Information entropy method for measuring the axial displacement of a bead and its application to analyzing the trapping force of optical trap

Abstract

It is often necessary to follow the axial movement of a micron particle, such as the one trapped in optical trap, in addition to its radial movement. A new method based on the information entropy is developed for measuring the axial displacement, which is then used to reconsider the drag force method for measuring the radial trapping force and stiffness in an optical tweezers system. It is found that the new equilibrium position of the bead displaces not only radially but also axially when the surrounding viscous fluid flows at constant lateral velocity. The result implies that the trap stiffness measured in such a way is not really for the same horizontal plane. In addition, the measured trajectory of the bead (both radial and axial displacements) shows that the sphere escapes from the optical trap upward in stead of radially when the fluid velocity reaches the critical value. The fact indicates that the escape force is not the maximal radial trapping force as commonly accepted. It also deduced that the axial movement of the bead is one of error sources for trapping force calibration using the drag-force method.