-Kai

2008-01-01

302

Euler-Bessel and Euler-Fourier Transforms Robert Ghrist

) An extension of spatially variant apodization (SVA) to Euler-Bessel transforms, with applications to sidelobe variant apodization (SVA) to mitigate sidelobe phenomena. AMS classification scheme numbers: 65R10,58C35, including localization and shape discrimination. This last application utilizes an extension of spatially

Ghrist, Robert W.

303

Fourier-transform spectroscopy and potential construction of the (2)(1)? state in KCs.

The paper presents an empirical pointwise potential energy curve (PEC) of the (2)(1)? state of the KCs molecule constructed by applying the Inverted Perturbation Approach routine. The experimental term values in the energy range E(v', J') ? [15?407; 16?579] cm(-1) involved in the fit were based on Fourier-Transform spectroscopy data obtained with 0.01 cm(-1) accuracy from the laser-induced (2)(1)? ? X(1)?(+) fluorescence spectra. Buffer gas Ar was used to facilitate the appearance of rotation relaxation lines in the spectra, thus enlarging the (2)(1)? data set and allowing determination of the ?-splitting constants. The data set included vibrational v' ? [0, 28] and rotational J' ? [7, 274] quantum numbers covering about 67% of the potential well. The present PEC reproduces the overall set of data included in the fit with a standard deviation of 0.5 cm(-1). The obtained value of the ?-doubling constant q = + 1.8 × 10(-6) cm(-1) for J' > 50 and v' ? [0, 6] is in an excellent agreement with q = + 1.84 × 10(-6) cm(-1) reported in Kim, Lee, and Stolyarov [J. Mol. Spectrosc. 256, 57-67 (2009)]. PMID:25854245

Birzniece, I; Nikolayeva, O; Tamanis, M; Ferber, R

2015-04-01

304

867 Description of the absorption spectrum of iodine recorded by means of Fourier Transform 2014 An in extenso analysis of the (B-X) I2 iodine absorption spectrum recorded by means of Fourier.1 HISTORICAL. - First, let us recall that the study of the absorption spectrum of iodine by means of Fourier

Paris-Sud XI, UniversitÃ© de

305

Adaptive motion mapping in pancreatic SBRT patients using Fourier transforms

Recent studies suggest that 4DCT is unable to accurately measure respiratory-induced pancreatic tumor motion. In this work, we assessed the daily motion of pancreatic tumors treated with SBRT, and developed adaptive strategies to predict and account for this motion. The daily motion trajectory of pancreatic tumors during CBCT acquisition was calculated using a model which reconstructs the instantaneous 3D position in each 2D CBCT projection image. We developed a metric (termed "Spectral Coherence," SC) based on the Fourier frequency spectrum of motion in the SI direction, and analyzed the ability of SC to predict motion-based errors and classify patients according to motion characteristics. The amplitude of daily motion exceeded the predictions of pre-treatment 4DCT imaging by an average of 3.0 mm, 2.3 mm, and 3.5 mm in the AP, LR, and SI directions. SC was correlated with daily motion differences and tumor dose coverage. In a simulated adaptive protocol, target margins were adjusted based on SC, resulting in...

Jones, Bernard L; Miften, Moyed

2015-01-01

306

Fast Inverse Nonlinear Fourier Transform For Generating Multi-Solitons In Optical Fiber

The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier transform in WDM systems with an appropriately defined nonlinear Fourier transform (NFT). The computational complexity of NFTs is a topic of current research. In this paper, a fast inverse NFT algorithm for the important special case of multi-solitonic signals is presented. The algorithm requires only $\\mathcal{O}(D\\log^{2}D)$ floating point operations to compute $D$ samples of a multi-soliton. To the best of our knowledge, this is the first algorithm for this problem with $\\log^{2}$-linear complexity. The paper also includes a many samples analysis of the generated nonlinear Fourier spectra.

Wahls, Sander

2015-01-01

307

The kinetics of air oxidation of a series of bituminous coals were investigated by using diffuse reflectance infrared Fourier transform (DRIFT) spectrometry. Four bituminous coals were ground to three particle sizes and oxidized at 150, 200 and 250Â°C. Activation energies and rate constants for the air oxidation of these coals were determined by tracking the decrease in the intensity of

TeVrucht

1989-01-01

308

A new instrument has been designed, built, and tested for high performance Fourier transform ion cyclotron resonance mass spectrometry (FTICRMS) that allows operation at gas pressures of up to ?20 Torr in the ion source and up to ?0.01 Torr in the ion trap. FTICRMS performance is not compromised at these pressures due to an external, high throughput ion source

M. L. Mandich; A. M. DeSantolo

1998-01-01

309

Improvements to the utility of Fourier transform ion cyclotron resonance mass spectrometry for analytical mass spectrometry are presented. Various ion packet decay models are investigated for both singly and multiply charged ions. A new ion trap allows for determination of the cyclotron radius of the ion packet with improved sensitivity. The cyclotron radius of the ion packet can be measured

Limbach

1992-01-01

310

Electron capture dissociation (ECD) efficiency in a 9.4 T Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer varies periodically with the time interval between ion and electron injection. The observed modulation frequency correlates to within 1% with ion magnetron frequency, most probably due to misalignment between the ion beam and the electron beam. The optimum ECD conditions are obtained by

Yury O. Tsybin; Christopher L. Hendrickson; Steven C. Beu; Alan G. Marshall

2006-01-01

311

There are approximately 109 proteins in a cell. A hotspot in bioinformatics is how to identify a protein's subcellular localization, if its sequence is known. In this paper, a method using fast Fourier transform-based support vector machine is developed to predict the subcellular localization of proteins from their physicochemical properties and structural parameters. The prediction accuracies reached 83% in prokaryotic

Zhimeng WANG; Lin JIANG; Menglong LI; Lina SUN; Rongying LIN

2007-01-01

312

Apodization Functions for Fourier Transform Spectroscopy Margaret K. Tahic and David A. Naylor

Apodization Functions for Fourier Transform Spectroscopy Margaret K. Tahic and David A. Naylor margaret.tahic@uleth.ca and naylor@uleth.ca Abstract: The three Norton-Beer apodizing functions provide a reduction in the sidelobe amplitude of FTS instrumental line shapes. We extend this series of apodizing

Naylor, David A.

313

Investigation of infrared Fourier-Transform spectroscopy for oral cancer detection

A system was developed using a Fourier Transform-n spectrometer to investigate spectral differences between malignant, benign and healthy oral tissue in the near-infrared range (2.0-2.5 microns). A hamster model for oral squamous cell carcinoma...

Cooney, Kevin Michael

1998-01-01

314

Amplified dispersive Fourier-transform imaging for ultrafast displacement sensing and barcode and, more importantly, enables fast real-time measurements. Here we describe a novel ultrafast barcode. This technique amplifies and simultaneously maps the spectrally encoded barcode into a temporal waveform

Jalali. Bahram

315

Experiments performed in a Fourier transform ion cyclotron resonance (FTICR) mass spectrometer are evaluated to produce quantitatively reliable mass spectra in which the ion population in the trapped-ion cell is proportional to the image current. Generation of signal intensity profiles as a function of excitation voltage is described for analyzing ion cloud evolution in response to the effect of system

Riegner

1993-01-01

316

Soil is a complex environmental medium, particularly with respect to its biological and organic characteristics. Analytical approaches based on specific aspects of biological or organic variation may fail to detect broader differences in function or composition. Fourier transform infrared spectroscopy (FT-IR) spectra provide a more comprehensive description of soil characteristics in the form of complex multivariate data sets. Soils at

Geoffrey N. Elliott; Hilary Worgan; David Broadhurst; John Draper; John Scullion

2007-01-01

317

Refined Fourier-transform method of analysis of full two-dimensional digitized interferograms

NASA Astrophysics Data System (ADS)

A refined Fourier-transform method of analysis of interference patterns is presented. The refinements include a method of automatic background subtraction and a way of treating the problem of heterodyning. The method proves particularly useful for analysis of long sequences of interferograms.

Lovri?, Davorin; Vu?i?, Zlatko; Gladi?, Jadranko; Demoli, Nazif; Mitrovi?, Slobodan; Milas, Mirko

2003-03-01

318

In this article, the design and fabrication of a Fourier transform spectrometer, based on a thermally actuated tunable grating, are presented. Grooves of a binary grating are filled with nitrobenzene, the refractive index of which highly depends on temperature. Through the application of heat, the temperature of the nitrobenzene is changed, which in turn changes the efficiency of the grating.

Mohammadreza Riahi

319

By use of coherent terahertz synchrotron radiation, we experimentally tested a holographic Fourier transform spectrometer coupled to an array detector to determine its viability as a spectral device. Somewhat surprisingly, the overall performance strongly depends on the absorptivity of the birefringent lithium tantalate pixels in the array detector.

Nikolay I. Agladz, John Klopf, Gwyn Williams, Albert J. Sievers

2010-06-01

320

A Fractional Fourier Transform Analysis of a Bubble Excited by an Ultrasonic Chirp

A Fractional Fourier Transform Analysis of a Bubble Excited by an Ultrasonic Chirp Euan Barlow. 2 #12;1 Introduction When a bubble is insonified by an ultrasonic signal it oscillates perturbation of the bubble's radius to show that using an ultrasonic chirp signal as the forcing function

Mottram, Nigel

321

We report the first use of a polarizing Fourier transform spectrometer on the James Clerk Maxwell Telescope. Solar spectra have been measured through four of the submillimeter and millimeter atmospheric windows. The repeatability is shown to be excellent, with signal-to-noise ratios exceeding 100 per spectral element per scan. The spectra also show good agreement with synthetic atmospheric transmission spectra over

D. A. Naylor; T. A. Clark; G. R. Davis; W. D. Duncan; G. J. Tompkins

1993-01-01

322

Fourier transform infrared spectroscopy in high-pressure studies on proteins

Several aspects of the application of Fourier transform infrared spectroscopy (FTIR) in high-pressure studies on proteins are reviewed. Basic methodological considerations regarding spectral band assignments, quantitative analysis, and choice of pressure calibrants are also placed within the scope of this paper. This work attempts to evaluate recent developments in the field of high-pressure FTIR of proteins and its prospects for

Wojciech Dzwolak; Minoru Kato; Yoshihiro Taniguchi

2002-01-01

323

This paper presents a viable approach and a new teaching and learning paradigm to enhance the effectiveness of teaching fast Fourier transform [1] and significantly improve the learning outcomes. By using the smart mobile devices, this approach establishes the links among concepts, abstract representations, and realistic applications which are often lacking in traditional instruction. Several mobile apps for real time

Zhengzhe Li; Teng Zhao; Dong Ren; Yang Zhang; Lei Wang

2012-01-01

324

Technology Transfer Automated Retrieval System (TEKTRAN)

The automated quantification of three greenhouse gases, ammonia, methane and nitrous oxide, in the vicinity of a large dairy farm by open-path Fourier transform infrared (OP/FT-IR) spectrometry at intervals of 5 minutes is demonstrated. Spectral pretreatment, including the detection and correction ...

325

This paper addresses two fundamental issues involved in the reconstruction of a multidimensional sequence from either the phase or magnitude of its Fourier transform. The first issue relates to the uniqueness of a multidimensional sequence in terms of its phase or magnitude. Although phase or magnitude information alone is not sufficient, in general, to uniquely specify a sequence, a large

M. Hayes

1982-01-01

326

Iterative reconstruction of speech from short-time Fourier transform phase and magnitude spectra

Iterative reconstruction of speech from short-time Fourier transform phase and magnitude spectra dimensional, signal reconstruction (specifically speech signals) from the magnitude spectrum and the phase magnitude spectrum, and (iii) a signal can be reconstructed to within a scale factor from its magnitude

327

Fast and accurate computation of the Fourier transform of an image Gregory Beylkin

function f. Namely, we compute for --N m, n N (with a given accuracy ) the integrals * ,1 1 · f(m,n) = I I in image processing to simply take the FFT of the pixel values of the image in order to evaluate the Fourier transform. Due to the jump discontinuities of the function f, the accuracy of such a computation

Beylkin, Gregory

328

Recent Applications of Fourier Transform Infrared Spectrophotometry in Herbal Medicine Analysis

Fourier transform infrared spectroscopy (FTIR) is a fast and nondestructive analytical method. Associated with chemometrics, it is a powerful tool for the pharmaceutical industry. It is becoming a suitable technique for analysis of herbal medicine. This review focuses on the recent developments and updates for the qualitative and quantitative analysis of herbal medicine using FTIR. Moreover, it can be implemented

Andrei A. Bunaciu; Hassan Y. Aboul-Enein; Serban Fleschin

2011-01-01

329

On the use of windows for harmonic analysis with the discrete Fourier transform

This paper makes available a concise review of data windows and their affect on the detection of harmonic signals in the presence of broad-band noise, and in the presence of nearby strong harmonic interference. We also call attention to a number of common errors in the application of windows when used with the fast Fourier transform. This paper includes a

FREDRIC J. HARRIS

1978-01-01

330

Technology Transfer Automated Retrieval System (TEKTRAN)

This study deals with transferring the near-infrared (NIR) calibration models for quality assessment of barley between two instruments with different resolutions and number of data points, a Fourier transform instrument (master) and a dispersive instrument (slave). A file of spectra from 206 ground ...

331

A test for second order stationarity of a time series based on the Discrete Fourier Transform

A test for second order stationarity of a time series based on the Discrete Fourier Transform property, we construct a Portmanteau type test statistic for testing stationarity of the time series. It is shown that under the null of stationarity, the test statistic is approximately a chi square distribution

Subba Rao, Suhasini

332

Several field tests of a Fourier transform infrared (FTIR) spectrometer have been conducted. he results indicate that effective use of this type of instrument in the field of continuous emissions monitoring (CEM) is possible under the proper conditions, and within limits currentl...

333

Characteristic Length Scale of Bicontinuous Nanoporous Structure by Fast Fourier Transform

We propose a method derived from fast Fourier transform (FFT) process to measure the characteristic length scale of bicontinuous nanoporous structures. By rotationally averaging the FFT power spectrum of a nanoporous micrograph from scanning electron microscope (SEM) or transmission electron microscope (TEM), a significant peak in the power spectrum can be obtained, which reflects the characteristic length scale of the

Takeshi Fujita; Ming Wei Chen

2008-01-01

334

Amplified Dispersive FourierTransform Imaging for Ultrafast Displacement Sensing and Barcode Reading

Dispersive Fourier transformation is a powerful technique in which the spectrum of an optical pulse is mapped into a time-domain waveform using chromatic dispersion. It replaces a diffraction grating and detector array with a dispersive fiber and single photodetector. This simplifies the system and, more importantly, enables fast real-time measurements. Here we describe a novel ultrafast barcode reader and displacement

Keisuke God; Kevin K. Tsi; Bahram Jalali

335

Far infrared Fourier-transform spectroscopy of mono-deuterated hydrogen peroxide HOOD

Far infrared Fourier-transform spectroscopy of mono-deuterated hydrogen peroxide HOOD Doris-1, Tsukuba, Ibaraki 305-8569, Japan a r t i c l e i n f o Keywords: Deuterated hydrogen peroxide Far infrared phase spectrum of singly deuterated hydrogen peroxide, HOOD, in its vibrational ground state, recorded

Giesen, Thomas

336

Technology Transfer Automated Retrieval System (TEKTRAN)

Our presentation will focus on continuing efforts to examine secondary cell wall development in cotton fibers using infrared Spectroscopy. Cotton fibers harvested at 18, 20, 24, 28, 32, 36 and 40 days after flowering were examined using attenuated total reflection Fourier transform-infrared (ATR FT-...

