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首页> 外文期刊>Optical engineering >Application of the time-invariant linear filter approximation to parametrization of surface metrology with high-quality x-ray optics
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Application of the time-invariant linear filter approximation to parametrization of surface metrology with high-quality x-ray optics

机译：时不变线性滤波器近似在高质量X射线光学器件表面计量学参数化中的应用

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摘要

We investigate the time-invariant linear filter (TILF) approach to optimally parameterize the surface metrology of high-quality x-ray optics considered as a result of a stationary uniform random process. The approach is a generalization of autoregressive moving average (ARMA) modeling of one-dimensional slope measurements with x-ray mirrors considered. We show that the suggested TILF approximation has all the advantages of one-sided autoregressive and ARMA modeling, allowing a high degree of confidence when fitting the metrology data with a limited number of parameters. Compared to ARMA modeling, the TILF approximation gains in terms of better fitting accuracy and the absence of the causality limitation. Moreover, the TILF approach can be directly generalized to two-dimensional random fields. With the determined model parameters, the surface topography of prospective beamline optics can be reliably forecast before they are fabricated. These forecast metrology data, containing essential and reliable statistical information about the existing optics which are fabricated by the same vendor and technology, but generally, have different sizes, and slope and height root-mean-square variations, are vitally needed for numerical simulations of the performance of new x-ray beamlines and those under upgrade.
机译：我们研究了时不变线性滤波器（TILF）的方法，以对作为稳定均匀随机过程结果的高质量X射线光学器件的表面度量进行最佳参数化。该方法是考虑了X射线镜的一维斜率测量的自回归移动平均（ARMA）建模的一般化。我们表明，建议的TILF逼近具有单面自回归和ARMA建模的所有优点，当使用有限数量的参数拟合度量数据时，可以提供很高的置信度。与ARMA建模相比，TILF近似在更好的拟合精度和因果关系的限制方面获得了收益。此外，TILF方法可以直接推广到二维随机场。利用确定的模型参数，可以在制造前瞻性束线光学器件之前可靠地预测其表面形貌。这些预报计量数据包含有关由相同厂商和技术制造的现有光学器件的基本且可靠的统计信息，但通常具有不同的尺寸，并且斜率和高度均方根变化非常重要。新的X射线束线和正在升级的束线的性能。

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