The linear translation stages play an important role in computer numerical control machine tools, coordinate measuring machines and semiconductor lithograph equipment. Six geometric motion errors are associated with a precision linear stage. High precision simultaneous measurement of multiple degrees of freedom is essential for the multiple-dimension motion calibration of the ultra-precision linear translation stage. In this paper, a laser heterodyne interferometer for simultaneous measurement of displacement and roll angle based on the acousto-optic modulator is proposed. In this optical configuration, a stabilize single-frequency laser (f₀) and two acousto-optic modulators are used to generate the laser source. The frequency shifts of the two AOMs are f₁ and f₂, respectively. The positive first order diffraction beams of two AOMs, f₀+f₁ and f₀+f₂, are merged into one orthogonally and linearly polarized beam with a frequency offset of (f₁-f₂) as the laser source for the roll measurement-unit. A half wave plate (HWP) is utilized as the roll sensing plate to magnify the tiny roll angle into an observable phase shift based on the change of polarization state. The resolution of the roll measurement system is determined by the amplification factor which can be enhanced by a multi-reflection cavity made of a specifically arranged assembly square pyramidal mirror and a folding mirror. The zeroth beam f₀ and the positive first order beam f₀+f₁ provided by two AOMs forms two space separated beams for the displacement measurement, which can eliminate the periodic nonlinearity error. The optical system of the simultaneous measurement of displacement and roll angle were setup. The experimental results showed good repeatability and good consistency.

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Jingya Qi, Zhao Wang, Junhui Huang, and Jianmin Gao, "Laser heterodyne interferometer for simultaneous measurement of displacement, and roll-angle based on the acousto-optic modulators," Proc. SPIE 10678, Optical Micro- and Nanometrology VII, 1067806 (Presented at SPIE Photonics Europe: April 25, 2018; Published: 24 May 2018); https://doi.org/10.1117/12.2307316.