EZ-RTE

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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Theory
The specific intensity

of light in a three-dimensional infinite medium with a point source at the origin obeys the following RTE.

where

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.

Input

μ_a: the absorption coefficient ( > 0 ).
μ_s: the scattering coefficient ( > 0 ).
g: the scattering asymmetry parameter ( 0 ≤ g ≤ 1 ).

* The computation might be difficult for μ_a ≫ μ_s since in this case U becomes very small.

Output
In the left panel, we plot

In the right panel,

are shown.

Change log

[December 23, 2022] The JavaScript version was released.
The initial Java version can be found here (July 15, 2013).