337

The design of a multi-purpose external ion source Fourier transform ion cyclotron resonance mass spectrometer for rapid microscale analyses of complex mixtures is presented. Rapid microscale analyses are carried out using several desorption and ionisation techniques, and benefit from a hydrocarbon-free UHV (Ultra High Vacuum) system. Two different techniques for polymer analysis will be discussed. “In source” filament pyrolysis is

Ron M. A. Heeren; Jaap J. Boon

1996-01-01

338

This paper gives the main results obtained at Laboratoire Aimé Cotton, using Fourier transform spectroscopy (FTS) in the visible and UV ranges. After a rapid historical survey, a description of the fourth generation interferometer, which is specially designed to record visible and UV light will be given. Typical results in emission and absorption spectroscopy, including the metrological applications, will follow.

Paul Luc

1995-01-01

339

NASA Astrophysics Data System (ADS)

This paper gives the main results obtained at Laboratoire Aimé Cotton, using Fourier transform spectroscopy (FTS) in the visible and UV ranges. After a rapid historical survey, a description of the fourth generation interferometer, which is specially designed to record visible and UV light will be given. Typical results in emission and absorption spectroscopy, including the metrological applications, will follow.

Luc, Paul

1995-07-01

340

Degradation of polymer/substrate interfaces Â an attenuated total reflection Fourier transform. The durability of such polymer coated adhesively bonded joint structures depends upon the stability of the interfaces between the polymer and the substrate it is coated on. It is economically important to have

341

Differentiating orange juices using fourier transform infrared spectroscopy (FT-IR)

Technology Transfer Automated Retrieval System (TEKTRAN)

Fourier transform infrared spectroscopy (FT-IR) is compared to various instrumental and physical/chemical methods for differentiating commercial orange juice products. Statistical models were generated using the data from an electronic nose (e-nose), a head space gas chromatograph (GC), a mass spec...

342

The ultra-high mass resolving power and high mass accuracy of Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) have been shown to be well suited for the characterization of highly complex mixtures. Petroleum mixtures, arguably the most complex on the planet, have been extensively characterized by FT-ICR MS. This new field of \\

Donald Francis Smith

2007-01-01

343

We report a study of the coagulation of whole blood by oscillatory shear Fourier transform mechanical spectroscopy. The results include the first identification of the Gel Point of coagulating blood in terms of the Chambon–Winter Gel Point criterion and we show how this may be used as an appropriate basis for detecting the establishment of an incipient clot in samples

P. A. Evans; K. Hawkins; P. R. Williams; R. L. Williams

2008-01-01

344

The Fourier transform infrared examination of the combustion products of a selection of forest materials has been undertaken in order to guide future detection of biomass burning using satellite remote sensing. Combustion of conifer Pinus strobus (white pine) and deciduous Prunus serotina (cherry), Acer rubrum (red maple), Friglans nigra (walnut), Fraxinus americana (ash), Betula papyrifera (birch), Querus alba (white oak)

Diomaris Padilla

2008-01-01

345

USE OF A FOURIER TRANSFORM SPECTROMETER AS A REMOTE SENSOR AT SUPERFUND SITES

A Fourier transform infrared remote sensor (FTIR-RS) was used to measure chemical emissions at the Shaver's Park Superfund site in northwestern Georgia. he system was bistatic with a source/receiver at one end of a 250 path and a retroreflector at the other end. he source/receive...

346

Rendering falling snow using an inverse Fourier transform Michael S. Langer

Rendering falling snow using an inverse Fourier transform Michael S. Langer School of Computer snow, non-photorealistic rendering Methods for rendering falling snow typically use particle sys- tems we present an alter- native method for rendering falling snow which does not use parti- cles

Langer, Michael

347

Study on europium doped hydroxyapatite nanoparticles by Fourier transform infrared spectroscopy were conducted on europium doped hydroxyapatite, Ca10-xEux(PO4)6(OH)2 nanocrystalline powders (Eu demonstrates that the antimicrobial activity of Eu:HAp nanoparticles is dependent on the europium concentration

Boyer, Edmond

348

Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform

ERIC Educational Resources Information Center

We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g…

Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos

2010-01-01

349

Technology Transfer Automated Retrieval System (TEKTRAN)

Over 32,000 interferograms measured during open-path Fourier transform infrared (OP/FT-IR) measurements at dairy and hog farms were evaluated for anomalies. Five types of anomalies could be distinguished: a reduction in the interferogram intensity because of weather-related optical misalignment; an ...

350

A neural-network based analog fault diagnostic system is developed for nonlinear circuits. This system uses wavelet and Fourier transforms, normalization and principal component analysis as preprocessors to extract an optimal number of features from the circuit node voltages. These features are then used to train a neural network to diagnose soft and hard faulty components in nonlinear circuits. Our neural

Farzan Aminian; Mehran Aminian

2001-01-01

351

The techniques of Fourier transform spectroscopy combined with large aperture telescopes and advances in detector technology now permit infrared (at a wavelength greater than 1 micron) observations of the surfaces of small solar system objects such as asteroids and satellites. The results demonstrate that this activity can produce important new compositional information related to the origin and evolution of the

H. P. Larson; Uwe Fink

1977-01-01

352

This article presents a fast algorithm for the efficient solution of the Helmholtz equation. The method is based on the translation theory of the multipole expansions. Here, the speedup comes from the convolution nature of the translation operators, which can be evaluated rapidly using fast Fourier transform algorithms. Also, the computations of the translation operators are accelerated by using the

Eng Teo Ong; Heow Pueh Lee; Kian Meng Lim

2004-01-01

353

Realistic 3D image reconstruction in CGH with Fourier transform optical system

NASA Astrophysics Data System (ADS)

In CGH, peculiar rendering techniques are necessary to express realistic 3D images because CGHs have parallax. We have proposed the calculation method with the ray tracing method that expresses the hidden surface removal, shading and so on. However, resolutions of current output devices are not high enough to display CGH, so the size of reconstructed images is restricted and viewing zone and visual field are very narrow. To enlarge the size of reconstructed images, the Fourier transform optical system is used. Then we introduce the technique to apply calculation method of CGH with ray tracing method to the Fourier transform optical system in this paper. The Fourier transform optical system reverses the depth of images and reconstructs pseudo stereoscopic 3D images in front of a hologram. We solved this problem by reconstructing images at the back of hologram plane and observing conjugate images. Moreover, we conducted elimination of unnecessary light including 0-th order light. We conducted optical reconstructions that show proposed method is able to make realistic CGHs implementing the hidden surface removal in the Fourier transform optical system.

Ichikawa, Tsubasa; Yamaguchi, Kazuhiro; Sakamoto, Yuji

2013-03-01

354

A commercial Fourier transform interferometer system with telescopic optics has been installed in a van and used to make long-path absorption and single-ended emission measurements of gaseous pollutant concentrations at a number of geographical locations. The system covers the in...

355

Technology Transfer Automated Retrieval System (TEKTRAN)

A new chemometric method based on absorbance ratios from Fourier transform infrared spectra was devised to analyze multicomponent biodegradable plastics. The method uses the BeerLambert law to directly compute individual component concentrations and weight losses before and after biodegradation of c...

356

Transmission line fault location estimation by Fourier & wavelet transforms using ANN

Nowadays, power supply has become a business commodity. The quality and reliability of power needs to be maintained in order to obtain optimum performance. Therefore, it is extremely important that transmission line faults from various sources be identified accurately, reliably and be corrected as soon as possible. In this paper, a comparative study of the performance of Fourier transform and

A. Abdollahi; S. Seyedtabaii

2010-01-01

357

Fourier transform spectroscopy around 3 microns with a broad difference frequency comb

We characterize a new mid-infrared frequency comb generator based on difference frequency generation around 3.2 microns. High power per comb mode (>10-7 W/mode) is obtained over a broad spectral span (>700 nm). The source is used for direct absorption spectroscopy with a Michelson-based Fourier transform interferometer.

Meek, Samuel A; Guelachvili, Guy; Hänsch, Theodor W; Picqué, Nathalie

2013-01-01

358

Complex Acquisition of the Fourier Transform Imaging of an Arbitrary Object

A scheme to a complex-valued acquisition of the Fourier transform imaging was proposed. The main idea is to project the real and the imaginary parts of a diffraction field to intensity distributions respectively. The whole procedure was algorithm independent and needs no a priori knowledge of an arbitrary objet. An example was demonstrated with a numerical modeling and its results.

Minghui Zhang; Jianfei Xu; Xianfu Wang

2009-05-13

359

ATMOSPHERIC MEASUREMENTS OF TRACE POLLUTANTS; LONG PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY

Described are the results of a four-year study to measure trace pollutant concentrations in polluted atmospheres by kilometer pathlength Fourier transform infrared (FT-IR) absorption spectroscopy. The study covers selected smog episodes during the years 1976 to 1979. During 1976 ...

360

Mammalian cell growth studied in situ by fourier transform infrared spectroscopy

Fourier transform infrared techniques were used to monitor mammalian cell growth plated on attenuated total reflection (ATR) crystals. Consistently, the growth kinetics plots generated from the obtained spectra demonstrated a sigmoidal curve representing a sequence of slow, rapid, then tapering cell growth which correlated well with non-spectral cell growth determinations. Significant advantages over traditional methods of measuring cell growth kinetics

Timothy B. Hutson; Ming J. W. Chang; Joseph T. Keller; David J. Long

1988-01-01

361

Ordered fast Fourier transforms on a massively parallel hypercube multiprocessor

NASA Technical Reports Server (NTRS)

The present evaluation of alternative, massively parallel hypercube processor-applicable designs for ordered radix-2 decimation-in-frequency FFT algorithms gives attention to the reduction of computation time-dominating communication. A combination of the order and computational phases of the FFT is accordingly employed, in conjunction with sequence-to-processor maps which reduce communication. Two orderings, 'standard' and 'cyclic', in which the order of the transform is the same as that of the input sequence, can be implemented with ease on the Connection Machine (where orderings are determined by geometries and priorities. A parallel method for trigonometric coefficient computation is presented which does not employ trigonometric functions or interprocessor communication.

Tong, Charles; Swarztrauber, Paul N.

1991-01-01

362

1685 Description of the absorption spectrum of bromine recorded by means of Fourier transform An in extenso analysis of the (B-X ) Br2 bromine absorption spectrum recorded by means of Fourier Transform and extensive studies of the (B-X) bromine system have already been made [2-6], in the paper of Barrow Clark

Paris-Sud XI, UniversitÃ© de

363

Progress Towards Chirped-Pulse Fourier Transform Thz Spectroscopy

NASA Astrophysics Data System (ADS)

New opportunities are provided by the development of higher power THz frequency multiplier sources, the development of a broadband Chirped-Pulse FTMW spectroscopy technique at microwave and mm Wave frequencies, and recently demonstrated heterodyne hot electron bolometer detection technology in the THz frequency region with near quantum noise-limited performance and high spectral resolution. Combining these three technologies and extending the chirped-pulse technique to 0.85 THz enables a host of new applications. NIST is currently pursing applications as a point sensor for greenhouse gases, volatile organic compounds, and potentially human breath. The generation and detection of phase stable chirped pulses at 850 GHz will be demonstrated. A description of the experimental setup and preliminary data will be presented for nitrous oxide. G.G. Brown, B.C. Dian, K.O. Douglass, S.M. Geyer, S. Shipman and B.H. Pate, Rev.Sci.Instrum. 79 (2008) 053103. E. Gerecht, D. Gu, L. You, K.S. Yngvesson, IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. 56, (2008) 1083.

Douglass, Kevin O.; Plusquellic, David F.; Gerecht, Eyal

2010-06-01

364

NASA Astrophysics Data System (ADS)

Low-coherence interferometric setups in the Fourier domain can experience false structures after the Fourier transform procedure due to signal saturation; in fact, these structures are located at multiple frequencies of the original signal, also referred to as harmonics. This study aids in a better understanding of this phenomenon. The aim of the present work was to show that these features can be used to improve differential axial resolution in highly reflective samples. Using an optical coherence tomography system and calibrated step height standards, it was possible to achieve a resolution greater than the light source coherence length.

Raele, Marcus Paulo; Tarelho, Luiz Vicente Gomes; da Silva Azeredo, Carlos Leonardo; Couceiro, Iakyra Borrakuens; Freitas, Anderson Zanardi

2014-07-01

365

An evolving factor analysis procedure with concentration constraints (gradient concentration window) was applied to the analysis of data sets of aqueous Fourier transform infrared (FT-IR) spectra of carboxylic acids (acetic, malonic and succinic acids) collected in experiments with varying pH. Besides the calculation of the number of acid-base systems, this procedure allowed the calculation of the FT-IR spectra of the

Adélio A. S. C. Machado; César J. S. Oliveira

1996-01-01

366

Discrimination of Unitary Transformations and Quantum Algorithms

Quantum algorithms are typically understood in terms of the evolution of a multi-qubit quantum system under a prescribed sequence of unitary transformations. The input to the algorithm prescribes some of the unitary transformations in the sequence with others remaining fixed. For oracle query algorithms, the input determines the oracle unitary transformation. Such algorithms can be regarded as devices for discriminating amongst a set of unitary transformations. The question arises: "Given a set of known oracle unitary transformations, to what extent is it possible to discriminate amongst them?" We investigate this for the Deutsch-Jozsa problem. The task of discriminating amongst the admissible oracle unitary transformations results in an exhaustive collection of algorithms which can solve the problem with certainty.

David Collins

2008-11-09

367

A fast partial Fourier transform (FPFT) for data compression and filtering.

A discrete Fourier transform (DFT) or the closely related discrete cosine transform (DCT) is often employed as part of a data compression scheme. This paper presents a fast partial Fourier transform (FPFT) algorithm that is useful for calculating a subset of M Fourier transform coefficients for a data set comprised of N points (M < N). This algorithm reduces to the standard DFT when M = 1 and it reduces to the radix-2, decimation-in-time FFT when M = N and N is a power of 2. The DFT requires on the order of MN complex floating point multiplications to calculate M coefficients for N data points, a complete FFT requires on the order of (N/2)log{sub 2}N multiplications independent of M, and the new FPFT algorithm requires on the order of (N/2)log{sub 2}M + N multiplications. The FPFT algorithm introduced in this paper could be readily adapted to parallel processing. In addition to data compression, the FPFT algorithm described in this paper might be useful for very narrow band filter operations that pass only a small number of non-zero frequency coefficients such that M << N.

