Parameter Detection of Thin Films From Their X-Ray Reflectivity by Support Vector Machines

Strauß, Daniel J. ; Steidl, Gabriele ; Welzel, Udo

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URN: urn:nbn:de:bsz:180-madoc-16090
Document Type: Working paper
Year of publication: 2001
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Mathematik und Informatik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Classification: MSC: 41A30 41A63 49N45 49N10 ,
Subject headings (SWD): Röntgenaufnahmetechnik , Reflektometrie , Hilbert-Kern , Dünnschichttechnik , Radiale Basisfunktion
Keywords (English): Support vector machines , reproducing kernel Hilbert spaces , radial basis functions , X-ray reflectometry, optical matrix method
Abstract: Reflectivity measurements are used in thin film investigations for determining the desity and the thickness of layered structures and the roughness of external and internal surfaces. From the mathematical point of view the deduction of these parameters from a measured reflectivity curve represents an inverSe ptoblem. At present, curve fitting procedures, based to a large extent on expert knowledge are commonly used in practice. These techniques suffer from a low degree of automation. In this paper we present a new approach to the evaluation of reflectivity measurements using support vector machines. For the estimation of the different thin film parameters we provide sparse approximations of vector-valued functions, where we work in parallel on the same data sets. Our support vector machines were trained by simulated reflectivity curves generated by the optical matrix method. The solution of the corresponding quadratic programming problem makes use of the SVMTorch algorithm. We present numerical investigations to assess the performance of our method using models of practical relevance. It is concluded that the approximation by support vector machines represents a very promising tool in X-ray reflectivity investigations and seems also to be applicable for a much broader range of parameter detection problems in X-ray analysis.
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