10. Radiometry#
Term |
Symbol |
Description |
Equation |
Units |
|---|---|---|---|---|
Flux or Power |
\(\Omega\) |
Watts (lumens) |
||
Intensity |
\(I\) |
Source power emitted per unit solid angle |
\(\frac{d\Phi}{d\Omega}\) |
W/sr (lm/sr=cd) |
Exitance |
\(M\) |
Power emitted from a sourcer per unit area of the source |
\(\frac{d\Phi}{dA}\) |
W/m^2 (lm/m^2) |
Irradiance |
\(E\) |
Power falling on a unit target area |
\(\frac{d\Phi}{dA}\) |
W/m^2 (lm/m^2) |
Radiance |
\(L\) |
Source power per unit area per unit solid angle |
\(\frac{d\Phi}{d\Omega dA}\) |
W/m^2 sr (lm/m^2 sr) |
Solid angle is a measure of the 2d arc on the surface of a sphere. It is similar to the length of an arc.
\[
d\theta = \frac{\text{length of an arc}}{r} \mathrm{rad}
\]
For a whole circle,
\[
\theta = \frac{2 \pi r}{r} = 2 \pi \ \mathrm{rad}
\]
For a solid angle,
\[
d\Omega = \frac{\text{surface area of section}}{r^2} \mathrm{steradians}
\]
For a whole sphere,
\[
\Omega = \frac{4 \pi r^2}{r^2} = 4 \pi \ \mathrm{sr}
\]