Why don’t we use a differential area normal to the beam in the first place, instead of projecting a non-normal one?
Besides that, radiance is often described as an measure for how bright an object appears, wouldn't that be a property of the interaction of light with a surface?
I'm still having trouble to see why that would be a problem. I would be glad if you or someone else could illustrate it with an example like this:
Suppose there is a surface segment ##d A## inside a sphere and the sphere emits light on the inside like a Lambertian radiator. If I measure the...
Radiance is defined as radiant flux per solid angle per projected area normal to the beam direction: ##L = \frac{d^2 \Phi}{d \vec\omega \cdot d A_\perp}## where ##A_\perp = A \cos \theta## and ##\theta## is the angle between the beam direction ##\vec\omega## and the surface normal. I kind of...