Exact derivation of aperture errors in antenna measurements

Antenna-pattern measurements are generally undertaken by placing the antenna under test (usually the receiving antenna) sufficiently far from the transmitting antenna that the receiving antenna is illuminated with a plane wave. Gain measurements, whether by substitution, paired horns, or integration of the area under the beam pattern, depend upon the same criterion. A true plane wave is only achieved by separating the two antennas by an infinite distance, but it has been shown by Milne (1950) that small departures from a plane wave do not usually seriously degrade the measurement. The authors consider three aspects of the fields across a linear aperture. The finite spacing between the antennas produces a phase deviation and an amplitude taper. If we are only interested in the apparent gain loss, we need to combine both tapers into an illumination efficiency. It is surprising how little the illumination loss is when the phase deviation and amplitude taper are large. The formulation is given in terms of linear apertures, and can be easily extended to circular or rectangular apertures by adjusting the limits of the integrals.