In the early 1990’s [App. Opt. 32(19), 3344-531 (1993)], Church and Takacs pointed out that the specification of surface figure and finish of x-ray mirrors must be based on their performance in the beamline optical system. In the present work, we demonstrate the limitations of specification, characterization, and performance evaluation based on the totally statistical approach, including root-mean-square (rms) roughness and residual slope variation, evaluated over the spatial frequency bandwidths that are system specific, and a more refined statistical description of the surface morphology based on the power spectral density (PSD) distribution. We show that the limitations are fatal, especially, in the case of highly collimated coherent x-ray beams, like beams from X-ray Free Electron Lasers (XFELs). The limitations arise due to the deterministic character of the surface profile data for a definite mirror, while the specific correlation properties of the surface are essential for the performance of the entire x-ray optical system. As a possible way to overcome the problem, we treat a method, suggested in [Opt. Eng. 51(4), 046501, 2012] and based on an autoregressive moving average (ARMA) modeling of the slope measurements with a limited number of parameters. The effectiveness of the approach is demonstrated with an example peculiar to the x-ray optical systems under design at the European XFEL.

Date Published: 17 September 2014
PDF: 19 pages
Proc. SPIE 9209, Advances in Computational Methods for X-Ray Optics III, 92090F (17 September 2014); doi: 10.1117/12.2062085

Published in SPIE Proceedings Vol. 9209:
Advances in Computational Methods for X-Ray Optics III
Manuel Sanchez del Rio; Oleg Chubar, Editor(s)