Single-shot Phase Retrieval from a Fractional Fourier Transform Perspective

TL;DR

This paper introduces a novel single-shot phase retrieval method using fractional Fourier transform measurements combined with self-supervised neural networks, effectively recovering signals from a single intensity measurement.

Contribution

It presents a new FrFT-based measurement model and a self-supervised reconstruction scheme that improve phase retrieval accuracy and relax previous measurement requirements.

Findings

Effective retrieval of amplitude and phase from a single measurement

Addresses aliasing artifacts in Fresnel diffraction calculations

Reduces need for oversampled or multiple measurements

Abstract

The realm of classical phase retrieval concerns itself with the arduous task of recovering a signal from its Fourier magnitude measurements, which are fraught with inherent ambiguities. A single-exposure intensity measurement is commonly deemed insufficient for the reconstruction of the primal signal, given that the absent phase component is imperative for the inverse transformation. In this work, we present a novel single-shot phase retrieval paradigm from a fractional Fourier transform (FrFT) perspective, which involves integrating the FrFT-based physical measurement model within a self-supervised reconstruction scheme. Specifically, the proposed FrFT-based measurement model addresses the aliasing artifacts problem in the numerical calculation of Fresnel diffraction, featuring adaptability to both short-distance and long-distance propagation scenarios. Moreover, the intensity measurement in the FrFT domain proves highly effective in alleviating the ambiguities of phase retrieval and relaxing the previous conditions on oversampled or multiple measurements in the Fourier domain. Furthermore, the proposed self-supervised reconstruction approach harnesses the fast discrete algorithm of FrFT alongside untrained neural network priors, thereby attaining preeminent results. Through numerical simulations, we demonstrate that both amplitude and phase objects can be effectively retrieved from a single-shot intensity measurement using the proposed approach and provide a promising technique for support-free coherent diffraction imaging.