EXPERIMENTAL VERIFICATION OF PROPER KIRCHHOFF THEORY OF WAVE SCATTERING FROM KNOWN RANDOMLY ROUGH SURFACES

Backscattered measurements of acoustics waves returned from three known surfaces of different roughnesses were made at four different frequencies. Two surfaces are made of mild steel and one of rubber polymer. The reflection coefficients were measured and found to be approximately constant over the scattering angles ranging from 0° to 30° from the vertical. The correlation functions and the standard deviations of the surface heights were calculated from the surface profiles obtained with a depth gauge. The correlation lengths and the standard deviations were found to be 6.00 27.75 mm and 0.74 1.08 mm, respectively. The range of the working wavelengths is from 1 to 3 mm. Thus, all parameters needed in the Kirchhoff's scattering law are known. Comparison with the usual Kirchhoff's theory [P. Beckman and W. K. Klemperer, “Interpretation of the Angular Dependence of Backscattering from the Moon and Venus,” Nat. Bur. Stand. Radio Sci. 69D, 1669 1676 (Dec. 1965); T. Hagfors, “Relationship of Geometric Optics and Autocorrelation Approaches to the Analysis of Lunar and Planetary Radar.” J. Geol. Res. 71, 379 383 (1966)] shows serious disagreement. It is found that this is due to an overapproximation in evaluating the Kirchhoff's integral. When the integral is properly evaluated, very good agreement between theory and experimental results is obtained. This appears to be the first theory that is capable of explaining both the angular and frequency behaviors of the return signal. We restrict our backscatter angles to be within 30° so that we are sure that the Kirchhoff's theory applies, and no polarization, shadowing, or multiple scattering effects are significant. Thus, the results obtained apply equally well to electromagnetic scattering. The distributions of the surface slopes are also calculated from the surface profiles so that geometric optics theories of wave scattering (which may be considered to be a special case of the Kirchhoff's theory can also be checked. © 1969, Acoustical Society of America. All rights reserved.