We first obtain a frequency-space equation of diffraction tomography for the electric field vector, within the first-order Born approximation, using a simplified formalism resulting from using three-dimensional spatial frequencies and replacing outgoing waves by linear combinations of homogeneous plane waves. A coherent optical diffraction tomographic microscope is then described, in which a sample is successively illuminated by a series of plane waves having different directions, each scattered wave is recorded by phase-shifting interferometry, and the object is then reconstructed from these recorded waves. The measurement process in this device is analysed taking into account the illuminating wave, the wave scattered by the sample, the reference wave, and the phase relations between these waves. This analysis yields appropriate equations that take into account the characteristics of the reference wave and compensate random phase shifts. It makes it possible to obtain a high-resolution three-dimensional frequency representation in full conformity with theory. The experimentally obtained representations show index and absorptivity with a resolution limit of about a quarter of a wavelength, and have a depth of field of about 40 microm.