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Antenna efficiency is the ratio of the measured gain and calculated directivity.
The directivity is usually calculated from the aperture size and wavelength.
Gain measurement is best done on an open range; in aperture antennas the beam is often formed far away from the aperture; this is difficult to do in an anechoic chamber.
Using the near-field to far-field procedure is mainly useful to measure the full radiation pattern than the main beam while the main beam width determines the gain.
Details can be found in many books and manuals, also Agilent white paper.
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