The input power of accelerator structure is normally fed through a coupling slot(s) on the outer wall of the accelerator structure via magnetic coupling. While providing perfect matching, the coupling slots may produce non-axial-symmetric fields in the coupler cell that can induce emittance growth as the beam is accelerated in such a field. This effect is especially important for low emittance beams at low energies such as in the injector accelerators for light sources. In this paper, we present studies of multipole fields of different rf coupler designs and their effect on beam emittance for an X-band photocathode gun being jointly designed with LLNL, and X-band accelerator structures. We will present symmetrized rf coupler designs for these components to preserve the beam emittance. Show Partial Abstract