Journal ArticleDOI
Fast FFT-based algorithm for phase estimation in speckle imaging
TLDR
The algorithm uses the fast Fourier transform to diagonalize and decouple the system of equations which results from the application of the least-squares criterion and is accurate and stable, and is perhaps an order of magnitude faster than the best iterative method.Abstract:
This paper describes a fast direct algorithm for obtaining least-squares phase estimates from arrays of noisy phase differences. The algorithm uses the fast Fourier transform to diagonalize and decouple the system of equations which results from the application of the least-squares criterion. It is accurate and stable, and is perhaps an order of magnitude faster than the best iterative method. The effectiveness of the algorithm has been demonstrated by using it in connection with the Knox–Thompson speckle-imaging procedure to restore an optical object perturbed by simulated atmospheric turbulence. Representative results are discussed in the paper.read more
Citations
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Journal ArticleDOI
Wave-front estimation from wave-front slope measurements
TL;DR: In this paper, the problem of wavefront estimation from wave-front slope measurements has been examined from a least-squares curve fitting model point of view, and a new zonal phase gradient model is introduced and its error propagator, which relates the mean square wavefront error to the noisy slope measurements, has been compared with two previously used models.
Journal ArticleDOI
Wavefront reconstruction using iterative Fourier transforms
Francois Roddier,Claude Roddier +1 more
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Modal estimation of a wave front from difference measurements using the discrete Fourier transform
TL;DR: In this paper, it was shown that a wave front can be reconstructed from its discrete differences by a simple multiplicative filtering operation in the spatial-frequency domain by using complex exponentials as basis functions in a modal expansion.
Journal ArticleDOI
Solution to the shearing problem
TL;DR: A new, to the authors' knowledge, approach for the evaluation of lateral shearing interferograms is presented, based on an extension of the difference measurements that allows for reconstruction of that part of the underlying wave front whose information is contained in the given difference measurements.
References
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Journal Article
Attainment of Diffraction Limited Resolution in Large Telescopes by Fourier Analysing Speckle Patterns in Star Images
Journal ArticleDOI
Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements
TL;DR: In this article, the problem of fitting a wavefront distortion estimate to a (single-instant) set of phase-difference measurements has been formulated as an unweighted least-square problem.
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Wave-front reconstruction for compensated imaging
TL;DR: In this paper, the authors analyzed the conversion from phase differences to phases and derived the optimal linear estimator in terms of least noise propagation for a compensated imaging (CI) system.
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Active optics: A new technology for the control of light
TL;DR: Active optical systems as mentioned in this paper are those in which real-time control over optical wavefronts is employed to optimize system perference in the presence of random distrurbances, such as interference.
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Matrix formulation of the reconstruction of phase values from phase differences
TL;DR: The phase reconstruction problem is formulated in terms of a vector-matrix multiplication and it is shown that previous solution methods are equivalent to this general description, and the errors in reconstruction are analyzed.