National Aeronautics and Space Administration


Date of this Version



Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1476–1487


This article is a U.S. government work, and is not subject to copyright in the United States.


We test several convolution and deconvolution models on phase curves at small phase angles (0.0011° < α < 1.51°) that have the highest phase angle sampling to date.These curves were provided by cameras on board several NASA missions (Clementine/UVVIS, Galileo/SSI and Cassini/ISS) when the Sun had different apparent angular radii (α = 0.266°, 0.051°, 0.028°). For the smallest phase angles, the brightness of the objects (Moon, Europa and the Saturn’s rings) exhibits a strong round-off below the angular size of the Sun. The brightness continues to increase below α before finally flattening at 0.4α. These behaviors are consistent with the convolution models tested. A simple deconvolution model is also used and agrees with laboratory measurements at extremely small phase angles that do not show any flattening [Psarev V, Ovcharenko A, Shkuratov YG, Belskaya I, Videen G. Photometry of particulate surfaces at extremely small phase angles.