Abstract
Multi-dimensional, correlated particle tracking is a key technology to reveal dynamic processes in living and synthetic soft matter systems. In this paper we present a new method for tracking micron-sized beads in parallel and in all three dimensions - faster and more precise than existing techniques. Using an acousto-optic deflector and two quadrant-photo-diodes, we can track numerous optically trapped beads at up to tens of kHz with a precision of a few nanometers by back-focal plane interferometry. By time-multiplexing the laser focus, we can calibrate individually all traps and all tracking signals in a few seconds and in 3D. We show 3D histograms and calibration constants for nine beads in a quadratic arrangement, although trapping and tracking is easily possible for more beads also in arbitrary 2D arrangements. As an application, we investigate the hydrodynamic coupling and diffusion anomalies of spheres trapped in a 3 × 3 arrangement.
Highlights
Position tracking of particles has gained tremendous interest during the last years since a particle’s trajectory r(t) delivers an image of the interaction with its environment
The precision of a tracking system defines the resolution Δr of the position histogram or of p(r) [9], which can be down to a few nanometers and which is usually independent of the optical resolution δx ≈ λ/2 of a conventional microscope
In this paper we present a method, where time multiplexed optical tweezers can trap N different particles in N traps and determine their 3D positions by using sequential back-focal plane (BFP) interferometric tracking
Summary
Position tracking of particles has gained tremendous interest during the last years since a particle’s trajectory r(t) delivers an image of the interaction with its environment. A fast and precise tracking system is even more indispensable for measuring dynamic interactions such as in micro-rheology [10] or for processes out of thermal equilibrium [11] In this case analysis of correlations [12] or of power spectral densities allows the measurement of processes inside living cells [13], or the hydrodynamic interaction of particles in a fluid [14,15]. In this paper we present a method, where time multiplexed optical tweezers can trap N different particles in N traps and determine their 3D positions by using sequential BFP interferometric tracking (here N = 9). This enables an independent calibration of both particle displacements and optical forces of N different particles in N different traps within seconds. Due to the high tracking rate of 100/N ≈11 kHz, we show cross-correlation results of many particle hydrodynamic couplings
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