  In this work we consider the inverse problem of reconstructing the optical
properties of a layered medium from an elastography measurement where optical
coherence tomography is used as the imaging method. We hereby model the sample
as a linear dielectric medium so that the imaging parameter is given by its
electric susceptibility, which is a frequency- and depth-dependent parameter.
Additionally to the layered structure (assumed to be valid at least in the
small illuminated region), we allow for small scatterers which we consider to
be randomly distributed, a situation which seems more realistic compared to
purely homogeneous layers. We then show that a unique reconstruction of the
susceptibility of the medium (after averaging over the small scatterers) can be
achieved from optical coherence tomography measurements for different
compression states of the medium.
