New method of a tomographic microscopy with spatially incoherent illumination is proposed. Earlier, in our works for reconstruction of a refractive index with spatial distribution of 3D phase samples, a method of tomographic microscopy with the coherent light was used. Main disadvantage of this scheme is use of a coherent light, which brings to appearance the phase noise in projection data. Spatially incoherent tomographic microscope is based on the Linnik phase-shifting interference microscope reflected type. Using interferometry with large source of the monochromatic light allows greatly improve a quality of phase projections by averaging of interference patterns. For tomographic mode of Linnik microscope working and obtaining the oblique illumination of sample method for displacing a light source is used. Observation angle range for 100 X oil-immersion objective, N.A. equals 1.25, is 90 degrees. This method allows realizing a two-dimensional scanning trajectory for sample observation. Particularities of tomography for the phase objects, placed near plane mirror, are considered. So, a viewing angle range can be reduced to 90 degree, and sample is complement by its mirror reflection. The iterative algorithms for limited-angle tomographic reconstruction were used. Experimental results on three-dimensional reconstruction of the single human blood cell (erythrocyte) are presented.