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 threedimensional 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.