Specification of x-ray mirrors in terms of system performance: new twist to an old plot

Valeriy V Yashchuk,Liubov V Samoylova,Igor V Kozhevnikov

doi:10.1117/1.oe.54.2.025108

Abstract

In the early 1990s, 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. We demonstrate the limitations of specification, characterization, and performance evaluation based on conventional statistical approaches, including root-mean-square roughness and residual slope variation, evaluated over spatial frequency bandwidths that are system specific, and a more refined description of the surface morphology based on the power spectral density distribution. We show that these 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 by Yashchuk and Yashchuk in 2012, based on an autoregressive moving average modeling of the slope measurements with a limited number of parameters. The effectiveness of the approach is demonstrated with an example specific to the x-ray optical systems under design at the European XFEL.

Highlights

The unique properties of modern synchrotron radiation sources and x-ray free electron lasers (XFELs), including their high flux and brightness, and, in the case of XFEL, high coherence and time resolution, make them indispensable tools in the exploration in physics, chemistry, biology, and material science
We demonstrate the limitations of specification, characterization, and performance evaluation based on conventional statistical approaches, including root-mean-square roughness and residual slope variation, evaluated over spatial frequency bandwidths that are system specific, and a more refined description of the surface morphology based on the power spectral density distribution
We investigate the applicability of the power spectral density (PSD)-based evaluation of beamline performance of prospective x-ray optics for XFELs, for the case when dedicated optical systems deliver the beams over distances of hundreds of meters

Summary

Introduction

The unique properties of modern synchrotron radiation sources and x-ray free electron lasers (XFELs), including their high flux and brightness, and, in the case of XFEL, high coherence and time resolution, make them indispensable tools in the exploration in physics, chemistry, biology, and material science. The uniqueness of the optics and the limited number of proficient vendors makes the fabrication of state-of-the-art x-ray optics extremely time consuming and expensive. The numerical simulation of the performance of optics for new beamlines and those under upgrade requires refined and reliable information about the expected surface slope and height distributions of the planned x-ray optics before they are fabricated. Such information should be based on metrology data from existing mirrors, fabricated by the same vendor and technology, but may have different desired sizes, as well as slope and height root-mean-square (rms) variations

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