  Diffraction microtomography in coherent light is foreseen as a promising
technique to image transparent living samples in three dimensions without
staining. Contrary to conventional microscopy with incoherent light, which
gives morphological information only, diffraction microtomography makes it
possible to obtain the complex optical refractive index of the observed sample
by mapping a three-dimensional support in the spatial frequency domain. The
technique can be implemented in two configurations, namely, by varying the
sample illumination with a fixed sample or by rotating the sample using a fixed
illumination. In the literature, only the former method was described in
detail. In this report, we precisely derive the three-dimensional frequency
support that can be mapped by the sample rotation configuration. We found that,
within the first-order Born approximation, the volume of the frequency domain
that can be mapped exhibits a missing part, the shape of which resembles that
of an apple core. The projection of the diffracted waves in the frequency space
onto the set of sphere caps covered by the sample rotation does not allow for a
complete mapping of the frequency along the axis of rotation due to the finite
radius of the sphere caps. We present simulations of the effects of this
missing information on the reconstruction of ideal objects.