Smith, Mark William

2010-07-01

368

A metal object is computer visualized by registration of the amplitudes of the transmitted through the object short acoustic pulses. The pulses are separated by time, because of the presence of holes and internal compact components in the longitudinal section (structure along the propagation direction of acoustic wave). The acoustic field transmitted through the object is composited from a field presenting Fourier transformation of the hole shape and field, transmitted through the metal components in the longitudinal section of the object. A computer Fourier transformation of the digital data of the amplitude fields transmitted through the object components is performed instead of converging lens. The Fourier series of the object obtained as digital data after the transformation is multiplied with a term, describing the angle distribution of the field on spatial frequencies. The reconstruction of the image of the metal components is performed by reverse transformation, i.e. summing up in all spatial frequencies. 3D visualization of the transmitted through the hole acoustic field determines the hole geometry (circular, square, rectangular). It is shown that at the transmission of a short acoustic pulse through the components with different thicknesses and holes, presenting Fourier and non-Fourier transformation can be registered separately in contrast to the optics. PMID:17395232

Andreeva, A; Burova, M; Burov, J

2007-06-01

369

The C library \\texttt{libkww} provides functions to compute the Kohlrausch-Williams-Watts function, i.e.\\ the Laplace-Fourier transform of the stretched (or compressed) exponential function $\\exp(-t^\\beta)$ for exponents $\\beta$ between 0.1 and 1.9 with sixteen-digits accuracy. Analytic error bounds are derived for the low and high frequency series expansions. For intermediate frequencies the numeric integration is enormously accelerated by using the Ooura-Mori double exponential transformation. The source code is available from the project home page \\url{http://apps.jcns.fz-juelich.de/doku/sc/kww}.

Joachim Wuttke

2012-09-01

370

Tropical Forest Biomass Estimation from Vertical Fourier Transforms of Lidar and InSAR Profiles

NASA Astrophysics Data System (ADS)

Structural forest biomass estimation from lidar or interferometric SAR (InSAR) has demonstrated better performance than radar-power-based approaches for the higher biomasses (>150 Mg/ha) found in tropical forests. Structural biomass estimation frequently regresses field biomass to some function of forest height. With airborne, 25-m footprint lidar data and fixed-baseline C-band InSAR data over tropical wet forests of La Selva Biological Station, Costa Rica, we compare the use of Fourier transforms of vertical profiles at a few frequencies to the intrinsically low-frequency “average height”. RMS scatters of Fourier-estimated biomass about field-measured biomass improved by 40% and 20% over estimates base on average height from lidar and fixed-baseline InSAR, respectively. Vertical wavelengths between 14 and 100 m were found to best estimate biomass. The same airborne data acquisition over La Selva was used to generate many 10’s of repeat-track L-band InSAR baselines with time delays of 1-72 hours, and vertical wavelengths of 5-100 m. We will estimate biomass from the Fourier transforms of L-band radar power profiles (InSAR complex coherence). The effects of temporal decorrelation will be modeled in the Fourier domain to try to model and reduce their impact. Using L-band polarimetric interferometry, average heights will be estimated as well and biomass regression performance compared to the Fourier transform approach. The more traditional approach of using L-band radar polarimetry will also be compared to structural biomass estimation.

Treuhaft, R. N.; Goncalves, F.; Drake, J.; Hensley, S.; Chapman, B. D.; Michel, T.; Dos Santos, J. R.; Dutra, L.; Graca, P. A.

2010-12-01

371

A Discussion of the Discrete Fourier Transform Execution on a Typical Desktop PC

NASA Technical Reports Server (NTRS)

This paper will discuss and compare the execution times of three examples of the Discrete Fourier Transform (DFT). The first two examples will demonstrate the direct implementation of the algorithm. In the first example, the Fourier coefficients are generated at the execution of the DFT. In the second example, the coefficients are generated prior to execution and the DFT coefficients are indexed at execution. The last example will demonstrate the Cooley- Tukey algorithm, better known as the Fast Fourier Transform. All examples were written in C executed on a PC using a Pentium 4 running at 1.7 Ghz. As a function of N, the total complex data size, the direct implementation DFT executes, as expected at order of N2 and the FFT executes at order of N log2 N. At N=16K, there is an increase in processing time beyond what is expected. This is not caused by implementation but is a consequence of the effect that machine architecture and memory hierarchy has on implementation. This paper will include a brief overview of digital signal processing, along with a discussion of contemporary work with discrete Fourier processing.

White, Michael J.

2006-01-01

372

Transformations between symmetric sets of quantum states

We investigate probabilistic transformations of quantum states from a `source' set to a `target' set of states. Such transforms have many applications. They can be used for tasks which include state-dependent cloning or quantum state discrimination, and as interfaces between systems whose information encodings are not related by a unitary transform, such as continuous-variable systems and finite-dimensional systems. In a probabilistic transform, information may be lost or leaked, and we explain the concepts of leak and redundancy. Following this, we show how the analysis of probabilistic transforms significantly simplifies for symmetric source and target sets of states. In particular, we give a simple linear program which solves the task of finding optimal transforms, and a method of characterizing the introduced leak and redundancy in information-theoretic terms. Using the developed techniques, we analyse a class of transforms which convert coherent states with information encoded in their relative phase to symmetric qubit states. Each of these sets of states on their own appears in many well studied quantum information protocols. Finally, we suggest an asymptotic realization based on quantum scissors.

Vedran Dunjko; Erika Andersson

2012-06-22

373

MightySat II.1 Fourier-transform hyperspectral imager payload performance

NASA Astrophysics Data System (ADS)

Using a new microsat called MightySat II as a platform, Kestrel Corporation is designing and building the first Fourier transform hyperspectral imager (FTHSI) to be operated from a spacecraft. This payload will also be the first to fly on the Phillips Laboratory MightySat II spacecraft series, a new, innovative approach, to affordable space testing of high risk, high payoff technologies. Performance enhancements offered by the Fourier transform approach have shown it to be one of the more promising spaceborne hyperspectral concepts. Simulations of the payload's performance have shown that the instrument is capable of separating a wide range of subtle spectral differences. Variations in the return from the Georges Bank and shoals are discernible and various types of coastal grasses (sea oats and spartina) can be isolated against a sand background.

Otten, Leonard J.; Sellar, R. Glenn; Rafert, J. Bruce

1995-12-01

374

Gaseous effluent monitoring and identification using an imaging Fourier transform spectrometer

We are developing an imaging Fourier transform spectrometer for chemical effluent monitoring. The system consists of a 2-D infrared imaging array in the focal plane of a Michelson interferometer. Individual images are coordinated with the positioning of a moving mirror in the Michelson interferometer. A three dimensional data cube with two spatial dimensions and one interferogram dimension is then Fourier transformed to produce a hyperspectral data cube with one spectral dimension and two spatial dimensions. The spectral range of the instrument is determined by the choice of optical components and the spectral range of the focal plane array. Measurements in the near UV, visible, near IR, and mid-IR ranges are possible with the existing instrument. Gaseous effluent monitoring and identification measurements will be primarily in the ``fingerprint`` region of the spectrum, ({lambda} = 8 to 12 {mu}m). Initial measurements of effluent using this imaging interferometer in the mid-IR will be presented.

Carter, M.R.; Bennett, C.L.; Fields, D.J.; Hernandez, J.

1993-10-01

375

Multiple-image encryption based on phase mask multiplexing in fractional Fourier transform domain.

A multiple-image encryption scheme is proposed based on the phase retrieval process and phase mask multiplexing in the fractional Fourier transform domain. First, each original gray-scale image is encoded into a phase only function by using the proposed phase retrieval process. Second, all the obtained phase functions are modulated into an interim, which is encrypted into the final ciphertext by using the fractional Fourier transform. From a plaintext image, a group of phase masks is generated in the encryption process. The corresponding decrypted image can be recovered from the ciphertext only with the correct phase mask group in the decryption process. Simulation results show that the proposed phase retrieval process has high convergence speed, and the encryption algorithm can avoid cross-talk; in addition, its encrypted capacity is considerably enhanced. PMID:23722815

Liansheng, Sui; Meiting, Xin; Ailing, Tian

2013-06-01

376

NASA Astrophysics Data System (ADS)

A laboratory instrument that utilizes broadband laser ultrasonics and two-dimensional Fourier transformation for signal processing has been developed to characterize the properties of various foils and plates. Laser ultrasonics generation is achieved by using a pulsed laser which deposits pulsed laser energy on the surface of the specimen. The displacement of the resulting broadband ultrasonic modes is monitored using a two-wave mixing photorefractive interferometer. By means of the two-dimensional Fourier transformation of the detected spatial and temporal displacement wave forms, the image of density of state (DOS) for the excited ultrasound is obtained, and from it the materials properties are extracted. Results are presented for a 150?m thick paper sample, a 50?m stainless steel foil, and a 1.27mm thick aluminum plate. The DOS image demonstrates the ability to measure the properties of each generated ultrasonic modes and provides a direct, nondestructive, measure of elastic moduli of the tested specimens.

Zhang, Xinya; Jackson, Ted; Lafond, Emmanuel

2005-02-01

377

NASA Astrophysics Data System (ADS)

A fast Fourier transform accelerated Ewald method for the computation of the vector electromagnetic rectangular cavity Green's function in terms of the electric field due to electric currents is presented and used in a boundary integral formulation. The Ewald summation technique suffers from the high-frequency breakdown when it is applied to Green's functions of wave problems. In the case of the rectangular cavity Green's function, the number of necessary terms in the spectral series grows, therefore, cubically with frequency for a given accuracy. To counteract the high-frequency breakdown, the evaluation of the spectral series is accelerated with an inverse fast Fourier transform in this work. At high frequencies, a speed-up of up to four orders of magnitude is achieved. As an application example, a reverberation chamber containing a metallic enclosure and a mode-stirrer is modeled.

Gruber, M. E.; Koenen, C.; Eibert, T. F.

2015-01-01

378

Simulation of micromechanical behavior of polycrystals: finite elements vs. fast Fourier transforms

In this work, we compare finite element and fast Fourier transform approaches for the prediction of micromechanical behavior of polycrystals. Both approaches are full-field approaches and use the same visco-plastic single crystal constitutive law. We investigate the texture and the heterogeneity of the inter- and intragranular, stress and strain fields obtained from the two models. Additionally, we also look into their computational performance. Two cases - rolling of aluminium and wire drawing of tungsten - are used to evaluate the predictions of the two mode1s. Results from both the models are similar, when large grain distortions do not occur in the polycrystal. The finite element simulations were found to be highly computationally intensive, in comparison to the fast Fourier transform simulations.

Lebensohn, Ricardo A [Los Alamos National Laboratory; Prakash, Arun [IWM FREIBURG

2009-01-01

379

Subwavelength Fourier-transform imaging without a lens or a beamsplitter

NASA Astrophysics Data System (ADS)

The fourier-transform patterns of an object are usually observed in the far-field region or obtained in the near-field region with the help of lenses. Here we propose and experimentally demonstrate a scheme of Fourier-transform patterns in the Fresnel diffraction region with thermal light. In this scheme, neither a lens nor a beamsplitter is used, and only one single charge coupled device (CCD) is employed. It means that dividing one beam out of a light source into signal and reference beams is not as necessary as the one done by the use of a beamsplitter in usual ghost interference experiments. Moreover, the coincidence measurement of two point detectors is not necessary and data recorded on a single CCD are sufficient for reconstructing the ghost diffraction patterns. The feature of the scheme promises a great potential application in the fields of X-ray and neutron diffraction imaging processes.

Liu, Rui-Feng; Yuan, Xin-Xing; Fang, Yi-Zhen; Zhang, Pei; Zhou, Yu; Gao, Hong; Li, Fu-Li

2014-05-01

380

Improved fourier-transform ion-cyclotron-resonance mass spectrometry of large biomolecules

Initial results from a Fourier-transform mass spectrometer with a 6.2 Tesla magnet using electrospray ionization show substantial\\u000a improvements in resolution, mass accuracy, mass range, signal\\/noise, and tandem mass spectromehy capabilities compared to\\u000a our earlier 2.8 T instrument that demonstrated the first unit resolution mass spectra of molecules as large as myoglobin (17\\u000a kDa). The new instrument exhibits greater than 106

Steven C. Beu; Michael W. Senko; John P. Quinn; Fred W. McLafferty

1993-01-01

381

With unmatched mass resolution, mass accuracy, and exceptional detection sensitivity, Fourier Transform Ion Cyclotron Resonance\\u000a Mass Spectrometry (FTICR-MS) has the potential to be a powerful new technique for high-throughput metabolomic analysis. In\\u000a this study, we examine the properties of an ultrahigh-field 12-Tesla (12T) FTICR-MS for the identification and absolute quantitation\\u000a of human plasma metabolites, and for the untargeted metabolic fingerprinting

Jun Han; Ryan M. Danell; Jayanti R. Patel; Dmitry R. Gumerov; Cameron O. Scarlett; J. Paul Speir; Carol E. Parker; Ivan Rusyn; Steven Zeisel; Christoph H. Borchers

2008-01-01

382

Electron capture dissociation (ECD) efficiency in a 9.4T Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer varies periodically with the time interval between ion and electron injection. The observed modulation frequency correlates to within 1% with ion magnetron frequency, most probably due to misalignment between the ion beam and the electron beam. The optimum ECD conditions are obtained by correctly

Yury O. Tsybin; Christopher L. Hendrickson; Steven C. Beu; Alan G. Marshall

2006-01-01

383

This paper describes our effort in optimizing the experimental parameters for electron capture dissociation (ECD) of peptides\\u000a in a commercially available Fourier-transform mass spectrometer. Using a built-in electrically heated filament electron gun,\\u000a it was demonstrated that good quality ECD spectra of peptides (MW < 2500) could be obtained by irradiating the isolated peptide\\u000a molecule-ions with a short pulse (50 ms)

T.-W. Dominic Chan; W. H. Herman Ip

2002-01-01

384

Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform

Wave-front reconstruction with the use of the fast Fourier transform (FFT) and spatial filtering is shown to be computationally tractable and sufficiently accurate for use in large Shack-Hartmann-based adaptive optics systems (up to at least 10,000 actuators). This method is significantly faster than, and can have noise propa- gation comparable with that of, traditional vector-matrix-multiply reconstructors. The boundary problem that

Lisa A. Poyneer; Donald T. Gavel; James M. Brase

2002-01-01

385

A Method to Generate Artificial 2D Shape Contour Based in Fourier Transform and Genetic Algorithms

\\u000a This work presents a simple method to generate 2D contours based in the small number of samples. The method uses the Fourier\\u000a transform and genetic algorithms. Using crossover and mutation operator news samples were generated. An application case is\\u000a presented and the samples produced were tested in the classifier construction. The result obtained indicated the method can\\u000a be a good

