New approach to radiative transfer and related atmospheric correction problems

Henry Berger; Thomas Hay; Eugene A. Margerum

doi:10.1117/12.363608

5 October 1999 New approach to radiative transfer and related atmospheric correction problems

Henry Berger, Thomas Hay, Eugene A. Margerum

Proceedings Volume 3763, Propagation and Imaging through the Atmosphere III; (1999) https://doi.org/10.1117/12.363608
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

Most atmospheric correction codes are based in part or in whole on the radiative transfer equation (RTE), which is an integrodifferential equation. It is well known to be an ad hoc equation, which can and has produced incorrect answers. This paper initiates a new way of exploring where the RTE can produce unphysical answers in parameter-ratio ranges of genuine concern. The exploration begins with formulating a new technique for rigorously transforming the scalar RTE, without approximation, into a `pure' partial differential equation (PDE), i.e., one involving only partial derivatives of finite and relative small order. The virtue of this approach is that there are only a small number of analytical and numerical techniques for dealing with integrodifferential equations compared to the vast array of techniques for PDEs. A variety of tools are developed that are more powerful than needed for the particular physical problems to demonstrate the robustness of the technique. An atmosphere is then considered where Rayleigh scattering is dominant and its PDE derived, apparently for the first time. A class of nonlinear integrodifferential equations were also transformed into linear PDEs and solved for a multiplicity of solutions.

Citation Download Citation

Henry Berger, Thomas Hay, and Eugene A. Margerum "New approach to radiative transfer and related atmospheric correction problems", Proc. SPIE 3763, Propagation and Imaging through the Atmosphere III, (5 October 1999); https://doi.org/10.1117/12.363608

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