Nonredundant NF-FF transformation by a bi-polar scanning facility

antennas, the required size of the conventional FF range becomes prohibitively large. Moreover, the development and the spreading of NF-FF transformation techniques employing planar, cylindrical or spherical scanning systems is justified from the fact that each approach has its own particular advantages, depending on the antenna under test (AUT) and the measurement requirements. Last but not the least, NF facilities provide a controlled and secure environment, and all weather capability. Among the NF-FF transformation techniques, that employing the plane-polar scanning has attracted considerable attention due to its particular characteristics [1]. In such a scanning the antenna rotates while the probe travels in a linear motion, so that the NF data are acquired in concentric rings centered on the AUT. The large computer time, required in the earliest approach [1] to reconstruct the far-field, has been drastically reduced by recovering the plane-rectangular data from the plane-polar ones, thus enabling the use of FFT [2]. In [3], by exploiting the quasi-bandlimitation properties of electromagnetic (EM) fields [4], an optimal sampling interpolation (OSI) algorithm has been developed to recover the plane-rectangular data from the plane-polar ones. It minimizes the truncation error and is stable with respect to errors affecting the data. Moreover, at variance of the previous approaches [1, 2], the number of samples for each ring stays bounded even if the ring radius goes toward infinity and, on increasing the measurement plane distance, the radial step can be significantly larger than that previously adopted. However, when the radius of the scanning zone approaches infinity, the overall number of samples becomes unbounded. This shortcoming has been overcome in [5, 6], where field representations over a plane from a nonredundant number of samples, which stays finite also for an unbounded scanning plane, have been developed. They have been obtained by considering proper geometrical modellings of AUT and by exploiting the results [7] concerning the nonredundant representations of the EM fields radiated by sources enclosed in arbitrary convex domains with rotational symmetry and observed on surfaces having the same symmetry. The bi-polar scanning proposed by Rahmat-Samii et alii in [8, 9] represents a convenient alternative to collect NF data over a plane. In such a scanning the AUT rotates axially, whereas the probe is attached to the end of an arm which rotates around an axis parallel to the AUT one. This allows to collect the NF data on a grid consisting of concentric rings and radial arcs (see Fig. 1). The bi-polar scanning maintains all the advantages of the plane-polar one while providing a simple and cost-effective measurement system. In fact, since the arm is fixed at only one point and the probe is attached at its end, the bending is constant and this allows to maintain the planarity. Moreover, rotational movements are preferable to the linear ones, since rotating tables are more accurate than linear positioners.