Stereoscopic 3D PIV

Conventional 2D planar PIV technique measures projections of 3D velocity vectors onto the 2D plane defined by the light sheet. It is not capable of measuring 

2 Calibration and 3D Reconstruction. To reconstruct the true 3D (X,Y,Z) displacements from two 2D (x,y) displacements as observed by the two cameras, a numerical model is necessary that describes how each of the two cameras image the flow field onto their CCD chips. Using the camera imaging models, four equations (which may be linear or nonlinear) with three unknowns are obtained. 

Instead of a theoretical model that requires careful measurements of distances, angles, and so on, an experimental calibration approach is preferred. The experimental calibration estimates the model parameters based on the images of a calibration target as recorded by each camera. A linear imaging model that works well for most cases, the pinhole camera model, is based on geometrical optics. This leads to the following direct linear transform equations, where x,y are image coordinates, and X,Y,Z are object coordinates. This physics-based model cannot describe nonlinear phenomena such as lens distortions. 

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