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Reconstruction of the Lambert Curve in a Scattering Medium by Using Pulsed Sounding

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Abstract

Under study is some mathematical model of the radiation transfer process in a scattering medium initiated by a pulsed point isotropic source. We inspect the 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 .

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Funding

The authors were supported by the Russian Foundation for Basic Research (project no. 20–01–00173) and the Ministry of Education and Science of the Russian Federation and Deutscher Akademischer Austauschdienst (DAAD) according to the Program “Mikhail Lomonosov.”

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Authors and Affiliations

  1. Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok, 690041, Russia

    V. A. Kan & I. V. Prokhorov

  2. Far-Eastern Federal University, Vladivostok, 690950, Russia

    V. A. Kan

Authors
  1. V. A. Kan
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  2. I. V. Prokhorov
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Corresponding authors

Correspondence to V. A. Kan or I. V. Prokhorov.

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Translated by L.B. Vertgeim

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Kan, V.A., Prokhorov, I.V. Reconstruction of the Lambert Curve in a Scattering Medium by Using Pulsed Sounding. J. Appl. Ind. Math. 14, 321–329 (2020). https://doi.org/10.1134/S1990478920020106

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  • DOI: https://doi.org/10.1134/S1990478920020106

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