Multiple-Exposure PTV With Variable Time Steps

Abstract

Recording multiple exposures of the tracer particles onto a single digital image has the potential to simplify the hardware needed for 3D PTV measurements. A sequence with equal time intervals leads to the well-known directional ambiguity problem. Instead, a sequence with irregular time-intervals (two or more) allows resolving the ambiguity. Two fundamental criteria are introduced that determine whether a set of particle samples corresponds to a physical trace for a given neighborhood: the kinematic similarity criterion imposes similarity (i.e. proportionality) between the length travelled by the particle and time elapsed. Additionally, the trace regularity criterion favors sets with minimum fluctuations of the velocity vector. A numerical algorithm, based on combinatorial analysis is presented, whereby all possible sets are scrutinized and the set of particles yielding the minimum disparity from the above criteria corresponds to the physical trace. The algorithm is demonstrated using 3D experimental data and results are benchmarked against the state-of-the-art time-resolved analysis Shakethe-Box (single-frame, single-exposure).