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A calculation is made of the luminance and polarization of light due to single and double reflections from the faces of particles in a surface composed of random, irregular particles using equations of electromagnetic waves and materials with a complex index of refraction. Some geometric properties of shadows are derived and used. Good agreement is obtained between these results and measurements of polarized light from Mars, Mercury, and the moon, including the phenomenon of negative polarization at small phase angles. Negative polarization is found to be caused by shade and shadows affecting the double-reflected rays. Graphical results are provided for materials of varied real and complex indices of refraction. The model can be used to calculate polarization and luminance of rough astronomical bodies and surfaces as a function of the viewing angle. Calculated ratios of single-reflected, double-reflected, and randomly diffused light can be related to the surface structure and optical properties of the material.
Milo Wolff (Sun,) studied this question.