| As the key technology in the field of modern manufacturing and information industries,high-precision displacement measurement plays an important role in national economic development and technology advancement.In order to achieve the long-range,high-precision and high-stability displacement measurement,with the combination of heterodyne interferometry and grating technology,a one-dimensional(1D)and a two-dimensional(2D)heterodyne interferometric grating displacement measurement systems are respectively developed in this thesis.The comprehensive theoretical analysis and experimental investigations about the proposed two heterodyne interferometric grating displacement measurement systems are conducted,and the main innovation works can be summarized as follows:1.The symmetrical 1D heterodyne interferometric grating displacement measurement system with high fringe contrast that we previously proposed is modified.With the reasonable utilization of the short-period metrological grating and the deliberate placement of the half-wave plate,the modified system gets shorter optical signal period,higher signal-to-noise ratio,and stronger disturbance rejection capability compared with the initial one.Based on the constructed novel 1D measurement system,the experiments including the small-range displacements of step,square wave and sine wave motion trajectories,the long-range displacement of round-trip motion trajectory,and the static stability of the system are consecutively conducted.The results reveal that the developed 1D heterodyne interferometric grating displacement measurement system can achieve the practical displacement resolution of 0.45 nm,measurement repeatability of 0.25 nm,system stability of ±1.5 nm with 10 minutes,and the standard deviation of 24.67 nm under 10 mm round-trip movement.It proves that the 1D measurement system has successfully realized the nanometric displacement measurement accuracy.2.A novel 2D heterodyne interferometric grating displacement measurement system based on diagonal diffraction orders is proposed.With the utilization of the(±1,±1)diffraction orders and the cooperation with the suitable 2D metrological gratings,the proposed system can simultaneously achieve the "three high" characteristics,which includes the high fringe contrast,high signal-to-noise ratio and high optical subdivision.Based on the constructed 2D measurement system,the experiments including the step,square wave,sine wave and triangular wave linear trajectories,circular,octagonal and square planar motion trajectories,and the static stability of the system are successively developed.The results illustrate that the practical displacement resolution of 1.07 and 2.42 nm,measurement repeatability of 2.16 and 2.52 nm,system stability of ±4 nm and ±6.5 nm within 10 minutes can be achieved for the X and Y directions,respectively.Additionally,the system is also proved to capable for 2D straightness error measurement.3.A 2D single-layer metrological grating with planar cross rectangular structure is proposed.With the deliberate designation of the surface profile of the 2D grating,the diffraction efficiencies of the grating for TE and TM polarization are equivalent,which is beneficial to simultaneously achieve the high fringe contrast,high signal-to-noise ratio and high optical subdivision.Based on the Fourier optics theory,the Fresnel-Kirchhoff diffraction integral,and the rigorous coupled wave theory,the structure parameters of the proposed 2D single-layer cross-grating are optimized.The results reveal that the equivalent diffraction efficiency of 18.32% for TE and TM polarizations can be achieved with the grating pitch of 1 ?m,duty cycle of 0.5,and normalized depth of 0.3.Meanwhile,a 2D single-layer cross-grating with pitch of 4 ?m is fabricated with the mask lithography method,and its diffraction characteristics are tested as well.It reveals that the experimental results are coincident with the theoretical analysis,and the capability of the proposed 2D grating for optical metrology is verified.4.A 2D double-layer metrological grating with overlapped cross rectangular structure is proposed.With the comprehensive consideration of the diffraction characteristics and the fabrication process,a 2D grating which can be comprised by the orthogonally overlapping of two equal-depths 1D grating is proposed.It also possesses the "three high" characteristics and can be easily fabricated with the short period.Both the Fourier optics theory and the rigorous coupled wave theory are utilized to analyze the 2D double-layer cross-grating.It reveals that the 2D double-layer cross-grating has similar diffraction characteristics with the 2D single-layer cross-grating.The diffraction efficiency of 17.41% for TE and TM polarization can be achieved with the grating pitch of 1.2 ?m,duty cycle of 0.3,and normalized depth of 0.31.With the combination of holographic lithography and lithography-etch-lithography-etch double patterning technology,a 2D double-layer cross-grating with pitch of 2 ?m is manufactured and its diffraction characteristics are tested as well.The results reveal that the experiments are reasonable consistent with the theoretical analysis.5.The general mathematical model of the geometric errors for 2D grating displacement measurement systems is constructed.With the combinative consideration of the impact of the imperfection fabrication and assembly of 2D gratings to the overall performance of 2D measurement systems,cooperated with the comparative study of the single-diffraction and the double-diffraction optical configurations,the general mathematical model of the geometric errors for the 2D symmetrical grating displacement measurement system is established.The results reveal that the imperfection fabrication and assembly of 2D gratings would cause the cosine errors and coupling errors in 2D grating displacement measurement systems.Meanwhile,the coupling errors are more serious than the cosine errors,which is the dominant component of the geometric errors.Additionally,both the cosine errors and the coupling errors are independent of the diffraction times,the diffraction orders and the optical subdivision multiple,just determined by the angle error and the measurement displacement.These conclusions about the geometric errors would be helpful to the systems integration and the error evaluation and compensation of 2D displacement measurement systems.6.A 2D geometric error compensation method combined the self-calibration and the comparative calibration technology is proposed.Based on the exhaustive study of the characteristics of the geometric errors,a strategy that combines the self-calibration and the comparative calibration is developed to compensate the geometric errors.By establishing of the mappings among the grating measurement displacement,translational motion displacement,and ideal orthogonal displacement,the geometric errors are effectively compensated with the linear translation stage and linear laser interferometer.The numerical simulations with the linear and circular motion trajectories under various measurement errors are first conducted.Then the experimental verification with the linear round-trip motion trajectories is developed.The results reveal that the proposed geometric error compensation method can effectively compensate the geometric errors of the 2D grating displacement measuring system. |
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