Kirchhoff diffractals

Abstract

We study the angular properties of plane waves backscattered from random fractal curves and surfaces (diffractals). For this purpose we apply the physical optics (Kirchhoff) approximation without resorting to the high-frequency limit. The fractals of interest are described by Gaussian random processes possessing power-law spectra with and without a large-scale cutoff. We show that if the wavelength of the incident field is of order of the topothesy, small variations of its value may alter the angular pattern of the backscattered power qualitatively. The most important prediction is a peak which Kirchhoff diffractals exhibit under specific conditions at a particular angle of incidence. The position of the peak is linked to the dimension of the topothesy and provides a good possibility for experimental measurement of these intrinsic parameters of the fractal surfaces. The effect of large-scale cut-off which determines the RMS height of the surface is also studied.