Application of time-invariant linear filter approximation to parametrization of one- and two-dimensional surface metrology with high quality x-ray optics

Valeriy V. Yashchuk; Yury N. Tyurin; Anastasia Y. Tyurina

doi:10.1117/12.2024662

27 September 2013 Application of time-invariant linear filter approximation to parametrization of one- and two-dimensional surface metrology with high quality x-ray optics

Valeriy V. Yashchuk, Yury N. Tyurin, Anastasia Y. Tyurina

Author Affiliations +

Proceedings Volume 8848, Advances in X-Ray/EUV Optics and Components VIII; 88480H (2013) https://doi.org/10.1117/12.2024662
Event: SPIE Optical Engineering + Applications, 2013, San Diego, California, United States

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.

Citation Download Citation

Valeriy V. Yashchuk, Yury N. Tyurin, and Anastasia Y. Tyurina "Application of time-invariant linear filter approximation to parametrization of one- and two-dimensional surface metrology with high quality x-ray optics", Proc. SPIE 8848, Advances in X-Ray/EUV Optics and Components VIII, 88480H (27 September 2013); https://doi.org/10.1117/12.2024662

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