## Applications of algorithmic differentiation to phase retrieval algorithms

JOSA A, Vol. 31, Issue 7, pp. 1348-1359 (2014)

http://dx.doi.org/10.1364/JOSAA.31.001348

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### Abstract

In this paper, we generalize the techniques of reverse-mode algorithmic differentiation to include elementary operations on multidimensional arrays of complex numbers. We explore the application of the algorithmic differentiation to phase retrieval error metrics and show that reverse-mode algorithmic differentiation provides a framework for straightforward calculation of gradients of complicated error metrics without resorting to finite differences or laborious symbolic differentiation.

© 2014 Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(000.4430) General : Numerical approximation and analysis

(010.7350) Atmospheric and oceanic optics : Wave-front sensing

(100.5070) Image processing : Phase retrieval

**ToC Category:**

Image Processing

**History**

Original Manuscript: April 2, 2014

Revised Manuscript: April 4, 2014

Manuscript Accepted: April 22, 2014

Published: June 9, 2014

**Citation**

Alden S. Jurling and James R. Fienup, "Applications of algorithmic differentiation to phase retrieval algorithms," J. Opt. Soc. Am. A **31**, 1348-1359 (2014)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-7-1348

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