  We continue the development of X-ray tomography in sub-Riemannian geometry.
Using the Fourier Transform adapted to the group structure, we generalize the
Fourier Slice Theorem to the class of H-type groups. The Fourier Slice Theorem
expresses the X-ray transform as the composition of a Fourier restriction and
multiplication operator. We compute the spectral resolution for the resulting
operator-valued multiplier, which we use to show that an integrable function on
an H-type group is determined by its integrals over sub-Riemannian geodesics.
We also relate the support of the X-ray transform $If$ to the support of $f$ in
frequency space. These results given explicit answers to the injectivity
question in a class of geometries with an abundance of conjugate points.
