A full three-dimensional characterization of defocusing digital particle image velocimetry

The paradigm set forth by Pereira et al (2000 Exp. Fluids 29 S78–84) was an important milestone in capturing the optical geometry of a three-dimensional defocusing digital particle image velocimetry (DDPIV) design within a set of systematic equations. However, the opportunity to improve upon their pseudo-three-dimensional conceptual implementation of the two-dimensional equations exists by revisiting the derivations of these equations and revising some of their assumptions in order to define a modified set of equations for a true full-three-dimensional derivation. This paper introduces this newly revised set of equations that will explicitly and more accurately represent the three-dimensional DDPIV measurement system. A three-dimensional geometric uncertainty model has also been established through uncertainty analysis. Finally, a discussion of the differences and benefits of the new system of equations is presented.