Share Email Print

Proceedings Paper

Fourier decomposition of sharply peaked phase functions: Legendre expansions versus trapezoidal rule
Author(s): Alain Sei
Format Member Price Non-Member Price
PDF $14.40 $18.00
cover GOOD NEWS! Your organization subscribes to the SPIE Digital Library. You may be able to download this paper for free. Check Access

Paper Abstract

Most numerical methods used in radiation transfer problems decompose the radiation field in Fourier series and solve a reduced radiative transfer equation for each Fourier mode. Classically, Legendre polynomials expansions provide the kernels of these reduced transfer equations. For highly peaked phase functions, the Legendre series expansion converges very slowly. We show in this paper that this expansion can advantageously be replaced by a direct numerical evaluation using the trapezoidal rule. The improvement afforded by this direct evaluation yields highly accurate results with orders of magnitude fewer arithmetic operations than the Legendre series, avoids the very slow convergence of the Legendre series and exploits instead the rapid decay of the Fourier coefficients for exponential convergence, and finally bypasses the need for phase function truncations.

Paper Details

Date Published: 29 September 2009
PDF: 13 pages
Proc. SPIE 7475, Remote Sensing of Clouds and the Atmosphere XIV, 74750J (29 September 2009); doi: 10.1117/12.828842
Show Author Affiliations
Alain Sei, Northrop Grumman Aerospace Systems (United States)

Published in SPIE Proceedings Vol. 7475:
Remote Sensing of Clouds and the Atmosphere XIV
Richard H. Picard; Klaus Schäfer; Adolfo Comeron; Evgueni I. Kassianov; Christopher J. Mertens, Editor(s)

© SPIE. Terms of Use
Back to Top