The Phase Center of Horn Antennas

OR CERTAIN applicat.ions, for example, a very precise interferometer, it is necessary to know t.he phase center of a horn ant.enna and t.he dependence of the pha.se cent,er on the shape of the horn. The phase center is defined as the center of curvature of the intersection of a far-field phase surface wit.11 a plane containing the horn axis. Previous work in this a.rea has been done by Baur [I]. He bases his work on t.he Iiirchhoff a,pproximation [a], and he derives an elegant method for determining the phase center of the E plane. Because I<irchhoff's approximation is used as a starting point,, the problem is basically treat.ed as a scalar problem. The solution is therefore primarily applicable to sectoral horns. A slight,ly different, approach to t.he problem was taken by Hu [3], where a plot, of the phase of the far field is used to determine the phase center. This met,hod requires a. suitable choice of coordina.te system and phase constant,s; Hu evaluat.ed the results for sectora.1 horns. Ujiie et al. [4] recognized that. different. phase centers will result for the E and N planes; they proceed to show only results for circular apertures m-it.11 phase distribut,ions which are a function of radius alone. For many applications such as diagona.1 and rectangular horns, the problem must be treated as a vector problem. Consequent,ly, the locat,ion of t.he phase cent,er will be derived here from the general expressions for the far field. To determine the phase center, it is necessary to use a second-order approximat.ion t,o the field at the horn aperture. While t.he far-field equations for horns [a] are generally ca,lculated by neglecting t,he fact, that the horn aperhre does not coincide with a phase front, such simplification cannot be afforded here. For square and diagonal horns discussed in this paper the integrat,ion is carried out over the horn aperture; however, a correction for the phase front is int,roduced. The phase front of the source is