Maur ´ icio Falvo; J oBatista Florindo; Odemir Martinez Bruno

386

Fourier transform infrared spectrophotometry (FTIR) is a valuable technique for monitoring thin films used in semiconductor device manufacture. Determinations of the constituent contents in borophosphosilicate (BPSG), phosphosilicate (PSG), silicon oxynitride (SiON:H,OH), and spin-on-glass (SOG) thin films are a few applications. Due to the nature of the technique, FTIR instrumentation is one of the most extensively computer-dependent pieces of equipment that

J. N. Cox; J. Sedayao; G. Shergill; R. Villasol; D. M. Haaland

1990-01-01

387

A method for estimating the magnitude-squared coherence function for two zero-mean wide-sense-stationary random processes is presented. The estimation technique utilizes the weighted overlapped segmentation fast Fourier transform approach. Analytical and empirical results for statistics of the estimator are presented. The analytical expressions are limited to the nonoverlapped case; empirical results show a decrease in bias and variance of the estimator

G. CLIFFORD CARTER; CHARLES H. KNAPP; ALBERT H. NUTTALL

1973-01-01

388

Fourier transform microwave spectra and ab initio calculation of N-ethylformamide

A peptide molecule: N-ethylformamide HCONHCH2CH3 (NEFA) was investigated by Fourier transform microwave spectroscopy in order to determine molecular structure, potential barrier to methyl internal rotation, and nuclear quadrupole coupling constant of the nitrogen atom. All the three (a, b and c) types of transitions were observed; they were split into hyperfine structure components due to nitrogen nuclear quadrupole coupling. The

Keisuke Ohba; Tsuyoshi Usami; Yoshiyuki Kawashima; Eizi Hirota

2005-01-01

389

Fourier transform infrared spectroscopy techniques for the analysis of drugs of abuse

Cryogenic deposition techniques for Gas Chromatography\\/Fourier Transform Infrared (GC\\/FT-IR) can be successfully employed in urinalysis for drugs of abuse with detection limits comparable to those of the established Gas Chromatography\\/Mass Spectrometry (GC\\/MS) technique. The additional confidence of the data that infrared analysis can offer has been helpful in identifying ambiguous results, particularly, in the case of amphetamines where drugs of

Kathryn S. Kalasinsky; Barry K. Levine; Michael L. Smith; Joseph J. Magluilo; Teresa Schaefer

1994-01-01

390

Cryogenic Fourier transform spectrometer for infrared spectral calibrations from 4 to 20 micrometers

We present initial performance data from a cryogenic Fourier transform spectrometer (Cryo-FTS) designed for lowbackground spectral infrared calibrations. The Cryo-FTS operates at a temperature of approximately 15 K and has been integrated into an infrared transfer radiometer containing a calibrated Si:As blocked impurity band (BIB) detector. Because of its low operating temperature, the spectrometer exhibits negligible thermal background signal and

Solomon I. Woods; Simon G. Kaplan; Timothy M. Jung; Adriaan C. Carter; Raju U. Datla

2010-01-01

391

Two rapid spectroscopic approaches for whole-organism fingerprinting—pyrolysis mass spectrometry (PyMS) and Fourier transform infrared spectroscopy (FT-IR)—were used to analyse 22 production brewery Saccharomyces cerevisiae strains. Multivariate discriminant analysis of the spectral data was then performed to observe relationships between the 22 isolates. Upon visual inspection of the cluster analyses, similar diVerentiation of the strains was observed for both approaches. Moreover,

M. TIMMINS; DAVID E. QUAIN; ROYSTON GOODACRE

1998-01-01

392

Differentiation of Fusarium spp. by Fourier Transform Infrared (FT-IR) spectroscopy

Fourier Transform Infrared (FT-IR) spectroscopy, in combination with chemometrics, was investigated as a simple method to\\u000a differentiateFusarium spp. Strains were grown on solid culture plates for sporulation. Spectral data of spores ofFusarium spp. were recorded within the range from 4000 to 400 cm?1. Hierarchical cluster analysis (HCA) and principal components analysis (PCA) were used to study the clusters in the

Ming Nie; Kan Bao; Ming Xiao; Jia-Ming Chen; Jiang-Lan Luo; Wei-Qiong Zhang; Jia-Kuan Chen; Bo Li

2006-01-01

393

Principal component anal. (PCA) and partial least squares discriminant anal. (PLS-DA) were used to classify acetaminophen-contg. medicines using their attenuated total reflection Fourier transform IR (ATR-FT-IR) spectra. Four formulations of Tylenol (Arthritis Pain Relief, Extra Strength Pain Relief, 8 H Pain Relief, and Extra Strength Pain Relief Rapid Release) along with 98% pure acetaminophen were selected for this study because

Huggins Z. Msimanga; Robert J. Ollis Jr.

2010-01-01

394

Non-invasive fibre optic Fourier transform-infrared reflectance spectroscopy on painted layers

Fibre optic Fourier transform-infrared (FT-IR) reflectance spectroscopy has recently made it possible to perform completely non-invasive investigations on works of art and, in particular, on painted layers. The use of chalcogenide fibre optics can overcome most of the limitations due to the size of the objects under investigation, and permits the acquisition of spectra in a wide mid-IR range that

M Bacci; M Fabbri; M Picollo; S Porcinai

2001-01-01

395

Silage quality is typically assessed by the measurement of several individual parameters, including pH, lactic acid, acetic acid, bacterial numbers, and protein content. The objective of this study was to use a holistic metabolic fingerprinting approach, combining a high-throughput microtiter plate-based fermentation system with Fourier transform infrared (FT-IR) spectroscopy, to obtain a snapshot of the sample metabolome (typically low-molecular-weight compounds)

Helen E. Johnson; David Broadhurst; Douglas B. Kell; Michael K. Theodorou; Roger J. Merry; Gareth W. Griffith

2004-01-01

396

Color image encryption based on fractional Fourier transforms and pixel scrambling technique

Color image encryption based on fractional Fourier transform (FRT) and pixel scrambling technique is presented in this paper. In general, color (RGB) image cannot be directly encrypted using a traditional setup for optical information processing, because which is only adapted to process two-dimensional gray image. In the proposed method, a three-dimensional RGB image is decomposed to three two-dimensional gray images

Jianlin Zhao; Hongqiang Lu; Qi Fan

2007-01-01

397

Fourier transform spectroscopy: from organizing MISFITS to FTing it in a truck

Open-cell long-path Fourier transform infrared (FT-IR) spectroscopy has become a common technique for the monitoring of fugitive emission of VOCs in the atmosphere. Our entry into the study of VOCs in the atmosphere is presented in a historical context. The evolution of our techniques for carrying out field studies is described. Some representative examples of our monitoring activities are given

Wanda G. Fateley; Robert M. Hammaker; Martin L. Spartz; Mark R. Witkowski; Tim L. Marshall; Charles T. Chaffin; M. D. Tucker; John M. Poholarz; V. D. Makepeace; Billy J. Fairless; Jody L. Hudson; Joseph Arello; M. J. Thomas

1994-01-01

398

On a Relative Fourier–Mukai Transform on Genus One Fibrations

We study relative Fourier–Mukai transforms on genus one fibrations with section, allowing explicitly the total space of the fibration to be singular and non-projective. Grothendieck duality is used to prove a skew–commutativity relation between this equivalence of categories and certain duality functors. We use our results to explicitly construct examples of semi-stable sheaves on degenerating families of elliptic curves.

Igor Burban; Bernd Kreussler

2006-01-01

399

Near-field Fourier transform polarimetry by use of a discrete space-variant subwavelength grating

We present a unique method for real-time polarization measurement by use of a discrete space-variant subwavelength grating. The formation of the grating is done by discrete orientation of the local subwavelength grooves. The complete polarization analysis of the incident beam is determined by spatial Fourier transform of the near-field intensity distribution transmitted through the discrete subwavelength dielectric grating followed by

Gabriel Biener; Avi Niv; Vladimir Kleiner; Erez Hasman

2003-01-01

400

Using single buffers and data reorganization to implement a multi-megasample fast Fourier transform

NASA Technical Reports Server (NTRS)

Data ordering in large fast Fourier transforms (FFT's) is both conceptually and implementationally difficult. Discribed here is a method of visualizing data orderings as vectors of address bits, which enables the engineer to use more efficient data orderings and reduce double-buffer memory designs. Also detailed are the difficulties and algorithmic solutions involved in FFT lengths up to 4 megasamples (Msamples) and sample rates up to 80 MHz.

Brown, R. D.

1992-01-01

401

For ions formed by plasma desorption (PD) in a Fourier-transform mass spectrometer, high resolution measurements are demonstrated,\\u000a such as 65,000 (FWHH) for the protonated molecularion of gramicidin S (MW 1140.7). Resolution is substantially improved by\\u000a delaying measurements until a significant ion concentration has built up in the cell, and by collisionally deactivating the\\u000a orbital kinetic energy of the ions. This

Evan R. Williams; Fred W. McLafferty

1990-01-01

402

The photon noise-limited performances of a Fourier transform (FT) seismometer for ground-based asteroseismological observations are computed. Simulations are conducted for a set of stars close to solar type, with V magnitude equal to 4 and vsini from 0 to 40 km s-1, extended to 100 km s-1 and 8500 K in order to include delta Scuti stars. Two instrumental configurations

Benoît Mosser; Jean-Pierre Maillard; François Bouchy

2003-01-01

403

This paper summarizes the design and development of the Panchromatic Imaging Fourier Transform Spectrometer (PanFTS) for the NASA Geostationary Coastal and Air Pollution Events (GEO-CAPE) Mission. The PanFTS instrument will advance the understanding of the global climate and atmospheric chemistry by measuring spectrally resolved outgoing thermal and reflected solar radiation. With continuous spectral coverage from the near-ultraviolet through the thermal

Yen-Hung Wu; Richard Key; Stanley Sander; Jean-Francois Blavier; David Rider

2011-01-01

404

Fast Fourier transform: A solution for digital signal processing in incoherent scatter experiments?

NASA Astrophysics Data System (ADS)

The use of digital signal processing based on modulation methods which lead to a high demand for computing power was addressed. A possible way of using fast Fourier transform based computations in different incoherent scatter implications is described. It turns out that surprisingly few different algorithms are needed to solve the high computing power problem in a very general way. Standard FIR filters are not necessarily needed, but there are applications for them in phase coded experiments using pulse to pulse approach.

Turunen, Tauno

405

Electrospray ionization (ESI) in combination with Fourier transform ion cyclotron resonance (FTICR) mass spectrometry provides\\u000a for mass analysis of biological molecules with unrivaled mass accuracy, resolving power and sensitivity. However, ESI FTICR\\u000a MS performance with on-line separation techniques such as liquid chromatography (LC) and capillary electrophoresis has to\\u000a date been limited primarily by pulsed gas assisted accumulation and the incompatibility

Michael W. Senko; Christopher L. Hendrickson; Mark R. Emmett; Stone D. H. Shi; Alan G. Marshall

1997-01-01

406

Nontargeted metabolome analysis by use of Fourier transform ion cyclotron mass spectrometry

Advanced functional genomic tools now allow the parallel and high-throughput analyses of gene and protein expression. Although this information is crucial to our understanding of gene function, it offers insufficient insight into phenotypic changes associated with metabolism. Here we introduce a high-capacity Fourier Transform Ion Cyclotron Mass Spectrometry (FTMS)¿based method, capable of nontargeted metabolic analysis and suitable for rapid screening

Asaph Aharoni; Vos de C. H; C. A. Maliepaard; G. Kruppa; R. J. Bino; D. Goodenough; Dayan B. Goodenowe

2002-01-01

407

Fourier transform infrared (FTIR) spectroscopy with transmission cell is described to predict anisidine value of palm olein.\\u000a The calibration set was prepared by mixing the thermally oxidized palm olein and the unoxidized palm olein with certain ratios\\u000a (w\\/w) covering a wide range of anisidine values. A partial least square (PLS) regression technique was employed to construct\\u000a a calibration model. This

Y. B. Che Man; G. Setiowaty

1999-01-01

408

The purpose of this testing program is to obtain uncontrolled and controlled hydrogen chloride (HCl) and speciated hydrocarbon Hazardous Air Pollutants (HAPs) emissions data from lime production plants to support a national emission standard for hazardous air pollutants (NESHAP). This report presents data from the Fourier Transform Infrared Spectroscopy (FTIR) measurements. FTIR source testing was conducted for the following purposes: Quantify HCl emission levels; and Gather screening (i.e., qualitative) data on other HAP emissions.

Toney, M.L.

1999-07-01

409

IUP MAI3 -M54 Mini-projet : FFT (transforme de Fourier Rapide) sur Hypercube

IUP MAI3 - M54 Mini-projet : FFT (transformÃ©e de Fourier Rapide) sur Hypercube L'objectif premier implÃ©mentation de la FFT sur un hypercube en supposant qu'Ã l'initialisation, le processeur 0 detient le vecteur calcul (pour le rÃ©aliser, vous vous aiderez du TD sur le FFT parallÃ¨le vue en cours et vous supposerez

Dumas, Jean-Guillaume

410

IUP MAI3 -TD M54 FFT : transforme de Fourier Rapide sur Hypercube

IUP MAI3 - TD M54 FFT : transformÃ©e de Fourier Rapide sur Hypercube Soit n N, nous notons N = 2n la dimension du vecteur f dont nous sou- haitons faire la FFT. Soit rang le numÃ©ro d'un processeur performant FFT(G,g,m) qui calule la FFT de g de taille 2m et retourne le rÃ©sultat dans G. (a) Si p = 1 (cad

Dumas, Jean-Guillaume

411

Metabolic fingerprinting of lichen Usnea baileyi by Fourier transform infrared spectroscopy

NASA Astrophysics Data System (ADS)

The lichen Usnea baileyi collected from different environments was characterised using Fourier transform infrared spectroscopy. This preliminary study was done to determine the effects of different environment populations on U. baileyi chemical composition. Results showed that the absorbance peaks of Golf Course 2 (GCU2) are more intense compared to Taman Awana (TA), Jalan Awana (JA) and Jalan Gohtong (JG). U. baileyi contains of dibenzofurans, depsides, depsidones, xanthones and terpenoids.

Bakar, Siti Zaharah Abu; Latip, Jalifah; bin Din, Laily; Samsuddin, Mohd Wahid

2014-09-01

412

Fourier transform intracavity laser absorption spectra of the 6 nu 1 band of CHD3

Absorption spectra in the 16 100–16 320 cm?1 region have been recorded for gaseous CHD3 at room temperature with 0.12 cm?1 resolution using a Fourier transform intracavity laser absorption technique. Two bands belonging to the N=6 polyad, 61 (6?1) and 62 (5?1+2?5), were identified and a rotational analysis for 61 including transitions up to J=13, verified by means of ground-state

C. Domingo; A. del Olmo; R. Escribano; D. Bermejo; J. M. Orza

1992-01-01

413

A Fourier transform method for powder diffraction based on the Debye scattering equation.

