It is shown that the scattered fields are almost space bandlimited functions. The effective bandwidth W is introduced and evaluated for a very general scattering system, as well as the error made using functions bandlimited to w > W for representing the scattered field. The effective bandwidth is very simply related to the maximum dimension of the scattering system; the error drops to negligible values for modest increases of w compared to W , in the case of large scatterers. Important consequences of the above general results are finally stressed.

On the spatial bandwidth of scattered fields

An optimal sampling interpolation algorithm is developed that allows the accurate recovery of scattered or radiated fields over a sphere from a minimum number of samples. Using the concept of the field equivalent (spatial) bandwidth, a central interpolation scheme is developed to compute the field in theta , phi coordinates, starting from its samples. The maximum allowable sample spacing and error upper bounds are also rigorously derived. Several simulated examples of pattern reconstruction are presented, for both the cases of field and power pattern interpolation. The interpolation error, as a function of the retained sample number, has been also evaluated and compared with the theoretical upper bounds. The algorithm stability versus randomly distributed errors added to the exact samples is demonstrated. >

Optimal interpolation of radiated fields over a sphere

A new computational approach is presented which allows fast analysis of radiation from large reflector antennas. For an aperture a Fourier transform (FT) relationship does exist between far-field and aperture distribution. Accordingly, the far field can be exactly reconstructed from the knowledge of approximately one sample per lobe (Shannon-Whittaker theorem applied at Nyquist rate). The finite reflector curvature introduces an extra factor in the radiation integral so that the radiation integral is no longer a FT. In order to overcome this difficulty a new pseudosampling expansion, which explicitly takes into account the extra factor, is developed. For parabolic reflector the sampling functions are related to the Fresnel integrals, and the far field can be exactly reconstructed in terms of aperture far-field samples, which can be computed using the fast Fourier transform (FFT). Numerical computations and error analysis show the excellent performance of the method, which can be generalized to deal with arbitrary reflector surfaces and near-field evaluation.

Reflector antenna fields--An exact aperture-like approach

The newly developed pseudo-sampling representation is applied for computing the far field of an offset parabolic reflector with a cluster feed illumination. A new comb-type fast Fourier transform (FFT) algorithm is used in a computer program. Both precision and computational time are analyzed, demonstrating the excellent performance of the method.

Efficient computation of the far field of parabolic reflectors by pseudo-sampling algorithm

A new computational approach is presented, which allows fast analysis of radiation from reflector antennas. The basic idea is the Fourier transform (FT) relationship between far-field and aperture distributions. Accordingly, the far field can be exactly reconstructed from the knowledge of spatial samples at angular rate ka sin θ cosϕ = n π ka sin θ sin ϕ = m π, where a is the aperture radius (Shannon-Whittaker theorem applied at Nyquist rate). The conclusion is that the aperture far field can be sampled at approximately one point per lobe. The finite reflector curvature introduces an extra term in the radiation integral which modifies the (finite) aperture/far-field FT relationship. There are two ways to overcome this difficulty: (1) consider an infinite aperture, thereby saving the FT relationship, but losing the spatially band-limited property and (2) reformulate the Shannon-Whittaker theorem in such a way as to take into account the extra (curvature) term. The first approach requires truncation of the infinite aperture to an assigned degree of approximation in the far-field computation. This states an equivalence between the field radiated by the reflector and the field radiated by an equivalent aperture of larger radius. Accordingly, the far field can still be reconstructed using the field radiated by the reflector, sampled at a higher rate (slightly higher for large dishes). These samples can be computed using physical optics or asymptotic techniques, whichever is appropriate. The second approach is based on a new sampling representation, which explicitly takes into account the extra term in the radiation integral. For a quadratic type of term, i.e., for parabolic reflectors, the sampling functions are the complementary error functions, and the far field can be exactly reconstructed in terms of the far field of an equivalent aperture. These samples can be computed using the fast Fourier transform, therefore further gaining in time saving. Computations showing the excellent performances of the two methods have been made, indicating the significant advantages provided in reflector antenna analysis.

G. Delia

Papers

Computation of radiation from reflector antennas - An optimal strategy