  Motivated by non-destructive testing of optical fiber, we consider the
problem of determining the index of refraction of a two-dimensional medium from
magnitude of the total field resulting from known incident plane waves at a
fixed frequency. The finiteness of the fiber cross section allows us to assume
that the index of refraction is variable over a compact set. The measurement
set is a closed curve, e.g., a circle of fixed radius, containing the fiber
cross section. We use complex geometric optics (CGO) solutions to show that the
inverse problem for the unknown index of refraction is unique in $C^{k}$ for
large enough $k$. The key tool in this work is the multi-term expansion of the
CGO solutions which we rely on to address the uniqueness question.

Analysis of PDEs