Modelling, identification, and control of a spherical particle trapped in an optical tweezer

Abstract

AbstractWe provide an introduction to modelling, identification, and control of a spherical particle trapped in an optical tweezer. The main purpose is to analyse the properties of an optical tweezer from a control systems point of view. By representing the non‐inertial dynamics of a trapped particle using a stochastic differential equation, we discuss probability distributions and compute first mean exit times. Within the linear trapping region, experimentally measured mean passage times for a 9.6‐µm diameter polystyrene bead show close agreement with theoretical calculations. We apply a recursive least squares method to a trapped 9.6‐µm diameter polystyrene bead to study the possibility of obtaining faster calibrations of characteristic frequency. We also compare the performance of proportional control, LQG control, and nonlinear control to reduce fluctuations in particle position due to thermal noise. Assuming a cubic trapping force, we use computer simulations to demonstrate that the nonlinear controller can reduce position variance by a factor of 65 for a 1‐µm diameter polystyrene bead under typical conditions. Copyright © 2005 John Wiley & Sons, Ltd.