Abstract
We present a generalization of the non-iterative phase retrieval in X-ray phase contrast imaging applicable for an arbitrary linear shift-invariant (LSI) imaging system with a non-negligible amount of free space propagation (termed as Fresnel-like). Our novel approach poses no restrictions on the propagation distance between optical elements of the system. In turn, the requirements are only demanded for the transfer function of the optical elements, which should be approximable by second-order Taylor polynomials. Furthermore, we show that the method can be conveniently used as an initial guess for iterative phase retrieval, resulting in faster convergence. The proposed approach is tested on synthetic and experimentally measured holograms obtained using a Bragg magnifier microscope – a representative of Fresnel-like LSI imaging systems. Finally, the algorithm is applied to a whole micro-tomographic scan of a biological specimen of a tardigrade, revealing morphological details at the spatial resolution of 300 nm – limiting resolution of the actual imaging system.
Highlights
Phase retrieval is one of the most challenging topics in X-ray full-field phase-contrast tomographic imaging
We present a generalization of the non-iterative phase retrieval in X-ray phase contrast imaging applicable for an arbitrary linear shift-invariant (LSI) imaging system with a non-negligible amount of free space propagation
We present a theoretical treatment for phase retrieval based on contrast transfer function (CTF) approach
Summary
Phase retrieval is one of the most challenging topics in X-ray full-field phase-contrast tomographic imaging. We present a theoretical treatment for phase retrieval based on contrast transfer function (CTF) approach ( called Born approximation [10]) It uses only single intensity measurement per tomographic projection and at the same time, it relaxes the restrictions put on the propagator of the whole setup, allowing us to treat the cases with an arbitrary amount of free space propagation. This is followed by the Conclusion, which summarizes the potential of the proposed method, especially when applied to the case of X-ray imaging with Bragg Magnifier
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