Topics in Particle and Dispersion Science

Radiometry: Lambertian light source

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An elementary lambertian light source with an area dA_n is, by definition, a source whose radiance, L, is independent of direction, ξ, in a hemisphere into which the source radiates (Figure 1). The reference to the hemisphere implies that the source is flat (plane). Given that L = const, one has:

I(ξ )	= L dA(ξ )
	= L dAn cos ξ
	= I0 cos ξ	(1)

for 0 ≤ ξ ≤ π/2, where ξ is the angle between ξ and the outward normal, n, to the plane of the lambertian source, and where the definitions of radiance and intensity are used. For π/2 < ξ ≤ π, we have I(ξ) = 0. Here, I₀, is the intensity of radiation emitted by the source in a direction of the normal to area dA_n.

Two useful equations follow from Equation 1 (see also Problem: A plane lambertian source):

I0 = Φ / π

(2)

L = E / π

(3)

where Φ is the power output of the lambertian source, and E is the irradiance generated by that source. See also Problem: Distribution of irradiance in an image of a uniform lambertian sphere

The above discussion applies to light sources that are either direct (i.e., radiant) or indirect (i.e., diffusely reflecting or transmitting material illuminated by another source).

CITATION: Jonasz M. 2009. Radiometry: Lambertian light source (www.tpdsci.com/Tpc/RdmLambSrc.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY: Published: 19-Jan-2009 Modified: 28-Jun-2009 Peer-reviewed: PENDING

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