| Due to the outstanding advantages of high signal-to-noise ratio,wide dynamic range and direct traceability to the length standard,heterodyne laser interferometric systems have been widely used in various precision measurement applications,therefore,it is significant to improve the displacement measurement accuracy of laser heterodyne interference.This dissertation is supported by the National Natural Science Foundation of China,which is “Research on Measurement Method of Laser Multi-degree-of-freedom Precision Motion Parameters Based on Faraday's Effect”(Grant No.51605445).By studying the angle error analysis based on Faraday effect and compensation method,a laser heterodyne interferometer with rotational error compensation is proposed to reduce or eliminate the influence of rotational error on the displacement measurement.The proposed interferometer can not only improve the measuring accuracy of displacement,but also achieve three degrees of freedom parameters simultaneously measurement.In this dissertation,based on the measurement and compensation methods of laser heterodyne interference displacement at home and abroad,a laser heterodyne interferometer with rotational error compensation based on Faraday effect is proposed.The optical configuration of the proposed interferometer is designed based on the orthogonal return method for linearly polarized beam.The mathematical model and the displacement measurement expression are established by analyzing the influence of rotational error on the displacement measurement.The coupling effect of axial displacement on rotational angle measurement and the rotational angle range used for compensation on displacement measurement is discussed,and the uncertainty of the system is analyzed and evaluated.The overall scheme of signal processing for the measurement system is designed,including the laser heterodyne interference signal processing scheme,the beam position detection signal processing scheme and the PC computer software.To verify the feasibility of the proposed signal processing method,the signal processing board with FPGA is developed,and the integer fringe counting test and the combination of integer and fraction fringe counting experiments are performed.For verifying the feasibility and effectiveness of the proposed interferometer for displacement measurement with rotational error compensation,a serious of experiments are performed as follows:(1)Angle measurement comparison experiment.The experiment results show that the system's angular resolution can reach 0.0001° and the ADU module can be used for rotational error detection in displacement measurement.(2)Rotational angle compensation experiment.The reflector is rotated with the M-038.DG1 to produce the rotational error,and when the rotational error reaches 0.12°,the maximum displacement deviation before compensation is 6.268 ?m.After compensation by the proposed method,the maximum displacement deviation is 11.8nm with the standard deviation of 4.7 nm,and the experimental results demonstrate that the proposed method has a significant compensation effect.(3)Displacement measurement with rotational error compensation experiment.The proposed interferometer and the Renishaw interferometer simultaneously measured the same displacement provided by the XML350 stage with a displacement increment of 1mm.The experimental results indicate that the displacement deviation obtained by the proposed interferometer without compensation is in agreement with that obtained by the Renishaw interferometer.The displacement measured value is compensated by the rotational error value measured by the ADU module,and the maximum displacement deviation of the compensated displacement value is effectively reduced.These experimental results verify the effectiveness of the rotational error compensation method that can be applied in precision measurement and improve the accuracy of displacement measurement. |
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