A heterodyne laser interferometer is used to study acoustic wave fields excited in a 1.8 GHz AlN thin film bulk acoustic wave resonator. The electrical response of the resonator exhibits a strong thickness resonance onto which spurious modes, caused by lateral standing plate waves, are superposed. Optical interferometer measurements are used to extract dispersion curves of the laterally propagating waves responsible for the spurious responses. A discrete eigenmode spectrum due to the finite lateral dimensions of the resonator is observed. An equivalent circuit model for a multimode resonator is fitted to the mechanical resonator response extracted along a single curve in the dispersion diagram, and is used to determine properties, such as Q-values, of the individual lateral eigenmodes. Measured wave field images, extracted dispersion curves, and the eigenmode spectrum with the model fitting results are presented.