A new near-field sampling representation from samples on planar spirals

A new convenient scanning geometry, the bi-polar one, has been introduced which allows simpler mechanical movements of the positioning system, thus enhancing its reliability and reducing its cost. In order to further reduce the complexity of the measurement set up as well as the time required for data acquisition, a continuous movement of the positioning system has been suggested leading to measurement points lying on a planar spiral. An effective exploitation of this new scanning system demand for a non-redundant field representation over a spiral (in order to get the minimum number of measurements required and the corresponding samples positions) allowing an efficient interpolation scheme for the evaluation of the field over the scanning plane, typically on a regular rectangular grid of /spl lambda//2 spaced points. In the past a large amount of effort has been devoted in the determination of a non-redundant and numerically efficient representation of the fields on canonical scanning surfaces in order to state the minimum number of required samples, their locations and to develop efficient interpolation algorithms. New field interpolation series allowing the use of a finite number of samples either on a bounded as well as unbounded observation line have been introduced at the University of Naples. Taking into account these results, a new interpolation series of the near-field on a planar spiral is introduced. Furthermore, an interpolation scheme is applied which allows one to evaluate the field on all the measurement planes from samples on a spiral line.