## Phase retrieval by propagation for localized images

JOSA A, Vol. 25, Issue 11, pp. 2784-2790 (2008)

http://dx.doi.org/10.1364/JOSAA.25.002784

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### Abstract

We present an algorithm for phase retrieval based on improvements to the methods developed by
Bates [see Optik
61, 247 (1982)
]. Specifically, we have developed a more precise way of calculating phase differences between adjacent *actual* sampling points. This leads to a reduction in the error buildup in a recursive phase propagation scheme. Our approach has the advantage of having no adjustable parameters. We present a few examples of how this method can lead to improved image reconstructions.

© 2008 Optical Society of America

**OCIS Codes**

(100.3190) Image processing : Inverse problems

(100.5070) Image processing : Phase retrieval

**ToC Category:**

Image Processing

**History**

Original Manuscript: June 12, 2008

Manuscript Accepted: August 17, 2008

Published: October 21, 2008

**Citation**

David Montiel, Mark Sutton, and Martin Grant, "Phase retrieval by propagation for localized images," J. Opt. Soc. Am. A **25**, 2784-2790 (2008)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-11-2784

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### References

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- The solution to the phase problem is not unique in 1D. In the most general case (for a complex image), there can be up to 22M−1 different sets of phases compatible with a set of 2M+1 given magnitudes al. This is consistent with the fact that there are two possible choices for the sign of each phase difference (ωl) between adjacent samples .
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