5 January 2001 Global optimization and reflectivity data fitting for x-ray multilayer mirrors by means of genetic algorithms
Author Affiliations +
The x-ray reflectivity of a multilayer is a non-linear function of many parameters (materials, layer thicknesses, densities, roughness). Non-linear fitting of experimental data with simulations requires to use initial values sufficiently close to the optimum value. This is a difficult task when the space topology of the variables is highly structured, as in our case. The application of global optimization methods to fit multilayer reflectivity data is presented. Genetic algorithms are stochastic methods based on the model of natural evolution: the improvement of a population along successive generations. A complete set of initial parameters constitutes an individual. The population is a collection of individuals. Each generation is built from the parent generation by applying some operators (e.g. selection, crossover, mutation) on the members of the parent generation. The pressure of selection drives the population to include 'good' individuals. For large number of generations, the best individuals will approximate the optimum parameters. Some results on fitting experimental hard x-ray reflectivity data for Ni/C multilayers recorded at the ESRF BM5 are presented. This method could be also applied to the help in the design of multilayers optimized for a target application, like for an astronomical grazing-incidence hard X-ray telescopes.
© (2001) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Manuel Sanchez del Rio, Manuel Sanchez del Rio, Giovanni Pareschi, Giovanni Pareschi, "Global optimization and reflectivity data fitting for x-ray multilayer mirrors by means of genetic algorithms", Proc. SPIE 4145, Advances in X-Ray Optics, (5 January 2001); doi: 10.1117/12.411624; https://doi.org/10.1117/12.411624

Back to Top