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. 2017 Jun 19;7:3819. doi: 10.1038/s41598-017-02979-4

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Steady-state spatially resolved reflectance from the three-layered scattering medium with an absorption coefficient of the lower semi-infinite layer of $μ_{a}^{(3)} = 0.02 {mm}^{- 1}$ and a refractive index of n _m = 1.4 due to a perpendicularly incident Gaussian beam with a beam radius of ρ _w = 0.5 mm. The refractive index of the surrounding medium is n ₀ = 1.0. For N ≥ 9, the Monte Carlo simulation and the P _N solution agree well. For the Monte Carlo simulation, 10¹¹ Photons were calculated.