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Based on phase retrieval, lensless coherent imaging and in particularholography offers quantitative phase and amplitude images. This is ofparticular importance for spectral ranges where suitable lenses arechallenging, such as for hard x-rays. Here, we propose a phase retrievalapproach for inline x-ray holography based on Tikhonov regularization appliedto the full nonlinear forward model of image formation. The approach can beseen as a nonlinear generalization of the well-establishedcontrast-transfer-function (CTF) reconstruction method. While similar methodshave been proposed before, the current work achieves nonlinear, constrainedphase retrieval at competitive computation times. We thus enablehigh-throughput imaging of optically strong objects beyond the scope of CTF.Using different examples of inline holograms obtained from illumination by ax-ray waveguide-source, we demonstrate superior image quality even for sampleswhich do not obey the assumption of a weakly varying phase. Since the presentedapproach does not rely on linearization, we expect it to be well suited alsofor other probes such as visible light or electrons, which often exhibit strongphase interaction.

Fast algorithms for nonlinear and constrained phase retrieval in near-field X-ray holography based on Tikhonov regularization