Editing Particle image velocimetry (section)

===Stereoscopic PIV===
[[Stereoscopic]] PIV utilises two cameras with separate [[angle|viewing angle]]s to extract the z-axis displacement. Both cameras must be focused on the same spot in the flow and must be properly calibrated to have the same point in focus.

In fundamental fluid mechanics, displacement within a unit time in the X, Y and Z directions are commonly defined by the variables U, V and W.  As was previously described, basic PIV extracts the U and V displacements as functions of the in-plane X and Y directions.  This enables calculations of the <math>U_x</math>, <math>V_y</math>, <math>U_y</math> and <math>V_x</math> velocity gradients.  However, the other 5 terms of the velocity gradient tensor are unable to be found from this information.  The stereoscopic PIV analysis also grants the Z-axis displacement component, W, within that plane.  Not only does this grant the Z-axis velocity of the fluid at the plane of interest, but two more velocity gradient terms can be determined:  <math>W_x</math> and <math>W_y</math>.  The velocity gradient components <math>U_z</math>, <math>V_z</math>, and <math>W_z</math> can not be determined.
The velocity gradient components form the tensor:

:<math>
\begin{bmatrix}
 U_x & U_y & U_z \\
 V_x & V_y & V_z \\ 
 W_x & W_y & W_z \\
\end{bmatrix}
</math>