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| Transmission function in the small-angle approximation .. : SAA and exact solutions | Parent topic |
Fig.1. Top panel: Dependence of the transmission function, T (Eq. 5 in Transmission function in the small-angle approximation for a medium illuminated at normal incidence), at an observation angle, γ = 1°, on optical thickness, τ, according to the small-angle approximation solution (Eq. 6 in that topic), Ta (dark-blue line), and the exact numerical solution, Ta (light-blue line) of the RTE, both for a medium with spherical and homogeneous particles having a gamma-function PSD (parameters: α = 6, Deff = 8 µm) and a refractive index of 1.52 - 0.008i relative to that of the surrounding medium. The exact numerical solution is described by Rozanov and Kokhanovsky (2006). Calculations have been performed for a wavelength of λ = 0.5 µm. The phase function and other relevant optical properties of the particles were calculated according to Mie theory. See also a tab-delimited data file. Bottom panel: Relative error of the approximate solution for the transmission function. For τ < ~10, the error is essentially random, due to a limited accuracy of the exact numerical solution of the RTE. A section between τ = 20 and 50 is a straight line between the results for these two values of τ. See also a tab-delimited data file.
| CITATION: Kokhanovsky A. A. 2007. Transmission function in the small-angle approximation (SAA) for a medium illuminated at normal incidence: SAA and exact solutions (www.tpdsci.com/Tpc/RTSAANmlTsmCmp.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 14-Feb-2007 Modified: 05-Feb-2007 Peer-reviewed: PENDING |
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