Lissajous microscanners are very attractive in compact laser scanning applications such as endomicroscopy or pro-projection display owing to high mechanical stability and low operating voltages. The scanning frequency serves as a critical factor for determining the scanning imaging quality. Here we report the selection rule of scanning frequencies that can realize high definition and high frame-rate (HDHF) full-repeated Lissajous scanning imaging. The fill factor (FF) monotonically increases with the total lobe number of a Lissajous curve, i.e., the sum of scanning frequencies divided by the great common divisor (GCD) of bi-axial scanning frequencies. The frames per second (FPS), called the pattern repeated rate or the frame rate, linearly increases with GCD. HDHF Lissajous scanning is achieved at the bi-axial scanning frequencies, where the GCD has the maximum value among various sets of the scanning frequencies satisfying the total lobe number for a target FF. Based on this selection rule, the experimental results clearly demonstrate that conventional Lissajous scanners substantially increase both FF and FPS by slightly modulating the scanning frequencies at near the resonance within the resonance bandwidth of a Lissajous scanner. This selection rule provides a new guideline for HDHF Lissajous scanning in compact laser scanning systems.
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