Monte-Carlo simulation of optical trap stiffness measurement

Abstract

The high precision calibration of optical trap stiffness is the foundation of the weak force measurement in an optical tweezers system. And the accuracy of the trap stiffness measurement is limited by the bandwidth of the acquisition system. In this article, such an influence is analyzed and discussed. The stiffness measuring process using an acquisition system with a finite acquisition time is numerically simulated by using Monte-Carlo method. Then the simulated results are analyzed by thermal motion analysis method to deduce the trap stiffness for different trapping system and for measuring systems with different acquisition time. As a comparison the power spectrum analysis method is used to study the thermal motion of the bead and to compute the trap stiffness for the same acquisition system, from which it is concluded that the bandwidth of the acquisition system is determined by its acquisition time, not the sampling frequency. The influence of the finite acquisition time or the limited bandwidth on the trap stiffness measurement is discussed. The numerical simulation shows that the measured position, which is here the average position within the acquisition time, shifts to the trap center due to the trapping force, which gives an alternative interpretation for the deviation of the measured stiffness from the true trap stiffness.