A two-axis optical imaging system using a Lissajous scan pattern with non-integer frequency ratio is presented. A waveguide with precisely tuned mechanical resonant frequencies is constructed by dip coating two fibres with a transparent polymer. Motion is achieved by mounting a waveguide cantilever at 45° on a single piezoelectric actuator with a dual-frequency drive. Confocal signal collection is achieved using a mode-stripping detector, and feedback signals needed for frequency and phase locking are derived from intermittent reflection from an apertured mirror. The first scan axis is locked to the resonance of one of the modes, while the second scan axis is locked to the correct phase at the desired frequency ratio. Accurate acquisition of two-dimensional images is demonstrated.