Tomographic phase microscopy (TPM) is an emerging optical microscopic technique for bioimaging. TPM uses digital holographic measurements of complex scattered fields to reconstruct three-dimensional refractive index (RI) maps of cells with diffraction-limited resolution by solving inverse scattering problems. In this paper, we review the developments of TPM from the fundamental physics to its applications in bioimaging. We first provide a comprehensive description of the tomographic reconstruction physical models used in TPM. The RI map reconstruction algorithms and various regularization methods are discussed. Selected TPM applications for cellular imaging, particularly in hematology, are reviewed. Finally, we examine the limitations of current TPM systems, propose future solutions, and envision promising directions in biomedical research.
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