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

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.