ALI improved theoretical lunar photometric function

The theoretical photometric function for the lunar surface previously proposed by the author, which successfully predicted variations of brightness for areas between selenographic longitudes of +600, has been improved so that it better agrees with observations in the limb regions. The modification consists of wrinkling the porous, open surface of the previous model into a series of steep-sided depressions. For formal mathematical reasons, the depressions used are cylindrical troughs whose axes are parallel to lines of lu- minance longitude. However, the primary reqnirement is that the surface must be densely covered ( 90%) with features whose walls make steep angles ( 45Q) with the local horizontal, and that these walls must be visible even at glancing angles. This model is consistent with radar-reflection data which indicate that the moon is rough on a subcentimeter scale. Hence, the size of these depressions is inferred to be centimeters and millimeters. These features are probably primary and secondary meteorite craters and ejecta debris, which saturate the lunar surface on a small scale.