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Applied Optics

Applied Optics


  • Vol. 43, Iss. 12 — Apr. 20, 2004
  • pp: 2418–2430

Optical phase retrieval by use of first Born- and Rytov-type approximations

Timur E. Gureyev, Timothy J. Davis, Andrew Pogany, Sheridan C. Mayo, and Stephen W. Wilkins  »View Author Affiliations

Applied Optics, Vol. 43, Issue 12, pp. 2418-2430 (2004)

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The first Born and Rytov approximations of scattering theory are introduced in their less familiar near-field versions. Two algorithms for phase retrieval based on these approximations are then described. It is shown theoretically and by numerical simulations that, despite the differences in their formulation, the two algorithms deliver fairly similar results when used for optical phase retrieval in the near and intermediate fields. The algorithms are applied to derive explicit solutions to four phase-retrieval problems of practical relevance to quantitative phase-contrast imaging and tomography. An example of successful phase reconstruction by use of the Born-type algorithm with an experimental x-ray image is presented.

© 2004 Optical Society of America

OCIS Codes
(090.0090) Holography : Holography
(100.3190) Image processing : Inverse problems
(100.5070) Image processing : Phase retrieval
(110.7440) Imaging systems : X-ray imaging
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(340.7440) X-ray optics : X-ray imaging

Original Manuscript: October 27, 2003
Revised Manuscript: January 21, 2004
Published: April 20, 2004

Timur E. Gureyev, Timothy J. Davis, Andrew Pogany, Sheridan C. Mayo, and Stephen W. Wilkins, "Optical phase retrieval by use of first Born- and Rytov-type approximations," Appl. Opt. 43, 2418-2430 (2004)

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