Distortion compensation for generalized stereoscopic particle image velocimetry

Optical distortion due to inaccurate optical alignment, lens nonlinearity, and/or refraction by optical windows, fluid interfaces, and other optical elements of an experiment causes inaccuracy by introducing variable magnification. Since fractional changes in the magnification have a one-to-one effect on the accuracy of measuring the velocity, it is important to compensate for such distortions. A general experimental calibration procedure is described which determines the magnification matrix of a distorted imaging system, and an algorithm is presented to compute accurate velocity field displacements from measurements of distorted PIV images. These procedures form a basis for generalized stereoscopic PIV procedures which permit easy electronic registration of multiple cameras and accurate recombination of stereoscopic displacement fields to obtain the three-dimensional velocity vector field.