Single-shot quantitative phase gradient microscopy using physics-based untrained neural network phase retrieval

Single-shot quantitative phase gradient microscopy (ss-QPGM) enables quantitative phase imaging (QPI) based on differential interference contrast (DIC) microscopy. In ss-QPGM, the analyzer is replaced by a quarter-wave plate and a polarization camera, allowing for phase gradient extraction from a single intensity measurement. The quantitative phase image is reconstructed via numerical integration, but direct integration along a single axis introduces artifacts and phase errors due to missing frequency response along the axis of orthogonal to the shear axis and noise-induced streak lines. In this work, we propose a phase retrieval method for ss-QPGM using an untrained neural network (UNN), which integrates physical priors without requiring paired ground truth and input datasets, overcoming the limitations of traditional regularization methods such as Tikhonov regularization and the alternating direction method of multipliers (ADMM) with total variation (TV) regularization. We demonstrate that the UNN approach not only offers superior phase reconstruction but also alleviates artifacts induced by missing frequency response along the axis and noise-induced streak lines, as shown by phase images of a calibrated target and biological samples.