Why is the BRDF a quotient of two differentials?

Question

I am not sure if this is the rigth place to ask this question but i can not think of an better. Can somebody explane to me why the BRDF is an quotient of two differentials and not a quotient of undifferentiated quantities for outcoming radicance and irradiance? In the best case with some scribbles. All the explantions i could find to this topic is the one of Wikipedia: "The reason the function is defined as a quotient of two differentials and not directly as a quotient between the undifferentiated quantities, is because other irradiating light than dEi(ωi), which are of no interest for fr(ωi , ωr), might illuminate the surface which would unintentionally affect Lr(ωr), whereas d⁡Lr (ωr) is only affected by dEi(ωi)." (https://en.wikipedia.org/wiki/Bidirectional_reflectance_distribution_function) I do not understand this explation.

I hope some of you can help me and i am very thankfully for every trie.

P.S.: I hope I do not sound like an six year old but english is not my mothertoung.

Answer 1

BRDF describes the ratio of outgoing light to incoming light. The BRDF function depends on 'differentiating' individual components of the incoming and outgoing light. Specifically, we break the light ray into individual photons, or differentiated elements of the light ray for computation.

I hope this sheds some light on the BRDF function.

Some extended discussions on the topic:

• StackOverflow: Can an infinite be undifferentiated?
• Github: Approximating BRDF