Study On Nonlinear Error Measurement Of Laser Interferometer Based On Beat-frequency Fabry-Perot Interferometry

In recent years,with the rapid development of nano scale ultra precision machining,chip manufacturing and other high-tech fields,the measurement and measurement of micro displacement become more and more important.As an important instrument in the field of displacement measurement and measurement,laser interferometer is widely used,and its measurement accuracy is also improving to sub nanometer or even PI meter level.However,due to the influence of many factors in the practical application process,a series of errors will be produced,among which the periodic nonlinear error has the most significant impact on the measurement results of laser interferometer,and the nonlinear error exists.It limits the further development of laser interferometer in industrial application.Therefore,it is very important and urgent to measure and analyze the errors of laser interferometer,especially the periodic non-linear errors,and improve the traceability system of micro displacement measurement.In this dissertation,through the improvement of beat frequency F-P interferometry combined with discrete Fourier transform,the high-precision,traceable,error measurement that can obtain the total nonlinear error and each order component is realized.The experimental device is built to measure and verify the nonlinear error of commercial laser interferometer,and the measurement results are analyzed.The main research work is as follows:(1)The characteristics and shortcomings of the existing research methods of laser interferometer nonlinear error measurement at home and abroad are summarized,and the nonlinear error measurement method based on beat frequency method and Perot interference method is adopted.According to the working principle of laser interferometer,the principle of periodic nonlinear error of laser interferometer caused by polarization aliasing and frequency aliasing is derived,and the mathematical expression of nonlinear error related to the wavelength and the change of measured displacement is given;(2)The principle of the beat frequency method and the interference method is introduced.The relationship between the displacement and the beat frequency signal variation is deduced,which shows that the error measurement results can be directly traced to the advantages of time and frequency.In order to solve the problem that the traditional comparison method can only obtain the total error,the discrete Fourier transform is used to process the error data measured by the beat frequency method and the Perot interference method,and the phase and amplitude of the first-order and second-order components of the nonlinear error are separated.(3)The nonlinear error measurement device of laser interferometer based on beat frequency method and Perot interference method is designed and built.Aiming at the limitation of current measurement range and accuracy,the optical path design of the system is improved.The control algorithm of frequency adjustment is optimized by using generalized nonlinear Preisach model,which improves the measurement efficiency and accuracy of the system.(4)The system performance of the measurement device designed in this paper is verified by different experimental analysis,and the performance of each module of the measurement device is verified respectively.The non-linear error of the commercial laser interferometer is measured by the device.The uncertainty of the measurement result is analyzed,and the expanded uncertainty is better than 0.3 nm,which shows that the scheme can be used for the non-linear error of the laser interferometer.Effective measurement and the traceability of measurement results.