Model-independent inversion of x-ray or neutron reflectivity data

A technique is described for the model-independent analysis of x-ray or neutron reflectivity data. Rather than trying to find just one optimum solution, the idea is to find the set of solutions that are feasible. The approach is based on inversion of the missing phase information using a feasible set approach coupled with a genetic algorithm search for the set of solutions. It does not require previous knowledge of the chemical constituents or any type of initial model, thus adding a higher degree of objectivity to the analysis. The algorithm is tested on both simulated data and observed data. Issues regarding inversion problems and multisolution algorithms, such as the uniqueness of the solutions, are also briefly discussed.