Geodesic
Reconstruction of the Lambert curve in a scattering medium by using pulsed sounding
Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 2, pp. 81-92

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Under study is some mathematical model of the radiation transfer process in a scattering medium initiated by a pulsed point isotropic source. We inspect inverse problem of finding a diffusely reflecting curve by using the two integral overdetermination conditions on the solution of the radiative transfer equation. Some nonlinear differential equation is obtained for the function that describes the shape of the desired curve in the case of the single scattering approximation. Numerical analysis of the inverse problem solution is carried out to check the stability under perturbations of the initial data.
Keywords: inverse problem, radiation transfer equation, pulsed irradiation, volume scattering. .
Mots-clés : diffuse reflection 
@article{SJIM_2020_23_2_a5,
     author = {V. A. Kan and I. V. Prokhorov},
     title = {Reconstruction of the {Lambert} curve in a scattering medium by using pulsed sounding},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {81--92},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2020_23_2_a5/}
}
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V. A. Kan; I. V. Prokhorov. Reconstruction of the Lambert curve in a scattering medium by using pulsed sounding. Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 2, pp. 81-92. http://geodesic.mathdoc.fr/item/SJIM_2020_23_2_a5/