We have two different terms, for example, let's talk about scattering only.
- Scattering coefficient
- Scattering cross-section
These two terms are supposed to have different physical meaning. I read it from the PBR-book - Chapter 11 :
Absorption is described by the medium’s absorption cross section, , which is the probability density that light is absorbed per unit distance traveled in the medium.
But the wikipedia told me:
The SI unit of attenuation coefficient is the reciprocal metre (m−1). Reference
And this:
This is also commonly expressed as: $\sigma = \alpha /n$, where $\alpha$ is the absorption coefficient, $n$ is the atomic number density Reference
So I suppose xxx cross-section and xxx coefficient should be different, therefore should have different unit. But it seems that, in rendering, these two terms are interchangeable? Like in mitsuba and PBRT we will set $\sigma$ instead of $\mu$, although they are just names. In rendering, the so-called cross-section (in PBR-book) has the same unit as xxx coefficient ($m^{-1}$), but they should be distinguished by $N$, which should have the unit of $m^{-3}$.
My confusion is what exactly are we setting in those renderers, and in theory, which term is the correct term to use? And, whether there is anything more work I should do, to convert the unitless distance in those renderers to be a physical value (Like multiply $\sigma_x$ by N)?
