Vol. 19, issue 12, article # 9

Budak V.P., Melamed O.P. Modified method of spherical harmonics for determination of the point spread function of a turbid medium layer. // Atmospheric and oceanic optics. 2006. V. 19. No. 12. P. 940-945.
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Abstract:

We have developed a method of solution of radiative transfer equation for the case of a point isotropic source, based on the spherical harmonics method. The convergence of the method has been improved by subtracting from the general solution of the small-angle component containing all the peculiar features of the solution. Thus, the solution is obtained for remaining smooth function containing no singularities. To maintain the stability of solution with the increase of the optical depth, scaling is applied. The numerical calculations made clearly show the physical idea of the small-angle approximation, i.e., the neglect of dispersion of the scattered photon trajectories and backscattering.

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