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Zeitschrift für Analysis und ihre Anwendungen


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Volume 12, Issue 2, 1993, pp. 319–326
DOI: 10.4171/ZAA/563

Published online: 1993-06-30

On the Solution of an Ill-Posed Non-Linear Fredholm Integral Equation Connected with an Inverse Problem of Thin Film Optics

H. Schachtzabel[1], H.-A. Braunss[2] and B. Hofmann[3]

(1) Universität Potsdam, Germany
(2) Universität Potsdam, Germany
(3) Technische Hochschule, Zittau, Germany

We carry out a theoretical analysis of the simultaneous identification of geometrical thick-ness and refractive index profile for inhomogeneous single layer systems from indirect mea-surements. The problem leads to a non-linear integral equation of the first kind with smooth kernel. We present a uniqueness theorem for monotone solutions referring to the Hausdorff moment problem.

Keywords: Non-linear integral equations, optics

Schachtzabel H., Braunss H.-A., Hofmann B.: On the Solution of an Ill-Posed Non-Linear Fredholm Integral Equation Connected with an Inverse Problem of Thin Film Optics. Z. Anal. Anwend. 12 (1993), 319-326. doi: 10.4171/ZAA/563