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Opt Express. 2010 Dec 6;18(25):25771-85. doi: 10.1364/OE.18.025771.

Nonlinear phase retrieval from single-distance radiograph.

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Laboratorium f¨ur Applikationen der Synchrotronstrahlung Karlsruher Institut für Technologie, Postfach 6980, D-76128 Karlsruhe, Germany.


Phase contrast in the object plane of a phase object is retrieved from intensity contrast at a {\sl single} object-detector distance. Expanding intensity contrast and phase shift in the detector plane in powers of object-detector distance, phase retrieval is performed beyond the solution to the linearized transport-of-intensity equation. The expansion coefficients are determined by the entire paraxial wave equation. The Laplacian of the phase shift in the object plane thus is written as a local expression linear in the intensity contrast and nonlinear in the phase shift in the object plane. A perturbative approach to this expression is proposed and tested with simulated phantom data.

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