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Curved Surface
If a surface is an ideal diffuse radiator, Lambert’s cosine law says that the radiant
intensity observed is directly proportional to the cosine of the angle θ between the
observer’s line of sight and the surface normal, as Eq. 3.32 quantifies.
where I e is the radiant intensity in W sr −1 .
I e (θ) = I e (θ = 0) cosθ, (3.32)
Figure 3.37.: Lambert’s cosine law [50].
In Figure 3.37 on the right, dA denotes an area element of the detector surface,
dS is an area element of the radiator surface. The radiant flux Φ e in W, which dA
receives from dS, is proportional to the angle θ, the area dS, dA, and inversely
proportional to r 2 . r is the distance between the two elements dA and dS. This
leads to
dΦ e = L e
dAdS
r 2 cos θ = L e dΩ dS cos θ, (3.33)
where dΩ = dA/r 2 is the solid angle in sr. The radiance, L e , measures the radiant
flux that is emitted from a unit surface and falls within a unit solid angle, in
W sr −1 m −2 .
82 3. Experimental Setup