Extension of Chandrasekhar's formula to a nonhomogeneous Lambertian surface and comparison with the 6S formulation
Applied Optics, Vol. 46, Issue 13, pp. 2471-2480 (2007)
http://dx.doi.org/10.1364/AO.46.002471
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Abstract
The classical Chandrasekhar's formula, which relates the surface albedo to the top of the atmosphere radiance, rigorously applies to a homogeneous Lambertian surface. For a nonhomogeneous Lambertian surface in a plane-parallel atmosphere, an extension of this formula was proposed in the 1980s and has been implemented recently in the 6S algorithm. To analyze this extension, the rigorous formula of the top of the atmosphere signal in a plane-parallel atmosphere bounded by a nonhomogeneous Lambertian surface is derived. Then the 6S algorithm extension is compared to the exact formula and approximations and their validity is examined. The derivation of the exact formula is based on the separation of the radiation fields into direct and diffuse components, on the introduction of the Green's function of the problem, and on integrations of boundary values of the radiation fields with Green's function.
© 2007 Optical Society of America
OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1310) Atmospheric and oceanic optics : Atmospheric scattering
(010.1320) Atmospheric and oceanic optics : Atmospheric transmittance
(280.1310) Remote sensing and sensors : Atmospheric scattering
(290.4210) Scattering : Multiple scattering
ToC Category:
Atmospheric and ocean optics
History
Original Manuscript: October 26, 2006
Revised Manuscript: December 18, 2006
Manuscript Accepted: December 19, 2006
Published: April 9, 2007
Virtual Issues
Vol. 2, Iss. 6 Virtual Journal for Biomedical Optics
Citation
Alain Sei, "Extension of Chandrasekhar's formula to a nonhomogeneous Lambertian surface and comparison with the 6S formulation," Appl. Opt. 46, 2471-2480 (2007)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-46-13-2471
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