Bidirectional reflectance spectroscopy. IV - The extinction coefficient and the opposition effect

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Astronomical Spectroscopy, Bidirectional Reflectance, Celestial Bodies, Extinction, Light Scattering, Reflected Waves, Amplitudes, Asteroids, Europa, Lunar Surface, Oberon

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An analytical model is developed for the opposition effect (heiligenshein) in the case of light scattering from a semi-infinite, particulate medium with particles that are large relative to the wavelength. The effect is common for natural materials, and comprises a brightness surge in light diffusively reflected from a surface at near zero phase. A generalized expression is devised for the extinction coefficient of a particulate medium. Models are developed for step function and hyperbolic tangent distributions of light scattered from a stratified medium and exhibiting the opposition effect. A maximum brightness amplitude increase of 0.753 is projected for the effect. Greater values must have other causes.

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