PRINCIPLE UNDULATORY INVARIANCE IN PHOTOMETRY OF ATMOSPHERELESS CELESTIAL BODIES

The strict invariance of light scattered by a surface with a complicat ed 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 funct ion: g x (lunar-like scattering law) + (I - g) x (Lambert law) to desc ribe the light scattering behavior of atmosphereless bodies as a funct ion 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 degre e of surface optical heterogeneity, respectively. Using disk-integrate d photometric observations of the Moon, Mercury, and dozens of asteroi ds, 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 m easurements of a planet's phase curve allows one to estimate the Hausd orff-Besicovitch dimension, if the surface is treated as a fractal. Fo r the Moon it is 2.4, very close to that predicted for a classic Brown ian process. Using photographic images of the Moon at phase angles of 1-degrees, 6-degrees, 12-degrees, and 96-degrees, maps and images of t he parameters delta0 and g were obtained for the western part of the l unar 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 t he delta0 and (1-degrees/6-degrees) images suggests that delta0 is cha racteristic of the opposition effect. Anomalies in the regional distri butions of the parameters delta0 and g, as well as of the phase coeffi cients (1-degrees/6-degrees) and (12-degrees/96-degrees) and the color ratio, indicate mare areas of different age and composition. Ejecta o f young craters also appear. In the future we plan to refine the model to include the effects of coherent backscattering and surface roughne ss on the meso- and macrorelief scales. (C) 1994 Academic Press, Inc.