We consider the inverse scattering problem arising in an optical coating deposited onto photovoltaic solar cells. Our objective is to optimize the space-dependent refractive index in this inhomogeneous cover to enhance the efficiency of the solar cells. The relevant model yields a boundary value problem for the one-dimensional Helmholtz equation, from which we derive an equivalent integral equation formulation. The resulting inverse problem is nonlinear and ill-posed. Firstly, we use the Born approximation to linearize the mathematical model. For regularizing, we apply the method of the Approximate Inverse. For the purpose of comparison, we also make numerical tests using Tikhonov-Phillips as a regularization method. Secondly, we treat the nonlinear problem using the method of the Approximate Inverse for the quadratic problem. Numerical results are presented to compare the efficiency of the methods.
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