I am reading the book Physically Based Rendering (Pharr, Humphreys). In the chapter on lights, they talk about approximating the total emitted power of different kinds of lights. For example, a point light's total power is
intensity * 4 * pi. Here 4pi represents a solid angle over the entire sphere.
This makes sense to me because intensity * solid angle = power (or radiant flux if you will). You can see this by the units as well. Intensity is W/sr and solid angle is sr, so
W/sr * sr = W and power is measured in watts. It checks out.
However, I don't understand the corresponding calculation for the
DiffuseAreaLight. From my understanding of the book they calculate the total power emitted from a diffuse area light as
emitted radiance * area * pi.
Since the unit of radiance is W/(sr*m^2) multiplying area gives W/sr. This makes me think the pi factor represents solid angle - but why only 1pi? I would have guessed 2pi since each point on the area light would radiate in a complete hemisphere (corresponding to 2pi steradians).
You can find the actual code mentioned in the book here.
What am I misunderstanding? Why does
total emitted power = emitted radiance * area * pi for diffuse area lights make sense?