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摘要: 本文首次提出并构建了自准直仪光电探测器失调的数学模型。基于该模型，分析了光电探测器相对于理论像面处于空间任意位置和朝向时对自准直仪测角的影响。结果表明，探测器失调造成的测角误差随准直物镜焦距f的增大而减小，随自准直仪到被测镜面的距离L以及待测角度θ的增大而增大。计算发现，当f=300 mm，L=100 mm，θ=20″时，因探测器失调引起的测角误差达到0.004 5″。文章进一步分析了各种探测器失调误差单独作用时对自准直仪测角的影响，验证了模型的正确性，并发现探测器离焦对自准直仪的影响最大。根据本文计算结果，选择长焦距的成像物镜、减小测量距离、提高光电探测器沿轴向的安装精度是减小光电探测器失调对自准直仪影响的关键。基于提出的数学模型，可以系统地计算探测器失调对自准直仪测角的影响，进而为构建更加完善的自准直仪误差模型奠定基础。Abstract: As one of the key errors in autocollimators, misalignment of the photodetector is analyzed and modeled carefully in this paper. Effect of misalignment of the photodetector on angle measurements is characterized, when the photodetector in any position and orientation in space with respect to the theoretical image plane of autocollimators. It is shown that the angular measurement errors of autocollimators induced by a misaligned photodetector increase with greater measuring range L, larger angle θ and smaller focal length f of the collimating object lens. When f=300 mm, L=100 mm, θ=20″, the angular measurement error caused by a misaligned photodetector is 0.004 5″. The effects of each photodetector misalignment error on angle measurements in autocollimators are characterized. The model proposed in this paper is validated. Among all kinds of photodetector misalignment errors, the defocusing error has the greatest influences on autocollimators. Hence, it is critical to choose an imaging objective with longer focal length, reduce the measurement distance, and improve the installation accuracy of the photodetector along the axis. The model proposed in this paper helps to systematically obtain the angular measurement errors caused by a misaligned photodetector, which will play a key role in building a better error analysis model for autocollimators.
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Key words:
- autocollimator /
- angular measurement accuracy /
- misaligned photodetector /
- error analysis
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图 2 CCD阵面失调的自准直仪光路
Figure 2. Optical path of autocollimator with a misaligned CCD array
图 3 自准直仪CCD阵面失调建模流程图
Figure 3. Flowchart of CCD misalignment modeling of autocollimator
图 4 自准直仪CCD阵面失调导致的测角误差
Figure 4. Angular measurement errors of autocollimators with a misaligned CCD
图 5 CCD失调参数一定时，自准直仪测角误差随焦距f和测量距离L的变化关系
Figure 5. The relationship between measurement errors of autocollimators and focal length f, and measuring length L when CCD misalignment parameters are constant
图 7 自准直仪测角误差随CCD阵面平移误差的变化曲线
Figure 7. Angular measurement errors in autocollimator varying with translation error of CCD
图 9 自准直仪测角误差随CCD阵面离焦误差的变化曲线
Figure 9. Angular measurement errors of autocollimators varying with defocusing errors of CCD
图 10 自准直仪CCD阵面出现倾斜误差
Figure 10. Inclination angle errors occuring in CCD of autocollimator
图 11 自准直仪测角误差随CCD阵面倾斜误差的变化曲线
Figure 11. Angular measurement errors in autocollimator varying with inclination angle error of CCD
表 1 CCD阵面失调参数
Table 1. Misalignment parameters of CCD
失调参数 最小值 最大值 取样数 a/mm −0.1 0.1 11 b/mm −0.1 0.1 11 c/mm −0.1 0.1 11 $\alpha $/(″) −360 360 11 $\beta $/(″) −360 360 11 $\gamma $/(″) −360 360 11 
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表 2 CCD阵面失调导致的测角误差
Table 2. Angular measurement errors induced by a misaligned CCD
f, L/mm $\theta $/(″) 20 200 2 000 f=300, L=100 0.004 5 0.046 0.53 f=300, L=1 000 0.016 0.16 1.8 f=500, L=1 000 0.004 1 0.042 0.51
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