Displacement measurement based on moire technique and polarization modulation

Abstract

A method to measure displacements based on Moire technique and polarization modulation is presented and analyzed with Fourier transform and Jones matrix in this paper. A collimated laser beam illuminates a scale grating moved in the direction perpendicular to its groove. The scale grating is imaged on a two-phase index grating through a 4f system with an aperture in its frequency plane to form Moire fringes. The scale grating and the index grating have same grating period and their line and space ratio is 1:1. Two sections of the index grating are imaged on two parts of a bi-cell detector through a telecentric system, thereby the displacement of the scale grating can be obtained by detecting the Miore signals on the detector. Before the index grating, a polarizer and a Savart plate are placed. In the telecentric system, a photoelastic modulator between two quarter-wave plates and an analyzer are arranged. Thus the polarization modulation of the Moire signals is realized. The polarization modulation improves the measurement accuracy of the displacement. The analysis shows the displacement measuring method is of nanometer accuracy. In experiments, we verified the feasibility of the method. The repeatability of the method was less than 12nm.