# Confusion about data types in Jensen's subsurface scattering paper

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?

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.