  Based on phase retrieval, lensless coherent imaging and in particular
holography offers quantitative phase and amplitude images. This is of
particular importance for spectral ranges where suitable lenses are
challenging, such as for hard x-rays. Here, we propose a phase retrieval
approach for inline x-ray holography based on Tikhonov regularization applied
to the full nonlinear forward model of image formation. The approach can be
seen as a nonlinear generalization of the well-established
contrast-transfer-function (CTF) reconstruction method. While similar methods
have been proposed before, the current work achieves nonlinear, constrained
phase retrieval at competitive computation times. We thus enable
high-throughput imaging of optically strong objects beyond the scope of CTF.
Using different examples of inline holograms obtained from illumination by a
x-ray waveguide-source, we demonstrate superior image quality even for samples
which do not obey the assumption of a weakly varying phase. Since the presented
approach does not rely on linearization, we expect it to be well suited also
for other probes such as visible light or electrons, which often exhibit strong
phase interaction.

Image and Video Processing;Optics