Opt Express 2011 Jun 20;1913:12066-73. doi: 10.1364/OE.19.012066.

Single-distance phase retrieval at large phase shifts.

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For coherent X-ray imaging of pure phase objects we study the reliability of linear relations in phase-retrieval algorithms based on a single intensity map after free-space propagation. For large phase changes and/or large propagation distances we propose two venues of working beyond linearity: Projection onto an effective, linear and local model in Fourier space and expansion of intensity contrast in powers of object-detector distance. We apply both algorithms successfully to simulated data.

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