Research On Electro-optic Modulated Dual-homodyne Interferometry For Nanometer Displacement Measurement

The further development of ultra-precision,integrated circuits,MEMS and other processing and manufacturing technologies has brought greater challenges to displacement measurement technology.Laser interferometry has been widely used in the precision displacement measurement because of its high-accuracy,large-range and direct traceability to the meter.Typical laser interferometry includes laser homodyne(signal frequency)interferometry and laser heterodyne(dual-frequency)interferometry.Compared with heterodyne laser interferometers,homodyne laser interferometers has no problems about polarization mixing or frequency mixing caused by polarization ellipticity or nonorthogonality of the laser beams.However,the measurement accuracy of the homodyne interferometer is limited by the DC-offset drift,the AC-amplitude variation and non-orthogonal phase of the interference signals.In order to solve the problems exist in the homodyne interferometry,and further improve the measurement accuracy of the homodyne interferometer,an electro-optic modulated dual-homodyne interferometer for large displacement measurement with nanometer accuracy is proposed in this thesis.Firstly,the displacement measurement principle is deduced in detail,the optical configuration is designed and the displacement measurement is achieved by detecting the phase difference of two interference signals produced by the dual-homodyne interferometer.A time-domain zero-crossing phase detection method based on linear phase modulation and an arctangent approach phase generation carrier(PGC-Arctan)demodulation method based on phase modulation combining sinusoidal and triangular signals are proposed.In the signal processing system of the linear phase modulated dual-homodyne interferometer,a zero-phase filter to preprocess the interference signals and a phase difference detection PC program are designed based on LabVIEW workbench.In the signal processing system of the phase modulated dual-homodyne interferometer combining sinusoidal and triangular signals,PGC-Arctan phase demodulation based on FPGA+ARM is designed and the ellipse fitting method is adopted to compensate the nonlinear error.To verify the feasibility of the proposed phase-modulated dual-homodyne interferometry based on the electro-optic modulator for nanometer displacement measurement,the dual-homodyne interferometer was constructed and debugged,and the corresponding signal processing tests and displacement measurement experiments were performed for the two modulation methods,respectively.For the linear phase modulation,the phase difference measurement stability experiment shows that the variation of phase difference is about 0.2? per minute in 6 hours,which meets the experimental requirements.Taking the displacement of the precision stage as a reference,the mean and standard deviation of the displacement error in the nanometer range do not exceed 1 nm;the mean value of the displacement error in the micrometer range is within 1 nm,and the standard deviation of the displacement error is 1.42 nm~3.21 nm.Using the commercial interferometer(Agilent 5519A)as a reference,the displacement measurement results with millimeter range show that the average error is-0.046 ?m~0.107 ?m and the standard deviation is 0.032 ?m~0.287 ?m.For the phase modulation combining sinusoidal and triangular signals,the ellipse fitting experiment verifies the effectiveness and accuracy of designed four-parameter ellipse fitting algorithm fulfilled by FPGA+ARM,and the time consuming of each ellipse fitting is about 12.05 ?s.The necessity and contrast experiments for the real-time correction of the quadrature signals in PGC-Arctan phase demodulation shows the compensation effect of the ellipse fitting correction technique on the nonlinear error in phase demodulation.The nonlinear error experimental results show that the designed dual-homodyne interferometer has a nonlinear error of less than 0.1 nm.When using the commercial interferometer(Renishaw XL80)as a reference,the experimental results of the displacement measurements with millimeter range show that the standard deviation is 27.4 nm and the maximum error is-60.5 nm.The above experimental results verify the feasibility and effectiveness of the proposed electro-optic modulated dual-homodyne interferometry for nanometer displacement measurement.