Generalized photoclinometry for Mariner 9

Abstract

The present investigation develops a new theory for the photoclinometric determination of topography when the photometric function of the planetary surface (or that which corresponds to the mean optical depth of emergent scattered solar radiation from an optically thick planetary atmosphere) is not restricted beyond the expectation that it is a function of phase angle, angle of incidence, and angle of emergence. Several versions of such an operational theory, which differ according to the auxiliary conditions employed to achieve mathematical determinacy, together with several approaches to the numerical analysis, have been evolved. The differences in the numerical methods arise from a variable trade-off between computing speed and stability and computer storage requirements. Although the computer encoding process is not yet fully operational, a first result has been worked out for an early frame in the Mariner 9 mission in which the dust-laden atmosphere appears to exhibit standing-wave patterns. Provided the assumption of homologous departures from plane-parallel atmospheric configuration is valid, the photoclinometric implication is that laminar flow lines in the optically viewable dust layer undergo a near-sinusoidal rise and fall of about 40 to 50m. Regardless of assumption, the resulting surface is a rigorous mean-emission surface.