Currents Reconstruction by Means of a New 2D Extrapolation Matrix

The equivalent currents reconstructed on the surface of an antenna from its far field measurements have a limited resolution. This is because just the visible part of the spectrum, i.e. the inner part of the circle of radius k (the wavenumber), can be obtained with this technique. The zero padding technique is used for improving the precision; however this technique does not improve the resolution and additional methods must be applied. One of the most used is the Gerchberg-Papoulis algorithm. This technique obtains the non visible spectrum from just the visible region and the maximum size of the antenna. The main disadvantage of this algorithm is that, since it is iterative, it takes a long processing time for achieving a good resolution. A direct form of this algorithm, called the extrapolation matrix, has been proposed, however its result is not the same as the result of the iterative method for 2D cases. In this paper a new 2D extrapolation matrix for obtaining the same result as the iterative algorithm is proposed.