Physics-informed deep learning transport-of-intensity quantitative phase imaging: accurate phase retrieval under partially coherent illumination

Achieving both high reconstruction accuracy and computational efficiency is a long-standing challenge in computational imaging, particularly in phase retrieval—a classic nonlinear inverse problem. This challenge becomes even more pronounced under partially coherent illumination, where a more complex nonlinear image formation model must be inverted, making the phase retrieval process either dependent on restrictive approximations or prohibitively time-consuming. Here, we present physics-informed deep learning transport-of-intensity quantitative phase imaging (PDL-TIQPI), a novel framework that synergizes deep learning with physical models through the alternating direction method of multipliers (ADMM). By integrating the weak object transfer function into the forward image formation model, PDL-TIQPI embeds physical priors into the pseudo-inverse mapping process, improving both accuracy and efficiency while mitigating boundary artifacts and eliminating reliance on weak object approximations. Notably, our method achieves high-precision QPI with minimal training data—fewer than 100 datasets. Experimental validation demonstrates that PDL-TIQPI not only reaches theoretical resolution limits but also resolves fine subcellular structures in live HeLa cells, demonstrating its potential for imaging non-weak objects. By unifying physical modeling and deep learning, PDL-TIQPI significantly reduces training demands, enhances generalization, and offers a robust, efficient solution to the partially coherent phase retrieval problem. Its versatility and robustness set a new benchmark for non-interferometric QPI techniques, paving the way for advanced applications in label-free cell imaging and beyond.