Interpolating algorithm for far-field calculations in the bi-polar method

In the bi-polar technique, the near-field to far-field transform can be calculated by the following three methods: interpolation/FFT, Jacobi-Bessel expansion and Fourier-Bessel expansion. The Jacobi-Bessel and Fourier-Bessel methods operate directly on the measured data located in the nodes of a bi-polar sampling grid. In these two methods a judicious choice of the expansion centre (which typically corresponds to the expected central axis of the antenna main beam) must be made. If the expansion centre fails to correspond to the central axis of the main beam, a fast convergence will not be achieved. Hence, these two methods are not recommended for the measurements of multi-beam, steerable-beam, steerable-null, or shaped-beam antennas. For such measurements the interpolation/FFT method is best suited, as in this approach no troublesome choices need to be made. Furthermore, the interpolation/FFT method has the inherent advantage of allowing direct application when the bi-polar sampling grid has been thinned in order to reduce the redundancy of the sampling points and, consequently, to shorten the duration of the measurement. Therefore we decided to use this method in our laboratory