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Davidoiu V, Sixou B, Langer M, et al. Non-linear iterative phase retrieval based on Frechet derivative. Opt Express. 2011;19(23):22809-19doi: 10.1364/OE.19.022809.
Davidoiu, V., Sixou, B., Langer, M., & Peyrin, F. (2011). Non-linear iterative phase retrieval based on Frechet derivative. Optics express, 19(23), 22809-19. https://doi.org/10.1364/OE.19.022809
Davidoiu, V, et al. "Non-linear iterative phase retrieval based on Frechet derivative." Optics express vol. 19,23 (2011): 22809-19. doi: https://doi.org/10.1364/OE.19.022809
Davidoiu V, Sixou B, Langer M, Peyrin F. Non-linear iterative phase retrieval based on Frechet derivative. Opt Express. 2011 Nov 07;19(23):22809-19. doi: 10.1364/OE.19.022809. PMID: 22109160.
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Opt Express. 2011 Nov 07;19(23):22809-19. doi: 10.1364/OE.19.022809.

Non-linear iterative phase retrieval based on Frechet derivative.

Optics express

V Davidoiu, B Sixou, M Langer, F Peyrin

Affiliations

  1. CREATIS, CNRS UMR5220, Inserm U630, INSA-Lyon, Universite Lyon 1, Universite de Lyon, F-69621 Villeurbanne Cedex, France. [email protected]

PMID: 22109160 DOI: 10.1364/OE.19.022809

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.

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