A New Look at Fundamentals of the Photometric Light Transport and Scattering Theory. Part 3: Bridges to Multi-Dimensional Problems
Authors: Persheyev S., Rogatkin D.A. | Published: 12.04.2018 |
Published in issue: #2(77)/2018 | |
DOI: 10.18698/1812-3368-2018-2-60-72 | |
Category: Physics | Chapter: Optics | |
Keywords: scattering, absorption, light transport, radiative transport equations, two-dimensional problems, orthogonal scattering approach, pencil-like beam |
In previous two parts of the article, one-dimensional (1D) scattering processes were taken into detailed consideration. All main typical 1D scattering problems of different complexities were discussed and solved using different approaches. It gave the opportunity to find ways to improve the theory, two-fluxes Kubelka --- Munk approach, in particular. It was shown that scattering and absorption processes inside the light-scattering medium are not independent, so the formulation of first coefficients of transport differential equations as the simplest sum of scattering and absorption coefficients is wrong. Inaccuracy in this formulation leads to inaccuracies in results. In this final part of the article, as a completion, the analysis of some spatial light-scattering problems, mainly two-dimensional (2D) problems as the simplest multidimensional problems for consideration, is presented. The detailed analysis of several important 2D approximations, such as a pure backscattering approximation, single-scattering one for a pencil-like beam, and an orthogonal-scattering approach opens the way to have a new look at several nuances of formulation of the 2D or 3D initial transport equations, as well. For example, a new unknown form of the radiative transport equation of the fourth-order is proposed for the case of the orthogonal scattering approach
References
[1] Ishimaru A. Wave propagation and scattering in random media. New York, London, Academic Press, 1978. 572 p.
[2] Davison B. Neutron transport theory. Oxford University Press, 1957. 450 p.
[3] Case K.M., Zweifel P.F. Linear transport theory. Addison-Wesley Publ. Co., 1967. 342 p.
[4] Farrell T.J., Patterson M.S., Wilson B. A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo. Med. Phys., 1992, vol. 19, no. 4, pp. 879–888. DOI: 10.1118/1.596777
[5] Tuchin V.V. Handbook of optical biomedical diagnostics PM107. SPIE Press, 2002. 1110 p.
[6] Rogatkin D.A. Basic principles of organization of system software for multifunctional noninvasive spectrophotometric diagnostic devices and systems. Biomedical Engineering, 2004, vol. 38, iss. 2, pp. 61–65. DOI: 10.1023/B:BIEN.0000035722.72246.bf
[7] Yoon G., Welch A.J., Motamedi M., Van Gemert M.C.J. Development and application of three-dimensional light distribution model for laser irradiated tissue. IEEE J. Quant. Electr., 1987, vol. 23, no. 10, pp. 1721–1733.
[8] Rogatkin D.A. An approach to the solution of multidimensional problems of the theory of light scattering in turbid media. Quantum Electronics, 2001, vol. 31, no. 3, pp. 279–281. DOI: 10.1070/QE2001v031n03ABEH001932
[9] Liemert A., Kienle A. Light transport in three-dimensional semi-infinite scattering media. J. Opt. Soc. Am. A, 2012, vol. 29, iss. 7, pp. 1475–1481. DOI: 10.1364/JOSAA.29.001475
[10] Machida M. Singular eigenfunctions for three-dimensional radiative transport equation. J. Opt. Soc. Am. A, 2014, vol. 31, iss. 1, pp. 67–74. DOI: 10.1364/JOSAA.31.000067
[11] Sandoval C., Rim A.D. Extending generalized Kubelka — Munk to three-dimensional radiative transfer. Applied Optics, 2015, vol. 54, iss. 23, pp. 7045–7053. DOI: 10.1364/AO.54.007045
[12] Rogatkin D., Shumskiy V., Tereshenko S., Polyakov P. Laser-based non-invasive spectrophotometry — an overview of possible medical application. Photonics and Lasers in Medicine, 2013, vol. 2, no. 3, pp. 225–240.
[13] Persheev S., Rogatkin D.A. A new look at fundamentals of the photometric light transport and scattering theory. Part 2: One-dimensional scattering with absorption. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2017, no. 6, pp. 65–78. DOI: 10.18698/1812-3368-2017-6-65-78
[14] Guseva I.A., Tarasov A.P., Rogatkin D.A. New form of the transport equation for the case of 2D orthogonal scattering approximation in biooptics. Proc. 2016 Int. Conf. Laser Optics, 2016, pp. S2−23.
[15] Persheev S., Rogatkin D.A. A new look at fundamentals of the photometric light transport and scattering theory. Part 1: One-dimensional pure scattering problems. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2017, no. 5, pp. 78–94. DOI: 10.18698/1812-3368-2017-5-78-94
[16] Rogatkin D.A. Scattering of electromagnetic waves by a randomly rough surface as a boundary problem of laser radiation interaction with light-scattering materials and media. Optics and Spectroscopy, 2004, vol. 97, iss. 3, pp. 455–463. DOI: 10.1134/1.1803651
[17] Giddings T.E., Kellems A.R. Analytical model for radiative transfer including the effects of a rough material interface. Applied Optics, 2016, vol. 55, iss. 24, pp. 6606–6616. DOI: 10.1364/AO.55.006606