Computational approaches in 3D quantitative phase Imaging: Current and future trends in cellular imaging

Phase retrieval methods are essential in computational imaging, enabling high-resolution, non-invasive imaging across various fields. This review focuses on the Transport of Intensity Equation (TIE) and its role in Quantitative Phase Imaging (QPI). We compare TIE with Shack-Hartmann and Pyramid wavefront sensors, as well as iterative methods like the Gerchberg-Saxton (GS) algorithm. While iterative methods offer flexibility, TIE provides a rapid, low-cost solution, making it ideal for real-time phase recovery. Advancements in spatial light modulators (SLMs) and electrically tunable lenses (ETLs) have enhanced TIE, achieving nanometer-scale sensitivity in milliseconds. Despite challenges in clinical translation, TIE has demonstrated potential in cellular morphology analysis and dynamic studies. This review highlights key strengths, limitations, and future directions for phase retrieval in computational imaging.