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The beam spread function of a turbid medium (BSF) characterizes the irradiance distribution generated by that medium illuminated by a unidirectional source (collimated beam) of light contained in it. The irradiance distribution is measured at a spherical surface of radius, r, centered at the light source location. The concept of BSF (and of a closely-related point spread function) enables one to use the formalism of the theory of linear optical systems in evaluating properties of an image of an object viewed through the turbid medium (for example, Mertens LE and Replogle 1977, see also Point spread function.
The BSF can be formally defined as follows (for example, Mertens LE and Replogle 1977):
| BSF(θ, φ, r) = E(θ, φ, r) / P0 | (1) |
where θ, φ are the polar coordinates of the irradiance observation point, relative to the location of the point source, r is the distance between the irradiance meter and the light source, E is the irradiance field, and P0 is the outgoing power of the unidirectional source. As follows from Equation 1, the unit of so defined BSF is m-2. The geometry of the BSF measurement is shown in Figure 1. Given the equivalence of BSF and PSF the relatively simple measurement of BSF yields simultaneously the PSF.
It follows from Equation 1 that
| ∫S BSF(u, r) dA(u) = 1 | (2) |
where S is the area of a sphere of radius r surrounding the unidirectional source and u is the unit vector of direction defined by the angles θ and φ.
In practice, the BSF is understood to be defined at an image plane tangent to the spherical surface, S, at the intersection of that surface and the light source axis. Hence, the normalization condition (Equation 2) is only approximately fulfilled (for example, Du H and Voss 2004).
See also Point spread function vs. beam spread function
| CITATION: Jonasz M. 2009. Beam spread function of turbid medium (www.tpdsci.com/Tpc/ImgTmBsfDef.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 19-Jan-2009 Modified: 27-Jun-2009 Peer-reviewed: 12-Feb-2009 |
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