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Determination of the axial stiffness of an optical trap with information entropy signals

Optical tweezers has been used to manipulate micro-sized particles for many years, and has been widely used in various applications. The axial trapping stiffness is one of the most important parameters to evaluate the trapping ability of an optical tweezers. In this paper, we calibrated the axial optical stiffnesses for micro-sized polystyrene spheres. When an external force was applied to particle held by an optical trap, the particle was displaced from the trap center by an amount proportional to the applied force. We displaced the particle from the trap center by applying triangular waves of varying velocity, and the varying velocity was obtained by altering the frequency of the triangular waves. In this case the particle has two balance position distributed at two-side of the trap center. The calibration of the axial position was critical to the measurement of axial optical stiffness. In this paper, the axial displacement between the balance position and the trap center was calibrated with image information entropy signals. According to Stokes Law, when the axial displacement of the particle relative to the external force was known, the axial optical stiffness can be measured, and this method was known as viscous drag method. The stiffnesses for a 2μm-diameter at different trapped depth were measured. Typical values for axial optical stiffness of our optical tweezers were between 4.0 and 7.5 pN/μm when the laser power was 35mW. Dependence of axial optical trapping stiffness on the diameter of the particles was measured with viscous drag method. At last, the origin of the measurement error was discussed.