A new interpretation of X-ray reflectivity in real space for low contrast multilayer systems I. Mathematical algorithm and numerical simulations

Abstract It is shown that X-ray specular reflectivity may be described in terms of canonical distribution functions (CDFs) p j ( z ) which is a probability to find an element of sort j at a depth z from the sample surface. The problem reduces to determine K CDFs, where K is the number of elements in the multilayer sample. Using the properties of the canonical functions, we have introduced the interface function p int ( z ) and use it as one unknown function at solving the integral equation. The integral Fredholm equation of the first kind belongs to the class of ill-posed problems and for solving it needs special methods. We use the Tikhonov regularization method. This method is applied to study the low contrast multilayer systems.