Mathematical Topics from 3D Graphics - 3D Math Primer for Graphics and Game Development - page 355

Imagine that a certain amount of radiant flux is emitted from a 1 m 2
surface, while that same amount of power is emitted from a different surface
that is 100 m 2 . Clearly, the smaller surface is “brighter” than the larger
surface; more precisely, it has a greater flux per unit area, also known as
flux density. The radiometric term for flux density, the radiant flux per
unit area, is called radiosity, and in the SI system it is measured in watts
per meter. The relationship between flux and radiosity is analogous to
the relationship between force and pressure; confusing the two will lead to
similar sorts of conceptual errors.
Several equivalent terms exist for radiosity. First, note that we can
measure the flux density (or total flux, for that matter) across any cross-
sectional area. We might be measuring the radiant power emitted from
some surface with a finite area, or the surface through which the light
flows might be an imaginary boundary that exists only mathematically
(for example, the surface of some imaginary sphere that surrounds a light
source). Although in all cases we are measuring flux density, and thus the
term “radiosity” is perfectly valid, we might also use more specific terms,
depending on whether the light being measured is coming or going. If the
area is a surface and the light is arriving on the surface, then the term
irradiance is used. If light is being emitted from a surface, the term radiant
exitance or radiant emittance is used. In digital image synthesis, the word
“radiosity” is most often used to refer to light that is leaving a surface,
having been either reflected or emitted.
When we are talking about the brightness at a particular point, we
cannot use plain old radiant power because the area of that point is in-
finitesimal (essentially zero). We can speak of the flux density at a single
point, but to measure flux, we need a finite area over which to measure. For
a surface of finite area, if we have a single number that characterizes the
total for the entire surface area, it will be measured in flux, but to capture
the fact that different locations within that area might be brighter than
others, we use a function that varies over the surface that will measure the
flux density.
Now we are ready to consider what is perhaps the most central quantity
we need to measure in graphics: the intensity of a “ray” of light. We can
see why the radiosity is not the unit for the job by an extension of the ideas
from the previous paragraph. Imagine a surface point surrounded by an
emissive dome and receiving a certain amount of irradiance coming from
all directions in the hemisphere centered on the local surface normal. Now
imagine a second surface point experiencing the same amount of irradiance,
only all of the illumination is coming from a single direction, in a very
thin beam. Intuitively, we can see that a ray along this beam is somehow
“brighter” than any one ray that is illuminating the first surface point. The
irradiance is somehow “denser.” It is denser per unit solid area.