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Determining parametric TIS behavior from optical fabrication metrology data

Optical manufacturers often have to deal with a specification on the total integrated scatter (TIS) or "Haze" from a given mirror surface. It is frequently thought that TIS or BRDF measurements are required to assure compliance with these specifications. TIS is determined by the spatial frequency banded-limited "relevant" rms surface roughness, the wavelength of light and the angle of incidence. For short-wavelength (EUV/X-ray) applications, even state-of-the-art optical surfaces can scatter a significant fraction of the total reflected light. In this paper we show that the TIS can be accurately predicted, even for moderately rough surfaces, directly from the surface metrology data. We present parametric plots of the TIS for optical surfaces with arbitrary roughness, surface correlation widths and incident angles. Surfaces with both Gaussian and ABC or K-correlation power spectral density (PSD) functions have been modeled. These parametric TIS predictions provide insight and understanding regarding optical fabrication tolerances necessary to satisfy specific optical performance requirements.