Geodesic
Determination of a diffuse reflecting surface under pulsed irradiation
Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 2, pp. 206-215

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An inverse problem of determining a diffusely reflecting surface under given functionals of the radiation flux density for a nonstationary radiation transfer equation is considered. Assuming the point pulsed source and the single scattering approximation, authors obtained the nonlinear differential equation. The solution has been obtained in a few quadratures to determine the profile of the Lambert surface. The computational experiments were carried out on test examples. 
@article{DVMG_2018_18_2_a7,
     author = {V. A. Kan and I. V. Prokhorov},
     title = {Determination of a diffuse reflecting surface under pulsed irradiation},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {206--215},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2018_18_2_a7/}
}
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V. A. Kan; I. V. Prokhorov. Determination of a diffuse reflecting surface under pulsed irradiation. Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 2, pp. 206-215. http://geodesic.mathdoc.fr/item/DVMG_2018_18_2_a7/