Focal shifts in parabolic reflectors

Given a parabolic reflector, the maximum directivity is not always achieved by placing the feed at the focal point. Depending on the nature of the feed, the maximum directivity can be obtained by axially displacing the feed either toward or away from the reflector. For low-tapered feeds, the shift should be toward the reflector. This result is similar to an optical phenomenon called the focal shift. We find that this positive shift depends mainly on the Fresnel number of the reflector. For highly tapered feeds, the shift should be away from the reflector. This negative shift becomes significant when the reflector aperture is small, in units of wavelength. A unified view is presented to explain both the positive shift and the negative shift in terms of spillover, aperture illumination efficiency and phase asynchronism. For a system with optimum aperture edge taper, no focal shift can exist.