Angular displacement mechanisms are widely used in X-ray diffraction and the nrad resolution is essential for high resolution X-ray diffractor. A multi-pass differential interferometer is designed to improve the resolution of the angel to ~ 10 nrad by increasing the optical pass length. For common interferometer based on Michelson interferometry, nonlinearity is caused by phase mixing due to the imperfect of polarization optical components in both homodyne and heterodyne interferometers. In this angular measurement interferometer, the laser beam of the reference path and measuring path are separated to eliminate the mixture and to reduce the nonlinearity. The four-pass design of the reference and measuring beam improve the resolution. The performance of the interferometer can be used measure the small angle generated by compact piezo driven flexure hinge stage.
This paper presents the control and non-linear calibration of large-scale two-dimensional nanometer displacement stage. The stage consists of a monolithic compliant mechanism, which using flexible hinge superimposed branch as a transmission part, driven by three piezoelectric actuators, To certify excellent performance of the stage, a micro-displacement measurement system which based on the measurement principle of a laser interferometer was setted up, then comparison of several stage parameters accomplished between before and after calibration. Based on the measurement of optical path and composition of dual-frequency laser interferometer, a experimental study on nano-positiong stage was carried out. The non-linear calibration method which based on newton-steffensen accelerated iteration are described; The accuracy of the calibration method was verified through experiments. Experiments show that: before calibration, the maximum nonlinearity error of x-axis and y-axis were 4.012μm and 2.875μm. after calibration, the maximum non-linearity of the x-axis is 8 nm and the maximum nonlinearity error of the y-axis is 10 nm, Meanwhile, a mathematical model is established to calculate the coupled displacement and yaw angle, The actual coupled displacement and yaw angle of X/Y were limited to 380nm and 1.4μrad.