Hybrid Transport-of-Intensity and Polarization Differential Phase Contrast for Extended Spatial-Frequency Phase Imaging

Abstract

The Transport-of-Intensity Equation (TIE) and polarization differential phase contrast (pDPC) exhibit transfer characteristics that limit their use as standalone quantitative phase imaging modalities. TIE provides stable recovery of low spatial frequencies but attenuates fine structure, while pDPC enhances phase gradients but is intrinsically insensitive near zero frequency. We present a hybrid reconstruction framework that combines a single-shot pDPC measurement with an in-focus-defocused TIE image pair and fuses the resulting phase estimates in the Fourier domain using frequency-selective weighting. The illumination geometry is co-designed to enforce angular separation between modalities, enabling high-frequency phase-gradient acquisition in a single exposure while preserving low-frequency sensitivity through low-numerical-aperture symmetric illumination. The proposed method requires three intensity measurements without requiring interferometric stability or sequential asymmetric illumination. Experimental results demonstrate improved phase fidelity across spatial frequencies, reduced halo artifacts, and enhanced recovery of both smooth and fine structural features. This approach provides a compact and robust method that moves towards extended spatial-frequency phase imaging for dynamic and resource-constrained applications.