A fast Fourier transform algorithm is introduced into the method recently defined for calculating powder diffraction patterns by means of the Debye scattering equation (DSE) [Thomas (2010). Acta Cryst. A66, 64-77]. For this purpose, conventionally used histograms of interatomic distances are replaced by compound transmittance functions. These may be Fourier transformed to partial diffraction patterns, which sum to give the complete diffraction pattern. They also lead to an alternative analytical expression for the DSE sum, which reveals its convergence behaviour. A means of embedding the DSE approach within the reciprocal-lattice-structure-factor method is indicated, with interpolation methods for deriving the peak profiles of nanocrystalline materials outlined. Efficient calculation of transmittance functions for larger crystallites requires the Patterson group symmetry of the crystals to be taken into account, as shown for ?- and ?-quartz. The capability of the transmittance functions to accommodate stacking disorder is demonstrated by reference to kaolinite, with a fully analytical treatment of disorder described. Areas of future work brought about by these developments are discussed, specifically the handling of anisotropic atomic displacement parameters, inverse Fourier transformation and the incorporation of instrumental (diffractometer) parameters. PMID:22011464

Thomas, Noel William

2011-11-01

414

Infrared small target enhancement via phase spectrum of Quaternion Fourier Transform

NASA Astrophysics Data System (ADS)

Small target enhancement is one of the crucial stages in infrared small target detection. In this paper, we propose a new method using phase spectrum of Quaternion Fourier Transform to enhance small targets while suppressing backgrounds for infrared images. This is inspired by the property that regularly Gaussian-like shape small targets could be considered as attractively salient signal in infrared images and the location information of such signal is implicitly contained in the phase spectrum from frequency domain. Formally, in the proposed method, we adopt the phase spectrum of Quaternion Fourier Transform instead of using traditional Fourier Transform to enhance the targets since the quaternion provides at most four data channels than only one for the latter, which could be helpful to broad types of background clutters by adding more information. For the construction of the quaternion, we present a second-order directional derivative filter via facet model to compute four second order directional derivative maps from four directions respectively as the four data channels. This filter is used to suppress noises and distinguish the targets and backgrounds into separably different textures so that it would boost the robustness of small target enhancement. In experiments, some typical infrared images with various scenes are tested to validate the effectiveness of the proposed method. The results demonstrate that our method actually has good performance and outperforms several state-of-the-art methods, which can be further used for infrared small target detection and tracking.

Qi, Shengxiang; Ma, Jie; Li, Hang; Zhang, Shuiping; Tian, Jinwen

2014-01-01

415

NASA Astrophysics Data System (ADS)

We explore efficient transformation of structure-borne propagating waves into low-power electricity using patterned polymer piezoelectrics integrated with an elastoacoustic mirror configuration. Fourier transform-based spatial optimization of a piezoelectric energy harvester domain weakly coupled to a thin plate housing a continuous elliptical elastoacoustic mirror is presented. Computational modeling and experimental testing are employed to quantify performance enhancement in power generation using the presented approach. Excellent agreement is observed between numerical simulations and experimental measurements. Specifically, dramatic enhancement of the harvested power output is reported by patterning the electrodes of a rectangular polyvinylidene fluoride piezoelectric energy harvester in the elliptical mirror domain.

Carrara, M.; Kulpe, J. A.; Leadenham, S.; Leamy, M. J.; Erturk, A.

2015-01-01

416

The Fourier modal method (FMM) has advanced greatly by using adaptive coordinates and adaptive spatial resolution. The convergence characteristics were shown to be improved significantly, a construction principle for suitable meshes was demonstrated and a guideline for the optimal choice of the coordinate transformation parameters was found. However, the construction guidelines published so far rely on a certain restriction that is overcome with the formulation presented in this paper. Moreover, a modularization principle is formulated that significantly eases the construction of coordinate transformations in unit cells with reappearing shapes and complex sub-structures. PMID:24787828

Küchenmeister, Jens

2014-04-21

417

Quantum Simulation of Noncausal Kinematic Transformations

NASA Astrophysics Data System (ADS)

We propose the implementation of Galileo group symmetry operations or, in general, linear coordinate transformations in a quantum simulator. With an appropriate encoding, unitary gates applied to our quantum system give rise to Galilean boosts or spatial and time parity operations in the simulated dynamics. This framework provides us with a flexible toolbox that enhances the versatility of quantum simulation theory, allowing the direct access to dynamical quantities that would otherwise require full tomography. Furthermore, this method enables the study of noncausal kinematics and phenomena beyond special relativity in a quantum controllable system.

Alvarez-Rodriguez, U.; Casanova, J.; Lamata, L.; Solano, E.

2013-08-01

418

Quantum simulation of noncausal kinematic transformations.

We propose the implementation of Galileo group symmetry operations or, in general, linear coordinate transformations in a quantum simulator. With an appropriate encoding, unitary gates applied to our quantum system give rise to Galilean boosts or spatial and time parity operations in the simulated dynamics. This framework provides us with a flexible toolbox that enhances the versatility of quantum simulation theory, allowing the direct access to dynamical quantities that would otherwise require full tomography. Furthermore, this method enables the study of noncausal kinematics and phenomena beyond special relativity in a quantum controllable system. PMID:24033011

Alvarez-Rodriguez, U; Casanova, J; Lamata, L; Solano, E

2013-08-30

419

We present a methodology for probing light-matter interactions in prototype photovoltaic devices consisting of an organic semiconductor active layer with a semitransparent metal electrical contact exhibiting surface plasmon-based enhanced optical transmission. We achieve high-spectral irradiance in a spot size of less than 100??m using a high-brightness laser-driven light source and appropriate coupling optics. Spatially resolved Fourier transform photocurrent spectroscopy in the visible and near-infrared spectral regions allows us to measure external quantum efficiency with high sensitivity in small-area devices (<1?mm2). This allows for rapid fabrication of variable-pitch sub-wavelength hole arrays in metal films for use as transparent electrical contacts, and evaluation of the evanescent and propagating mode coupling to resonances in the active layer. PMID:25705085

Camino, Fernando E.; Nam, Chang-Yong; Pang, Yutong T.; Hoy, Jessica; Eisaman, Matthew D.; Black, Charles T.; Sfeir, Matthew Y.

2014-01-01

420

Quantum Algorithms Using the Curvelet Transform

The curvelet transform is a directional wavelet transform over R^n, which is used to analyze functions that have singularities along smooth surfaces (Candes and Donoho, 2002). I demonstrate how this can lead to new quantum algorithms. I give an efficient implementation of a quantum curvelet transform, together with two applications: a single-shot measurement procedure for approximately finding the center of a ball in R^n, given a quantum-sample over the ball; and, a quantum algorithm for finding the center of a radial function over R^n, given oracle access to the function. I conjecture that these algorithms succeed with constant probability, using one quantum-sample and O(1) oracle queries, respectively, independent of the dimension n -- this can be interpreted as a quantum speed-up. To support this conjecture, I prove rigorous bounds on the distribution of probability mass for the continuous curvelet transform. This shows that the above algorithms work in an idealized "continuous" model.

Yi-Kai Liu

2009-03-25

421

Introduction to Quantum Simulation

NASA Technical Reports Server (NTRS)

This viewgraph presentation addresses the problem of efficiently simulating the evolution of a quantum system. The contents include: 1) Quantum Simulation; 2) Extracting Answers from Quantum Simulations; 3) Quantum Fourier Transform; 4) Eigenvalue Estimation; 5) Fermionic Simulations.

Williams, Colin P.

2005-01-01

422

This second paper in a series of two reports on the performance of a new instrument for studying chemical reaction dynamics and kinetics at low temperatures. Our approach employs chirped-pulse Fourier-transform microwave ...

Abeysekera, Chamara

423

A measurement platform is introduced that combines a bilayer cantilever probe with a Fourier transform infrared spectrometer to measure absolute spectral absorptance between wavelengths of 3??m and 18??m directly and ...

Hsu, Wei-Chun

424

Technology Transfer Automated Retrieval System (TEKTRAN)

Analysis of DNA samples of Salmonella serotypes (Salmonella Typhimurium, Salmonella Enteritidis, Salmonella Infantis, Salmonella Heidelberg and Salmonella Kentucky) were performed using Fourier transform infrared spectroscopy (FT-IR) spectrometer by placing directly in contact with a diamond attenua...

425

Time-resolved Fourier transform Raman spectroscopy of the highly fluorescent chromophore 9,10-diphenylanthracene (DPA) in cyclohexane and ethanol is described. Raman spectra of the first excited singlet state of DPA were obtained with 100-ps...

Jas, Gouri S.; Wan, Chaozhi; Johnson, Carey K.

1995-05-01

426

Precise measurement of the resolution in light microscopy using Fourier transform

The resolution power of light microscope has been accurately measured ({+-}5%) by Fourier transform of various object images and further evaluation of the highest spatial frequency in Fourier spectrum. Any unknown shape plane object with a shape feature's size smaller than the resolution to be measured was shown to provide a reliable resolution test. This simple method gives a direct measurement of the resolution power as defined by Abbe [Archiv. F. Mikroskopische Anat. 9, 413 (1873)]. The results have been justified by comparison to a standard resolution measurement by using calibrated periodic line patterns. Notably, the approach is applicable in super-resolution light microscopy (transmission, reflection, and fluorescence), where calibrated resolution targets do not occur. It was conveniently implemented by using a compact disk as a test object and free IMAGEJ imaging software.

Vainrub, Arnold [Department of Anatomy, Physiology and Pharmacology, College of Veterinary Medicine, Auburn University, Auburn, Alabama 36849 (United States)

2008-04-15

427

Precise measurement of the resolution in light microscopy using Fourier transform.

The resolution power of light microscope has been accurately measured (+/-5%) by Fourier transform of various object images and further evaluation of the highest spatial frequency in Fourier spectrum. Any unknown shape plane object with a shape feature's size smaller than the resolution to be measured was shown to provide a reliable resolution test. This simple method gives a direct measurement of the resolution power as defined by Abbe [Archiv. F. Mikroskopische Anat. 9, 413 (1873)]. The results have been justified by comparison to a standard resolution measurement by using calibrated periodic line patterns. Notably, the approach is applicable in super-resolution light microscopy (transmission, reflection, and fluorescence), where calibrated resolution targets do not occur. It was conveniently implemented by using a compact disk as a test object and free IMAGEJ imaging software. PMID:18447570

Vainrub, Arnold

2008-04-01

428

Fractional Fourier plane image encryption technique using radial hilbert-, and Jigsaw transform

NASA Astrophysics Data System (ADS)

A new method for image encryption using integral order radial Hilbert transform (RHT) filter in the fractional Fourier transform (FRT) domain has been proposed. The technique is implemented using the popular double random phase encoding method in the fractional Fourier domain. The random phase masks (RPMs), integral orders of the RHT, fractional orders of FRT, and indices of the Jigsaw transform (JT) have been used as keys for encryption and decryption. Simulation results have been presented and the schematic representation for optical implementation has been proposed. The mean-square-error and signal-to-noise ratio between the decrypted image and the input image have been calculated for the correct as well as incorrect orders of the RHT. Effect of occlusion and noise on the performance of the proposed scheme has also been studied. The robustness of the technique has been verified against attack using partial windows of the correct random phase masks. Similar investigations have also been carried out for the chosen-, and the known-plain-text attacks.

Joshi, Madhusudan; Shakher, Chandra; Singh, Kehar

2010-07-01

429

Content measurement of textile mixture by Fourier transform near infrared spectroscopy

NASA Astrophysics Data System (ADS)

A new method for accurate measurement of content of textile mixture based on Fourier transform near infrared spectroscopy is put forward. The near infrared spectra of 56 samples with different cotton and polyester contents were obtained, in which 41 samples, 10 samples and 5 samples were used for the calibration set, validation set and prediction set respectively. The wavelet transform (WT) was utilized for the spectra data compression. From the linear and nonlinear perspective, multivariable linear regression (MLR) model based on the Lambert - Beer's law and back propagation (BP) neural network model based on WT were developed. It indicates that the prediction accuracy of WT-ca3-BP network model is 2% for calibration sample and 4% for validation sample, which is much higher than the MLR model and is suitable for the prediction of unknown samples. On the basis of not changing the structure of the WT-ca3-BP network model, calibration and validation samples were utilized fully to be re-set to new calibration samples, which upgraded this model. The upgraded WT-ca3-BP network model was applied to predict unknown samples. Experimental results show that this approach based on Fourier transform Near Infrared Spectroscopy can be used to quantitative analysis for textile fiber.

Liu, Li; Yan, Li; Xie, Yaocheng; Li, Songzhang; Xia, Ge; Zhou, Libin

2009-11-01

430

Acetaminophen is a widely prescribed drug used to relieve pain and fever; however, it is a leading cause of drug-induced liver injury and a burden on public healthcare. In this study, hepatotoxicity in mice post oral dosing of acetaminophen was investigated using liver and sera samples with Fourier Transform Infrared microspectroscopy. The infrared spectra of acetaminophen treated livers in BALB/c mice show decrease in glycogen, increase in amounts of cholesteryl esters and DNA respectively. Rescue experiments using L-methionine demonstrate that depletion in glycogen and increase in DNA are abrogated with pre-treatment, but not post-treatment, with L-methionine. This indicates that changes in glycogen and DNA are more sensitive to the rapid depletion of glutathione. Importantly, analysis of sera identified lowering of glycogen and increase in DNA and chlolesteryl esters earlier than increase in alanine aminotransferase, which is routinely used to diagnose liver damage. In addition, these changes are also observed in C57BL/6 and Nos2?/? mice. There is no difference in the kinetics of expression of these three molecules in both strains of mice, the extent of damage is similar and corroborated with ALT and histological analysis. Quantification of cytokines in sera showed increase upon APAP treatment. Although the levels of Tnf? and Ifn? in sera are not significantly affected, Nos2?/? mice display lower Il6 but higher Il10 levels during this acute model of hepatotoxicity. Overall, this study reinforces the growing potential of Fourier Transform Infrared microspectroscopy as a fast, highly sensitive and label-free technique for non-invasive diagnosis of liver damage. The combination of Fourier Transform Infrared microspectroscopy and cytokine analysis is a powerful tool to identify multiple biomarkers, understand differential host responses and evaluate therapeutic regimens during liver damage and, possibly, other diseases. PMID:23029070

Deobagkar-Lele, Mukta; Rakshit, Srabanti; Kumar B. N., Vinay; Umapathy, Siva; Nandi, Dipankar

2012-01-01

431

Slit Function Measurement of An Imaging Spectrograph Using Fourier Transform Techniques

NASA Technical Reports Server (NTRS)

Knowledge of a spectrograph slit function is necessary to interpret the unresolved lines in an observed spectrum. A theoretical slit function can be calculated from the sizes of the entrance slit, the detector aperture when it functions as an exit slit, the dispersion characteristic of the disperser, and the point spread function of the spectrograph. A measured slit function is preferred to the theoretical one for the correct interpretation of the spectral data. In a scanning spectrometer with a single exit slit, the slit function is easily measured. In a fixed grating/or disperser spectrograph, illuminating the entrance slit with a near monochromatic light from a pre-monochrmator or a tunable laser and varying the wavelength of the incident light can measure the slit function. Even though the latter technique had been used successfully for the slit function measurements, it had been very laborious and it would be prohibitive to an imaging spectrograph or a multi-object spectrograph that has a large field of view. We explore an alternative technique that is manageable for the measurements. In the proposed technique, the imaging spectrograph is used as a detector of a Fourier transform spectrometer. This method can be applied not only to an IR spectrograph but also has a potential to a visible/UV spectrograph including a wedge filter spectrograph. This technique will require a blackbody source of known temperature and a bolometer to characterize the interferometer part of the Fourier Transform spectrometer. This pa?er will describe the alternative slit function measurement technique using a Fourier transform spectrometer.

