# Term confusion about volume scattering

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)?

• Normally publications refer to the "scattering coefficient" is the "out scattering coefficient" which is the probability of a photon, being out scattered. Where as the "scattering cross-section" is usually computed as part of the "absorption cross-section". Which is a measure of how likely a photon is going to absorbed as it travels through a medium. They are related but separate concepts. Most models use a unitless combination of the two called the scattering coefficient. But alone they do have units. If the two are not separated out internally then combining them seems like a good approach. Mar 28, 2023 at 22:41
• @pmw1234 Thanks for the comment. I just found that they might be separated in other related fields lile optics, but not in CG. Since I wish my rendering to correspond well with realistic data, I don't want any misunderstanding in the parameter settings in the renderer. Mar 29, 2023 at 10:10