Recently the theory of linear coupling between the ordinary (O) and extraordinary (X) electron cyclotron waves in the vicinity of critical (cut-off) plasma density was generalized for two-dimensionally inhomogeneous plasma configurations, in particular taking into account the variation of a magnetic field on flux surfaces in tokamaks and stellarators. One of the new features of two-dimensional mode conversion is the existence of optimal quasi-optical beams of a finite aperture exhibiting perfect (no reflection) transformation instead of an optimal plane wave specific for one-dimensional geometry. In this paper such wave structures are analysed in more detail keeping in mind its importance for experiments on electron cyclotron resonance heating and diagnostics of overdense magnetized plasma based on linear mode conversion in modern stellarators and spherical tokamaks.