Park, Hongwoo; Swimyard, Bruce; Jakobsen, Peter; Moseley, Harvey; Greenhouse, Matthew

2004-01-01

432

NASA Technical Reports Server (NTRS)

The development of a prototype, ground-based, Sun-pointed Michelson interferometric spectrometer is described. Its intended use is to measure the atmospheric amount of various gases which absorb in the near-infrared, visible, and near-ultraviolet portions of the electromagnetic spectrum. Preliminary spectra which contain the alpha, 0.8 micrometer, and rho sigma tau water vapor absorption bands in the near-infrared are presented to indicate the present capability of the system. Ultimately, the spectrometer can be used to explore the feasible applications of Fourier transform spectroscopy in the ultraviolet where grating spectrometers were used exclusively.

Parsons, C. L.; Gerlach, J. C.; Whitehurst, M.

1982-01-01

433

Planetary infrared astronomy using a cryogenic postdisperser on Fourier transform spectrometers

NASA Technical Reports Server (NTRS)

High resolution infrared spectra of planets from ground-based observatories were analyzed and instrumentation to improve sensitivity was developed. A cryogenic postdisperser (a narrow bandpass spectral filter) for use with Fourier transform spectrometers (FTS's) at facility observatories was constructed. This instrument has improved the sensitivity of FTS observations at 8 to 20 microns by about an order of magnitude. Spectra of Jupiter, Saturn and Comet Halley were obtained using the postdisperser with FTS facilities at the Kitt Peak 4-meter and McMath telescopes. Spectral resolution as high as 0.01/cm was achieved.

Jennings, D. E.; Kunde, V. G.; Hanel, R. A.; Maguire, W. C.; Lamb, G. M.

1986-01-01

434

The feasibility of utilizing a gas chromatograph-tandem quadrupole-Fourier transform ion cyclotron resonance mass spectrometer\\u000a (GC-MS\\/MS-FTICRMS) to analyze chlorinated-dioxins\\/furans (CDDs\\/CDFs) and mixed halogenated dioxins\\/furans (HDDs\\/HDFs) was\\u000a investigated by operating the system in the GC-FTICRMS mode. CDDs\\/CDFs and mixed HDDs\\/HDFs could be analyzed at 50,000 to\\u000a 100,000 resolving power (RP) on the capillary gas Chromatographic time scale. Initial experiments demonstrated that 1

Vince Y. Taguchi; Robert J. Nieckarz; Ray E. Clement; Stefan Krolik; Robert Williams

2010-01-01

435

Numerical simulations of turbulent fluid flows. I - Fast Fourier transform method

NASA Astrophysics Data System (ADS)

A brief review on turbulent flow problems is presented. The large eddy simulation technique is promising for detail numerical analyses of turbulent flows using existing computers. A computer program TURBINE has been developed, in which the Poisson equation for pressure is solved by using the fast Fourier transform technique and the tri-diagonal matrix algorithm to improve numerical accuracy and cpu time. The program was tested with use of an exactly solvable problem proposed by Taylor. Good numerical accuracy was obtained and cpu time was decreased to about 1/30 as compared with SOLA program based on a pressure iteration technique.

Sakai, K.; Sekiya, T.

1984-10-01

436

Using complex roots of unity and the Fast Fourier Transform, we design a new thermodynamics-based algorithm, FFTbor, that computes the Boltzmann probability that secondary structures differ by base pairs from an arbitrary initial structure of a given RNA sequence. The algorithm, which runs in quartic time and quadratic space , is used to determine the correlation between kinetic folding speed and the ruggedness of the energy landscape, and to predict the location of riboswitch expression platform candidates. A web server is available at http://bioinformatics.bc.edu/clotelab/FFTbor/. PMID:23284639

Senter, Evan; Sheikh, Saad; Dotu, Ivan; Ponty, Yann; Clote, Peter

2012-01-01

437

An isocratic online liquid chromatography Fourier transform infrared procedure has been developed for the determination of\\u000a glycolic acid in cosmetics. The method involves the ultrasound-assisted extraction of glycolic acid from the samples with\\u000a an acetonitrile:phosphate buffer (25 mM, pH 2.7) (3:97 v\\/v). The extracts were centrifuged and filtered before their injection\\u000a into the chromatography system, which was equipped with a C18

J. Kuligowski; A. Breivogel; G. Quintás; S. Garrigues; M. de la Guardia

2008-01-01

438

High Throughput Proteomics Using Fourier Transform Ion Cyclotron Resonance Mass Spectrometry

The advent of high throughput proteomics technology for global detection and quantitation of proteins creates new opportunities and challenges for those seeking to gain greater understanding of cellular machinery. Here, we review recent advances in high-resolution capillary liquid chromatography coupled to Fourier transform ion cyclotron resonance (FTICR) mass spectrometry along with its potential application to high throughput proteomics. These technological advances combined with quantitative stable isotope labeling methodologies provide powerful tools for expanding our understanding of biology at the system-level.

Qian, Weijun; Camp, David G.; Smith, Richard D.

2004-06-01

439

Quantitative analysis of oils and fats by Fourier transform Raman spectroscopy

NASA Astrophysics Data System (ADS)

The rapid analysis of fats and oils is of great importance in the food industry. It is shown that Fourier transform Raman spectroscopy may be used for this purpose. Good quality spectra, free of fluorescence, may be obtained and the spectra may be interpreted in terms of changes in total unsaturation, cis/trans isomer ratios and the number of double bonds in the hydrocarbon chains. Quantitative analysis of total unsaturation and cis/trans is possible and offers considerable improvements in speed when compared with conventional methods.

Sadeghi-Jorabchi, H.; Wilson, R. H.; Belton, P. S.; Edwards-Webb, J. D.; Coxon, D. T.

440

Deformation measurements of dragonfly's wings in free flight by using Windowed Fourier Transform

NASA Astrophysics Data System (ADS)

Grating Projection method was used to measure the height distribution of dragonfly's wings in free flight. Then the fringe patterns on the dragonfly were recorded by a high-speed CCD camera. Since the fringe patterns recorded in such a way have poor contrast and brightness, Windowed Fourier Transform (WFT), which is insensitive to noise and fringe amplitude, was used to process the fringe patterns to extract the phase. Finally, the height distributions of dragonfly's wings in free flight were obtained by using the Weighted Least-Squares Phase Unwrapping method. The choice of integration limits and the size of the window of WFT are briefly discussed here

Cheng, Peng; Hu, Jinsong; Zhang, Guofeng; Hou, Lei; Xu, Boqin; Wu, Xiaoping

2008-02-01

441

Set-up for broadband Fourier-transform multidimensional electronic spectroscopy.

We present a compact passively phase-stabilized ultra-broadband 2D Fourier transform setup. A gas (argon)-filled hollow core fiber pumped by an amplified Ti:Al_{2}O_{3} laser is used as a light source providing spectral range spanning from 420 to 900 nm. Sub-10-fs pulses were obtained using a deformable mirror-based pulse shaper. We probe the nonlinear response of Rhodamine 101 using 90 nm bandwidth and resolve vibrational coherences of 150 fs period in the ground state. PMID:25680035

Al Haddad, A; Chauvet, A; Ojeda, J; Arrell, C; van Mourik, F; Auböck, G; Chergui, M

2015-02-01

442

Universal and special keys based on phase-truncated Fourier transform.

We propose a novel optical asymmetric cryptosystem based on a phase-truncated Fourier transform. Two decryption keys independent of each other are generated. They are referred to as universal key and special key, respectively. Each of them can be used for decryption independently in absence of the other. The universal key is applicable to decrypt any ciphertext encoded by the same encryption key, but with poor legibility. On the contrary, the special key is adequate for legible decryption, but only valid for one ciphertext corresponding to the specified plaintext. A set of simulation results show the interesting performance of two types of de cryption keys. PMID:25339784

Qin, Wan; Peng, Xiang; Meng, Xiangfeng; Gao, Bruce

2011-08-01

443

Digital Fourier Transform Holography applied to investigate mechanical deformation in polymers

NASA Astrophysics Data System (ADS)

In the present work a state of deformation has been analyzed using a Digital Fourier Transform Holography method. A simple shear test using single lap joint specimen was performed. The material tested was polydimethylsiloxane, which is a rubber-like material characterized by large deformations. The displacement of the single lap joint was estimated by means of the digital holography and was associated to polymer deformation. Some classical constitutive models available in the literature were used to evaluate important material parameters. The results indicate that the proposed approach is an alternative procedure for applications related to experimental mechanics, which provide full-field and noncontact measurements.

Oliveira, G. N.; Rodrigues, D. M. C.; Nunes, L. C. S.; Santos, P. A. M. dos

2012-12-01

444

Diffuse reflectance mid-infrared Fourier transform spectroscopy of cellulose-based materials

NASA Astrophysics Data System (ADS)

Diffuse Reflectance mid-Infrared Fourier Transform (DRIFT) spectroscopy has been applied to the analysis of cellulose-based materials including wood, paper, and paper products. High-quality DRIFT spectra representing 1 mm spatial resolution on the substrate were obtained from different locations on the sample using a mechanical positioning technique. The analysis of the spectra results in spectral images showing the spatial variation in the chemistry of the sample. Chemical variations in cellulose-based samples have been observed due to variations in ink content, coating thickness, and concentration of phenyl and carbonyl groups associated with lignin.

Parks, J. E.; Blair, D. S.; Powell, G. L.

1998-06-01

445

Fourier transform C-13 NMR analysis of some free and potassium-ion complexed antibiotics.

NASA Technical Reports Server (NTRS)

Fourier transforms of the noise-decoupled, natural abundance C-13 NMR free induction decays of the cyclic antibiotic valinomycin and its potassium-ion complex have been obtained at 25.2 MHz. Comparisons are made with C-13 NMR spectra taken at 22.6 MHz of the cyclic antibiotic nonactin and the synthetic polyether dicyclohexyl-18-crown-6 and their potassium complexes. The results obtained suggest that conformational rearrangements of the molecule as a whole can compete with direct interactions between carbons and the potassium ion in determining C-13 chemical shift differences between the free and complexed species.

Ohnishi, M.; Fedarko, M.-C.; Baldeschwieler, J. D.; Johnson, L. F.

1972-01-01

446

Determination of doubly labeled water by gas-phase Fourier transform infrared spectroscopy.

Both 2H (deuterium) and 18O (oxygen 18) in isotopically enriched water have been detected by gas-phase Fourier transform infrared (FTIR) spectroscopy at 2,720 and 3,661.8 cm-1, respectively. A linear relationship between varying concentrations of each of these isotopes and their absorbance at the above frequencies indicates that gas-phase FTIR may provide a rapid and potentially less expensive approach to measure doubly labeled water in biological fluids for the estimation of energy expenditure and total body water. PMID:7854152

Khaled, M A; Krumdieck, C L; Ong, J L

1995-01-01

447

Fourier-transform infrared spectroscopy (FT-IR) using a photoacoustic sampling cell was used to obtain high-quality infrared spectra of various fiber-reinforced epoxy composites and the corresponding resin matrixes. Photoacoustic spectroscopy (PAS) offers the advantages of having little or no sample preparation for high-quality spectra to be obtained, and no alignment of the infrared incident beam is necessary. This makes PAS an ideal sampling method for in-field testing of composite laminates. The spectra revealed information on the degree of cure of the resin system by monitoring the 915/cm absorption band and the type of reinforcement material used (glass or Kevlar).

Sloan, J.M.

1986-07-01

448

NASA Astrophysics Data System (ADS)

A leaky loop Fourier Transform spectrometer is presented in 700-1000nm spectral bandwidth. This integrated optic spectrometer is made without moveable parts. The contrast and the shape of the interferogram created at the end of the component are controlled by the gap evolution between the bend waveguide and the planar waveguide. Glass ion exchange has been chosen to obtain a high fringe contrast. A linear camera set directly at the end of the component allows interferences capture from 780nm to 850nm and the light vertical scattering due to the waveguides surface roughness is used to characterize the optical loop behavior.

Creux, A.; Morand, A.; Benech, P.; Martin, B.; Grosa, G.; Cassagnettes, C.; Barbier, D.; Le Coarer, E.

2013-03-01

449

Realization of a NIR compact static Fourier transform spectrometer in glass integrated optics

NASA Astrophysics Data System (ADS)

The realization and characterization of the leaky loop integrated Fourier transform spectrometer (LLIFTS) in integrated optics are described. The component is compact, costless with no moveable parts. The principle lies on a two-beam interferometer in planar design using a leaky loop waveguide structure. The radiated part leaking from the loop induces an interference pattern at the end of the component. The structure has the advantage of controlling the shape of the interference pattern. Ion exchange technology used here requires only a single lithography step. Measurements have been made in the near infrared domain with wavelength resolution of 11 nm.

Martin, B.; Morand, A.; Jocou, L.; Benech, P.; Grosa, G.; Le Coarer, E.; Kern, P.

2010-02-01

450

The spontaneous loss of coherence catastrophe (SLCC) is a frequently observed, yet poorly studied, space-charge related effect in Fourier-transform ion cyclotron resonance mass spectrometry (FTICR-MS). This manuscript presents an application of the filter diagonalization method (FDM) in the analysis of this phenomenon. The temporal frequency behavior reproduced by frequency shift analysis using the FDM shows the complex nature of the SLCC, which can be explained by a combination of factors occurring concurrently, governed by electrostatics and ion packet trajectories inside the ICR cell. PMID:19013078

Aizikov, Konstantin; Mathur, Raman; O’Connor, Peter B.

