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Phase shifting profilometry (PSP) is an effective technique to reconstruct the three-dimensional shape of object. In general, PSP needs three or more fringe patterns with phase-shifting accurately known to extract the phase distribution of objects. Therefore, the scene and the test objects should remain stationary during capturing the fringe patterns. However, the phase shifts may be unknown in an actual PSP measurement system, especially when measuring the moving object, that is, the phase-shift error may be introduced during the obtaining of the phase-shifting fringe patterns of moving object. In the dynamic measurement scenario, the use of fewer fringe patterns can realize the faster measurement speed and suppress the phase shift error introduced by the moving object. In this paper, a two-step PSP algorithm is proposed based on Lissajous ellipse fitting (LEF). The proposed method uses only two fringe patterns to extract the phase distribution of the object and can suppress the phase shift error caused by the moving object. However, in a practical PSP system, the spatiotemporally varying background intensity and modulation also significantly affect the phase accuracy extracted by LEF, and thus three error-suppressing methods are proposed to reduce the phase error caused by the non-uniform background intensity and modulation. In order to verify the effectiveness of the three error-suppressing methods, we analyze and compare their performances of error suppression under different background intensities and modulations. The advantages of three error-suppressing methods can be summarized as follows. 1) The mean and modulation correction technique has greater advantage than the other two when the background intensity and modulation vary with time. 2) When the background intensity and modulation are relevant to pixel position and the number of fringe patterns, the empirical mode decomposition normalization can more effectively suppress the influence of the non-uniform background intensity and modulation. In experiment, a two-step phase-shifting dynamic measurement based on LEF is conducted. Compared with the traditional PSP which needs at least three fringe patterns, the two-step PSP algorithm successfully extracts the phase with only two fringe patterns and suppresses the phase shift error caused by the motion of the object. Compared with Fourier transform profilometry (FTP), the two-step PSP algorithm can obtain very accurate phase distribution and retain many phase details. -
Keywords:
- fringe projection technology /
- phase reconstruction /
- phase shifting profilometry /
- phase shift error
[1] Li B W, Liu Z P, Zhang S 2016 Opt. Express 24 23289
Google Scholar
[2] Wu Y X, Cai X J, Zhu J J, Yue H M, Shao X P 2020 Opt. Lasers Eng. 127 105987
Google Scholar
[3] Feng S J, Zhang L, Zuo C, Tao T Y, Chen Q, Gu G H 2018 Meas. Sci. Technol. 29 122001
Google Scholar
[4] Pan B, Kemao Q, Huang L, Asundi A 2009 Opt. Lett. 34 416
Google Scholar
[5] Wang Y J, Zhang S, Oliver J H 2011 Opt. Express 19 8539
Google Scholar
[6] Isaac T, Heejoo C, Wook K D 2016 Opt. Express 24 27993
Google Scholar
[7] Lilley F, Lalor M J, Burton D R 2000 Opt. Eng. 39 187
Google Scholar
[8] Servin M, Garnica G, Estrada J C, Padilla J M 2014 Opt. Express 22 10914
Google Scholar
[9] Wang Y, Laughner J I, Efimov I R, Zhang S 2013 Opt. Express 21 5822
Google Scholar
[10] Lu L, Xi J T, Yu Y G, Guo Q H 2014 Opt. Lett. 39 6715
Google Scholar
[11] Cai Z W, Liu X L, Jiang H, He D, Peng X, Huang S J, Zhang S H 2015 Opt. Express 23 25171
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[12] Tao T Y, Chen Q, Da J, Feng S J, Hu Y, Zuo C 2016 Opt. Express 24 20253
