Topics in Particle and Dispersion Science

Radiometry: Axial irradiance due to an extended-area source

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Consider a disk-shaped extended-area lambertian light source and a point, P, at an axis co-axial with and perpendicular to that source, and located a distance, r, away (Figure 1). The irradiance, E, at that point in a plane perpendicular to the axis, due to the extended-area source with a radius, R, can be expressed as follows (for example, Freeman MH et al 2003, p. 354):

E = πLR 2 / (R 2 + r 2 )

(1)

where, L, is the radiance of the extended-area source. See also a related problem.

It follows from Equation 1 that for R << r, the irradiance of a co-axial point, P, falls off with the distance, r, as follows:

Ep	= πR 2 L / r 2
	= I / r 2	(2)

where, I, is the intensity of an incoherent "point source". The substitution of a product πR²L = AL (where A is the area of the disk-shaped "point source") by I as well as referring to the extended source as a "point source", are made possible by the assumption about the smallness of R (see also The size of an incoherent point source).

The last line of Equation 2 is known as the inverse square law for irradiance (for example, Freeman MH et al 2003, p. 347).

CITATION: Jonasz M. 2009. Radiometry: Axial irradiance due to an extended-area source (www.tpdsci.com/Tpc/RdmIrdExtAreaSrc.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY: Published: 15-Jan-2009 Modified: 18-Jun-2009 Peer-reviewed: 12-Feb-2009

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