Differential displacement measurement of the levitated particle using D-shaped mirrors in the optical tweezers

Displacement measurement using a D-shaped mirror is a key technology in optical tweezers, which have emerged as an important tool for precision measurement. In this paper, we first study the influences of installation errors for the D-shaped mirror on the displacement measurement. The calibration factor and sensitivity of the different installation parameters are quantified. The results show that the variation of the calibration factor obeys the cosine curve with the angle error, and the sensitivity increases exponentially with the translation error. Besides, we find that the translation error will also lead to crosstalk between transverse and axial displacement. Our work will contribute to improving the performance of optical tweezers for the application in precision measurement and basic physics.