X-ray near field holography has proven to be a powerful 2D and 3D imaging technique with applications ranging from biomedical research to material sciences. To reconstruct meaningful and quantitative images from the measurement intensities, however, it relies on computational phase retrieval which in many cases assumes the phase-shift and attenuation coefficient of the sample to be proportional. Here, we demonstrate an efficient phase retrieval algorithm that does not rely on this homogeneous-object assumption and is a generalization of the well-established contrast-transfer-function (CTF) approach. We then investigate its stability and present an experimental study comparing the proposed algorithm with established methods. The algorithm shows superior reconstruction quality compared to the established CTF-based method at similar computational cost. Our analysis provides a deeper fundamental understanding of the homogeneous object assumption and the proposed algorithm will help improve the image quality for near-field holography in biomedical applications
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.