Gerchberg–Saxton algorithm: Difference between revisions

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{{Short description|Algorithm for phase retrieval}}

[[File:Gerchberg-Saxton algorithm.jpg|thumb|400px|The Gerchberg-Saxton algorithm for iterative phase retrieval,. FT is Fourier transform.]]

The '''Gerchberg–Saxton (GS) algorithm''' is an iterative [[algorithm]] phase retrieval]] [[algorithm]] for retrieving the phase of a complex-valued wavefront from two intensity measurements acquired in two different planes.<ref>{{Cite journal|last=Gerchberg|first=R. W.|last2=Saxton|first2=W. O.|date=1972|title=A practical algorithm for the determination of the phase from image and diffraction plane pictures|url=http://www.u.arizona.edu/~ppoon/GerchbergandSaxton1972.pdf|archive-url=https://web.archive.org/web/20160328053000/http://www.u.arizona.edu/~ppoon/GerchbergandSaxton1972.pdf|url-status=dead|archive-date=March 28, 2016|journal=Optik|language=EN|volume=35|pages=237–246}}</ref> 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 [[Fourier transform]]. The original paper by Gerchberg and Saxton considered image and diffraction pattern of a sample acquired in an electron microscope.

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 one-dimensional signals.

The [[pseudocode]] 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".

The Gerchberg-Saxton algorithm is one of the most prevalent methods used to create [[computer-generated hologram]]s.<ref>{{Cite journal |last=Memmolo |first=Pasquale |last2=Miccio |first2=Lisa |last3=Merola |first3=Francesco |last4=Paciello |first4=Antonio |last5=Embrione |first5=Valerio |last6=Fusco |first6=Sabato |last7=Ferraro |first7=Pietro |last8=Antonio Netti |first8=Paolo |date=2014-01-01 |title=Investigation on specific solutions of Gerchberg–Saxton algorithm |url=https://www.sciencedirect.com/science/article/pii/S0143816613001942 |journal=Optics and Lasers in Engineering |volume=52 |pages=206–211 |doi=10.1016/j.optlaseng.2013.06.008 |issn=0143-8166|url-access=subscription }}</ref>

==Pseudocode algorithm==

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* [[Fourier optics]]

* [[Holography]]

* [[Computer-generated holography]]

* [[Adaptive-additive algorithm]]

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==External links==

* Dr W. Owen Saxton's pages [http://www-hrem.msm.cam.ac.uk/people/saxton/] {{Webarchive|url=https://web.archive.org/web/20080613024950/http://www-hrem.msm.cam.ac.uk/people/saxton/ |date=2008-06-13 }}, [https://www.murrayedwards.cam.ac.uk/fellows/dr-w-owen-saxton]

* [http://www.ysbl.york.ac.uk/~cowtan/fourier/coeff.html Graphical explanatory material by Kevin Cowtan]

* Dr W. Owen Saxton's pages [http://www-hrem.msm.cam.ac.uk/people/saxton/], [https://www.murrayedwards.cam.ac.uk/fellows/dr-w-owen-saxton]

* [http://www.optics.rochester.edu/workgroups/fienup/index.html Applications and publications on phase retrieval from the University of Rochester, Institute of Optics]

* [https://slmtoolbox.neocities.org/ SLM ToolBox]. A [[freeware]] Windows program for calculating holograms and displaying them on a [[spatial light modulator]]

* [https://www.creatgraphy.com/05/2020/allgemein/lightmodulation-gerchberg-saxton-algorithmus-gsa-660/ A Python-Script of the GS by Dominik Doellerer]

* MATLAB GS algorithms [https://ch.mathworks.com/matlabcentral/fileexchange/68647-gerchberg-saxton-phase-retrieval-algorithm/], [https://ch.mathworks.com/matlabcentral/fileexchange/65979-gerchberg-saxton-algorithm]

{{DEFAULTSORT:Gerchberg-Saxton algorithm}}