Scattering effects from microtopographic surface roughness are merely nonparaxial diffraction phenomena resulting from random phase variations in the reflected or transmitted wavefront. Rayleigh-Rice, Beckmann-Kirchhoff. or Harvey-Shack surface scatter theories are commonly used to predict surface scatter effects. Smooth-surface and/or paraxial approximations have severely limited the range of applicability of each of the above theoretical treatments. A recent linear systems formulation of nonparaxial scalar diffraction theory applied to surface scatter phenomena resulted first in an empirically modified Beckmann-Kirchhoff surface scatter model, then a generalized Harvey-Shack theory that produces accurate results for rougher surfaces than the Rayleigh-Rice theory and for larger incident and scattered angles than the classical Beckmann-Kirchhoff and the original Harvey-Shack theories. These new developments simplify the analysis and understanding of nonintuitive scattering behavior from rough surfaces illuminated at arbitrary incident angles.
Image degradation due to scattered radiation is a serious problem in many short-wavelength ͑x-ray and EUV͒ imaging systems. Most currently available image analysis codes require the scattering behavior ͓data on the bidirectional scattering distribution function ͑BSDF͔͒ as input in order to calculate the image quality from such systems. Predicting image degradation due to scattering effects is typically quite computation-intensive. If using a conventional optical design and analysis code, each geometrically traced ray spawns hundreds of scattered rays randomly distributed and weighted according to the input BSDF. These scattered rays must then be traced through the system to the focal plane using nonsequential ray-tracing techniques. For multielement imaging systems even the scattered rays spawn more scattered rays at each additional surface encountered in the system. In this paper we describe a generalization of Peterson's analytical treatment of in-field stray light in multielement imaging systems. In particular, we remove the smooth-surface limitation that ignores the scattered-scattered radiation, which can be quite large for EUV wavelengths even for state-of-the-art optical surfaces. Predictions of image degradation for a two-mirror EUV telescope with the generalized Peterson model are then numerically validated with the much more computation-intensive ZEMAX ® and ASAP ® codes.
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