Detection of nanometer displacement in optical-tweezers and its related measuring errors

Optical Tweezers can be used in measuring nanometer displacements of a particle with several micron diameters. Methods of measurement and data processing, error sources were analyzed. The dynamic image analysis methods including the gray centroid method and new developed methods (exponent centroid method and parabolic fit method) are discussed and compared. A numerical simulation method was developed to evaluate errors caused by these different methods and compared the errors of three data processing methods. The result shows that the parabolic fit method has a high precision with fewer computing time when the background noise is the main noise source. The position of a fixed particle was measured by the quadrant detect (QD) method and the dynamic image analysis method. The measurement standard deviation is 1 nm and 0.3 nm respectively. Based on nanometer displacement measurement, the trap stiffness could be got. Finally, a sub-PicoNewton external force which is applied on the particle was measured successfully. It shows that the resolution of force measurement can reach femto Newton order.