Shadowgraph imaging is a promising technique for volumetric velocity measurements, which features with high framing rate, long depth focus, and a cheap light source. The main objective of current study is to develop a camera calibration algorithm for collimated shadowgraph systems, which is an essential procedure for 3D PTV strategies. First, the optical model of a two-view collimated shadowgraph system is established, which can be described by the orthographic projection model. The image distortion effect is also taken into consideration. Then, the calibration algorithm is developed using a flexible planar-target-based method. Aiming for 3D PTV applications, the extrinsic parameters including rotation and translation relationships between the two camera imaging coordinates have been derived. The ambiguity for sign confirmation of the extrinsic parameters has been solved by introducing extra information from the relative position of the two views. Moreover, extrinsic parameters self-calibration (EPSC) has been implemented to deal with unavoidable camera drifts during the experiments. The results indicate that the EPSC is effective to remove the global system error in the current two-view system. The proposed calibration algorithm has been verified by synthetic images, which has shown a mean reprojection error less than 0.1 pixel. In a water jet experiment, the mean reprojection error is around 0.3 pixel (about 0.019 mm in reality) after the board calibration. The relative error evaluated from the reconstruction points is less than 1%. The reprojection error can be further reduced to less than 0.1 pixel after refining through EPSC algorithm. The results indicate that the proposed calibration procedure is effective and feasible for collimated shadowgraph imaging systems. The 3D-particle positions of a sample frame have been reconstructed successfully. It is believed that the high-quality shadowgraph images can offer high precision measurements for further particle tracking velocimetry.
The volumetric Lagrangian measurements of droplet or turbulent flow using particle tracking methods have attracted intensive attentions recently. The performance of three-dimensional particle tracking velocimetry (3D PTV) is highly relying on the algorithms. Most of the existing 3D PTV algorithms are developed for multi-view systems, which cannot be applied directly to two-view systems due to the lack of enough geometry constraints. In the current study, three different 3D PTV algorithms applicable for two-view systems have been investigated parametrically using synthetic data. The imaging model is established on a two-view collimated shadowgraph imaging setup, which features with high framing rate, large test volume and long depth focus. The performance of three algorithms has been tested under different image particle densities and displacement-spacing ratios. The correctness of 3D reconstruction and tracking, as well as the number of ghost particles are obtained and compared comprehensively. The results indicate that significant improvement has been achieved through dedicated designed algorithms. The comparative study has revealed the potential of each algorithm with extremely limited geometry constraints in two-view systems, which may serve as guidance for choosing appropriate algorithms under different test conditions.
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