Radiometric and photometric quantities

Radiometric or
photometric quantity

Formula

Definition of radiometric quantities

Radiant power [W]
Luminous flux [lm]

Φe/v = dQe/v/dt

Radiant power Φe is defined as the total power dQe emitted by a light source per unit time dt.

Radiant intensity [W/sr]
Luminous intensity
[lm/sr = cd]

Ie/v = dΦe/v/dΩ

dΩ = dA/r²

Radiant intensity Ie is defined as the radiant power dΦe emitted per unit solid angle dΩ. The unit solid angle dΩ is calculated from the area dA of the surface area of a sphere and the distance r² of this area from the center of the sphere.

Irradiance [W/m²]
Luminous intensity [lm/m² = lux]

Ee/v = dΦe/v/dA

Irradiance Ee is a radiometric quantity that does not relate to a light source but to a detector area in the space. Irradiance is calculated from the ratio of the radiant power dΦe and the area of the detector dA.

Radiance [W/sr m²]
Luminance [cd/m²]

Le/v = dΦe/v/dA dΩ

Radiance Le is measured for extended, i.e. not point, light sources and is defined as the radiant power dΦe emitted from an area dA per unit solid angle dΩ.

Note: Subscript "e" relates to "radiometric" and "v" to "photometric"

The V(λ) curve is used in photometry to convolute the radiometric quantity that is a function of the wavelength λ with the sensitivity function of the human eye in the wavelength range from 380 nm to 780 nm. The photometric quantity luminous flux Φv is then obtained by integrating radiant power Φe(λ) as follows:

The unit of luminous flux Φv is the lumen [lm]. Factor Km = 683 lm/W establishes the relationship between the (physical) radiometric unit watt and the (physiological) photometric unit lumen. All other photometric quantities are also obtained from the integral of their corresponding radiometric quantity weighted with the V(λ) curve.