Abstract. We present an optical tomographic diffractive microscope, a device able to image a complex refractive index distribution in three dimensions. Theoretical foundations are first recalled: diffraction under the first Born approximation explains the link between diffracted beam, object frequencies and physical properties of the object. We then describe our experimental setup, recording 2-D interferograms in the image space, and detail the image reconstruction process underlying our tomographic microscope, which involves 2-D transforms of the recorded interferograms, a peculiar 3-D mapping of the data, and a final 3-D Fourier reconstruction. We apply tomographic reconstruction to diatom skeletons, unicellular algae with cell walls made of silica, and compare it to holographic reconstruction. We further apply it to pollen grains and show differences between the real and imaginary parts of the measured complex refractive index. Finally, we also recall alternative tomographic methods.