The energy density for the three-dimensional radiative transport equation (RTE) with anisotropic scattering is calculated without any approximation. See Report by Mihai V. Avram. The analytical solution is based on Machida, JOSAA, 2014. The density of light is obtained as a function of the distance from an isotropic source.

Chi Zhang and Manabu Machida (Hamamatsu University School of Medicine)
Hamamatsu, Japan, December 2022

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The specific intensity
of light in a three-dimensional infinite medium with a point source at the origin obeys the following RTE.
Here we assume linear scattering and the scattering phase function is given by
The energy density U is obtained as
where v is the speed of light in the medium. Since U is spherically symmetric, we measure U along the z-axis. We have
See the report for furhter details.

  • μa: the absorption coefficient ( > 0 ).
  • μs: the scattering coefficient ( > 0 ).
  • g: the scattering asymmetry parameter ( 0 ≤ g ≤ 1 ).
* The computation might be difficult for μa ≫ μs since in this case U becomes very small.

In the left panel, we plot
In the right panel,
are shown.

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