Non-Invasive Laser-Cross Calibration For Volumetric Flow Measurements In Closed Channels

The calibration of a multi-camera system is a crucial step of a 3D particle tracking velocimetry (3D-PTV) measurement and other optical velocimetry techniques, which are based on multi-camera setups. Conventional calibration methods for multi-camera systems are based on recording hardware targets in the cameras’ fields of view. In measurement volumes that are difficult to access, the insertion of such hardware targets is associated with an increased technical or mechanical effort or is eventually not possible. This work presents a calibration method without the use of a hardware target. Instead, crossing laser beams are introduced into the volume, which create unique calibration points due to their beam paths. The underlying algorithm for detecting the laser beams and the optimization of the calibration is explained. The influence of the beam diameter and positioning errors on the calibration quality are examined by using synthetic data, which is created in Blender (Free and Open 3D Creation Software under GNU GPL). The new laser cross calibration is compared to the calibration with a two-plane target by synthetic data and experimental data from a 3D-PTV measurement in a difficult-to-access volume in a transparent manifold. For the comparison, the synthetic data and the therefore known absolute positions of the lasercross allow to calculate the reconstruction error in addition to the widely used reprojection error. The ransac algorithm is used for the detection of the beam paths from the raw images. The ransac algorithm is well suited for this application, as it is stable against parasitic reflections while its subpixel accuracy is sufficient for this application with small beam diameters. The non-invasive calibration techniques have different advantages over the usage of a hardware target. Due to the in-situ calibration it is not necessary to move the camera setup, which can otherwise lead to errors in the alignment of the cameras to each other. The installing and deinstalling process of the calibration plate is not needed, which reduces the effort for the construction and further reduces errors. Hardware-targets need to be homogenously illuminated, which is not necessary with "self-illuminating" calibration targets like the laser cross. When having opposing cameras, hardware-targets need to be two-faced with front- and back-side being perfectly parallel and the calibration points need to be in defined geometric relation. Deviations can introduce systematic errors. With a non-invasive method like the laser cross there is no obstruction by the calibration plate itself.