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

TL;DR

This paper introduces a fast, nonlinear phase retrieval algorithm based on Tikhonov regularization for near-field X-ray holography, enabling high-quality, high-throughput imaging of strongly scattering objects beyond traditional linear methods.

Contribution

It presents a novel nonlinear, constrained phase retrieval method that generalizes the CTF approach, achieving competitive computation times for complex holographic imaging.

Findings

Superior image quality for strong phase objects

Effective nonlinear, constrained phase retrieval

Applicable to various probes like visible light and electrons

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.