The BRDF is defined as fr(wi, wo) = dL(wi) / dE(wo), where wi and wo are the incident and exitant solid angles.

According to wikipedia, this equation expands to fr(wi, wo) = dL(wi) / L(wi) * cos(theta) * dw. From what I can tell, this is the differential outgoing radiance divided by the incoming radiance along the incident solid angle, multiplied by the cosine of the azimuth angle (to account for the projected area term), multiplied by the differential solid angle.

My question is, if L is the energy evaluated along the incident differential solid angle, what does the differential of Radiance mean? To clarify, why do we need dL when L is effectively giving us the light energy along a single ray of light? Also, in the denominator, we have the radiance term, L, multiplied by the cosine of the angle (which I understand to be projecting the incident radiance onto the surface). Why is that L instead of dL?

Thanks.

**Edited by ZBethel, 27 May 2012 - 10:56 PM.**