The development of Radiative Transport Equation has a contribution term called the scattering phase density probability function. It account to scattering events from photons from a different solid angle direction that is scattered to the direction of interest.

∂u/∂t=-v∘∇u-v(μ_a+μ_s)u+∫〖vμ〗_s p_s (Ω^'→Ω)u(r,Ω^',t)ⅆΩ^'+q(r,Ω,t)

I am looking at the scattering phase density
∫〖vμ〗_s p_s (Ω^'→Ω)u(r,Ω^',t)ⅆΩ^'

After looking at the following source found the following plot of a Phase function

enter image description here

What troubles me is that this graph shows that the Phase function has magnitudes greater that 1. Is not a density probability function supposed to stay between 0 to 1?

  • 1
    $\begingroup$ A PDF (probability density function) does not have to stay between 0 and 1, but its CDF (cumulative density function) does. For example, a uniform distribution between 0 and 0.5 must have a PDF value of 2 in that interval. $\endgroup$ – nukeguy Feb 12 at 21:14

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