Assessment of camera models for use in planar velocimetry calibration

Abstract

Most planar imaging techniques require some sort of calibration to associate image coordinates with physical coordinates. A viewing arrangement in which the object plane (e.g. laser light-sheet) is parallel to the image plane involves a simple linear transformation consisting of translation, scaling and possibly rotation. This is no longer the case for oblique viewing arrangements or if lens distortion is present. In effect the normal viewing arrangement should be considered a special case of the oblique viewing arrangement. The calibration procedure for the more generalized oblique viewing arrangement typically requires high order mapping functions to transform image pixels to physical space coordinates. Additional calibration is necessary for multi-component measurements such as Doppler global velocimetry (DGV) or stereoscopic PIV. In these cases the positions of the cameras with respect to the image plane are required to reconstruct the three velocity components. A rather pragmatic approach is the direct measurement of the camera positions with respect to the object plane (Willert, 1997) which is not necessarily trivial in complex geometries involving windows or change of media (i.e. air-glass-water interface). The investigation was motivated by the need for reliable methods of camera calibration in various industrial wind tunnel and turbo-machinery applications of PIV and DGV. The use of translated (or multi-level) calibration targets is not always possible due to time constraints or setup complexity (i.e. measurements in curved channels). Even if translation targets were used, it was found that a larger number of calibration images or more complex camera models did not necessarily improve the final calibration result. Three implementations of pinhole-based camera models for use in common light-sheet imaging arrangements are described in the context of application to particle image velocimetry (PIV) and Doppler global velocimetry (DGV). Calibration data obtained from translated calibration targets was found to yield camera attitude within 0.1 degrees on a variety of different test cases with object distance varying as little as 2% depending on the choice of camera model. Calibration using data from a single plane is considered a viable alternative to manual triangulation of camera positions but is restricted to off-normal viewing directions. The presented calibration approach is considered a valuable tool for successful of three-component planar velocimetry in large scale facilities.