Algorithm for calculating the complex scattering function of a metal sphere

Abstract

A simple recurrent algorithm for calculating the complex scattering function of a metal sphere is proposed. The speed with which this function can be calculated by means of this algorithm is considered and it is shown that it is best to use cubic spline-interpolation of the complex scattering function of a spherical reflector to calibrate the high-frequency channel during measurements.When measuring radar scattering characteristics the need arises to calibrate the high-frequency channel of the measuring system, which at present is done using reflectors having a simple geometrical shape [1]. These include metal spheres, disks, cylinders, corner reflectors etc. The use of any of these reflectors in practice gives rise to certain difficulties. Thus, the complex scattering function of a cylinder can be calculated approximately only for certain ratios of its geometrical dimensions, the wavelength and the orientation of the plane of polarization [i]. In addition, the greater the geometrical dimensions of the cylinder the higher the requirements imposed on the accuracy with which it is orientated with respect to the electrical axis of the measuring system. A spherical reflector is free from these difficulties and the problem of calculating its complex scattering function has a strict mathematical solution over the whole frequency band [1]. This is particularly important when pulse measurements are being made of the radar characteristics, when low frequencies are present in the spectrum of the probing signal [2]. A spherical reflector also does not have to have any particular spatial orientation, and hence it is the most convenient for calibrating the radio-frequency channel of broadband measuring systems and is generally used for this purpose [2, 3].However, considerable difficulties arise when calculating the complex scattering function of a spherical reflector, since the formulas for calculating the energy and phase scattering functions of a metal sphere are fairly lengthy. The possibility of calculating the complex scattering functions of a sphere by a recurrent method was pointed out in [4, 6], but no specific algorithm for doing this was given. In practice, the complex scattering function is most often calculated in radar measurements by piecewise-linear interpolation of this function using a finite set of nodal points. The energy scattering function was calculated in this way in [5] and the phase scattering function was calculated in [6]. The spacing and range of variation of the argument of the nodal points were different in [5] and [6], which gives rise to practical difficulties. Moreover, the upper limit of the range of variation of the argument for the calculated values of the energy scattering function U(x) is insufficient, since the value of U(x) for x = 4 (the boundary between the resonance and optical scattering regions), obtained in [5], differs from its asymptotic value by approximately 10%. This gives rise to a nonuniqueness in the extrapolation of the energy scattering function for values of the argum...