Understanding BSDF Sampling in Mitsuba's Spectral Mode

[shiasin]

Hi,

I'm new to Mitsuba, so my question might be basic. I'm currently trying to implement my own BSDF in Mitsuba's spectral mode. As far as I know, in spectral mode, the refractive index varies across different wavelengths.

While working on my implementation, I noticed that Mitsuba samples four wavelengths at a time. Although the BSDF returns a spectral quantity with four values, it still uses a single BSDFSample3f object, which contains fields like wo and pdf. These fields can depend on the wavelength.

My question is: how does Mitsuba internally handle the fact that direction (wo) and pdf are shared across multiple wavelengths, even though the BSDF evaluation depends on wavelength-specific behaviour like refractive index?

[njroussel]

Hi @shiasin

As far as I know, in spectral mode, the refractive index varies across different wavelengths.

That is correct. However, FWIW I believe we don't model this in any of the existing materials.

how does Mitsuba internally handle the fact that direction (wo) and pdf are shared across multiple wavelengths, even though the BSDF evaluation depends on wavelength-specific behaviour like refractive index?

The solution to this, is to build one single geometric light path and evaluate it for 4 different wavelengths. Of course, with something like an ideal dielectric with a spectral-varying refractive index, there is only a single valid outgoing direction (wo) per wavelength. In practice, this would mean that you're wasting 3/4 of your computation -- the 3 other wavelengths will have 0 contribution for the selected (wo). But for "smooth" materials, we can still sample a single direction and evaluate the BSDF contribution for all 4 of them. This is known as hero-wavelength sampling.

[shiasin]

Thank you so much for your detailed explanation.