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ANALYSIS OF OPTICAL TOMOGRAPHY WITH NON-SCATTERING REGIONS

Published online by Cambridge University Press:  17 June 2002

Nuutti Hyvönen
Nuutti Hyvönen
Affiliation:
Helsinki University of Technology, Institute of Mathematics, PO Box 1100, FIN-02015 HUT, Finland
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Abstract

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This paper provides mathematical analysis of optical tomography in a situation when the examined object, for example the human brain, is strongly scattering with non-scattering inclusions. Light propagation in biological tissue is often modelled by the diffusion approximation of the radiative transfer equation. To be justified, the diffusion approximation demands that the medium is strongly scattering. Naturally, this is not true for non-scattering inclusions, for which some other model is needed. This is found through geometrical optics. Combination of the two models leads to an elliptic partial differential equation with boundary conditions on the outer boundary as well as on the boundaries of the non-scattering regions. The well-posedness of this forward problem is the main concern of this work.

AMS 2000 Mathematics subject classification: Primary 35Q60; 35R30

Keywords

optical tomographynon-scattering regionsradiative transfer equationdiffusion approximationinverse problems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 2 , June 2002 , pp. 257 - 276
Copyright
Copyright © Edinburgh Mathematical Society 2002