Radial-balanced phase transfer functions for accurate retrieval in quantitative differential phase contrast microscopy

Quantitative differential phase contrast microscopy (qDPC) is a potent quantitative phase imaging (QPI) technique for biological applications due to its high resolution and rapid image acquisition. Traditionally, qDPC employs an asymmetric 12 axis illumination pattern and reconstructs the phase using Tikhonov regularization. Numerous endeavors have been made to enhance qDPC performance, including reducing the number of illumination patterns and refining retrieval algorithms. However, a comprehensive theoretical framework linking illumination patterns to the radial profile of the phase transfer function (PTF) within qDPC microscopy remains largely unexplored, leading to suboptimal phase retrieval. To address this shortage, this study presents a rigorous mathematical derivation of this correlation and introduces an illumination pattern designed to achieve precise phase retrieval based on the desired PTF. The effectiveness of the proposed method was assessed through numerical computations using a customized phantom phase object, demonstrating a phase retrieval accuracy surpassing that of existing qDPC techniques. Further experiments with phase targets corroborated the numerical computation results, demonstrating the advancement of our approach.