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Proceedings Paper

Application of time-invariant linear filter approximation to parametrization of one- and two-dimensional surface metrology with high quality x-ray optics
Author(s): Valeriy V. Yashchuk; Yury N. Tyurin; Anastasia Y. Tyurina
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Paper Abstract

Numerical simulations of the performance of new x-ray beamlines and those under upgrade require sophisticated and reliable information about the expected surface slope and height distributions of prospective beamline optics before they are fabricated. Ideally, such information is based on metrology data obtained with existing optics, which are fabricated by the same vendor and technology, but generally, have different sizes, and slope and height rms variations. In a recent work [Opt. Eng. 51(4), 046501, 2012], it has been demonstrated that autoregressive moving average (ARMA) modeling of one-dimensional (1D) slope measurements with x-ray mirrors allows a high degree of confidence when fitting the metrology data with a limited number of parameters. With the parameters of the ARMA model, the surface slope profile of an optic with the desired specification can reliably be forecast. Here, we investigate the time-invariant linear filter (TILF) approach to optimally parameterize surface metrology of high quality x-ray optics thought of as a result of a stationary uniform random process. We show that the TILF approximation has all advantages of one-sided AR and ARMA modeling, but it additionally gains in terms of better fitting accuracy and absence of the causality limitation. Moreover, the suggested TILF approach can be directly generalized to 2D random fields. This work is supported by the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

Paper Details

Date Published: 27 September 2013
PDF: 13 pages
Proc. SPIE 8848, Advances in X-Ray/EUV Optics and Components VIII, 88480H (27 September 2013); doi: 10.1117/12.2024662
Show Author Affiliations
Valeriy V. Yashchuk, Lawrence Berkeley National Lab. (United States)
Yury N. Tyurin, Moscow State Univ. (Russian Federation)
Second Star Algonumerics (United States)
Anastasia Y. Tyurina, Scientific Systems Co., Inc. (United States)


Published in SPIE Proceedings Vol. 8848:
Advances in X-Ray/EUV Optics and Components VIII
Ali Khounsary; Shunji Goto; Christian Morawe, Editor(s)

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