Luminance

The notion of intensity does not provide access to the spatial distribution of the source's emitters, their geometry, or their relative importance. To characterize the radiation by its spatial and angular properties, we define the luminance.

Luminance is defined as the intensity per unit of apparent surface area in a given direction, i.e.

L S = dI S dA s cos θ s size 12{L rSub { size 8{S} } = { { ital "dI" rSub { size 8{S} } } over { ital "dA" rSub { size 8{s} } "cos"θ rSub { size 8{s} } } } } {}

where \(A_{S}\) is the source surface element and \(\theta_{S}\) is the angle between the source normal and the emission direction. We therefore have

L S = d 2 Φ dA s cos θ s d Ω s size 12{L rSub { size 8{S} } = { {d rSup { size 8{2} } Φ} over { ital "dA" rSub { size 8{s} } "cos"θ rSub { size 8{s} } d %OMEGA rSub { size 8{s} } } } } {}

Luminance is expressed in \(\text{Wm}^{-2}\text{sr}^{-1}\). Luminance is sometimes called shine or brightness. With the previous relationship it comes

d 2 Φ = L S dA s d Ω s cos θ s size 12{d rSup { size 8{2} } Φ=L rSub { size 8{S} } ital "dA" rSub { size 8{s} } d %OMEGA rSub { size 8{s} } "cos"θ rSub { size 8{s} } } {}
Figure 2.7 : luminance of a source

For a given point in space, the luminance generally depends on the direction of emission and the angular properties of the radiation coming from this location are defined by its luminance indicator. This indicator is the locus of the vector \(L_{S} (\psi,\zeta)\) whose origin kept fixed is the point considered.