Tomographic diffractive microscopy (TDM) is an advanced digital imaging technique, which combines the recording of multiple holograms with the use of inversion procedures to retrieve quantitative information on the sample. In this review, we discuss the basic theory of TDM in the framework of electromagnetism and draw a comparison with conventional widefield microscopes. We describe various implementations of TDM, highlighting their power of resolution. Finally, we present some research perspectives for increasing the potential of this promising new imaging modality.
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