8.2 Summary of Radiometric and Photometric Quantities
| Quantification of electromagnetic radiation … | Radiometric quantity | Spectral quantity | Photometric quantity | Quantity depends on |
| emitted by a source in total | radiant power | spectral radiant power | luminous flux | – |
| Φe | Φλ(λ) | Φv | ||
| W | W nm-1 | lm (lumen) | ||
| emitted in a certain direction | radiant intensity | spectral radiant intensity | luminous intensity | direction |
| Ie | Iλ(λ) | Iv | ||
| W sr-1 | W sr-1 nm-1 | lm / sr = cd | ||
| emitted by a location on a surface | radiant exitance | spectral radiant exitance | luminous exitance | position on source’s surface |
| Me | Mλ(λ) | Mv | ||
| W m-2 | W m-2 nm-1 | lm m-2 | ||
| emitted by a location on a surface in a certain direction | radiance | spectral radiance | luminance | direction and position on source’s surface |
| Le | Lλ(λ) | Lv | ||
| W sr-1 m-2 | W sr-1 m-2 nm-1 | lm sr-1 m-2 = cd m-2 | ||
| impinging upon a surface | irradiance | spectral irradiance | illuminance | position on irradiated surface |
| Ee | Eλ(λ) | Ev | ||
| W m-2 | W m-2 nm-1 | lm m-2 = lx |
Tab. 1: Radiometric and photometric quantities
Radiometric quantities
In the following relations, X has to be replaced with one of the symbols Φ, I, L or E:
Xe = ∞ ∫ Xλ(λ) dλ 0
or
Xe,range = λ2 ∫ Xλ(λ) dλ λ1
with λ1 and λ2 denoting the lower and the upper limit of the respective wavelength range (for instance, UV-A).
Photometric quantities
In the following relations, X has to be replaced with one of the symbols Φ, I, L or E:
Photopic vision
Xv = Km × ∞ ∫ Xλ(λ) × V(λ)dλ with Km = 683 lm / W 0
Scotopic vision
Xv = K'm × ∞ ∫ Xλ(λ) × V'(λ)dλ with K'm = 1700 lm / W 0
Basic integral relations between radiometric and photometric quantities
In the following, x has to be replaced either with e (denoting radiometric quantities) or v (denoting photometric quantities).
Φx = ∫ Ix dΩ 4π
Ix = ∫ Lx cos(ϑ) dA emitting surface
Mx = ∫ Lx cos(ϑ) dΩ 2π