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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 23 — Nov. 7, 2011
  • pp: 22809–22819

Non-linear iterative phase retrieval based on Frechet derivative

V. Davidoiu, B. Sixou, M. Langer, and F. Peyrin  »View Author Affiliations


Optics Express, Vol. 19, Issue 23, pp. 22809-22819 (2011)
http://dx.doi.org/10.1364/OE.19.022809


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Abstract

Several methods of phase retrieval for in-line phase tomography have already been investigated based on the linearization of the relation between the phase shift induced by the object and the diffracted intensity. In this work, we present a non-linear iterative approach using the Frechet derivative of the intensity recorded at a few number of propagation distances. A Landweber type iterative method with an analytic calculation of the Frechet derivative adjoint is proposed. The inverse problem is regularized with the smoothing L2 norm of the phase gradient and evaluated for several different implementations. The evaluation of the method was performed using a simple phase map, both with and without noise. Our approach outperforms the linear methods on simulated noisy data up to high noise levels and thanks to the proposed analytical calculation is suited to the processing of large experimental image data sets.

© 2011 OSA

OCIS Codes
(100.3190) Image processing : Inverse problems
(100.5070) Image processing : Phase retrieval
(110.7440) Imaging systems : X-ray imaging
(180.7460) Microscopy : X-ray microscopy

ToC Category:
Image Processing

History
Original Manuscript: May 4, 2011
Revised Manuscript: June 22, 2011
Manuscript Accepted: June 24, 2011
Published: October 26, 2011

Virtual Issues
Vol. 7, Iss. 1 Virtual Journal for Biomedical Optics

Citation
V. Davidoiu, B. Sixou, M. Langer, and F. Peyrin, "Non-linear iterative phase retrieval based on Frechet derivative," Opt. Express 19, 22809-22819 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-22809


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