Numerical computations on one-dimensional inverse scattering problems

In this note we present an approximate method to detemine the index of refraction of a dielectric obstacle. For simplicity we treat one-dimensional models of electromagnetic scattering. The governing equations yield a second-order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yields an additional initial condition. We approximate the index of refraction by a kth-order spline which can be written as a linear combination of B-splines. For N/2 distinct reflection coefficients, the resulting N/2 initial value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.