Application of Fourier Integrals for Determination of Antenna Far-Field Patterns from Measurements at Fresnel Distances

Abstract

A method for determination of antenna far-fields, based on a measurement at Fresnel distances, is presented. The method is applicable to highly directive antennas, measured in anechoic chambers, which size is not large enough to satisfy the far-field condition for the antenna under test (AUT). The method is based on an approximation of the accurate diffraction integral at Fresnel distances by a Fourier integral. According to the method, a quasi far-field radiation pattern of the AUT is measured at a Fresnel distance R, the measured pattern is used for a reconstruction of a distorted, due to the short range, aperture excitation, and the distorted aperture excitation is corrected magnitudewise and phasewise in accordance with ${R}$ and, then, forward propagated to the far-field. An advantage of the method is that it allows an accurate treatment of the distorted phase and the magnitude of the Green kernel in the diffraction integral, with respect to the ideal far-field, in contrast to the usual quadratic approximation of the phase and expansion in an infinite row of the exponential phase term. The method offers computational precision advantages over existing methods in shorter measurement distances R and low levels of sidelobes. The accuracy of the method improves as the directivity of the AUT gets higher. The measurement distance R must not be too short to smear too much the measured Fresnel pattern and to compromise the validity of the mentioned Fourier approximation of the diffraction integral.