Precision straightness and displacement measurement based on phase-modulated interferometric scheme with different modulation depths

Abstract

In this study, a novel straightness and displacement measurement method using a Wollaston prism-sensing phase-modulated interferometer (WPHI) is proposed to accurately measure straightness errors and the position of linear stages. In the proposed WPHI, a Wollaston prism assembly along with a semi-reflector serves as a sensing element to generate two straightness and one displacement measuring beams. By using an electro-optic phase modulator to modulate the linearly polarized laser beam at 45° to its optic axis, different modulation depths are introduced into the straightness and displacement measuring beams to obtain phase-modulated interference signals. Thus, the straightness error can be directly obtained from the change in the optical path difference between the two measuring beams, thereby avoiding any additional errors introduced by separately measuring the changes in the optical path of each beam. Moreover, a 2 × 2 array photodetector is used to simultaneously measure the displacement and rotational angles of stage to compensate for the influence of rotational errors on the displacement result. The experimental results showed that within a range of 4 m, the standard deviations of the straightness error and displacement measurements between the proposed WPHI and a commercial interferometer were 0.50 and 0.59 μm, respectively. Thus, the proposed WPHI has substantial applications in the fields of ultraprecision machine-tool control, precision motion stage testing, and displacement sensor calibration.