An Efficient Method for the Experimental Characterization of Periodic Multilayer Mirrors: A Global Optimization Approach

This study proposes a new approach to periodic multilayer mirrors (PMMs) characterizations based on measured X-ray reflectivity (XRR) data. Here, XRR data are used to reconstruct the internal structure of PMMs using grazing incidence XRR (GIXR). A mathematical model of electromagnetic wave reflection by PMMs is employed to implement forward prediction, which will then be used iteratively in a global optimization framework in order to reconstruct the PMM unknown structure parameters. A typical simulation of PMM often includes tens to thousands of unknown structure parameters, rendering standard curve fitting methods cumbersome and impractical. To make the PMM characterization method computationally feasible, this study combines implementation of the Levy flight particle swarm optimization (LFPSO) algorithm with a parallelized version of the electromagnetic solver X-Ray Calc in order to simplify the model parameter reconstruction process. Levy flight, a random walk wherein the Levy distribution is used to determine step size, is a more efficient search strategy for global optimization because of the long jumps made by the particles. It is demonstrated that a PMM model with up to thousands of structure parameters can be reconstructed within several seconds on a regular workstation. The algorithm is tested with both measured and theoretical XRR data using in-house fabricated PMMs with known structures. Excellent agreement with the actual structures is observed, which is attained in short computation time. The new approach avoids manual curve fitting and simplified GIXR analysis and is observed to scale linearly with the size of the PMM structure, making it attractive for X-ray optics systems involving large-and-complex reflecting mirrors.