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

Abstract

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.

3D imaging of neuronal inclusions and protein aggregates in human neurodegeneration by multiscale X-ray phase-contrast tomography

“…Projections were acquired and saved using the .tiff or .raw format. After flat field and dark image correction, operating in the holographic regime, phase retrieval was performed using either the contrast transfer function (CTF, [53,54]), the nonlinear Tikhonov (NLT, [55]) or a Paganin-based iterative scheme [56] (see supplementary information). On the phase retrieved projections, ring removal techniques were conducted (only random displacement at SR2-setup) as well as an automatic rotation axis correction.…”