Simplified single-shot geometries for quantitative phase imaging using the transport of intensity equation

The transport of intensity equation (TIE) has emerged as a powerful and versatile approach for retrieving phase information from intensity measurements. It offers label-free high-resolution imaging capability. In the TIE, at least two intensity recordings are required for phase retrieval for which either the sample or sensor is mechanically displaced, which creates an error in computation. Single-shot imaging is a technique where all essential intensity measurements needed to solve the TIE are captured simultaneously within a single exposure. Therefore, it overcomes the usual problems of the TIE. In this paper, we propose two simplified versions of single-shot experimental geometries following the Michelson interferometer architecture for phase imaging using the TIE. Through an optical experiment, we demonstrate the efficacy and versatility of the single-shot imaging technique with different object samples.