Design of an angle measurement system based on interferometric fringe imaging and its off-axis measurement accuracy
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摘要:
基于干涉条纹成像的测角系统测量精度随着测量范围的增大而下降，单纯提高精定位的细分倍数并不能提高测量精度。针对这一问题，本文围绕非成像系统的参数设计方法及大测量范围下的精度变化情况展开研究。建立了双光栅干涉系统及光楔阵列波前分割的数学模型，给出了近轴条件下非成像光学系统的参数设计方法。设计了一台一维高精度光学测角系统，并对该系统在整个测角范围内的测量误差进行了分析和计算。结果显示：利用本文提出的数学模型和方法，所设计的测角系统在[−5°，5°]的测量范围内，近轴区的测角分辨率为0.02″。随着测量范围的增大，干涉条纹相位非线性变化引起的精定位误差成为系统测角误差的主要来源，最大测量角度下精密轴的测量误差为0.42″。上述结果表明采用本文提出的模型和参数设计方法，可以设计出具有较高测角精度的光学测角系统。
Abstract:The accuracy of an angle measurement system based on interferometric fringe imaging decreases as the measurement range increases. Merely increasing the subdivision factor of precise positioning cannot improve the accuracy of the measurement. In this case, this paper primarily focuses on the parameter design method in non-imaging optical systems and accuracy changes under a wide measurement range. The mathematical models for the dual grating interference system and the wavefront segmentation of the optical wedge array were established, and a parameter design method for non-imaging optical systems under paraxial conditions was proposed. A one-dimensional high-precision angle measurement system was designed, and the measurement error of the system within the measurement range was analyzed and calculated. The results show that the designed angle measurement system achieves a resolution of 0.02" in the paraxial region with a measurement range of [−5°,5°] based on the mathematical model and method proposed in this paper. As the measurement range expands, the precision positioning errors resulting from nonlinear changes in the phase of interference fringes become the primary source of measurement errors. At the maximum measurement angle, the accuracy of the precision axis reduces to 0.42". The above results demonstrate that the proposed model and parameter design method can be employed to design an optical angle measurement system with high accuracy.
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图 1 基于干涉条纹成像的光学测角系统（a）结构示意图及（b）拓扑图
Figure 1. (a) Structural diagram and (b) topology of optical angle measurement system based on interferometric fringe imaging
图 2 单光楔对光束角度作用示意图
Figure 2. Schematic diagram of the effect of a single optical wedge on the beam angle
图 4 子像点与目标像点分布
Figure 4. Distribution of the sub-image spots and the target image spot
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