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NEW DEVELOPMENTS IN FREQUENCY DOMAIN OPTICAL TOMOGRAPHY. PART I. FORWARD MODEL AND GRADIENT COMPUTATION

DOI: 10.1615/ICHMT.2010.RAD-6.30
10 pages

Olivier F. Balima
Centre Universitaire de Rocherche sur I' Aluminium, Université du Québec a Chicoutimi, 555 Bd de l'Université Chicoutimi QC G7H 2B1Canada

Joan Boulanger
Gas Turbine Laboratory Institute for Aerospace Research - National Research Council Canada, Ottawa, ON, Canada, K1A 0R6

Andre Charette
Groupe de Recherche en Ingénierie des Procédés et Systèmes, Departement des Sciences Appliquées, Université du Québec à Chicoutimi, 555 Boulevard de l'Université, Chicoutimi, Québec, Canada, G7H 2B1

Daniel Marceau
Université du Québec à Chicoutimi, 555 Bd de l’Université Chicoutimi QC G7H 2B1Canada

Resumo

This paper deals with a gradient-based frequency domain optical tomography method where the collimated source direction is taken into account in the computation of both the forward and the adjoint models. The forward model is based on the least square finite element method associated to the discrete ordinates method where no empirical stabilization is needed. In this first part of the study, the forward model is highlighted with an easy handling of complex boundary condition through a penalization method. Gradient computation from an adjoint method is developed rigorously in a continuous manner through a Lagrangian formalism for the deduction of the adjoint equation and the gradient of the objective function. The proposed formulation can be easily generalized to stationary and time domain optical tomography by keeping the same expressions.

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