Numerical reconstruction of fine structure in obscured backscattering spectra

Revelation of details which are hidden in a backscattering spectrum due to finite apparatus resolution demands the numerical solution of a linear Fredholm integral equation of the first kind with only approximately known and near-singular kernel. Unphysical oscillations of the solution are largely avoided by properly chosen smoothness conditions. Adequate algebraization of the problem is achieved by approximation of the solution by a cubic spline function. Reliability of the approach is studied by mathematical experiments with realistic kernels.