外差干涉相位测量中信号串扰误差与补偿方法研究

Study on Signal Crosstalk Error and its Compensation Method in Phase Measurement for Heterodyne Interferometry

为了解决外差干涉相位测量中多通道采样信号间的串扰误差对相位测量精度的影响,提出了一种基于采样信号频谱分析的预补偿方法来实现信号串扰误差的补偿和消除。首先建立基于锁相放大的正交鉴相法的信号串扰误差理论模型,阐明了串扰系数、输入信号幅值比和串扰信号相位偏移对相位测量误差的影响;设计仿真实验验证了该误差模型和补偿方法的有效性;然后基于紧凑型FPGA开发平台设计了相位测量实验,结果表明该补偿方法能够有效消除信号串扰误差的影响,补偿后相位测量的最大误差从0.34°下降到0.01°;最后搭建了外差干涉仪并与高精度的压电位移平台进行比对,实验结果表明补偿后的信号处理系统能够满足外差干涉测量的应用需求。

Objective Heterodyne laser interferometers have been widely utilized in the field of precision measurement owing to their wide measurement range,high measurement accuracy,and robust measurement ability.With the development of high-precision science and technology,higher requirements have been proposed for the measurement accuracy of heterodyne laser interferometers,which is significantly affected by the phase measurement accuracy of the interference signal.In multichannel signal acquisition and processing,the crosstalk error between sampled signals is a familiar error source.In this study,the problem of signal crosstalk in interference signal processing is investigated,and a signal crosstalk error model is established.Accordingly,a pre-compensation method based on spectrum analysis is proposed to eliminate signal crosstalk errors and improve the phase measurement accuracy of the interference signal.Methods The signal crosstalk error was systematically examined through theoretical derivation,simulation analysis,and experimental verification to solve the problem of crosstalk between two sampled signals in heterodyne interferometry.First,a mathematical model of the signal crosstalk error was deduced,and a pre-compensation method based on spectrum analysis was proposed.Then,the influence of the crosstalk coefficient,signal amplitude ratio,and crosstalk signal phase offset on the signal crosstalk error was analyzed via simulation,and the crosstalk compensation method was verified.After the initial verification of the error model and compensation method through simulation,the signal processing algorithm was implemented based on the Red Pitaya FPGA board,and further verification was performed through a phase measurement experiment.The experimental results show that the actual measurement error is consistent with the theoretical calculation error and that the crosstalk compensation method can effectively eliminate the signal crosstalk error.Finally,a heterodyne interferometric measurement system was built to verify that the proposed signal processing system can meet the measurement requirements of practical applications.Results and Discussions This study deduces a mathematical model of the signal crosstalk error and proposes a precompensation method based on spectrum analysis.Then,the analysis and verification are conducted through simulations and experiments.According to the derived mathematical model of the signal crosstalk error,the crosstalk coefficient,signal amplitude ratio,and crosstalk signal phase offset affect the magnitude of the crosstalk error.The influence of these three factors on the signal crosstalk error is analyzed via simulation.The crosstalk coefficient and signal amplitude ratio significantly impact the size of the signal crosstalk error(Figs.3 and 4),and the phase offset of the crosstalk signal affects the size of the crosstalk signal error and the location of the extreme value distribution simultaneously(Fig.5).After the simulation analysis,the signal processing algorithm is implemented based on the Red Pitaya board,and a phase measurement experiment is performed(Fig.8).When the amplitude ratios of the two input signals are 1,2,and 3,the actual measurement and theoretical calculation errors are consistent(Fig.13).After compensating for the signal crosstalk error,the maximum measurement error drops from 0.34°to 0.01°(Fig.14).A phase measurement experiment verifies the correctness and effectiveness of the signal crosstalk error model and compensation method.Finally,a heterodyne interferometric measurement system is built to test the performance of the algorithm(Fig.16).In the range of 250μm,the measurement error is less than 5 nm(Fig.17),indicating that the signal processing algorithm can meet the needs of actual measurements.Conclusions Phase measurement accuracy is essential for accurate heterodyne laser interferometer measurements,and the signal crosstalk error is a common source in multichannel signal sampling processing.This study deduces the signal crosstalk error model and proposes a pre-compensation method based on spectrum analysis to solve the problem of crosstalk between the reference signal and measurement signal in heterodyne interferometry.The influence of the crosstalk coefficient,signal amplitude ratio,and crosstalk signal phase offset on the signal crosstalk error is analyzed via simulation.When both crosstalk coefficients are 0.01,the signal amplitude ratio is 10,and the phase offset of the crosstalk signal is 0,the maximum crosstalk error of the signal can reach 5.78°,which needs to be effectively compensated.In the phase measurement experiment,when the amplitude ratios of the two signals are 1,2,and 3,the actual measurement error is the same as the theoretical calculation error,proving that the signal crosstalk error model is correct.After the signal crosstalk error compensation,the measurement error drops from the maximum of 0.34°to 0.01°,proving that the crosstalk error compensation method is effective.In summary,this study systematically analyzes the signal crosstalk error.The proposed compensation method can effectively eliminate the signal crosstalk error and improve the phase-measurement accuracy of the heterodyne interference signal.