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

Abstract

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.

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

“…According to the previous research works of time-dependent light propagation [20][21][22], the characteristic length where the diffusion approximation holds has been evaluated at approximately 10/µ t with µ t = µ s + µ a . In our current conditions, the characteristic lengths are given as 0.89 cm for the volume fraction of 1% and 0.15 cm for 20%, respectively.…”

“…However, the dependence of light propagation on the volume fraction has not been fully clarified. In particular, a range of the volume fraction where the diffusion approximation holds, is unclear, although the length and time scales for the diffusion approximation have been extensively discussed [1,[20][21][22]. Because the volume fraction is a control parameter for phantom experiments, the information of the volume fraction range is helpful.…”

Special Issue on New Horizons in Time Domain Diffuse Optical Spectroscopy and Imaging

“…The M-th order delta-Eddington equation (dEM) is used as one effective approach to reduce the computational cost of a numerical solution to the RTE. The final paper in the issue by Fujii et al examined photon transport in 3D, homogeneous, highly forward-scattering media with different optical properties by using time-dependent RTE, dEM, and PDE and estimated the length and time scales in which the dEM is valid [26].…”