Perspective Camera Model with Refraction Correction for Optical Velocimetry Measurements in Complex Geometries

Camera calibration is among the most challenging aspects of the investigation of fluid flows around complex transparent geometries, due to the optical distortions caused by the refraction of the lines-of-sight at the solid/fluid interfaces. This work presents a camera model which exploits the pinhole-camera approximation and represents the refraction of the lines-of-sight directly via Snell's law. The model is based on the computation of the optical ray distortion in the 3D scene and dewarping of the object points to be projected. The present procedure is shown to offer a faster convergence rate and greater robustness than other similar methods available in the literature. Issues inherent to estimation of the refractive extrinsic and intrinsic parameters are discussed and feasible calibration approaches are proposed. The effects of image noise, volume size of the control point grid and number of cameras on the calibration procedure are analyzed. Finally, an application of the camera model to the 3D optical velocimetry measurements of thermal convection inside a polymethylmethacrylate (PMMA) cylinder immersed in water is presented. A specific calibration procedure is designed for such a challenging experiment where the cylinder interior is not physically accessible and its effectiveness is demonstrated by providing velocity field reconstructions.