On the Solution of an Ill-Posed Non-Linear Fredholm Integral Equation Connected with an Inverse Problem of Thin Film Optics

Abstract

We carry out a theoretical analysis of the simultaneous identification of geometrical thick-ness and refractive index profile for inhomogeneous single layer systems from indirect mea-surements. The problem leads to a non-linear integral equation of the first kind with smooth kernel. We present a uniqueness theorem for monotone solutions referring to the Hausdorff moment problem.