2009-01-01

451

A new Fourier Transform Ion Cyclotron Resonance mass spectrometer based on a permanent magnet with an atmospheric pressure ionization source was designed and constructed. A mass resolving power (full-width-at-half-maximum) of up to 80,000 in the electron ionization mode and 25,000 in the electrospray mode was obtained. Also, a mass measurement accuracy at low-ppm level has been demonstrated for peptide mixtures in a mass range of up to 1,200 m/z in the isotopically resolved mass spectra. PMID:17587594

Vilkov, Andrey N.; Gamage, Chaminda M.; Misharin, Alexander S.; Doroshenko, Vladimir M.; Tolmachev, Dmitry A.; Tarasova, Irina A.; Kharybin, Oleg N.; Novoselov, Konstantin P.; Gorshkov, Michael V.

2007-01-01

452

Matrix-assisted laser desorption ionization is used to obtain Fourier-transform ion cyclotron resonance mass spectra of model peptides (e.g., gramicidin S, angiotensin I, renin substrate, melittin, and bovine insulin). Matrix-assisted laser desorption ionization yields ions having appreciable kinetic energies. Two methods for trapping the high kinetic energy ions are described: (i) the ion signal for [M+H]+ ions is shown to increase with increasing trapping voltages, and (ii) collisional relaxation is used for the detection of [M+H]+ ions of bovine insulin. Images PMID:1378614

Solouki, T; Russell, D H

1992-01-01

453

NASA Technical Reports Server (NTRS)

New developments in infrared sensor technology have potentially made possible a new space-based system which can measure far-infrared radiation at lower costs (mass, power and expense). The Stationary Imaging Fourier Transform Spectrometer (SIFTS) proposed by NASA Langley Research Center, makes use of new detector array technology. A mathematical model which simulates resolution and spectral range relationships has been developed for analyzing the utility of such a radically new approach to spectroscopy. Calculations with this forward model emulate the effects of a detector array on the ability to retrieve accurate spectral features. Initial computations indicate significant attenuation at high wavenumbers.

Beecken, Brian P.; Kleinman, Randall R.

2004-01-01

454

A Fourier transform infrared (FTIR) transmission-based spectroscopic method was investigated for the simultaneous monitoring\\u000a of aldehyde formation and the determination of anisidine value (AV) in thermally stressed oils. Synthetic calibration standards\\u000a were prepared by adding known amounts of hexanal,t-2-hexenal andt,t-2,4-decadienal to canola oil (these compounds considered representative of aldehydic compounds formed during oxidation) plus\\u000a random amounts of other compounds representative

J. Dubois; F. R. van de Voort; J. Sedman; A. A. Ismail; H. R. Ramaswamy

1996-01-01

455

Incineration of chlorobenzene in a small laboratory incinerator was monitored by using Fourier transform infrared spectroscopy (FTIR) coupled with a heated long-path cell (LPC) to analyze and quantify flue gas emissions in near real time. The effects of operating conditions under stable and decreasing incineration temperatures on the destruction of chlorobenzene were studied. The results from the decreasing temperature experiments were found to be consistent with those from experiments at stable temperatures. This finding demonstrates that the FTIR/LPC, as a continuous emissions monitor, can effectively detect dynamic changes in the incinerator emissions and can contribute significantly to the safety of incinerators.

Mao, Zhuoxiong; McIntosh, M.J.; Demirgian, J.C.

1992-06-01

456

Analysis of stacking faults in gallium nitride by Fourier transform of high-resolution images

NASA Astrophysics Data System (ADS)

We present results of studying stacking faults (SFs) in gallium nitride (GaN) with the aid of Fourier transform of high-resolution transmission electron microscopy (HRTEM) images. Using this method, it is possible both to determine the SF type and to directly measure the corresponding displacement vector. This allowed us to explain the peculiarities of the contrast of HRTEM of structures with high SF density (above 106 cm-1). It is established that the displacement vector component in the (0001) plane in these structures can significantly differ from the expected value of that is typical of single SFs.

Kirilenko, D. A.; Sitnikova, A. A.; Kremleva, A. V.; Mynbaeva, M. G.; Nikolaev, V. I.

2014-12-01

457

A study of long-range proton coupling in nitroxide radicals has been performed with a numerical analysis program using the Fourier transform technique. The present method provides a means for further identification of radicals which is particularly useful for species that are otherwise indistinguishable. The superhyperfine structure of piperidine and pyrrolidine-1-oxyl derivatives, showing ..gamma..-nuclei coupling constants as small as 0.2 G, has been brought out. The results are in good agreement with those obtained by other resolution-enhancement methods. 17 references, 7 figures, 3 tables.

Trousson, P.; Lion, Y.

1985-05-09

458

Far-infrared Fourier transform spectroscopy of (C-12)(0-18)

This paper reports on high-accuracy Fourier transform measurements of the far-infrared spectrum of (C-12)(0--18) between 0.87 and 2.7 THz (32.9-91.2/cm). Precise rotational constants are determined, and transition frequencies up to J = 35-34 are given (with an accuracy better than 5 x 10 to the -7th), along with the previously available transition frequencies for (C-12)(0-16) and (C-13)(0-16). 11 refs.

De Natale, P.; Inguscio, M.; Orza, C.R.; Zink, L.R. (European Laboratory for Non Linear Spectroscopy, Florence (Italy))

1991-03-01

459

We implemented fast Gaussian gridding (FGG)-based non-uniform fast Fourier transform (NUFFT) on the graphics processing unit (GPU) architecture for ultrahigh-speed, real-time Fourier-domain optical coherence tomography (FD-OCT). The Vandermonde matrix-based non-uniform discrete Fourier transform (NUDFT) as well as the linear/cubic interpolation with fast Fourier transform (InFFT) methods are also implemented on GPU to compare their performance in terms of image quality and processing speed. The GPU accelerated InFFT/NUDFT/NUFFT methods are applied to process both the standard half-range FD-OCT and complex full-range FD-OCT (C-FD-OCT). GPU-NUFFT provides an accurate approximation to GPU-NUDFT in terms of image quality, but offers >10 times higher processing speed. Compared with the GPU-InFFT methods, GPU-NUFFT has improved sensitivity roll-off, higher local signal-to-noise ratio and immunity to side-lobe artifacts caused by the interpolation error. Using a high speed CMOS line-scan camera, we demonstrated the real-time processing and display of GPU-NUFFT-based C-FD-OCT at a camera-limited rate of 122 k line/s (1024 pixel/A-scan). PMID:21164690

Zhang, Kang; Kang, Jin U.

2010-01-01

460

A radix 4 delay commutator for fast Fourier transform processor implementation

NASA Astrophysics Data System (ADS)

This paper describes the development of a semicustom delay commutator circuit to suppor the implementation of high speed fast Fourier transform processors based on the McCellan and Purdy radix 4 pipeline FFT algorithm. The delay commutator is a 108,000 transistor circuit comprising 12,288 shift register stages and approximately 2000 gates of random logic realized with 2.5 micrometer design rule CMOS standard cell technology. It operates at a 10 MHz clock rate which processes data at a 40 MHz rate. The delay commutator is suitable for implementing processors that compute transforms of 16, 64, 256, 1024, and 4096 (complex) points. It is implemented as a 4 bit wide data slice to facilitate concatenation to accomodate common data word sizes and to use a standard 48 pin dual-in-line package.

Swartzlander, E. E., Jr.; Young, W. K. W.; Joseph, S. J.

1984-10-01

461

The isotope patterns of unknown analytes provide information that can be of great value in their identification as part of a mass spectrometry experiment. Determining the range of compounds that are consistent with an empirically observed isotope pattern requires, as an initial step, the calculation of the theoretical isotope patterns of all feasible candidate formulas, and this is not a trivial mathematical task. While algorithms based on the Fourier transform have been used for almost two decades to perform such calculation efficiently, they have hitherto not been able to provide the exact sets of masses and abundances that constitute the fundamental isotope pattern. This article presents a new approach to the treatment of such calculations, which involves arranging and manipulating the isotope patterns of distinct elements as multidimensional data structures. This enables the use of the multidimensional Fourier transform to calculate isotope patterns with an accuracy that is limited only by the errors of floating point arithmetic. The algorithm is both highly efficient and very easy to implement in many programming environments. An open-source implementation of the algorithm in the R programming language will be made publicly available and is also available upon request. PMID:24841326

Ipsen, Andreas

2014-06-01

462

Arithmetic Fourier Transform And Adaptive Delta Modulation: A Symbiosis For High Speed Computation

NASA Astrophysics Data System (ADS)

We present preliminary results on the VLSI design and implementation of a novel and promising algorithm for accurate high-speed Fourier analysis and synthesis. The Arithmetic Fourier Transform (AFT) is based on the number -theoretic method of Mobius inversion. Its computations proceed in parallel and the individual operations are very simple. Except for a small number of scalings in one stage of the computation, only multiplications by 0, +1, and -1 are required. If the input samples were not quantized and if ideal real-number operations were used internally, then the results would be exact. The accuracy of the computation is limited only by the input A/D conversion process, any constraints on the word lengths of internal accumulating registers, and the implementation of the few scaling operations. Motivated by the goal of efficient, effective, high-speed realization of the algorithm in an integrated circuit, we introduce further simplicities by the use of delta modulation to represent the input function in digital form. The result is that only binary (or preferably, ternary) sequences need to be processed in the parallel computations. And the required accumulations can be replaced by up/down counters. The dynamic range of the resulting transformation can be increased by the use of adaptive delta modulation (ADM).

Tufts, D. W.; Sadasiv, G.

1988-04-01

463

The ultrahigh resolution and sensitivity of electrospray ionization Fourier transform ion cyclotron resonance (ESI-FTICR) mass spectrometry have for the first time been exploited for the characterization of highly sialylated glycoproteins, using human alpha-1-acid glycoprotein as the model compound. An alternative approach to the widely used high-performance liquid chromatography (HPLC) and matrix-assisted laser desorption/ionization (MALDI) assays is described. This new method does not require any enzymatic or chemical digestion (removal of sialyl groups or deglycosylation), chemical derivatization (introduction of chromophore groups), or preliminary chromatographic separation (HPLC or electrophoresis). Following ESI and accumulation of ions in a hexapole ion guide, ions are injected into the ICR cell. A selected mass window from the overall ion population is isolated and axialized prior to detection. After acquisition and Fourier transform of the transient signal the resulted spectrum is evaluated in order to determine the charge state of the detected ions and the isotope pattern of the measured protein glycoform. The presence of ions from the same glycoform with different charge states was confirmed. The advantages and limitations of the technique are discussed. Future prospects and possible applications are indicated. PMID:15373434

Nagy, Kornél; Vékey, Károly; Imre, Tímea; Ludányi, Krisztina; Barrow, Mark P; Derrick, Peter J

2004-09-01

464

NASA Astrophysics Data System (ADS)

Kestrel Corporation and the Florida Institute of Technology have designed, and are now manufacturing, a Fourier transform visible hyperspectral imager system for use in a single engine light aircraft. The system is composed of a Sagnac-based interferometer optical subsystem, a data management system, and an aircraft attitude and current position sybsystem. The system is designed to have better than 5 nm spectral resolution at 450 nm, operates over the 440 nm to 1150 nm spectral band and has a 2D spatial resolution of 0.8 mrad. An internal calibration source is recorded with every frame of data to retain radiometric accuracy. The entire system fits into a Cessna 206 and uses a conventional downward looking view port located in the baggage compartment. During operation, data are collected at a rate of 15 Mbytes per second and stored direct to a disk array. Data storage has been sized to accommodate 56 minutes of observations. Designed for environmental mapping, this Fourier transform imager has uses in emergency response and military operations.

Otten, Leonard John, III; Butler, Eugene W.; Rafert, Bruce; Sellar, R. Glenn

1995-06-01

465

A fractional Fourier transform analysis of the scattering of ultrasonic waves

Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time–frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification.

Tant, Katherine M.M.; Mulholland, Anthony J.; Langer, Matthias; Gachagan, Anthony

2015-01-01

466

NASA Astrophysics Data System (ADS)

A multiple-image encryption scheme is proposed based on the asymmetric technique, in which the encryption keys are not identical to the decryption ones. First, each plain image is scrambled based on a sequence of chaotic pairs generated with a system of two symmetrically coupled identical logistic maps. Then, the phase-only function of each scrambled image is retrieved with an iterative phase retrieval process in the fractional Fourier transform domain. Second, all phase-only functions are modulated into an interim, which is encrypted into the ciphertext with stationary white noise distribution by using the fractional Fourier transform and chaotic diffusion. In the encryption process, three random phase functions are used as encryption keys to retrieve the phase-only functions of plain images. Simultaneously, three decryption keys are generated in the encryption process, which make the proposed encryption scheme has high security against various attacks, such as chosen plaintext attack. The peak signal-to-noise is used to evaluate the quality of the decrypted image, which shows that the encryption capacity of the proposed scheme is enhanced considerably. Numerical simulations demonstrate the validity and efficiency of the proposed method.

Sui, Liansheng; Duan, Kuaikuai; Liang, Junli; Zhang, Zhiqiang; Meng, Haining

2014-11-01

467

NASA Astrophysics Data System (ADS)

The geometric phase analysis (GPA), an important image-based deformation measurement method, has been used at both micro- and nano-scale. However, when a deformed image has apparent distortion, non-ignorable error in the obtained deformation field could occur by using this method. In this paper, the geometric phase analysis based on the windowed Fourier transform (WFT) is proposed to solve the above-mentioned issue, defined as the WFT-GPA method. In WFT-GPA, instead of the Fourier transform (FT), the WFT is utilized to extract the phase field block by block, and therefore more accurate local phase information can be acquired. The simulation tests, which include detailed discussion of influence factors for measurement accuracy such as window size and image noise, are conducted with digital deformed grids. The results verify that the WFT-GPA method not only keeps all advantages of traditional GPA method, but also owns a better accuracy for deformation measurement. Finally, the WFT-GPA method is applied to measure the machining distortion incurred in soft ultraviolet nanoimprint lithography (UV-NIL) process. The successful measurement shows the feasibility of this method and offers a full-field way for characterizing the replication quality of UV-NIL process.

Dai, Xianglu; Xie, Huimin; Wang, Qinghua

2014-06-01

468

Application of Fast Fourier Transform in thermo-magnetic convection analysis

NASA Astrophysics Data System (ADS)

Application of Fast Fourier Transform in thermo-magnetic convection is reported. Cubical enclosure filled with paramagnetic fluid heated from below and placed in the strong magnetic field gradients was investigated. The main aim of study was connected with identification of flow types, especially transition to turbulence. For this purpose the Fast Fourier Transform (FFT) analysis was applied. It was followed by the heat transfer characteristic for various values of magnetic induction gradient. The analysis was done at two Rayleigh numbers 7.89·105 and 1.86·106 with thermo-magnetic Rayleigh numbers up to 1.8·108 and 4.5·108 respectively. The presented results clearly indicate flow types and also demonstrate augmented heat transfer in dependence on magnetic induction gradient. Detailed analysis of flow transition to turbulent state was compared with transition line for natural convection reported in literature. The transition to turbulence in the case of thermo-magnetic convection of paramagnetic fluid was in very good agreement with transition in the case of natural convection.

