Limited-angle hybrid optical diffraction tomography system with total-variation-minimization-based reconstruction

Abstract

The case of diffraction tomography with limited angle of projections is discussed from the algorithmic and experimental points of view. To reconstruct a three-dimensional distribution of refractive index of a micro-object under study, we use a hybrid approach based on the simultaneous algebraic reconstruction technique (SART) enhanced by a compressed sensing reconstruction technique. It enables us to apply the standard computed tomography algorithms (which assume that the rays are traveling in straight lines through the object) for phase data obtained by means of digital holography. We present the results of analysis of a phantom and real objects obtained by applying SART with anisotropic total variation (ATV) minimization. The real data are acquired from an experimental setup based on a Mach–Zehnder interferometer configuration. Also, it is proven that in the case of simulated data, the limited number of projections captured in a limited angular range can be compensated by a higher number of iterations of the algorithm. We also show that the SART + ATV method applied for experimental data gives better results than the data replenishment algorithm.