Super-resolution, multi-plane phase retrieval via amplitude flow variants

Abstract

In the Fresnel regime, super-resolution multi-plane phase retrieval (MPPR) often requires upsampling the captured diffraction patterns via experimental or computational means to satisfy the sampling conditions imposed by the traditional angular spectrum method which quickly becomes computationally expensive for large upsampling ratios. Furthermore, the vanilla single-beam multiple-intensity reconstruction and amplitude-phase retrieval algorithms often used in MPPR are either susceptible to noise and misalignment, or suffer from slow convergence. In this paper, we introduce a new approach to super-resolution MPPR without requiring upsampling. Super-resolution is achieved by utilizing the shifted Fresnel propagator to perform forward and backward propagation, enabling the mapping of different pixel sizes between the sample and detector plane. In addition, we incorporate the gradient descent updates of amplitude flow variants due to their accelerated convergence speed as compared to the traditional MPPR methods. Our simulation studies show that the proposed algorithms are able to reconstruct the target sample with resolution limited only by the diffraction limit despite using a camera with much larger pixel sizes, corresponding to an upsampling ratio ≥7.0. We also demonstrate their robustness against noise and misalignment in experiment, outperforming the super-resolution equivalent of the standard APR algorithm in reconstruction quality and speed.