The theta variable controls the angle between the laser plane and the $x$-direction flow field displacement (in radians). Essentially, this variable controls how misaligned the laser sheet is to the direction of the 2-d flow direction and demonstrates the importance of aligning the laser sheet with the flow field. When these planes are misaligned, particles are gained/lost between images. Figure 1 demonstrates a series of particle images becoming brighter through time due to laser plane misalignment (image captured through a pulsed laser with long exposure).
Figure 1. Example observation of particle intensity changing through a series of images (left) and Synthetic image particle intensity changing due to a 2° prescribed sheet angle (right).
This loss and gain of particles results in a potential increase in the PIV algorithm error, as these algorithms rely on estimating the translation of particles from the first to second image.
Author: Jack Elliott
Date Published: June, 2022