The k (kappa) term essentially relates to the absorption property, ie indirectly to the albedo of the material (Ks0, see further).
Then I guess you could turn eta into a color, so that could express a Ks90 type color.
I’d like to see two explicit colors, Ks0 and Ks90 blended with a shlick approximation.
It’s also really easy to relate the index of refraction to the reflectivity (ie Ks0 without the color component): R = [ ( 1 - ior ) / ( 1+ ior ) ] ^2
For instance, glass, with ior 1/1.5, leads to Ks0 = 0.04.
Note the 1/1.5 here, because we are considering glass as seen in the air (ior 1), ie going from air medium into glass medium.
This assumes Ks90 is 1 (or white) for most materials, tinted for metallic surfaces (hence the colored kappa).
...all the extra constants/parameters may relate to some type of spectral representation: I was talking about two colors (Ks0 and Ks90), but you could imagine describing them better than in RGB space and you could also imagine having more than these two samples along the fresnel curve.
This is all about what you are trying to simulate. (For instance, jewelry may benefit a lot from this).
Unfortunately, ...the renderer itself is *not* spectral, so the extra data (on top of the 3 stimulus RGB) will do nothing with most lights.
If you consider the Shlick approximation, then Ks0 would be the value on one end and Ks90 on the other (if your fresnel was based on V.N, reflectivity would be Ks0 where V.N = 1 going towards Ks90 on glancing angles where V.N = 0).
I speak about V.N above (which is the approach most people in the industry have taken for years), but remember that physically based models should be based on H, the halfway vector: so substitute H.N.