Pyrda, L.

2014-08-01

469

Instrumental phase-based method for Fourier transform spectrometer measurements processing

Phase correction is a critical procedure for most space-borne Fourier transform spectrometers (FTSs) whose accuracy (owing to often poor signal-to-noise ratio, SNR) can be jeopardized from many uncontrollable environmental conditions. This work considers the phase correction in an FTS working under significant temperature change during the measurement and affected by mechanical disturbances. The implemented method is based on the identification of an instrumental phase that is dependent on the interferometer temperature and on the extraction of a linear phase component through a least-squares approach. The use of an instrumental phase parameterized with the interferometer temperature eases the determination of the linear phase that can be extracted using only a narrow spectral region selected to be immune from disturbances. The procedure, in this way, is made robust against phase errors arising from instrumental effects, a key feature to reduce the disturbances through spectra averaging. The method was specifically developed for the Mars IR Mapper spectrometer, that was designed for operation onboard a rover on the Mars surface; the validation was performed using ground and in-flight measurements of the Fourier transform IR spectrometer planetary Fourier spectrometer, onboard the MarsExpress mission. The symmetrization has been exploited also for the spectra calibration, highlighting the issues deriving from the cases of relevant beamsplitter emission. The applicability of this procedure to other instruments is conditional to the presence in the spectra of at least one spectral region with a large SNR along with a negligible (or known) beamsplitter emission. For the PFS instrument, the processing of data with relevant beamsplitter emission has been performed exploiting the absorption carbon dioxide bands present in Martian spectra.

Saggin, Bortolino; Scaccabarozzi, Diego; Tarabini, Marco

2011-04-20

470

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ? operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements. PMID:24628166

Ma, Q; Boulet, C; Tipping, R H

2014-03-14

471

NASA Technical Reports Server (NTRS)

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

Ma, Q.; Boulet, C.; Tipping, R. H.

2014-01-01

472

Retention time shift is one of the most challenging problems during the preprocessing of massive chromatographic datasets. Here, an improved version of the moving window fast Fourier transform cross-correlation algorithm is presented to perform nonlinear and robust alignment of chromatograms by analyzing the shifts matrix generated by moving window procedure. The shifts matrix in retention time can be estimated by fast Fourier transform cross-correlation with a moving window procedure. The refined shift of each scan point can be obtained by calculating the mode of corresponding column of the shifts matrix. This version is simple, but more effective and robust than the previously published moving window fast Fourier transform cross-correlation method. It can handle nonlinear retention time shift robustly if proper window size has been selected. The window size is the only one parameter needed to adjust and optimize. The properties of the proposed method are investigated by comparison with the previous moving window fast Fourier transform cross-correlation and recursive alignment by fast Fourier transform using chromatographic datasets. The pattern recognition results of a gas chromatography mass spectrometry dataset of metabolic syndrome can be improved significantly after preprocessing by this method. Furthermore, the proposed method is available as an open source package at https://github.com/zmzhang/MWFFT2. PMID:25645318

Zhang, Mingjing; Wen, Ming; Zhang, Zhi-Min; Lu, Hongmei; Liang, Yizeng; Zhan, Dejian

2015-03-01

473

Open-path Fourier Transform Infrared Spectroscopy (OP-FTIR) was used to conduct an air monitoring survey at a Fourier manufactured gas plant (FMGP) superfund site. This survey was performed in support and at the request of the Waste Management Division, U.S. EPA, Region VII. A three day study was conducted in which the OP- FTIR instrument was operated at several fenceline locations

Michael F. Davis; Joseph Arello; John R. Helvig; Jody L. Hudson; Melissa D. Tucker; John M. Poholarz; Robert M. Hammaker; William G. Fateley

1995-01-01

474

NASA Astrophysics Data System (ADS)

Fourier Domain Low Coherence Interferometry (fLCI) is a promising technique which combines the depth resolution of low coherence interferometry with the sensitivity of light scattering spectroscopy for probing the health of epithelial tissue layers. Our new fLCI system configuration utilizes a white light Xe arc lamp source and a 4-f interferometer which re-images light scattered from the sample onto the detection plane. The system employs an imaging spectrometer at the detection plane to acquire depth resolved profiles from 252 adjacent spatial points without the need for any scanning. The limited spatial coherence of the light source requires the resolution of adjacent spatial points for the generation of depth information. Depth-resolved spectral information is recovered by performing a short-time Fourier transform on the detected spectra, similar to spectroscopic optical coherence tomography. Wavelength dependent variations in scattering intensity are analyzed as a function of depth to obtain information about the neoplastic transformation of the probed cells. Previous studies have demonstrated fLCI as an excellent technique for probing the scatterer morphology of simple phantoms and of in vitro cancer cell monolayers. We now seek to assess the ability of the new fLCI system to measure the health of subsurface tissue layers using the hamster cheek pouch model. Seven hamsters will have one cheek pouch treated with the known carcinogen DMBA. At the conclusion of the 24 week treatment period the animals will be anesthetized and the cheek pouches will be extracted. We will use the fLCI optical system to measure the neoplastic transformation of the in situ subsurface tissue layers in both the normal and DMBA-treated cheek pouches. Traditional histological analysis will be used to verify the fLCI measurements. We expect our results to establish the feasibility of fLCI to distinguish between healthy and dysplastic epithelial tissues in the hamster cheek pouch.

Graf, Robert N.; Chen, Xiaoxin; Brown, William; Wax, Adam

2008-02-01

475

Continuous wavelet transform in quantum field theory

NASA Astrophysics Data System (ADS)

We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar ?4 theory, quantum electrodynamics, and quantum chromodynamics. The method of continuous wavelet transform in quantum field theory, presented by Altaisky [Phys. Rev. D 81, 125003 (2010)] for the scalar ?4 theory, consists in substitution of the local fields ?(x) by those dependent on both the position x and the resolution a. The substitution of the action S[?(x)] by the action S[?a(x)] makes the local theory into a nonlocal one and implies the causality conditions related to the scale a, the region causality [J. D. Christensen and L. Crane, J. Math. Phys. (N.Y.) 46, 122502 (2005)]. These conditions make the Green functions G(x1,a1,…,xn,an)=??a1(x1)…?an(xn)? finite for any given set of regions by means of an effective cutoff scale A=min?(a1,…,an).

Altaisky, M. V.; Kaputkina, N. E.

2013-07-01

476

Gridding-based direct Fourier inversion of the three-dimensional ray transform

NASA Astrophysics Data System (ADS)

We describe a fast and accurate direct Fourier method for reconstructing a function f of three variables from a number of its parallel beam projections. The main application of our method is in single particle analysis, where the goal is to reconstruct the mass density of a biological macromolecule. Typically, the number of projections is extremely large, and each projection is extremely noisy. The projection directions are random and initially unknown. However, it is possible to determine both the directions and f by an iterative procedure; during each stage of the iteration, one has to solve a reconstruction problem of the type considered here. Our reconstruction algorithm is distinguished from other direct Fourier methods by the use of gridding techniques that provide an efficient means to compute a uniformly sampled version of a function g from a nonuniformly sampled version of Fg, the Fourier transform of g, or vice versa. We apply the two-dimensional reverse gridding method to each available projection of f, the function to be reconstructed, in order to obtain Ff on a special spherical grid. Then we use the three-dimensional gridding method to reconstruct f from this sampled version of Ff. This stage requires a proper weighting of the samples of Ff to compensate for their nonuniform distribution. We use a fast method for computing appropriate weights that exploits the special properties of the spherical sampling grid for Ff and involves the computation of a Voronoi diagram on the unit sphere. We demonstrate the excellent speed and accuracy of our method by using simulated data.

Penczek, Pawel A.; Renka, Robert; Schomberg, Hermann

2004-04-01

477

NASA Astrophysics Data System (ADS)

The goal of our scattering experiments is to derive the distribution the differential cross-section and elucidate the dynamics of a bimolecular collision via pure rotational spectroscopy. We have explored the use of a data reduction model to directly transform rotational line shapes into the differential cross section and speed distribution of a reactive bimolecular collision. This inversion technique, known as Fourier Transform Doppler Spectroscopy (FTDS), initially developed by James Kinsey, deconvolves the velocity information contained in one-dimensional Doppler Profiles to construct the non-thermal, state-selective three-dimensional velocity distribution. By employing an expansion in classical orthogonal polynomials, the integral transform in FTDS can be simplified into a set of purely algebraic expressions technique; i.e. the Taatjes method. In this investigation, we extend the Taatjes method for general use in recovering asymmetric velocity distributions. We have also constructed a hypothetical asymmetric distribution from adiabatic scattering in Argon-Argon to test the general method. The angle- and speed-components of the sample distribution were derived classically from a Lennard-Jones 6-12 potential, with collisions at 60 meV, and mapped onto Radon space to generate a set of discrete Doppler profiles. The sample distribution was reconstructed from these profiles using FTDS. Both distributions were compared along with derived total cross sections for the Argon--Argon system. This study serves as a template for constructing velocity distributions from bimolecular scattering experiments using the FTDS inversion technique.

Monge, Josue Roberto

478

The Fourier transform infrared (FT-IR) spectral data of two nerve agent simulants, diisopropyl methyl phosphonate (DIMP) and dimethyl methyl phosphonate (DMMP), are used as test cases to determine the spectral resolution that gives optimal pattern recognition performance. DIMP is used as the target analyte for detection, while DMMP is used to test the ability of the automated pattern recognition methodology to detect the analyte selectively. Interferogram data are collected by using a Midac passive FT-IR instrument. The methodology is based on the application of pattern recognition techniques to short segments of single-beam spectra obtained by Fourier processing the collected interferogram data. The work described in this article evaluates the effect of varying spectral resolution on the pattern recognition results. The objective is to determine the optimal spectral resolution to be used for data collection. The results of this study indicate that the data with a nominal spectral resolution of 16 cm{sup -1} provide sufficient selectivity to give pattern recognition results comparable to that obtained by using higher resolution data. We found that, while higher resolution does not increase selectivity sufficiently to provide better pattern recognition results, lower resolution decreases selectivity and degrades the pattern recognition results. These results can be used as guidelines to maximize detection sensitivity, to minimize the time needed for data collection, and to reduce data storage requirements. (c) 2000 Society for Applied Spectroscopy.

Bangalore, Arjun S. [Chemical Technology Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439 (United States)] [Chemical Technology Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439 (United States); Demirgian, Jack C. [Environmental Research Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439 (United States)] [Environmental Research Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439 (United States); Boparai, Amrit S. [Chemical Technology Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439 (United States)] [Chemical Technology Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439 (United States); Small, Gary W. [Center for Intelligent Chemical Instrumentation, Department of Chemistry, Clippinger Laboratories, Ohio University, Athens, Ohio 45701-2979 (United States)] [Center for Intelligent Chemical Instrumentation, Department of Chemistry, Clippinger Laboratories, Ohio University, Athens, Ohio 45701-2979 (United States)

1999-11-01

479

NASA Astrophysics Data System (ADS)

Knowing that the gravitational lens deflection angle can be expressed as the convolution product between the dimensionless surface mass density ? (x) and a simple function of the scaled impact parameter vector x, we make use of the Fourier transform to derive its analytical expression for the case of mass distributions presenting a homoeoidal symmetry. For this family of models, we obtain the expression of the two components of the deflection angle in the form of integrals performed over the radial coordinate ?. In the limiting case of axially symmetric lenses, we obviously retrieve the well-known relation hat{? }(x) ? M(? |x|) x/|x|^2. Furthermore, we derive explicit solutions for the deflection angle characterized by dimensionless surface mass density profiles such as ? ? (? _c2+ ? 2)^{-? }; corresponding to the non-singular isothermal ellipsoid model for the particular case ? = 1/2. Let us insist that all these results are obtained without using the complex formalism introduced by Bourassa and Kantowski. Further straightforward applications of this Fourier approach are suggested in the conclusions of this work.

Wertz, O.; Surdej, J.

2014-01-01

480

NASA Astrophysics Data System (ADS)

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.

Georges, James A., III

2007-09-01

481

Purpose: Boyer and Mok proposed a fast calculation method employing the Fourier transform (FT), for which calculation time is independent of the number of seeds but seed placement is restricted to calculation grid points. Here an interpolation method is described enabling unrestricted seed placement while preserving the computational efficiency of the original method. Methods: The Iodine-125 seed dose kernel was sampled and selected values were modified to optimize interpolation accuracy for clinically relevant doses. For each seed, the kernel was shifted to the nearest grid point via convolution with a unit impulse, implemented in the Fourier domain. The remaining fractional shift was performed using a piecewise third-order Lagrange filter. Results: Implementation of the interpolation method greatly improved FT-based dose calculation accuracy. The dose distribution was accurate to within 2% beyond 3 mm from each seed. Isodose contours were indistinguishable from explicit TG-43 calculation. Dose-volume metric errors were negligible. Computation time for the FT interpolation method was essentially the same as Boyer's method. Conclusions: A FT interpolation method for permanent prostate brachytherapy TG-43 dose calculation was developed which expands upon Boyer's original method and enables unrestricted seed placement. The proposed method substantially improves the clinically relevant dose accuracy with negligible additional computation cost, preserving the efficiency of the original method.

Liu, Derek, E-mail: dmliu@ualberta.ca; Sloboda, Ron S. [Department of Medical Physics, Cross Cancer Institute, Edmonton, Alberta T6G 1Z2, Canada and Department of Oncology, University of Alberta, Edmonton, Alberta T6G 2R3 (Canada)] [Department of Medical Physics, Cross Cancer Institute, Edmonton, Alberta T6G 1Z2, Canada and Department of Oncology, University of Alberta, Edmonton, Alberta T6G 2R3 (Canada)

2014-05-15

482

The inductively coupled plasma (ICP) excitation source for analytical atomic spectroscopy has been studied with the one-meter Fourier-transform spectrometer (FTS) located at Kitt Peak National Observatory, Tucson, Arizona. The high resolution of this spectrometer combined with the comprehensive wavelength coverage of the Fourier transform technique, allows the use of the spectra for elucidation of spectraphysical properties such as excitation temperatures and line widths. From these studies, the analytical applicability of the ICP-FTS combination is evaluated for atomic spectrochemical measurements in the visible and ultraviolet. 4 figures, 1 table.

Faires, L.M.; Palmer, B.A.; Engleman, R. Jr.; Niemczyk, T.M.

1983-01-01

483

NASA Astrophysics Data System (ADS)

In this experiment we used an 800 nm laser to generate high-order harmonics in a gas cell filled with Argon. Of those photons, a harmonic with 42 eV was selected by using a time-preserving grating monochromator. Employing a modified Mach-Zehnder type Fourier transform spectrometer for the VUV/XUV it was possible to measure the temporal coherence of the selected photons to about 6 fs. We demonstrated that not only could this kind of measurement be performed with a Fourier transform spectrometer, but also with some spatial resolution without