Numerical technique for inverse problems of geometrical optics of inhomogeneous media

The synthesis of inhomogeneous lenses, the problems of phase tomography of one-dimensional gradient media in geometrical optics approximation, etc., can be reduced to nonlinear integral equations relatively to an unknown function of the index of refraction. These equations have closed-form solutions in a small number of particular cases. A new technique to solve these problems is proposed. According to this technique, we analyze a layered medium instead of an inhomogeneous one. As a result, we have a stepped-law function of the index of refraction variation. It is possible to decrease the difference between the stepped and the continuous-law functions by increasing the number of layers. Three modifications of this technique: ray, phase and combined, are used to investigate inhomogeneous media where the index of refraction is a function of the Cartesian coordinate or radius. The latter two provide the desired accuracy