An Efficient Method for the Experimental Characterization of Periodic
Multilayer Mirrors: A Global Optimization Approach
Abstract
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 X-ray reflectivity (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.