Another look at volume self-calibration: Calibration and self-calibration within a pinhole model of Scheimpflug cameras

We address calibration and self-calibration of tomographic PIV experiments within a pinhole model of cameras. A complete and explicit pinhole model of a camera equipped with a 2-tilt angles Scheimpflug adapter is presented. It is then used in a calibration procedure based on a freely moving calibration plate. While the resulting calibrations are accurate enough for Tomo-PIV, we confirm, through a simple experiment, that they are not stable in time, and illustrate how the pinhole framework can be used to provide a quantitative evaluation of geometrical drifts in the setup. We propose an original self-calibration method based on global optimization of the extrinsic parameters of the pinhole model. These methods are successfully applied to the tomographic PIV of an air jet experiment. An unexpected by-product of our work is to show that volume self-calibration induces a change in the world frame coordinates. Provided the calibration drift is small, as generally observed in PIV, the bias on the estimated velocity field is negligible but the absolute location cannot be accurately recovered using standard calibration data.