Analysis And Compensation Of Nonlinear Errors In A Laser Synthetic-wavelength Nanomeasurement Interferometer

In recent years, with the micro-electronics, ultra-precision machining and other high-tech rapid development, nano-displacement measurement techniques and instruments for large displacement measurement with nanometer accuracy are demanded. This thesis is supported by the National Natural Science Foundation of China (NSFC, No.50827501). In order to improve the technical performance of measuring long-range displacement with nanometer resolution, nonlinearity in the laser synthetic-wavelength nanomeasurement interferometer,measurement of the refractive index of air and wavelength correction are studied in detail.Based on the principle of laser synthetic-wavelength nanomeasurement interferometer, the optical structure and the signal processing system based on DSP, a model calculating nonlinearity and a new Jones matrix are established, and applied to analyses nonlinear error. Analysis and simulation study on nonlinearity in the laser synthetic-wavelength nanomeasurement interferometer are done. The results show that: (1) The nonlinearity caused by polarization ellipticity or nonorthogonality of the laser beams is related to deviation angle of the laser beams, the nonlinear error caused by the deviation angle of 5.7°is 0.09nm, the nonlinear error caused by the deviation angle of 1.7°is 1nm. (2) The nonlinear error caused by polarized light leakage&nonorthogonality of the polarization splitting directions of the polarizing beam splitter or the dihedron angle error of retroreflector is less than 0.05nm. (3) With the measurement range of 50μm, the nonlinear error caused by the angle installation error of polarizing beam splitter is caused mostly by the polarizing beam splitter not in measuring arm, the nonlinear error cased by the installation error angle more than 8°is form several nanometers to several tens of nanometers, 5°is 2nm. 1°is less than 1nm. (4) The nonlinear error casued by polarization properties of retroreflector with aluminum plating film is from 0.05nm to 0.1nm, the nonlinear error caused by retroreflector with silver plating film is from 0nm to 0.38nm. Base on the result of the simulation and analysis of nonlinearity in the laser synthetic-wavelength nanomeasurement interferometer, a new configuration of laser synthetic-wavelength interferometer is designed. The nonlinear error caused by angle installation error of polarizing beam splitter in the new design is reduced to from third to thirtieth compared to original design when the installation error angle is less than 5°. Hardware and software system for measuring the refractive index of air are developed. Four experiments with the step increment of displacements of 13μm, 3mm, 5mm and 8mm are carried out. The experimental results show that the average of the errors before wavelength correction are -4.42nm, -0.6μm, -0.78μm and -2.27μm, the average of the errors after wavelength correction are 0.91nm, 0.21μm, 0.55μm and -0.1μm, respectively. The feasibility of the system is verified experimentally.