Relationship of geometric optics and autocorrelation approaches to the analysis of lunar and planetary radar

The formal relationship is established between the geometric optic approach and the autocorrelation approach to the analysis of lunar and planetary radar echoes for a Gaussian autocorrelation function when the surface has Gaussian height statistics and introduces deep phase modulation on the incident wave. Similarly it is inferred that such an analogy also holds whenever the surface undulations contain structure no smaller than the wavelength of observation divided by the rms slope of the surface. If an appreciable amount of small-scale structure is present, it is shown that (1) the range of scales responsible for the scattering will include an increasing amount of small-scale structure with increasing angle of incidence and (2) no ample relationship appears to exist between the distribution of apparent surface slopes and the power backscattered as a function of angle of incidence.