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J Opt Soc Am A Opt Image Sci Vis. 2013 May 1;30(5):854-8. doi: 10.1364/JOSAA.30.000854.

Analytic expressions for the black-sky and white-sky albedos of the cosine lobe model.

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US Army Engineer Research and Development Center, Vicksburg, Mississippi 39180, USA.


The cosine lobe model is a bidirectional reflectance distribution function (BRDF) that is commonly used in computer graphics to model specular reflections. The model is both simple and physically plausible, but physical quantities such as albedo have not been related to the parameterization of the model. In this paper, analytic expressions for calculating the black-sky and white-sky albedos from the cosine lobe BRDF model with integer exponents will be derived, to the author's knowledge for the first time. These expressions for albedo can be used to place constraints on physics-based simulations of radiative transfer such as high-fidelity ray-tracing simulations.


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