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The point spread function (PSF) of a turbid medium characterizes the radiance field generated by that medium illuminated by a point source of light contained in it. The concept of PSF (and of a closely-related beam spread function) enables one to use the formalism of the theory of linear optical and electrical 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 vs. optical and modulation transfer functions). In a more general sense, the point spread function (PSF) may characterize both the effects of the turbid medium and of the imaging system itself (see Point and beam spread functions of seawater).
The PSF can be formally defined as follows (for example, Mertens LE and Replogle 1977):
| PSF(θ, φ, r) = L(θ, φ, r) / I0 | (1) |
where θ, φ are the polar coordinates of the direction of the radiance detector axis (a direction towards the point source is represented by θ = 0, φ undefined, hence, usually set to 0), r is the distance between the radiance detector and the point source, L is the radiance field generated by the turbid medium illuminated by the point source, and I0 is the intensity of the point source. As it follows from Equation 1, the unit of PSF is m-2. The geometry of the operational definition of the PSF is shown in Figure 1.
In many turbid media, the PSF is axially symmetrical. This leads to a considerable simplification when the transfer of image in such a medium is considered (see Point spread function vs. optical and modulation transfer functions).
The radiation pattern of the point source is a significant factor in the definition of the PSF. Mertens LE and Replogle 1977 use in their definition an unresolvable lambertian source, for which the angular intensity, I, pattern is as follows:
|
I(α ) = I0 cos α, 0 ≤ α ≤ π I(α ) = 0, π < α ≤ 2π |
(2) |
where α is the angle between the outward normal to the source plane and the direction from which the source is observed.
The normalization condition for PSF is as follows:
| ∫S PSF(u, r) dA(u) = 1 | (3) |
where S is the area of a sphere (of radius r) surrounding the source and u is the unit vector of direction defined by the angles θ and φ. See also Beam spread function: Definition.
See also Point spread function vs. beam spread function
| CITATION: Jonasz M. 2008. Point spread function of turbid medium (www.tpdsci.com/Tpc/ImgTmPsfDef.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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