A RAINBOW INVERSE PROBLEM

Alexis Blasselle (1) , Vincent Calvez (2) , Ayman Moussa (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 ENS de Lyon - École normale supérieure de Lyon
3 ENS Cachan - École normale supérieure - Cachan

Abstract. We consider the radiative transfer equation (RTE) with reflection in a three-dimensional domain, infinite in two dimensions, and prove an existence result. Then, we study the inverse problem of retrieving the optical parameters from boundary measurements, with help of existing results by Choulli and Stefanov. This theoretical analysis is the framework of an attempt to model the color of the skin. For this purpose, a code has been developed to solve the RTE and to study the sensitivity of the measurements made by biophysicists with respect to the physiological parameters responsible for the optical properties of this complex, multi-layered material.

Domains: Numerical Analysis [cs.NA]

Alexis Blasselle, Vincent Calvez, Ayman Moussa. A RAINBOW INVERSE PROBLEM. ESAIM: Proceedings, 2010, 30, pp.142-152. ⟨10.1051/proc/2010011⟩. ⟨hal-00518164v2⟩