Google Scholar
[13] Liu Z P, Zibley P C, Zhang S 2018 Opt. Express 26 12632
Google Scholar
[14] Wang Y, Liu Z P, Jiang C, Zhang S 2018 Opt. Express 26 34224
Google Scholar
[15] Feng S J, Zuo C, Tao T Y, Hu Y, Zhang M L, Chen Q, Gu G H 2018 Opt. Lasers Eng. 103 127
Google Scholar
[16] Lu L, Xi J T, Yu Y G, Guo Q H 2013 Opt. Express 21 30610
Google Scholar
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[18] Su X Y, Chen W J 2001 Opt. Lasers Eng. 35 263
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[19] 徐建亮, 汪敏, 潘慧, 刘晓辉, 戚晓利, 许四祥 2011 物理学报 60 074210
Google Scholar
Xu J L, Wang M, Pan H, Liu X H, Qi X L, Xu S X 2011 Acta Phys. Sin. 60 074210
Google Scholar
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[21] Li B W, An Y T, Zhang S 2016 Appl. Opt. 55 5219
Google Scholar
[22] Zhong J G, Weng J W 2005 Opt. Lett. 30 2560
Google Scholar
[23] Zhong M, Chen W J, Wang T, Su X Y 2013 Opt. Lasers Eng. 51 1138
Google Scholar
[24] Wang S J, Li W L, Wang Y, Jiang Y Y, Jiang S, Zhao R L 2012 J. Multimedia 7 429
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[25] Huang N E, Sheng Z, Long S R, Wu M C, Shih W H, Zeng Q, Yen N C, Tung C C, Liu H H 1998 Proc. Math. Phys. Eng. Sci. 454 903
Google Scholar
[26] Bernini M B, Galizzi, G E, Federico, A, Kaufmann, G H 2007 Opt. Lasers Eng. 45 723
Google Scholar
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图 1 PSP测量系统原理
Figure 1. Principle of PSP measurement system.
图 2 均匀背景强度和调制度下LEF方法的仿真结果 (a) 条纹图; (b) 相位分布; (c) 相位误差
Figure 2. Simulation results of LEF method under the uniform background intensity and modulation: (a) The fringe pattern; (b) the phase distribution; (c) the phase error.
图 3 不同背景强度下LEF方法的仿真结果
Figure 3. Simulation results of LEF method under different background intensities.
图 4 不同调制度下LEF方法的仿真结果
Figure 4. Simulation results of LEF method under different modulation.
图 5 参考相位
Figure 5. Reference phase.
图 6 仿真1下基归一化LEF的两步PSP测量相位分布
Figure 6. Phase distribution of two-step PSP based on the normalized LEF in simulation condition 1.
图 7 不同情况下基于归一化LEF的2步PSP测量相位误差
Figure 7. Phase error results of 2-step PSP based on the normalized LEF under different conditions.
图 8 随机噪声条件下3步相移方法、FTP和基于归一化LEF的两步PSP的测量结果
Figure 8. Measurement results of 3-step phase shift method, FTP and 2-step PSP based on the normalized LEF under random noise.
图 9 十步相移方法的测量结果 (a) 待测物体; (b) 物体的条纹图; (c) 十步相移方法提取的相位分步; (d) 图(c)中红色方框内的相位细节
Figure 9. Measurement results of ten-step phase shifting method: (a) Test object; (b) fringe pattern of the test object; (c) the reference phase distribution based on ten-step phase-shifting method; (d) the enlarged phase details in red rectangular of Fig. (c).
图 10 FTP的测量结果 (a) 相位分布; (b) 相位误差; (c) 图(a)中红色框内的相位细节
Figure 10. Measurement results of FTP: (a) Phase distribution; (b) phase error distribution; (c) the enlarged phase details in red rectangular of Fig. (a).
图 11 基于高斯滤波归一化、EMD归一化、均值和对比度矫正的LEF方法重建结果
Figure 11. Reconstructed results of LEF method based on Gaussian filter normalization, EMD normalization, mean and contrast correction.
图 12 运动物体的实验结果 (a) 三步相移方法提取的相位; (b) 基于高斯滤波归一化的两步PSP重建的相位; (c) 基于EMD归一化的两步PSP重建相位; (d) 基于均值和调制度矫正的两步PSP重建相位
Figure 12. Experimental results of moving objects: (a) The extracted phase by three-step phase shifting method; (b) the phase obtained from two-step PSP based on Gaussian filter normalization; (c) the phase estimated from two-step PSP based on EMD normalization; (d) the phase estimated from two-step PSP based on the mean value and modulation.
表 1 不同情况下基于LEF的两步PSP方法计算的相位误差均方根
Table 1. Root mean square of phase error calculated by two-step PSP based on the normalized LEF under different conditions.
