Comparing Speckle Imaging Methods

NASA Astrophysics Data System (ADS)

Speckle imaging techniques have been evolving since the fundamental idea was presented almost 40 years ago;(1) the critical insight demonstrated how moments of the Fourier transform of an ensemble of short exposures contain information out to the diffraction limit. Many variations on the theme have been implemented, but in all cases, an ensemble of short-exposure images is collected and then post-processed to restore the object. In this presentation, we will compare speckle imaging reconstruction results for several speckle imaging approaches. In particular, we will compare and contrast four methods: 1) Knox-Thompson, using a hidden phase-finder in the object spectrum phase reconstruction ;(2,3) 2) Knox-Thompson, using a phasor-based phase reconstruction; 3) Bispectrum, using only two bispectrum planes and a phasor-based phase reconstruction;(4) 4) Bispectrum, using four bispectrum planes and a phasor-based phase reconstruction. In each application of the four approaches, we first calculate the modulus of the object spectrum using a Wiener-Helstrom filter to remove the speckle transfer function. The methods then differ in their object spectrum phase reconstructions. The first method solves two-dimensional difference equations for the phase using the method described in Reference 3. There, we demonstrate that the object spectrum phase can be decomposed into a regular, single-valued function determined by the divergence of the phase gradient, as well as a multi-valued function determined by the circulation of the phase gradient; this second function has been called the "hidden phase." The standard least-squares solution to the two-dimensional difference equations always misses this hidden phase. Reference 3 develops a solution method that gives both the regular and hidden parts of the object spectrum phase. The next three methods all use phasor-based phase reconstruction algorithms. Here, we develop "least-squares" motivated iterative improvement algorithms that rapidly converge to the least-squares-best two-dimensional phasor array for the object spectrum. In our applications, we will implement all four methods on a simple binary star object at both moderate and low photon-per-frame light levels. Then, we will apply the four methods to several complex extended objects, once again varying the photons per frame. In the simulations, we will assume that the only aberrations are those introduced by atmospheric turbulence setting the ratio of the telescope diameter, D, to the Fried Parameter, r0, greater than or equal to ten.(5) In addition, we assume only photon noise in the short exposures while neglecting other noise sources. We will present numerous results, describing the strengths and weaknesses of each of the four methods applied to both simple and extended objects. References 1. A. Labeyrie, "Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images," Astron. Astrophys. 6, 85-87 (1970). 2. K. T. Knox and B. J. Thompson, "Recovery of images from atmospherically degraded short-exposure photographs," Astron. J. 193, L45-L48 (1974). 3. G. C. Dente, Speckle Imaging and Hidden Phase, Appl. Opt, vol. 39, No. 10, pg. 1480-1485, 2000. 4. G. R. Ayers, M. J. Northcott and J. C. Dainty, "Knox-Thompson and triple-correlation imaging through atmospheric turbulence," J. Opt. Soc. Am. 5, 963-985 (1987). 5. D. L. Fried, "Optical resolution through a randomly inhomogeneous medium for very long and very short exposures," J. Opt. Soc. Am. 56, 1372-1379 (1966).

Dente, G.; Tilton, M.; Ongstad, A.