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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
Ix =    ∫ Lx cos(ϑ) dA
emitting surface
Mx =    ∫ Lx cos(ϑ) dΩ