Note: Three-dimensional linearization of optical trap position detection for precise high speed diffusion measurements

Y.-H. Hsu and A. Pralle

Studies of the details of Brownian motion, hydrodynamic of colloids, or protein diffusion measurements all require high temporal and spatial resolution of the position detector and a means to trap the colloid. Optical trap based thermal noise imaging employing a quadrant photodiode as detector provides such a method. However, optical trapping requires an objective with high numerical aperture resulting in highly nonlinear position signal and significant cross-dependence of the three spatial directions. Local diffusion measurements are especially susceptible to distance errors. Here, we present a position calibration method, which corrects nonlinearities sufficiently to allow precise local diffusion measurement throughout the entire trapping volume. This correction permits us to obtain high-resolution two- and three-dimensional diffusion maps.

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