SPECTRUM OF A SIGNAL SCATTERED BY AN OSCILLATING INTERFACE V. D. Freilikher and I. M. Fuks Izvestiya VUZ. Radiofizika, Vol. 12, No. 1, pp. 114-121, 1969 UDC 621.372.8.09 The spectrum of a signal scattered at an oscillating interface between tv.;o media is calculated in the Kirchhoff approximation. It is shown that the spectrum is altered on scattering, but not only as a result of the Doppler shift, which is connected with the motion of the surface as a whole and leads to a shift of the frequency of the scattered field relative to the frequency of the incident field. The spectrum is also broadened, and there is an additional shift, associated with the finite angular width of the energy spectrum of surface waves and with the nonlinearity of their dispersion law. It is well known that the spectrum of an electromagnetic signal is altered when scattered by a moving object. This occurs for example ff the scattering takes place at the oscillating interface between two media. This phenomenon was first investigated in [1], which gave the spectra of signals reflected from the surface of the sea, and attempted to examine them theoretically. The spectrum of the scattered signal was studied by Bass [2] using the approximate method of small perturbations. It turned out that in first-order perturbation theory the spectrum is discre.te and consists of three frequencies: w0 and w• = ~00 + ~2(q• Here, w~ and k 0 are the frequency and wave vector of the incident plane wave; ~2(v) is the dispersion law for waves at the surface; q = k0 - n; n is a vector in the direction of the point of observation equal to the modulus of k0; n is the normal to the mean surface. Second-order perturbation theory gives a finite spectral width as the result of dissipative processes [3]. In addition to the sharply defined maxima in the spectrum at frequencies w~, experimental work [4] also revealed a spectral broadening which cannot be dealt with in the framework of the method of small perturbations. This broadening was explained using a combined sea-surface model (a small ripple superimposed on a large wave) [5]. The scattered field was represented as the sum of a zeroth-approximation field U0, scattered from a smooth large-scale surface, and a field which is of the first approximation in the heights and slopes of the small-scale ripple U 1. The paper referred to above only investigated the spectrum of a field U1, which is considerably in excess of U0 for scattering in directions far from specular. Backscattering (radar case) for grazing angles which are not very large is of particular relevance here. The present paper considers the signal spectrum in a range of angles close to specular. This case is the opposite of that considered in [5] in the sense that in this interval of directions the field U0, reflected from the large- scale surface and calculated without allowing for the ripple, turns out to be dominant (IU01 >> lull). w As usual, the spectrum of the field U is understood to be the following quantity: s(o,) =~ (u(t) u ~ (t + ~) ) e ..... d~. (1) --oe We note that U(t) can describe an acoustic as well as an electromagnetic wave field (in the latter case U(t) is a component of an appropriate vector). (.. ,) denotes an ensemble averaging of realizations of the random scattering surface. We assume that the transmitter and receiver are situated in the Fraunhofer zone relative to the reflecting surface z = [(r, t), so that it is sufficient to restrict attention to the scattering of a plane monochromatic wave. If the field of such a wave scattered at z = ~(r, t} is calculated by Kirchhoff's method, it follows from the results of [6] that oo s(,,) ~ ~ .[ ap.f a~:p {~[qp - ,,,~1 +~q,[~(,',, t~)-~(,.,, t,)]l~. (2) 89