Systems approach to identification of feedback enhanced optical tweezers

Feedback enhanced optical tweezers, based on Proportional and Integral (PI) control, are routinely used for increasing the stiffness of optical traps. Digital implementation of PI controller, using DSP or FPGA, enables easy maneuverability of feedback gains. In this paper, we report occurrence of a peak in the thermal noise power spectrum of the trapped bead as the proportional gain is cranked up, which imposes a limit on how stiff a trap can be made using position feedback. We explain the reasons for the deviant behavior in the power spectrum and present a mathematical formula to account for the anomaly, which is in very good agreement with the experimental observations. Further, we present a new method to do the closed loop system identification of feedback enhanced optical tweezers by applying a frequency chirp. The system model thus obtained greatly predicts the closed loop behavior of our feedback based optical tweezers system.