Axial deviation of an optically trapped particle in trapping force calibration using the drag force method

The axial deviation of the trapped particle in the lateral trap stiffness calibration and the maximal trapping force measurement has been reported, but has not yet been extensively analyzed in the literature. Due to the importance of the trapping force calibration in the applications, the axial deviation and the influence on the trap stiffness and the maximal trapping force measurement is analyzed both experimentally and theoretically. First, the trap stiffness calibration experiment is rechecked and more attention is paid to the axial displacement of the particle. The result confirms that the equilibrium position of the particle moves upward with the increase of the lateral displacement. In order to get better understanding of the phenomenon, the relation between the axial displacement and the lateral displacement is theoretically calculated by using the ray optics model. The comparison of the calculated result with the experimental one indicates that the particle equilibriums are not in the horizontal plane passing through the trap center, but are on a curved track where the external force is balanced with the trapping force. Then the relations between the trapping efficiency and the lateral displacement are derived, which shows that the experimentally calibrated trap stiffness is a reasonable approximation so long as the particle is kept in the central part of the trap. Finally, the difference between the maximal lateral trapping force and the escape force is discussed, and it is shown that the measured escape force is not as supposed to be the maximal lateral trapping force but far less than it.