A procedure is described for a detailed characterization of multilayer analyzers that can be effectively applied to their design, optimization, and application for absolute x-ray spectrometry in the 100 to 10,000 eV photon energy region. An accurate analytical model has been developed that is based upon a simple modification of the dynamical Darwin-Prins theory to extend its application to finite multilayer systems and to the low energy x-ray region. Its equivalence to the optical E&M solution of the Fresnel equations at each interface is demonstrated by detailed comparisons for the reflectivity of a multilayer throughout the angular range of incidence of 0° to 90°. A special spectrograph and an experimental method are described for the measurement of the absolute reflectivity characteristics of the multilayer. The experimental measurements at three photon energies in the 100 to 2000 eV region are fit by the analytical modified Darwin-Prins equation (MDP) for 1(0), generating a detailed characterization of two state-of-the-art multilayers: sputtered tungsten-carbon with 2d 70 A and a molecular lead stearate with 2d 100 A. The fitting parameters that are determined by this procedure are applied to help establish the structural characteristics of these multilayers.
B. L. Henke,
J. Y. Uejio,
H. T. Yamada,
R. E. Tackaberry,
"Characterization Of Multilayer X-Ray Analyzers: Models And Measurements," Optical Engineering 25(8), 258937 (1 August 1986). https://doi.org/10.1117/12.7973933