Camera calibration algorithm development for a two-view collimated shadowgraph system

Abstract

Shadowgraph imaging is a promising technique for volumetric velocity measurements, which features a high framing rate, long depth focus, and a cheap light source. The main objective of the current study is to develop a camera calibration algorithm for collimated shadowgraph systems, which is an essential procedure for 3D particle tracking velocimetry (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 towards 3D PTV applications, the extrinsic parameters, including rotation and translation relationships between the two camera imaging coordinates, have been derived. The ambiguity around the sign confirmation of the extrinsic parameters has been solved by introducing extra information from the relative positions 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 in removing the global system error in the current two-view system. The proposed calibration algorithm has been verified using synthetic images, which has shown a mean reprojection error of less than 0.1 pixels. In a water jet experiment, the mean reprojection error is around 0.3 pixels (about 0.019 mm in reality) after the board calibration. The relative error evaluated from the reconstruction points is less than 1%. 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 implementations of 3D PTV algorithms.