Analysis of the solution of the inverse refraction problem

The paper examines two methods for solving the inverse refraction problem involved in the radio probing of the atmosphere of the earth and other planets (Mars, Venus, etc.). Both methods consist in the reduction of the inverse problem to the solution of a Fredholm equation of the first kind, which can be obtained by the integral-transform technique. In the first method, the unknown function is expressed as a double Fourier cosine transform and Abel transform of the experimental function. In the second method, the problem of determining the refractive-index profile is solved by the double discrete Fourier transformation. The method based on digital filtering is shown to be more effective for determining the height dependence of the refractive index.