Particle Image Velocimetry (PIV) is a non-intrusive, two-dimensional, instantaneous velocity measurement technique. The measurements are performed by seeding the flow of a fluid with small particles and illuminating a region of interest with a thin sheet of powerful laser light. Then, sequential images of illuminated particles are captured either in pairs or in a double-exposed form by a CCD camera, depending on the method that the images are interrogated. In the case where the images are captured in pairs one obtains the velocity field via cross-correlation, whereas in the other case via auto-correlation. Below, the cross-correlation operation is described briefly by using numerically simulated PIV images that were created with Matlab. Image 1 and Image 2 show the simulated particle images at time instants t = t_1 and t = t_2, respectively. Particles are shifted by 4 pixels in positive x and y directions as they move from Image 1 to Image 2.
 

The average displacement, and consequently the average velocity, of the particles in the images are obtained by performing cross-correlation, which is a statistical method to determine the relation between the data contained in the images. As mentioned above, the prescribed relation between data contained in Image 1 and Image 2 is that particles move 4 pixels in positive x and y directions, so the resulting correlation function has a maximum value at this particular location. Below, contour and three-dimensional plots of the correlation function are shown. The peak is shifted by 4 pixels in each direction with respect to the center of the plotted area.
 

In the case of an actual PIV image however, the number of particles and the size of the image are much larger than the numerically simulated images shown above. Hence the image is divided into many small regions from which one velocity vector representing the average velocity of the particles contained only in that small region is obtained. This can be best described by an actual image and measured velocity field.

The image below is a real image of wavy vortex flow in a cylindrical Couette device investigated in our laboratory. The bright arcs at the top and the bottom (the bottom one is not as visible) are the outer and inner cylinder boundaries that become visible as the laser light sheet passes through the flow region of interest. The inner cylinder rotates in the CW direction and the outer cylinder is stationary. The white spots are individual tracer particles in the flow. The size of the image is 1K x 1K pixels. The average velocity of the tracer particles in a small 64 x 128 pixel interrogation region (subset of the image) is found using the cross-correlation for this region. Repeating this process over a grid of locations in the flow field provides an array of green velocity vectors. The length of the green vectors is proportional to the magnitude of the velocity. The orientation of the green vectors shows the direction of the flow. The velocity field shown below is obtain from a single pair of images. Ensemble averaging several realizations of velocity data produces even better results.