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.
Highlights
Elucidation of the photon scattering and transport in random media such as biological tissue volumes is crucial for biomedical optical imaging using the near-infrared light in the wavelength range from 700 to 1100 nm such as diffuse optical tomography [1,2,3], because the imaging technique uses light scattered by the media
Our objective is to examine photon transport especially in the scattering regime for various kinds of random media by using the time-dependent radiative transfer equation (RTE), dEM, and photon diffusion equation (PDE), and to evaluate a regime for the dEM to be valid as a function of μ0t and μ0t v
We investigated the temporal profiles of the fluence rate Φ(r, t) using the analytical solutions of the RTE (Equation (10)), dE0 (Equation (11) with M = 0), and PDE (Equation (12))
Summary
Elucidation of the photon scattering and transport in random media such as biological tissue volumes is crucial for biomedical optical imaging using the near-infrared light in the wavelength range from 700 to 1100 nm such as diffuse optical tomography [1,2,3], because the imaging technique uses light scattered by the media. There are mainly three kinds of systems of the imaging techniques: time-domain, steady-state, and frequency-domain systems. Time-dependent photon transport is basically classified into the two kinds of characteristic regimes (length and time scales): the ballistic and diffusive regimes corresponding to short and long source-detector (SD) distances and times after light incidence, respectively [5]. 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
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