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9 September 2009 Calculating BRDFs from surface PSDs for moderately rough optical surfaces
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Abstract
Image degradation due to scattered radiation is a serious problem in many short wavelength (X-ray/EUV) imaging systems. Most currently-available image analysis codes require the scatter behavior (BRDF data) as input in order to calculate the image quality from such systems. This BRDF data is difficult to measure and rarely available for the operational wavelengths of interest. Since the smooth-surface approximation is often not satisfied at these short wavelengths, the classical Rayleigh-Rice expression that indicates the BRDF is directly proportional to the surface PSD cannot be used to calculate BRDFs from surface metrology data for even slightly rough surfaces. We discuss the implementation of an FFTLog numerical Hankel transform algorithm that enables the practical use of the computationally intensive Generalized Harvey-Shack (GHS) surface scatter theory. The FFTLog Hankel transform algorithm is validated over the large dynamic range of relevant spatial frequencies required for short wavelength imaging applications, and BRDFs are calculated and displayed for increasingly short wavelengths that violate the smooth surface approximation implicit in the Rayleigh-Rice surface scatter theory.
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James E. Harvey, Narak Choi, Andrey Krywonos, and Jesus Grasa Marcen "Calculating BRDFs from surface PSDs for moderately rough optical surfaces", Proc. SPIE 7426, Optical Manufacturing and Testing VIII, 74260I (9 September 2009); https://doi.org/10.1117/12.831302
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