N 1 2 3 高斯滤波归一化/rad 0.0022 0.0729 0.0624 EMD归一化/rad 0.0216 0.0319 0.0608 均值和调制度矫正归一化/rad 0.0013 0.0805 0.0847 
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表 2 不同情况下基于LEF的两步PSP方法计算的相移误差均方根
Table 2. Root mean square of phase-shifting error calculated by two-step PSP based on the normalized LEF under different conditions.
N 1 2 3 高斯滤波归一化/rad 0 0.0125 0.0117 EMD归一化/rad 0.0017 0.0039 0.0108 均值和调制度矫正归一化/rad 0 0.0183 0.0206
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[1] Li B W, Liu Z P, Zhang S 2016 Opt. Express 24 23289
Google Scholar
[2] Wu Y X, Cai X J, Zhu J J, Yue H M, Shao X P 2020 Opt. Lasers Eng. 127 105987
Google Scholar
[3] Feng S J, Zhang L, Zuo C, Tao T Y, Chen Q, Gu G H 2018 Meas. Sci. Technol. 29 122001
Google Scholar
[4] Pan B, Kemao Q, Huang L, Asundi A 2009 Opt. Lett. 34 416
Google Scholar
[5] Wang Y J, Zhang S, Oliver J H 2011 Opt. Express 19 8539
Google Scholar
[6] Isaac T, Heejoo C, Wook K D 2016 Opt. Express 24 27993
Google Scholar
[7] Lilley F, Lalor M J, Burton D R 2000 Opt. Eng. 39 187
Google Scholar
[8] Servin M, Garnica G, Estrada J C, Padilla J M 2014 Opt. Express 22 10914
Google Scholar
[9] Wang Y, Laughner J I, Efimov I R, Zhang S 2013 Opt. Express 21 5822
Google Scholar
[10] Lu L, Xi J T, Yu Y G, Guo Q H 2014 Opt. Lett. 39 6715
Google Scholar
[11] Cai Z W, Liu X L, Jiang H, He D, Peng X, Huang S J, Zhang S H 2015 Opt. Express 23 25171
Google Scholar
[12] Tao T Y, Chen Q, Da J, Feng S J, Hu Y, Zuo C 2016 Opt. Express 24 20253
Google Scholar
[13] Liu Z P, Zibley P C, Zhang S 2018 Opt. Express 26 12632
Google Scholar
[14] Wang Y, Liu Z P, Jiang C, Zhang S 2018 Opt. Express 26 34224
Google Scholar
[15] Feng S J, Zuo C, Tao T Y, Hu Y, Zhang M L, Chen Q, Gu G H 2018 Opt. Lasers Eng. 103 127
Google Scholar
[16] Lu L, Xi J T, Yu Y G, Guo Q H 2013 Opt. Express 21 30610
Google Scholar
[17] Wang Z Y, Han B 2004 Opt. Lett. 29 1671
Google Scholar
[18] Su X Y, Chen W J 2001 Opt. Lasers Eng. 35 263
Google Scholar
[19] 徐建亮, 汪敏, 潘慧, 刘晓辉, 戚晓利, 许四祥 2011 物理学报 60 074210
Google Scholar
Xu J L, Wang M, Pan H, Liu X H, Qi X L, Xu S X 2011 Acta Phys. Sin. 60 074210
Google Scholar
[20] Hu Y, Chen Q, Zhang Y Z, Feng S J, Tao T Y, Li H, Yin W, Zuo C 2018 Appl. Opt. 57 772
Google Scholar
[21] Li B W, An Y T, Zhang S 2016 Appl. Opt. 55 5219
Google Scholar
[22] Zhong J G, Weng J W 2005 Opt. Lett. 30 2560
Google Scholar
[23] Zhong M, Chen W J, Wang T, Su X Y 2013 Opt. Lasers Eng. 51 1138
Google Scholar
[24] Wang S J, Li W L, Wang Y, Jiang Y Y, Jiang S, Zhao R L 2012 J. Multimedia 7 429
Google Scholar
[25] Huang N E, Sheng Z, Long S R, Wu M C, Shih W H, Zeng Q, Yen N C, Tung C C, Liu H H 1998 Proc. Math. Phys. Eng. Sci. 454 903
Google Scholar
[26] Bernini M B, Galizzi, G E, Federico, A, Kaufmann, G H 2007 Opt. Lasers Eng. 45 723
Google Scholar
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