http://en.wikipedia.org/wiki/Bidirectional_reflectance_distribution_function

The bidirectional reflectance distribution function is a four-dimensional function that defines how light is reflected at an opaque surface

http://www.cs.ucla.edu/~zhu/tutorial/An_Introduction_to_BRDF-Based_Lighting.pdf

In general, when light interacts with matter, a complicated light-matter dynamic occurs. This interaction depends on the physical characteristics of the light as well as the physical composition and characteristics of the matter.

That is, some of the incident light is reflected, some of the light is transmitted, and another portion of the light is absorbed by the medium itself.

A BRDF describes how much light is reflected when light makes contact with a certain material. Similarly, a BTDF (Bi-directional Transmission Distribution Function) describes how much light is transmitted when light makes contact with a certain material

http://www.cs.princeton.edu/~smr/cs348c-97/surveypaper.html

It is difficult to establish exactly how far one should go in elaborating the surface model. A truly complete representation of the reflective behavior of a surface might take into account such phenomena as polarization, scattering, fluorescence, and phosphorescence, all of which might vary with position on the surface. Therefore, the variables in this complete function would be:

incoming and outgoing angle incoming and outgoing wavelength incoming and outgoing polarization (both linear and circular) incoming and outgoing position (which might differ due to subsurface scattering) time delay between the incoming and outgoing light ray

www.studiobinder.com/blog/what-is-butterfly-lighting-definition