Recently, a new family of multi-resolution scan trajectories for high-speed scanning probe microscopy has been introduced based on Lissajous patterns. In this mode of imaging, the cantilever tip traverses the sample by following a pattern which is created by two single-tone harmonic waveforms interfering in a two dimensional plane. This paper provides a rigorous analysis of some of the fundamental properties of Lissajous scan trajectories, such as the imaging time and spatial resolution, and presents a step-by-step procedure which allows for the design of such trajectories. We also explore the multiresolution character of Lissajous scan trajectories which enables for a real-time preview of the sample in fractions of the overall imaging time. Experimental results are presented to substantiate the analytical results. © 2013 IFAC.