Radar Echo Variations of a Large Rough Sphere

The effect of surface roughness on the radar backscattering cross section of a perfectly conducting nominally spherical target is examined by applying the Kirchhoff method. It is shown that, for the type of roughness and sphere size to which the Kirchhoff method is applicable, the standard deviation of the cross section increases with frequency according to the law 2\TZ<r kt, until the first Fresnel zone reduces in size to the scale length of the roughness. At this point a knee in the curve occurs and its further course is determined by a more detailed statistical description of the surface. Here a is the nominal cross section, I, is the standard deviation of the surface height h and k = 2-rr/\, where X. is the wavelength. The average cross section is shown to be given by a 1 + 0{(kh)}l In o this connection, an error that may be significant, occurring in the work of Hiatt et al.on roughness effects, is pointed out. Some experimental results are reported which support the theoretical conclusions and, moreover, indicate that they may be useful even when the scale length of the roughness is smaller than the wavelength. Further theoretical results are included concerning the effect of rough ness on a general second order surface and the correlation function for the cross section. Accepted for the Air Force Stanley J. Wisniewski Lt Colonel, USAF Chief, Lincoln Laboratory Office