Two-dimensional grating line parameter calibration based on biaxial phase mapping
doi: 10.37188/CO.EN-2025-0020
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摘要:
二维光栅是平面光栅干涉仪实现高精度、多维位移测量的核心器件，其刻线密度和栅线正交性误差的检测与标校，一方面可提高光栅干涉仪的定位精度，另一方面可为二维光栅的制作提供反馈指导。本文提出一种利用正交外差金宝搏188软件怎么用 干涉仪同时标定二维光栅刻线密度和栅线正交性误差的方法，以待测光栅搭建二维光栅干涉仪，双轴金宝搏188软件怎么用 干涉仪为其提供位移参考，建立光栅干涉与金宝搏188软件怎么用 干涉的相位映射关系，通过任意两次位移获取的干涉相位信息，即可同时解算上述3项参数的同时获取光栅安装误差。使用1200 gr/mm的二维光栅验证了提出方法的可行性，X、Y方向刻线密度的标准差分别为0.012 gr/mm和0.014 gr/mm，栅线正交性误差的标准差为0.004°，安装误差标准差为0.002°。与原子力显微镜法进行了精度比对，X、Y方向刻线密度的一致性优于0.03 gr/mm、0.06 gr/mm，正交性误差优于0.008°。实验结果表明，提出方法可简单、高效的应用于二维光栅的栅线参数标定。
Abstract:The two-dimensional grating serves as a critical component in plane grating interferometers for achieving high-precision multidimensional displacement measurements. The calibration of grating groove density and orthogonality error of grating grooves not only improves the positioning accuracy of grating interferometers but also provides essential feedback for optimizing two-dimensional grating fabrication. This study proposes a method for simultaneous calibration of these parameters using orthogonal heterodyne laser interferometry. A two-dimensional grating interferometer is built with the grating to be measured, and a biaxial laser interferometer provides a displacement reference for it. The phase mapping relationship between grating interference and laser interference is established. The interference phase information obtained by any two displacements can simultaneously solve the above three parameters and obtain the grating installation error. The feasibility of the proposed method is verified by using a 1200 gr/mm two-dimensional grating. The standard deviation of the grating groove density in the X and Y directions is 0.012 gr/mm and 0.014 gr/mm, respectively. The standard deviation of the orthogonality error of grating grooves is 0.004°, and the standard deviation of the installation error is 0.002°. Compared with the atomic force microscope method, the consistency of the grating groove density in the X and Y directions is better than 0.03 gr/mm and 0.06 gr/mm, and the orthogonality error of grating grooves is better than 0.008°. The experimental results show that the proposed method can be simply and efficiently applied to the calibration of the grating line parameters of the two-dimensional grating.
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Figure 1. The schematic diagram of the optical path structure of the calibration system
Figure 2. The influence of orthogonality error of grating grooves error and grating installation error on displacement measurement
Figure 3. Experimental device photographs. (a) Layout of the 2D grating interferometer. (b) Layout of the laser interferometer. (c) 2D grating.
Figure 4. Stability test result diagrams. (a) Values measured by the X-direction laser interferometer. (b) Values measured by the Y-direction laser interferometer. (c) Measured values from the X-direction grating interferometer. (d) Measured values from the Y-direction grating interferometer.
Figure 5. Linear fitting data diagrams. (a) Results for plane displacement platform movement along the X-axis. (b) Results for plane displacement platform movement along the Y-axis.
Figure 8. Data solution result diagrams. (a) Grating installation error results. (b) Orthogonality error results for the grating lines. (c) X-direction grating groove density results. (d) Y-direction grating groove density results.
Figure 9. The AFM image and data acquisition schematic diagram of 2D grating (a)Measured images of AFM (b) Data acquisition schematic diagram
Figure 10. Comparison of results for the two measurement methods. (a) Comparison of grating groove density measurement results. (b) Comparison of orthogonality error of grating grooves error results.
Table 1. The solution results of the parameters to be measured
（xn,yn） θ(°) α(°) $ \rho $x(gr/mm) $ \rho $y(gr/mm) (1,5) 0.48016 − 1.07329 1199.99228 1199.90331 (2,5) 0.48820 − 1.08118 1199.99563 1199.90466 (3,5) 0.48496 − 1.07812 1200.02361 1199.90413 (4,5) 0.48669 − 1.07981 1200.02964 1199.90443 (5,5) 0.48652 − 1.07963 1200.01899 1199.90439 (5,4) 0.48654 − 1.07839 1200.01872 1199.87662 (5,3) 0.48653 − 1.07917 1200.01889 1199.88735 (5,2) 0.48668 − 1.06947 1200.01681 1199.88468 (5,1) 0.48653 − 1.07342 1200.01767 1199.87282 Average value 0.48587 − 1.07694 1200.01469 1199.89360 Standard deviation 0.002158 0.003702 0.01171085 0.01322980 
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Table 2. The results of the measurement of the 2D grating calibration area
Measuring field α(°) $ \rho $x(gr/mm) $ \rho $y(gr/mm) 1 − 1.07126 1200.03871 1199.94367 2 − 1.07313 1199.99825 1199.92325 3 − 1.07493 1200.01830 1199.92155 4 − 1.07138 1200.00781 1199.94672 5 − 1.07653 1200.03141 1199.90339 Average value − 1.07345 1200.01890 1199.92771 Standard deviation 0.002284 0.016573373 0.017786239
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