| 利特罗型光栅干涉仪的元件定位误差分析 |
| Element positioning error analysis of a Littrow grating interferometer |
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| 中文摘要: |
| 针对利特罗型光栅干涉仪的系统误差研究缺少更深入的量化数据的问题，对元件定位精度引起的利特罗型光栅干涉仪系统误差进行了研究，即分析光栅绕x、y、z轴旋转以及反射镜绕y轴旋转时导致的额外光程差所造成的系统误差对干涉仪的位移测量影响。建立光栅及反射镜绕轴旋转时的光程差变化引起的相关误差的数学模型，进行定量分析，并通过实验验证该数学模型的准确性。结果表明：光栅及反射镜绕x、z轴旋转时不会产生额外光程差；光栅绕y轴旋转时会产生系统误差，且误差会随着光栅常数和旋转角度的增大而增大；反射镜绕y轴旋转时，只有当两反射镜的旋转角度不同时才会产生误差，且误差会随着两反射镜旋转角度的增大而增大。对整个系统进行误差合成后得到：在高装配级别下，未定系统误差为± 3.12 μm；在一般级别下，未定系统误差为± 17.75 μm。通过该实验验证了理论仿真的正确性，为利特罗型光栅干涉仪的系统优化设计提供了技术参考与理论支持。 |
| 英文摘要: |
| Aiming at the lack of more in?depth quantitative data for the study of the systematic errors of Littrow?type grating interferometers, the systematic errors of Littrow?type grating interferometers caused by the positioning accuracy of the components, namely, the systematic errors of the interferometers caused by the additional optical path differences due to grating rotation around the x, y, and z axes as well as mirror rotation around the y axis, were investigated in terms of the impact of the systematic errors on the displacement measurements of the interferometers. A mathematical model of the error caused by the change in optical path difference when the grating and mirror rotate around the axes was established, quantitatively analyzed, and the accuracy of the mathematical model was verified by experiments. The results show that: when the grating and mirror rotate around the x and z axes, no additional optical path difference is generated; when the grating rotates around the y axis, the systematic error will be generated and increase with the increase of the grating constant and the rotation angle; when the mirror rotates around the y axis, the error will be generated only when the rotation angles of the two mirrors are different, and the error will increase with the increase of the rotation angle of the two mirrors. After synthesizing the errors of the whole system, the undefined system error is ± 3.12 μm in high assembly level, and ± 17.75 μm in general level, which verifies the correctness of the theoretical simulation, and provides technical reference and theoretical support for the system design of the Littrow?type grating interferometer. |
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| 中文关键词: 光栅干涉仪 利特罗型 误差分析 光程差 精密位移测量 |
| 英文关键词:grating interferometer Littrow type error analysis optical path difference precision displacement measurements |
| 基金项目: |
| DOI：10.11823/j.issn.1674-5795.2025.03.03 |
| 引用本文：赵金辉, 胡源.利特罗型光栅干涉仪的元件定位误差分析[J].计测技术,2025,45(3):37~44. |
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