Gerchberg–Saxton algorithm: Difference between revisions

Revision as of 04:45, 7 October 2024

Revision as of 00:56, 24 January 2025

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{{Short description|Algorithm for phase retrieval}}

[[File:Gerchberg-Saxton algorithm.jpg|thumb|400px|The Gerchberg-Saxton algorithm. FT is Fourier transform.]]

The '''Gerchberg–Saxton (GS) algorithm''' is an iterative [[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}}{{dead link|date=October 2024}}</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.