I'm reading through the light measurement handbook and page 28 is confusing me. I knew previously that lambertian diffuse reflections distribute the reflection of incoming intensity such that the surface looks equally bright from every direction from which it is measured (only dependent on incoming light direction and surface normal). Specifically, the measured radiance stays constant.
However, the page shows that the actual reflected energy (the text says energy, I'm assuming it's talking either about radiant flux or intensity) isn't actually uniformly distributed, but forms essentially a cosine lobe centered about the surface normal:
I'm assuming that the "uniform radiance" results somehow from the measured area in relation to Lambert's cosine law cancelling out this cosine distribution to somehow result in a uniform distribution. How can this be shown mathematically?
Also, how does this influence the light received by surfaces receiving this reflected energy? Are they lit such that every surface placed at equal distances to the surface receives the same amount of light, regardless of its orientation w.r.t. the surface normal, or do they essentially receive this cosine distribution?