Frequency-phase shift correction of interlaced lissajous trajectories for precise imaging in endoscopic scanning microscopy

• Dynamic discrepancies cause frequency and phase drift in Lissajous trajectory. • Mathematical description of shifted trajectories during scanning process. • Phase drifts by changes in driving frequency and damping ratio. • Lissajous trajectory shifts with the function of dynamical phase shift and slope. • Interlacing artifacts manifest due to shifted trajectories during resonance operation. Endoscopic scanners with a resonant scanning fibre cantilever have gained popularity in the biomedical field as optical imaging tools. However, precise characterisation of fibre cantilever-based scanners remains challenging, as the system is susceptible to dynamic discrepancies. To date, discussions regarding the dynamical influence of frequency and phase shift on reconstructed images in the Lissajous scanning system are limited. By looking into the theory behind the dynamic discrepancies, we have formulated mathematical expressions that describe the behaviour of frequency and phase shift on the frequency and phase response of the resonant scanning system. Phase drift occurs as a result of a mismatch between the driving signal and the resonance frequency, which modifies both the actual phase response and the Lissajous trajectory. The Lissajous trajectory shifts as a function of dynamical phase shift and slope. As a result, the coordinate for the Lissajous trajectory shifts in both vertical and horizontal coordinates, thereby causing image distortion and interlacing artifacts during image reconstruction. We verify the mathematical formulation by simulation and experimental confocal imaging of target samples with distinct features. A frequency shift of 0.1 Hz is sufficient to produce the interlacing artifacts. Our results establish that an accurate phase control in the Lissajous scanning system is required for clear, precise reconstructed images. The findings can be extended to non-resonant scanning systems and other scanning patterns. With the phase kept under control, any dynamical issues with a handheld endoscopic scanner can be mitigated to ensure distortion-free image reconstruction. More importantly, the main outcome of this study has proven the ability to reconstruct images precisely on target samples of various feature sizes without any interlacing effect.