Uniqueness of monotone solutions to a non-linear Fredholm integral equation
- 1 January 1991
- journal article
- research article
- Published by Taylor & Francis in Optimization
- Vol. 22 (5) , 765-774
- https://doi.org/10.1080/02331939108843718
Abstract
In this paper we carry out a theoretical analysis of the simultaneous identification of thickness and refractive index profile for inhomogeneous thin films from indirect measurements. The problem leads to a non-linear integral equation of the first kind with smooth kernel, for which solutions are well-determined with the exception of rearrangements of function values. Paying attention to monotone solutions we present a uniqueness theorem that allows us to apply descriptive regularization in order to stabilize the problem.Keywords
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