Asymmetric time sequence for multiple-exposure 3D PTV

Recording onto a single-frame multiple exposures of the tracer particles has the potential to simplify the hardware needed for 3D PTV measurements, especially when dealing with high-speed flows. The analysis of such recordings, however, is challenged by the unknown time tag of each particle exposure, alongside their unknown organization into physical trajectories (trajectory tag). Using a sequence of two or more illumination pulses with a constant time separation leads to the well-known directional ambiguity problem, whereby it is not possible to distinguish the direction of motion of the tracer particles. Instead, an irregular and asymmetric sequence of time separation for the illumination pulses allows recognizing the time tag of the unique sequence of positions in the image, composing the trace. A criterion is formulated here that recognizes unambiguously the trace pattern, based upon the principle of kinematic similarity. A combinatorial algorithm is proposed whereby a signal-to-noise ratio is introduced for every candidate trace. The approach is combined with an additional criterion that favors trace regularity (minimum velocity fluctuations). The algorithm is illustrated making use of particle motion examples. Furthermore, it is assessed using 3D experimental data produced with time-resolved analysis (single-frame, single-exposure) using the Shake-the-Box method. Traces with a three-pulse sequence yield a detection rate of 85%. The latter declines with the number of pulses. Conversely, the error rate rapidly vanishes with the samples number, which confirms the reliability of trace detection criterion when more pulses are comprised in the sequence.

Graphical abstract