The idea of a "phase-centre" for a feed antenna is frequently used when designing a system to be fed by the antenna. The phase-centre is loosely thought of as the point from which the beam emanates but that will be uniquely defined only for a beam which has a truly spherical phase-front and that is rarely the situation with a feed antenna, even in the far-field.
R. J. Wylde, R. J. Wylde,
"Phase and phase centres in quasi-optical systems", Proc. SPIE 1514, 15th International Conference on Infrared and Millimeter Waves, 15145P (1 December 1990); doi: 10.1117/12.2301615; https://doi.org/10.1117/12.2301615