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22. RAY OPTICS APPROXIMATION FOR RANDOM CLUSTERS
OF GAUSSIAN SPHERES
where
are the Legendre polynomials.
The two perpendicular slopes
are noncorrelating Gaussian random variables with zero means and standard
deviations
Here, is the correlation length that can be further related to a correlation
angle
where
is the second derivative of the correlation function with respect to
For example, the modified Gaussian correlation function depends on a
single parameter and can be phrased as
This function is a proper correlation function, since its Legendre
coefficients are all non-negative (Muinonen 1996),
where
and is a modified spherical Bessel function.