Single-shot phase retrieval: a holography-driven problem in Sobolev space

TL;DR

This paper develops a single-shot phase retrieval method in Sobolev space for dynamic signals using interference intensity measurements with a single reference wave, achieving exponential convergence.

Contribution

It introduces a novel single-shot PSDH framework based on nonnegative refinable functions and Sobolev space analysis, extending traditional multi-shot holography methods.

Findings

Exponential convergence of the approximation to the true signal.

Applicable to dynamic signals requiring single-shot measurements.

Theoretical connection to the transport of intensity equation (TIE).

Abstract

The phase-shifting digital holography (PSDH) is a widely used approach for recovering signals by their interference (with reference waves) intensity measurements. Such measurements are traditionally from multiple shots (corresponding to multiple reference waves). However, the imaging of dynamic signals requires a single-shot PSDH approach, namely, such an approach depends only on the intensity measurements from the interference with a single reference wave. In this paper, based on the uniform admissibility of plane (or spherical) reference wave and the interference intensity-based approximation to quasi-interference intensity, the nonnegative refinable function is applied to establish the single-shot PSDH in Sobolev space. Our approach is conducted by the intensity measurements from the interference of the signal with a single reference wave. The main results imply that the approximation version from such a single-shot approach converges exponentially to the signal as the level increases. Moreover, like the transport of intensity equation (TIE), our results can be interpreted from the perspective of intensity difference.