Measurement and calibration of the intensity transform function of the optical 3D profilometry system
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摘要:由于数字光栅投影仪的光强传递函数对于正弦投影条纹的质量以及相位测量精度起着至关重要的作用，本文提出了一种校正光学三维扫描仪光强传递函数的新方法。首先，分析了由于投影仪非线性响应引起的光栅谐波的相位测量误差；然后，通过投影一组不同灰度级的图像，并利用光功率计测出数字投影仪投出图像的亮度。接着，通过分析得到数字投影仪的非线性响应特性曲线，再经过数据处理，即可获得投影仪的光强传递函数；最后，对光强传递函数进行反函数逆变换，得到一个校正后的非正弦光栅，利用投影仪对该光栅的投影即可在被测物体表面上获得一个正弦光栅。数字投影仪对标准平板的测量结果表明，校正前平均误差为0.71 mm，校正后为0.55 mm；对于标准量块的测量，校正前的平均误差为0.62 mm，校正后为0.15 mm。上述结果表明，本文提出的方法可以减小由于系统非线性响应引起的测量误差并提高测量精度。Abstract:The light intensity transform function(ITF) of the digital grating projector plays a crucial role in the quality of sinusoidal projection fringes and the accuracy of phase measurement. Based on this, a new method of correcting the ITF of digital grating projector in optical 3D profilometry system is proposed in this paper. Firstly, the phase measurement error of the grating harmonics caused by the nonlinear response of the projector is analyzed. Then, the nonlinear of the digital projector is measured by projecting a set of images with different gray levels, and the brightness of these image on the digital projector is measured by optical power meter and the ITF of the projector can be obtained after data processing. Finally, an inverse transformation of ITF is implemened to obtain a corrected non-sinusoidal grating, which is then projected by the projector to obtain a sinusoidal grating on the surface of the measured object. Digital projector measurement experiments show that the average errors of standard panel are 0.71 mm and 0.55 mm before and after calibration, respectively; the average errors of standard block measurement are 0.62 mm and 0.15 mm before and after calibration. The above results show that the proposed method can reduce the measurement error caused by the nonlinear response of the system and improve the measurement accuracy.
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Key words:
- phase measurement/
- intensity transform function/
- nonlinear/
- calibration
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图 5反函数曲线(即：数字投影系统光强校正函数曲线)
Figure 5.Inverse function curve(namely ITF′s calibration curve of digital projection system)
表 1反函数数值解表
Table 1.Numerical solutions of inverse function
归一化的输出功率 归一化的输入灰度 归一化的输出功率 归一化的输入灰度 0 0.082 0.542 0.730 0.042 0.227 0.583 0.756 0.083 0.310 0.625 0.781 0.125 0.373 0.667 0.805 0.167 0.425 0.708 0.828 0.208 0.471 0.750 0.851 0.250 0.512 0.792 0.873 0.292 0.549 0.833 0.894 0.333 0.584 0.875 0.916 0.375 0.616 0.917 0.937 0.417 0.647 0.958 0.957 0.458 0.676 1 0.977 0.500 0.704 
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表 2标准平板测量结果
Table 2.Measurement results of standard panel
(mm) 1 2 3 4 5 6 7 8 9 标准 0 20 40 60 80 100 120 140 160 校正前 0.11 18.67 39.16 59.33 79.50 101.02 119.35 138.84 160.10 误差 0.11 1.33 0.84 0.67 0.50 1.02 0.65 1.16 0.1 校正后 -0.29 21.22 39.73 60.08 79.86 101.05 119.17 140.89 160.22 误差 0.29 1.22 0.27 0.08 0.14 1.05 0.83 0.89 0.22 下载:
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表 3标准量块测量结果比较
Table 3.Measurement results of standard block
(mm) 项目 校正前结果 校正后结果 面1位置 37.08 36.16 面2位置 25.50 24.11 高度差 11.58 12.05 绝对误差 0.62 0.15 相对误差 5.08% 1.23% 下载:
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