Effects of detection-beam focal offset on back-focal-plane displacement detection

High-resolution displacement detection can be achieved by analyzing the scattered light of the trapping beams from the particle in optical tweezers. In some applications where trapping and detecting beams must be separated, a detecting beam can be introduced for independent displacement measurement. However, the detecting beam focus possibly deviates from the center of the particle, which will affect the performance of displacement detection. Here, we detect the displacement of the particle by utilizing the forward scattered light of the detection beam from the particle. The effects of the lateral and axial offsets between the detection beam focus and the particle center on displacement detection are analyzed by the simulation and experiment. These results show that the lateral offsets will decrease the detection sensitivity and linear range. Moreover, it aggravates the crosstalk between the x-direction signal and the y-direction signal of the quadrant photodiode. Besides, the axial offsets also affect the detection sensitivity. More interestingly, an optimal axial offset can improve the sensitivity of displacement detection substantially. In addition, the influence of system parameters, such as particle radius a, numerical aperture of the condenser NAc, and numerical aperture of the objective NAo, on the optimal axial offset is also discussed. This work not only provides ideas for improving the performance of precision measurement by the method of forward scattered light detection but also expands the application of this method in fundamental physics.