Modeling surface topography of state-of-the-art x-ray mirrors as a result of stochastic polishing process: recent developments

Valeriy V. Yashchuk; Gary Centers; Yuri N. Tyurin; Anastasia Tyurina

doi:10.1117/12.2238260

8 September 2016 Modeling surface topography of state-of-the-art x-ray mirrors as a result of stochastic polishing process: recent developments

Valeriy V. Yashchuk, Gary Centers, Yuri N. Tyurin, Anastasia Tyurina

Author Affiliations +

Proceedings Volume 9962, Advances in Metrology for X-Ray and EUV Optics VI; 99620G (2016) https://doi.org/10.1117/12.2238260
Event: SPIE Optical Engineering + Applications, 2016, San Diego, California, United States

Abstract

Recently, an original method for the statistical modeling of surface topography of state-of-the-art mirrors for usage in xray optical systems at light source facilities and for astronomical telescopes [Opt. Eng. 51(4), 046501, 2012; ibid. 53(8), 084102 (2014); and ibid. 55(7), 074106 (2016)] has been developed. In modeling, the mirror surface topography is considered to be a result of a stationary uniform stochastic polishing process and the best fit time-invariant linear filter (TILF) that optimally parameterizes, with limited number of parameters, the polishing process is determined. The TILF model allows the surface slope profile of an optic with a newly desired specification to be reliably forecast before fabrication. With the forecast data, representative numerical evaluations of expected performance of the prospective mirrors in optical systems under development become possible [Opt. Eng., 54(2), 025108 (2015)]. Here, we suggest and demonstrate an analytical approach for accounting the imperfections of the used metrology instruments, which are described by the instrumental point spread function, in the TILF modeling. The efficacy of the approach is demonstrated with numerical simulations for correction of measurements performed with an autocollimator based surface slope profiler. Besides solving this major metrological problem, the results of the present work open an avenue for developing analytical and computational tools for stitching data in the statistical domain, obtained using multiple metrology instruments measuring significantly different bandwidths of spatial wavelengths.

Citation Download Citation

Valeriy V. Yashchuk, Gary Centers, Yuri N. Tyurin, and Anastasia Tyurina "Modeling surface topography of state-of-the-art x-ray mirrors as a result of stochastic polishing process: recent developments", Proc. SPIE 9962, Advances in Metrology for X-Ray and EUV Optics VI, 99620G (8 September 2016); https://doi.org/10.1117/12.2238260

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