Isotropic quantitative phase imaging with optimal differential phase contrast illumination scheme

Quantitative phase imaging (QPI), which provides unique imaging capabilities for optical thickness variation of living cells and tissues without the need for specific staining or exogenous contrast agents (e.g., dyes or fluorophores), has emerged as an invaluable optical tool for biomedical research. Differential phase contrast (DPC) is the most promising QPI approach to high resolution label-free cellular dynamic imaging because of its advantages of higher imaging efficiency, higher accuracy, and higher stability. Typically, illuminations in DPC systems are designed with 2-axis half-circle amplitude patterns, which however results in a non-isotropic phase transfer function (PTF). Furthermore, the frequency responses of the PTFs have not been fully optimized, leading to suboptimal phase contrast and signal-to-noise ratio (SNR) for phase reconstruction. In this paper, we derive the optimal illumination scheme to maximize the PTF response for both low and high frequencies (from 0 to 2NAobj ), and meanwhile achieve perfectly isotropic PTF with only 2-axis intensity measurements. We present the theoretical analysis, simulations, and experimental results demonstrating that our optimal illumination scheme is a simple, efficient, and stable approach for label-free quantitative cell imaging with subcellular resolution.