  We study an inverse uniqueness with a knowledge of spectral data in the
interior transmission problem defined by an index of refraction in a simple
domain. We expand the solution in such a domain into a series of one
dimensional problems. For each one dimensional problem, we apply a value
distribution theory in complex analysis to describe the eigenvalues of the
system. By the orthogonality of the one dimensional system, we consider the
uniqueness on the perturbation along each given incident angle.
