Single-distance phase retrieval algorithm for Bragg Magnifier microscope

Fast Fresnel propagation through a set of inclined reflecting planes applicable for X-ray imaging

We present a fast and accurate method for wave propagation through a set of inclined reflecting planes. It is based on the coordinate transformation in reciprocal space leading to a diffraction integral, which can be calculated only by using two 2D Fast Fourier Transforms and one 2D interpolation. The method is numerically tested, and comparisons with standard methods show its superiority in both computational speed and accuracy. The direct application of this method is found in the X-ray phase contrast imaging using the Bragg magnifier-an optics consisting of crystals asymmetrically diffracting in Bragg geometry.

Phase retrieval for arbitrary Fresnel-like linear shift-invariant imaging systems suitable for tomography

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.

Subsampled phase retrieval for temporal resolution enhancement in lensless on-chip holographic video

On-chip holographic video is a convenient way to monitor biological samples simultaneously at high spatial resolution and over a wide field-of-view. However, due to the limited readout rate of digital detector arrays, one often faces a tradeoff between the per-frame pixel count and frame rate of the captured video. In this report, we propose a subsampled phase retrieval (SPR) algorithm to overcome the spatial-temporal trade-off in holographic video. Compared to traditional phase retrieval approaches, our SPR algorithm uses over an order of magnitude less pixel measurements while maintaining suitable reconstruction quality. We use an on-chip holographic video setup with pixel sub-sampling to experimentally demonstrate a factor of 5.5 increase in sensor frame rate while monitoring the in vivo movement of Peranema microorganisms.