| In this dissertation, I provide an introduction to optical tweezers, including information about dynamics, construction, identification, and control. The main purpose is to analyze the properties of an optical tweezer from a control engineering point of view. The optical tweezer is widely used by biophysicists to study the mechanical properties of individual biological molecules.;Inertial and noninertial equations of motion are developed for both a linear trapping force and a cubic trapping force. By representing the noninertial dynamics of a trapped particle as a stochastic differential equation, probability distributions are discussed and first mean exit times are computed numerically. Experimentally measured mean passage times for a 9.6-micron diameter polystyrene bead within the linear trapping region show close agreement with theoretical calculations.;A recursive least squares method is applied to a trapped 9.6-micron diameter bead to study the possibility of obtaining faster calibrations of characteristic frequency. In spite of the asymmetry in the lateral optical trapping force, experimental calibration results for a sufficiently large square wave input are consistent with the average of off-line calibration results, within 7%. However, slight misalignments in the position detection system can significantly degrade the convergence rate and consistency of the on-line parameter estimates.;I also discuss and compare the application of PI control, LQG control, and nonlinear control to reduce fluctuations in particle position due to thermal noise. Assuming a cubic trapping force, I use computer simulations to demonstrate that the nonlinear controller can reduce position variance by a factor of 65 for a 1-micron diameter polystyrene bead under typical trapping conditions.;Guidelines for constructing and enhancing a research-grade optical tweezer system are also included. |
