Fast and accurate far-field evaluation from a non redundant, finite number of plane polar measurements

Among the near-field-far-field (NF-FF) measurement techniques, that using a plane-polar scanning has attracted considerable attention due to its particular characteristics. The main drawback of the earliest approach, i.e., the large computer time required to reconstruct the antenna far field, can be overcome by applying the bivariate Lagrange interpolation (BCI) to recover the plane-rectangular data from the plane-polar ones. This step enables the use of the fast Fourier transform (FFT) also in the plane-polar scanning. However, the very simple BCI technique is not tailored to interpolate electromagnetic fields and, accordingly, requires close spacings to reduce the interpolation error. Previously (see IEEE Trans. Antennas Propag., vol. 39, p.48, 1991) by exploiting the quasi-bandlimitation properties of the radiated or scattered fields, an optimal sampling interpolation algorithm of central type has been developed, which is accurate, fast and stable with respect to random errors affecting the data. The maximum allowable azimuthal spacing has been derived and it has been demonstrated that the radial step can be significantly larger than the usually adopted one. It must be stressed that, at variance of the classical approach, the number of samples for each ring stays bounded even if the ring radius approaches infinity. In this way, the problem of data redundancy in the plane-polar scanning, i.e., the determination of the minimum number of required samples, has been partially resolved. However, when the radius of the scanning zone approaches infinity, the number of required rings becomes again unbounded. The aim of this paper is to reconsider thoroughly the problem of the radial interpolation in order to determine the maximum spacing between rings. In this way, the problem of data redundancy will be fully resolved.<>