3D calibration of microsphere position in optical tweezers using the back-focal-plane interferometry method

This paper presents a method to directly calibrate the position of a trapped micro-sphere in optical tweezers utilizing its interference pattern formed at the back focal plane (BFP). Through finite difference time domain (FDTD) and scalar diffraction theorem, the scattering field complex amplitude of the near and far fields can be simulated after interference between the trapped sphere and focus Gaussian beam. The position of the trapped sphere can be recovered and calibrated based on a back focal plane interferometry (BFPI) algorithm. Theoretical results demonstrate that optical tweezers with a larger numerical aperture (NA) Gaussian beam will yield a better detection sensitivity but with a smaller linear range. These results were experimentally validated by trapping a microsphere in a single beam optical tweezer. We used an extra focused laser to manipulate the trapped sphere and then compared its position in the images and that obtained using the BFP method. The interference pattern from simulation and experiments showed good agreement, implying that the calibration factor can be deduced from simulation and requires no intermediate calculation process. These results provide a pathway to obtain the calibration factor, enable a faster and direct measurement of the sphere position, and show possibilities for adjusting the crosstalk and nonlinearity inside an optical trap.