10 August 2001 Direct and inverse problem in scatterometry of rough surfaces
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Abstract
Various optical methods are served for surface roughness measurements and have been applied for inspection of precise machined surfaces. These methods sometimes use scatterometry. Scatterometry of rough surfaces is based on scattering of light wave by surface irregularities. Essence of scatterometry consists of intensity and angular distribution of scattered light measurements. Scatter pattern is measured in one or two directions, depending on surface structure and its illumination. How will light be scattered from known irregular surface? It is the main question in direct problem of scatterometry. Research on dependence between measured distribution of scattered field and surface topography is the topic in inverse problem. Mathematical expression of this relation is based on various theories, primarily on the Rayleigh-Rice perturbation theory and on Kirchhoff theory. Direct and inverse problems in light scatter measurements of surface roughness are the subject of this paper. Theoretical and experimental studies of both these problems are presented. Computer techniques make possible to simulate and investigate direct and inverse problem for light scattering by rough surfaces. Investigations of both problems were carried on applying scalar Kirchhoff diffraction theory. Diffraction analysis of coherent light scattered from rough surface shows, that complex amplitude of light in Fraunhofer zone is proportional to two-dimensional Fourier transform complex amplitude of light in surface. Two-dimensional fast Fourier transform algorithm for computer simulation of diffraction field is applied. A discussion of modeling light scattered from periodical and random surfaces is also given.
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Czeslaw Lukianowicz, Czeslaw Lukianowicz, } "Direct and inverse problem in scatterometry of rough surfaces", Proc. SPIE 4517, Lightmetry: Metrology, Spectroscopy, and Testing Techniques Using Light, (10 August 2001); doi: 10.1117/12.435961; https://doi.org/10.1117/12.435961
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