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It is often necessary to know only the phase distribution from one of the planes, since the phase distribution on the other plane can be obtained by performing a
Fourier transform on the plane whose phase is known. Although often used for two-dimensional signals, the GS algorithm is also valid for
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for retrieving the phase of a complex-valued wavefront from two intensity measurements acquired in two different planes. Typically, the two planes are the image plane and the far field (diffraction) plane, and the wavefront propagation between these two planes is given by the
88:) Target and Source be the Target and Source Amplitude planes respectively A, B, C & D be complex planes with the same dimension as Target and Source Amplitude – Amplitude-extracting function: e.g. for complex
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error criterion is not satisfied B := Amplitude(Source) × exp(i × Phase(A)) C := FT(B) D := Amplitude(Target) × exp(i × Phase(C)) A := IFT(D)
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below performs the GS algorithm to obtain a phase distribution for the plane "Source", such that its
Fourier transform would have the amplitude distribution of the plane "Target".
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This is just one of the many ways to implement the GS algorithm. Aside from optimizations, others may start by performing a forward
Fourier transform to the source distribution.
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Memmolo, Pasquale; Miccio, Lisa; Merola, Francesco; Paciello, Antonio; Embrione, Valerio; Fusco, Sabato; Ferraro, Pietro; Antonio Netti, Paolo (2014-01-01).
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51:. The original paper by Gerchberg and Saxton considered image and diffraction pattern of a sample acquired in an electron microscope.
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Applications and publications on phase retrieval from the
University of Rochester, Institute of Optics
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200:"A practical algorithm for the determination of the phase from image and diffraction plane pictures"
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84:– the imaginary unit, √−1 (square root of −1) exp – exponential function (exp(x) =
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The
Gerchberg-Saxton algorithm is one of the most prevalent methods used to create
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132:| Phase – Phase extracting function: e.g. Phase(z) = arctan(y / x)
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226:"Investigation on specific solutions of Gerchberg–Saxton algorithm"
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FT – forward
Fourier transform IFT – inverse Fourier transform
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The
Gerchberg-Saxton algorithm. FT is Fourier transform.
139:Gerchberg–Saxton(Source, Target, Retrieved_Phase)
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287:A Python-Script of the GS by Dominik Doellerer
198:Gerchberg, R. W.; Saxton, W. O. (1972).
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230:Optics and Lasers in Engineering
242:10.1016/j.optlaseng.2013.06.008
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67:computer-generated holograms
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179:Adaptive-additive algorithm
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151:Retrieved_Phase = Phase(A)
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143:A := IFT(Target)
18:Gerchberg-Saxton algorithm
310:Digital signal processing
55:one-dimensional signals.
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291:MATLAB GS algorithms
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73:Pseudocode algorithm
272:2008-06-13 at the
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236:: 206–211.
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185:References
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