Confusion about data types in Jensen's subsurface scattering paper

Question

I am currently trying to implement Jensen's paper on subsurface scattering, but I am getting confused when I am trying to implement it in my pathtracer. I have questions about the data types of certain variables.

1. On page 3, $z_r$ is defined as $1 / \sigma_t'$, where $\sigma_t' = \sigma_s' + \sigma_a$. Based on Figure 5, $\sigma_s'$ and $\sigma_a$ are RGB values, which are Spectrum types in my pathtracer. However, $z_r$ is expected to be a distance above the surface, which I presume must be a float, not a Spectrum. How do I handle this discrepancy? Does each RGB wavelength have its own $z_r$?
2. There is a similar issue in the single scattering term in section 4. $s_o'$ is a distance along the refracted outgoing ray, which is presumably a float. However, the formula for this term uses $\sigma_t$, which is a Spectrum.
3. What about $\sigma_{tr}$? This value is $\sqrt{3\sigma_a\sigma_t'}$. Is this also a Spectrum or a float?

Answer 1

The heading row of Figure 5(b) says that the units of $\sigma_s'$ and $\sigma_a$ are inverse millimetres, that is, inverse distance. Hence, $1/\sigma_t'$ has units of distance.

If you send a beam of photons through a medium with scattering coefficient $\sigma$ and measure it at distance $l$, then the probability that a photon has made it that far without being scattered is $e^{-\sigma l}$. Since $l$ has units of distance, $\sigma$ must have units of inverse distance.