A simplified and versatile calibration method for multi-camera optical systems in 3D particle imaging.

This article describes a stereoscopic multi-camera calibration method that does not require any optical model. It is based on a measure of the light propagation within the measurement volume only instead of modeling its entire path up to the sensors. The calibration uses simple plane by plane transformations which allow us to directly link pixel coordinates to light rays. The appeal of the proposed method relies on the combination of its simplicity of implementation (it is particularly easy to apply in any sophisticated optical imaging setup), its versatility (it can easily handle index-of-refraction gradients, as well as complex optical arrangements), and its accuracy {we show that the proposed method gives better accuracy than commonly used techniques, based on Tsai's simple pinhole camera model [R. Tsai, J. Rob. Autom. 3, 323 (1987)], while its numerical implementation remains extremely simple}. Based on ideas that have been available in the fluid mechanics community, this method is a compact turn-key algorithm that can be implemented with open-source routines.

Estimating two-point statistics from derivatives of a signal containing noise: Application to auto-correlation functions of turbulent Lagrangian tracks.

This article describes a method for calculating moments and correlation functions of signal derivatives, which were rid of experimental noise without the use of filtering operations. The method is based on the computation of the ensemble-average of different time (or spatial) increments of the signal. The hypotheses are that the noise is white and not correlated with the signal; however, the method is also shown to work with colored noise. The method is first developed, considering white noise, and benchmarked with synthetic trajectories containing noise with variable signal-to-noise ratios. It is then tested on experimental trajectories in the context of Lagrangian tracking of particles in turbulent flows, either containing a short-correlated noise or a colored noise.

Stochastic dynamics of particles trapped in turbulent flows.

The long-time dynamics of large particles trapped in two nonhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different spatial symmetries and temporal behaviors. Because large particles are less and less sensitive to flow fluctuations as their size increases, we observe the emergence of a slow dynamics corresponding to back-and-forth motions between two attractors, and a super-slow regime synchronized with flow reversals when they exist. Such dynamics is substantially reproduced by a one-dimensional stochastic model of an overdamped particle trapped in a two-well potential, forced by a colored noise. An extended model is also proposed that reproduces observed dynamics and trapping without potential barrier: the key ingredient is the ratio between the time scales of the noise correlation and the particle dynamics. A total agreement with experiments requires the introduction of spatially nonhomogeneous fluctuations and a suited confinement strength.