  We present a Machine Learning-based method for tomographic reconstruction of
dense layered objects, with range of projection angles limited to $\pm
$10$^\circ$. Whereas previous approaches to phase tomography generally require
two steps, first to retrieve phase projections from intensity projections and
then perform tomographic reconstruction on the retrieved phase projections, in
our work a physics-informed pre-processor followed by a Deep Neural Network
(DNN) conduct the three-dimensional reconstruction directly from the intensity
projections. We demonstrate this single-step method experimentally in the
visible optical domain on a scaled up integrated circuit phantom. We show that
even under conditions of highly attenuated photon fluxes a DNN trained only on
synthetic data can be used to successfully reconstruct physical samples
disjoint from the synthetic training set. Thus, the need of producing a large
number of physical examples for training is ameliorated. The method is
generally applicable to tomography with electromagnetic or other types of
radiation at all bands.
