Asymmetric time-sequence for multiple-exposure 3D PTV

Abstract

Making use of a single-frame to record multiple exposures (ME) 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 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, coding the temporal information into a specific sequence of illumination pulses with irregular time separation results in a unique sequence of positions in the image, similar to a trace. The asymmetric pattern of the trace needs to be recognized, and a kinematic similarity criterion is introduced that selects traces most similar to the time sequence. Combining the latter with a criterion that favors trace regularity (minimum velocity fluctuations). The numerical implementation of the technique is challenged by the combinatorial growth of the calculations. The algorithm is applied to a 3D experiment and results are benchmarked against the time-resolved analysis (single-frame, single-exposure) with the Shake-the-Box method. Traces with a three-pulses 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. Potential methods to accelerate the ME recordings analysis are presented. The remaining bottlenecks hampering the direct application of the technique are also introduced and shortly discussed.