PRINCIPLE UNDULATORY INVARIANCE IN PHOTOMETRY OF ATMOSPHERELESS CELESTIAL BODIES

The strict invariance of light scattered by a surface with a complicated structure (e.g., a fractal-like surface) under stochastic isotropic perturbations of its structure leads to a differential equation, the general solution of which leads to a simple two-term photometric function: g x (lunar-like scattering law) + (I - g) x (Lambert law) to describe the light scattering behavior of atmosphereless bodies as a function of the viewing and illumination geometry. The model developed here includes two parameters, delta0 and g: the characteristic slope on a smoothing scale and the partition coefficient characterizing the degree of surface optical heterogeneity, respectively. Using disk-integrated photometric observations of the Moon, Mercury, and dozens of asteroids, the parameters delta0 and g, were found by an iterative numerical technique based on a least-squares routine. Correlations between these parameters and albedo are discussed. Using the model, multispectral measurements of a planet's phase curve allows one to estimate the Hausdorff-Besicovitch dimension, if the surface is treated as a fractal. For the Moon it is 2.4, very close to that predicted for a classic Brownian process. Using photographic images of the Moon at phase angles of 1-degrees, 6-degrees, 12-degrees, and 96-degrees, maps and images of the parameters delta0 and g were obtained for the western part of the lunar disk. In addition, images of the phase coefficients (1-degrees/6-degrees), (6-degrees/12-degrees), and (12-degrees/96-degrees) and the color ratio (0.65 mum/0.42 mum) are presented. A correlation between the delta0 and (1-degrees/6-degrees) images suggests that delta0 is characteristic of the opposition effect. Anomalies in the regional distributions of the parameters delta0 and g, as well as of the phase coefficients (1-degrees/6-degrees) and (12-degrees/96-degrees) and the color ratio, indicate mare areas of different age and composition. Ejecta of young craters also appear. In the future we plan to refine the model to include the effects of coherent backscattering and surface roughness on the meso- and macrorelief scales. (C) 1994 Academic Press, Inc.