Accurate and efficient computation of the 3D radiative transfer equation in highly forward-peaked scattering media using a renormalization approach

Fujii, Hiroyuki; Yamada, Yukio; Chiba, Go; Hoshi, Yoko; Kobayashi, Kazumichi; Watanabe, Masao

doi:10.1016/j.jcp.2018.07.047

Cited by 11 publications

(14 citation statements)

References 40 publications

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“…the N-value is determined so as to attain sufficient convergence of the results; and n is the refractive index of the medium. The verifications of Φ RTE (r, t) were confirmed by several independent works [23,32]. Using Φ LK , we can obtain the analytical form for the dEM Φ dEM (r, t):…”

Section: D Infinite Homogeneous Mediasupporting

confidence: 57%

“…Source and detector positions are set inside the medium to suppress the boundary effects because we compare the analytical solutions for infinite media with the numerical solutions for finite media. For the details for the numerical calculations, refer to [32,40]. The optical properties of the medium are set as µ a = 0.20 cm −1 , µ s = 100 cm −1 , g = 0.90, and n = 1.40; and the SD distance is set as r = 0.40 cm, corresponding to the scattering regime.…”

Section: Fundingmentioning

confidence: 99%

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Characteristic Length and Time Scales of the Highly Forward Scattering of Photons in Random Media

et al. 2019

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Background: Elucidation of the highly forward scattering of photons in random media such as biological tissue is crucial for further developments of optical imaging using photon transport models. We evaluated length and time scales of the photon scattering in three-dimensional media. Methods: We employed analytical solutions of the time-dependent radiative transfer, M-th order delta-Eddington, and photon diffusion equations (RTE, dEM, and PDE). We calculated the fluence rates at different source-detector distances and optical properties. Results: We found that the zeroth order dEM and PDE, which approximate the highly forward scattering to the isotropic scattering, are valid in longer length and time scales than approximately 10 / μ t ′ and 40 / μ t ′ v , respectively, where μ t ′ is the reduced transport coefficient and v the speed of light in a medium. The first and second order dEM, which approximate the highly forward-peaked phase function by the first two and three Legendre moments, are valid in the longer scales than approximately 4.0 / μ t ′ and 6.3 / μ t ′ v ; 2.8 / μ t ′ and 3.5 / μ t ′ v , respectively. The boundary conditions less influence the length scales, while they reduce the times scales from those for bulk at the longer length scale than approximately 4.0 / μ t ′ . Conclusion: Our findings are useful for constructions of accurate and efficient photon transport models. We evaluated length and time scales of the highly forward scattering of photons in various kinds of three-dimensional random media by analytical solutions of the radiative transfer, M-th order delta-Eddington, and photon diffusion equations.

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Section: D Infinite Homogeneous Mediasupporting

confidence: 57%

Section: Fundingmentioning

confidence: 99%

Characteristic Length and Time Scales of the Highly Forward Scattering of Photons in Random Media

et al. 2019

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“…We numerically calculated the RTE based on the finite difference method. We employed the third order upwind scheme for spatial discretization and discrete ordinate method (DOM) for angular discretization [30][31][32]. As discrete angular directions of light intensity, we used the level symmetric even (LSE) quadrature set [33] with the total number of the directions, N Ω = 48.…”

Section: Numerical Schemes and Conditions For The Rtementioning

confidence: 99%

“…Liu's method works well in the current condition where the anisotropy factor g is small. For details of the upwind scheme and DOM, see references [30][31][32], respectively. Although the references [31,32] focus on a case of highly forward peaked scattering rather than a case of weakly forward peaked scattering, they summarize the DOM with Liu's method.…”

Section: Numerical Schemes and Conditions For The Rtementioning

confidence: 99%

Numerical Study of Near-Infrared Light Propagation in Aqueous Alumina Suspensions Using the Steady-State Radiative Transfer Equation and Dependent Scattering Theory

et al. 2022

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Understanding light propagation in liquid phantoms, such as colloidal suspensions, involves fundamental research of near-infrared optical imaging and spectroscopy for biological tissues. Our objective is to numerically investigate light propagation in the alumina colloidal suspensions with the mean alumina particle diameter of 55 nm at the volume fraction range 1–20%. We calculated the light scattering properties using the dependent scattering theory (DST) on a length scale comparable to the optical wavelength. We calculated the steady-state radiative transfer and photon diffusion equations (RTE and PDE) using the DST results based on the finite difference method in a length scale of the mean free path. The DST calculations showed that the scattering and reduced scattering coefficients become more prominent at a higher volume fraction. The anisotropy factor is almost zero at all the volume fractions, meaning the scattering is isotropic. The comparative study of the RTE with the PDE showed that the diffusion approximation holds at the internal region with all the volume fractions and the boundary region with the volume fraction higher than 1%. Our findings suggest the usefulness of the PDE as a light propagation model for the alumina suspensions rather than the RTE, which provides accurate but complicated computation.

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“…One is to employ a cell-vertex finite volume method for discretization of the space for faster computing of the 2D TD-RTE [74]. The other is to employ a new renormalization approach to calculate the scattering integral for accurate and efficient computation of the 3D TD-RTE [75].…”

Section: Solving the Td-rte And Td-de Numericallymentioning

confidence: 99%

Time-Domain Near-Infrared Spectroscopy and Imaging: A Review

2019

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This article reviews the past and current statuses of time-domain near-infrared spectroscopy (TD-NIRS) and imaging. Although time-domain technology is not yet widely employed due to its drawbacks of being cumbersome, bulky, and very expensive compared to commercial continuous wave (CW) and frequency-domain (FD) fNIRS systems, TD-NIRS has great advantages over CW and FD systems because time-resolved data measured by TD systems contain the richest information about optical properties inside measured objects. This article focuses on reviewing the theoretical background, advanced theories and methods, instruments, and studies on clinical applications for TD-NIRS including some clinical studies which used TD-NIRS systems. Major events in the development of TD-NIRS and imaging are identified and summarized in chronological tables and figures. Finally, prospects for TD-NIRS in the near future are briefly described.

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Accurate and efficient computation of the 3D radiative transfer equation in highly forward-peaked scattering media using a renormalization approach

Cited by 11 publications

References 40 publications

Characteristic Length and Time Scales of the Highly Forward Scattering of Photons in Random Media

Characteristic Length and Time Scales of the Highly Forward Scattering of Photons in Random Media

Numerical Study of Near-Infrared Light Propagation in Aqueous Alumina Suspensions Using the Steady-State Radiative Transfer Equation and Dependent Scattering Theory

Time-Domain Near-Infrared Spectroscopy and Imaging: A Review

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