Quantifying and mitigating systematic errors in high-speed visualization of unsteady cavitating flows

Flow visualization experiments are crucial for characterizing the dynamics of unsteady cavitation flows. However, systematic errors caused by inaccuracies in high-speed camera assembly and multi-layer refractive effects can significantly compromise image fidelity. This study proposed an integrated calibration protocol that combined camera calibration with multi-layer planar refractive distortion correction. A nonlinear camera model was first employed to elucidate the origin of lens distortion and establish the rationale for correction, followed by the implementation of a camera calibration method to compensate for radial and tangential aberrations. A multi-layer planar refraction imaging model was then developed to define the applicability conditions of in-air calibration parameters for underwater scenarios. Using the Pinax theoretical framework, the forward projection equations for air–glass–water refraction were derived to enable precise coordinate transformations between the physical and virtual camera imaging planes. Systematic error reduction was quantified via reprojection error analysis. Finally, cavitation water jet visualization experiments were conducted to validate the calibration results, where the absolute error in nozzle-to-target distance measurements was evaluated. The synergistic application of these calibration methods effectively reduced systematic error by more than 95% and achieved a 70.64% reduction in absolute error. This study expands the applicability of in-air camera calibration, enhances the efficiency of refraction distortion correction, and provides a robust framework to improve measurement accuracy in flow visualization experiments.