Correction of misalignment errors in stereoscopic PIV systems

The main purpose of the present work is to correct errors occurring in a stereoscopic PIV system and caused by misalignments between the calibration plane and the measurement plane. The experimental measurements have been conducted using an angular stereoscopic system with Scheimpflug conditions and a PIV-calibration pattern has been mounted on stages which can translate in three dimensions and rotate around the vertical axis. In order to correct the errors in perspective, a calibration of the cameras has been done by setting the PIV-calibration pattern in different z-positions and utilizing different mapping functions of the physical plane coordinates (x, y, z); afterwards, a cross-correlation of the images recorded by the two cameras at the same instant has been used to calculate the disparity map and to obtain the equation of the measurement plane, i.e. an estimated value of the misalignment; finally, a reconstruction of the three-dimensional displacement field has been made: in this reconstruction the image has been de-warped inside the iterative deformation PIV process, in order to reduce the loss of image quality. A displacement field has been simulated to show the efficiency of the correction of misalignment errors. A correction of the formulae generally used in literature to estimate the viewing angles permits to obtain better results even for out of plane displacements.