On the Gerchberg-Papoulis algorithm for extrapolating antenna patterns

Summary form only given. The Gerchberg-Papoulis (G-P) iterative algorithm is a powerful method of extrapolating a band-limited time-domain function outside the time interval t in which it is known (Gerchberg, Optica Acta, 21, 9, pp. 709-720, 1974, Papoulis, IEEE Trans. Circuits and Systems, 22, 9, pp. 735-742, Sep. 1975). The method starts with the Fourier transform of the signal with zero padding outside the time interval t. The spectral data outside the known frequency band of the signal is deleted before performing inverse transform to obtain a new time domain signal. In this time-domain signal, the waveform in the time interval t is replaced by the original known time signal. Iterating the last three steps allows one to determine the entire time domain signal subject to numerical precision. Recently, this method has been employed successfully in constructing the front half space farfield antenna pattern using truncated planar near field data for a Gaussian tapered aperture distribution, uniform aperture distribution and a rectangular horn with no more than 50 iterations (Martini et al., IEEE Trans. Antennas Propagat., 56, 11, pp. 3485-3493, 2008). Martini et al. state that the G-P algorithm is suited to smoothly varying aperture distributions.The objective of this work is the application of the G-P technique for a wide range of aperture distributions to produce sum or difference patterns, and to understand the accuracy achievable as a function of the number of iterations, and the size of the truncated starting pattern. Initially we focus on one-dimensional aperture distributions since it may be easier to generalize the results. The contribution of the entire evanescent spectrum is incorporated using asymptotic evaluations. The effect of noise is investigated. The results will be applicable to the determination of the complete far-field pattern from the initial truncated near field data. Another application of this work is the determination of the far field at b- resight from a small number of near field samples in a surface perpendicular to the axis. In this case it will be interesting to know how few near field samples are needed to reconstruct the far-field in the boresight direction. The results of our investigation will be presented at the symposium.