Understanding Oren-Nayar reflectance model

Question

In the Oren–Nayar reflectance model, each facet is assumed to be Lambertian in reflectance. wiki

My understanding :

Law of reflection tells us that angle of incidence is equal to angle of reflection. So on a perfectly smooth surface, we get specular reflection. On a rough surface, an incident beam is scattered in a number of directions (each ray obeying law of reflection). To model this, a microfacet model is used which defines grooves (facets) on the surface. Now what does a lambertian facet mean? Are we assuming grooves on the already present grooves?

Answer 1

Lambertian BRDF is a theoretical model describing perfect diffuse reflection.

Microfacet BRDFs on the other hand are based on geometrical optics theory, where a surface is covered with microfacets and described by means of statistical distributions.

Oren-Nayar BRDF is an improvement over the theoretical Lambertian model, applying distribution of purely diffuse microfacets. So to answer your question - Lambertian microfacet is an entity itself not subject to microfacet theory, it's not a "groove with grooves". It's a purely theoretical concept used to apply microfacet theory to matte surfaces. There are many different BRDF models, only some of them follow geometrical optics like the microfacet models do, it is useful to keep in mind that microfacet is not a universal theory.

For further reading, I recommend the overview of BRDF models by Montes and Ureña, their classification was very enlightening to me at least.