X-ray diffraction imaging
The purpose of RCI-methods is the numerical reconstruction of a crystal surface to detect defects (dislocations, point defects, etc.). The experiment consists of the measuring of 2D-series of rocking curves with a CCD-detector. Thus obtained 3D-intensity distribution (x,y,Theta)(x,y are coordinates and Theta is the Bregg-angle) is the input information for development of our techniques (solution methods of inverse problems) - defining the crystal surface topology.
From a mathematical view inverse problems are operator equations, which have to be solved. These equations are typically ill-posed (instable according to Hadamard), i.e. they either are ambiguous or small changes in input data cause big changes in the output data (i.e. in the solution). Such artifacts should be avoided in the solution process by special techniques - regularization (stabilization). These in turn depend on properties of the operators (matrices).
We have developed numerical algorithms that lead to a stable solution of the inverse problem. These algoritms are being applied to specific problems.