Instructions

HD2402 - 9 - V1.3
2.2 RADIANCE
Radiance L
i
at a point of a surface is defined as the energetic flux d
2
Φ
I
that flows
through a surface dA per unit solid angle dΩ (Figure 2):
Ω⋅
Φ
=
ddA
d
L
i
2
Figure 2: radiance
The radiance measurement unit is [W/(m
2
sr)]; when calculated at different wave-
lengths, we obtain the spectral radiance [W/(m
2
nm sr)].
A solid angle is the angle subtended at a point P by a closed surface A. It is calculated
as the relation between the surface projected on a sphere of radius R with center in P
and R
2
. The measurement unit of a solid angle is the steradian [sr] and its value
ranges between 0 and 4π.
Radiance and irradiance are two different quantities. Radiance describes the angular
distribution of radiation while irradiance integrates radiance in all directions. The pri-
mary relation linking irradiance to radiance is:
(
) ωθφθ dLE
ii
)cos(,
∫
Ω
⋅=
If radiance is uniform, then the term L(θ,φ) can be taken out from the integral and the
expression is simplified as follows:
FLdE
i
i
i
L
⋅==
∫
Ω
ωθ )cos(
Where F depends only on geometry.
In these particular conditions, the radiance value can be obtained from that of the ir-
radiance: hence, the formula will be:
F
E
L
i
i
=
Remark: for small angles, F is actually the solid angle under which the observer
source is seen.
By using this reduction, HD2402 unit allows to calculate the radiance of the irradiance
measured values.