Some properties of radio waves reflected from the Moon and their relation to the lunar surface

Abstract

This report presents a theoretical discussion of the statistical properties of radio waves reflected from the moon. The discussion is based on the assumption of a large number of scattering areas simultaneously contributing to the signal. The properties of the echoes are usually described in terms of pulse broadening or by means of an average-power pulse response when very short pulses are transmitted. Here it is shown that the same type of information can be obtained by studying the correlation of complex amplitudes of two sine waves reflected from the moon at frequencies separated by Δω. By studying this correlation as a function of Δω it is possible to compute the power pulse response of the earth-moon-earth propagation circuit. It is suggested that this method will prove particularly useful in the study of the surface properties of more distant targets such as the planets. It is also shown how the correlation technique can be extended to a two-dimensional mapping of a rotating rough body. The properties of the echoes returned from the moon are related here to a crude statistical model of the lunar surface roughness. This model is shown to lead to a satisfactory account for the semispecular component of the return from the moon if a large-scale structure with rms slopes of 1/20 to 1/10 are assumed.