Stereoscopic particle tracking for 3D touch, vision and closed-loop control in optical tweezers

Force measurement in an interactive 3D micromanipulation system can allow the user to make delicate adjustments, and to explore surfaces with touch as well as vision. We present a system to achieve this on the micron scale using stereoscopic particle tracking combined with holographic optical tweezers, which can track particles with nanometre accuracy. 2D tracking of particles in each of the stereo images gives 3D positions for each particle. This takes less than 200 µs per image pair, using a 1D 'symmetry transform' applied to each row and column of a 2D image, which can maintain tracking of particles throughout the 10 µm axial range. The only parameters required are the geometry of the imaging system, and therefore there is no need to recalibrate for different particle sizes or refractive indices. Consequently, we can calculate the force exerted by the optical trap in real time at 1 kilohertz, allowing us to implement a force-feedback interface (with a loop rate of 400 Hz). In combination with our OpenGL hologram calculation engine, the system has a closed-loop bandwidth of 20 Hz. This allows us to stabilize trapped particles axially through active feedback, cancelling out some Brownian motion. For the weak traps we use here (spring constant k≈2 pN µm − 1), this results in a threefold increase in axial stiffness. We demonstrate the 3D interface by probing an oil droplet, mapping out its surface in the y–z plane.