It is proposed to use local tomography for optical studies of the internal structure of transparent phase microscopic objects, for example, living cells. From among the many local tomography methods that exist, the algorithms of back projection summation (in which partial derivatives of projections are used as projection data) are chosen. The application of local tomography to living cells is reasonable because, using optical phase microscopy, one can easily obtain projection data in the form of first-order derivatives of projections applying the methods of differential interference contrast and shear interferometry. The mathematical fundamentals of local tomography in differential projections are considered, and a computer simulation of different local tomography methods is performed. A tomographic phase microscope and the results of reconstructing a local tomogram of an erythrocyte from a set of experimental differential projections are described.
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