Three-Degree-of-Freedom Homodyne Wavefront Interferometry Using Fiber Array

Homodyne wavefront interferometry enables synchronous compensation of angle error in precision displacement measurement. However, the traditional decoupling method relies on image signal, and the measurement speed is typically only some \mu m/s. This article proposes a method that employs a fiber array for spatial sparse sampling, in order to achieve fast and simultaneous measurement of displacement, pitch, and yaw angles. A novel decoupling algorithm is developed to calculate the three degrees of freedom (3DoFs), based on an elliptic trajectory formed by a few sampling point inside an interference beam spot. The experimental results indicated that the prototype can achieve a measurement speed of 158.2 mm/s, while the resolution can achieve 0.6 nm and 0.13~\mu rad. The prototype was compared against a commercial interferometer and autocollimator; the difference was at nanometer and microrad levels. Further, the prototype was used to calibrate a commercial piezo stage. The maximum motion speed of the stage is 3.3 mm/s, within a motion range of 100~\mu m, the repeatability achieves 1 nm, and the linear error is below 10 nm.