1 December 1991 Underwater solar light field: analytical model from a WKB evaluation
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Abstract
An analytical expression for the underwater radiance distribution due to a purely 'delta function' sun is discussed. The expression derives from a WKB evaluation of the path integral solution for time-dependent radiative transfer, integrated over long times, and does not involve a small-angle approximation. However, a diffusion-limiting length scale previously found in the small-angle approximation also arises in this evaluation, suggesting that is plays a physically important role (independent of approximation schemes) in governing the structure and evolution of the radiance distribution. In its present form, the analytical expression reproduces the shape of the downwelling radiance distribution for angles as large as 90 degree(s), but is inadequate for the upwelling component. However, the poor modeling of the upwelling component is not a limitation of the WKB approximation, but is most likely due to the simplistic treatment of the phase function. An effort is underway to more carefully handle the phase function within this WKB framework.
© (1991) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Jerry Alan Tessendorf, Jerry Alan Tessendorf, "Underwater solar light field: analytical model from a WKB evaluation", Proc. SPIE 1537, Underwater Imaging, Photography, and Visibility, (1 December 1991); doi: 10.1117/12.49255; https://doi.org/10.1117/12.49255
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