Volume self-calibration for three-dimensional particle tracking velocimetry based on a stereoscopic shadowgraph system

Abstract The stereoscopic shadowgraph system can accommodate high framing rate, long depth of field, and high imaging quality for two-phase flow measurements. The system has been combined with three-dimensional (3D) particle tracking velocimetry (PTV) to implement time-resolved volumetric measurements. Due to inadequate constraints, the calibration residuals and system drift can cause deviations of the mapping function, leading to a large proportion of ghost particles. In this study, the extrinsic parameters self-calibration (EPSC) based on particle images is introduced to correct the mapping function error. The algorithm is implemented by minimizing the reprojection disparity, where the drift is transferred to the right camera by fixing the left camera as reference. Synthetic datasets are used to evaluate the influence of drifts and self-calibration algorithms on PTV processes within a wide range of 0.0039–0.0625 ppp particle image densities. The extrinsic parameters including both translation and rotation drifts are involved and the effect of sub-domain divisions during rotation drift is discussed. Results indicate that the deviated mapping functions greatly impact the accuracy of the 3D tracking process, and the EPSC algorithm can significantly reduce the reprojection error and the proportion of ghost particles. For translation drift between 0.57 and 1.13 pixels, more than 95% of true particles are tracked and the proportion of ghost particles is below 5% after EPSC process. For rotation drift with approximately a maximum 2 pixels disparity, the EPSC can also restore more than 95% and 55% true particles for the two datasets respectively. The current method is applied to the 3D flow field of an oscillating foil in still water, based on which reasonable particle trajectories are successfully resolved. The results indicate that the EPSC algorithm can effectively reduce the influence of system drift and improve the tracking accuracy of two-view PTV measurements. The current method has the potential to enable two-view volumetric PTV techniques to cope with scenarios of denser particle concentrations and achieve higher spatial resolution.