Topics in Particle and Dispersion Science

Radiometry: The size of an incoherent point source

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As suggested by, for example, Freeman MH et al 2003 (p. 354), Equation 1 and Equation 2 in Axial irradiance due to an extended area source provide, when combined, a criterion for the size of an incoherent lambertian "point source." Indeed, set an acceptable relative difference, ε, between the inverse square law irradiance, E_p(r) (Equation 2 cited above) for a point source, where r is the distance from the source, and irradiance, E (R, r) (Equation 1 cited above), due to a finite source with radius, R. One then has:

ε	= (Ep - E ) / E
	= R2 / r 2	(1)

Thus, the maximum radius, R, of a "point source" yielding a relative difference, ε, can be expressed as follows:

R ≤ r √ε

(2)

where r is the distance to the "point source" from an observation point. For example, if one can accept a 1% error (ε = 0.01), the maximum radius of the "point source" is 10% of the distance to the source, a useful "rule of thumb."

Another criterion of the size of the point source, useful in imaging applications, is the size which is unresolvable by the image detector (for example, Mertens LE and Replogle 1977).

CITATION: Jonasz M. 2009. Radiometry: The size of an incoherent point source (www.tpdsci.com/Tpc/RdmIncohPtSrc.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

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

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