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 (f<sub>0</sub>) and two acousto-optic modulators are used to generate the laser source. The frequency shifts of the two AOMs are f<sub>1</sub> and f<sub>2</sub>, respectively. The positive first order diffraction beams of two AOMs, f<sub>0</sub>+f<sub>1</sub> and f<sub>0</sub>+f<sub>2</sub>, are merged into one orthogonally and linearly polarized beam with a frequency offset of (f<sub>1</sub>-f<sub>2</sub>) 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 f<sub>0</sub> and the positive first order beam f<sub>0</sub>+f<sub>1</sub> 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.
The roll angle measurement method based on a heterodyne interferometer is an efficient technique for its high precision and environmental noise immunity. The optical layout bases on a polarization-assisted conversion of the roll angle into an optical phase shift, read by a beam passing through the objective plate actuated by the roll rotation. The measurement sensitivity or the gain coefficient G is calibrated before. However, a relative tilt between the laser and objective plate always exist due to the tilt of the laser and the roll of the guide in the field long rail measurement. The relative tilt affect the value of G, thus result in the roll angle measurement error. In this paper, a method for field calibration of G is presented to eliminate the measurement error above. The field calibration layout turns the roll angle into an optical path change (OPC) by a rotary table. Thus, the roll angle can be obtained from the OPC read by a two-frequency interferometer. Together with the phase shift, an accurate G in field measurement can be obtained and the measurement error can be corrected. The optical system of the field calibration method is set up and the experiment results are given. Contrasted with the Renishaw XL-80 for calibration, the proposed field calibration method can obtain the accurate G in the field rail roll angle measurement.