In general, only two velocity components are measured using standard PIV (2C-PIV). All the three velocity components can be measured and recorded using a stereoscopic approach, resulting in instantaneous 3D velocity vectors for the whole area.
A three component PIV (3C-PIV) is based on the same fundamental principle as human eye-sight: Stereo vision. Our two eyes see slightly different images of the world surrounding us, and comparing these images, the brain is able to make a 3-dimensional interpretation. With only one eye, it is perfectly able to recognise motion up, down or sideways, but it is difficult to judge distances and motion towards or away from you. Here, cameras play the role of "eyes". The most accurate determination of the out-of-plane displacement (i.e., velocity) is accomplished when there is 90° between the two cameras. The camera and the lens are aligned with an angle to the light sheet. Distortion of image fields occurs. Therefore the angle is kept so small that defocusing is acceptable. To overcome focusing problem in angular displacement, the Scheimpflug condition should be satisfied (The lens plane and the object plane and the image plane for each cameras has to intersect in a common line). The side effect by using method is to have a strong perspective distortion. Perspective distortion is avoided by using a second order mapping function (Raffel et al., 1998). Mapping function is the matrix which transforms the pixel coordinate system into real coordinate systems.
In this arrangement image plane, lens principle axis plane and object plane (Light sheet) meet at the same point, as shown in the Fig. 1. This configuration can be achieved by mounting the camera lens with an angular offset, as in the angular offset stereoscopic camera configuration and then tilting the camera body (with respect to the lens). The correct focus and tilt angles are achieved when all of the particles within the camera field of view are in good focus. The on-line update of the images captured by the camera makes this setup process straightforward.
The Scheimpflug arrangement allows one to keep the plane of best focus in the plane of light sheet for both air and water flows while having the camera view the light sheet from off-axis angle. The Scheimpflug configuration introduces perspective distortion to the images causing a rectangle in light sheet plane to be imaged as a trapezoid on the image sensor.
Photographic view of traversing arrangement for stereo PIV experiment.