一种非线性相位误差的全场补偿方法
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摘要
提出了一种非线性相位误差的全场补偿方法,通过对参考面相位的多次测量,提高了参考面的解相精度,提取出一个逼近理想值的期望相位面,并用该期望相位面检测非线性相位误差。重构待测物体时,可直接用物体展开相位值在查找表中查找对应的非线性相位误差,并以此对物体的展开相位进行全场补偿。采用所提方法重构已知具体高度的平面,平均绝对误差的最大值从0.48 mm减小到0.06 mm,方均根误差的最大值从0.55 mm减小到0.07 mm。
A full-field compensation method for nonlinear phase error is proposed. By measuring the reference plane for multiple times, the accuracy of phase unwrapping on the reference plane can be efficiently improved. An expected phase plane approaching to the ideal values can be extracted from these multiple measured phases on the reference plane. This expected phase plane can be used to detect the nonlinear phase error. When reconstructing the measured object, the nonlinear phase error can be directly searched in the look-up table with the unwrapped phase of the object, then the full-field unwrapping phase of the object be compensated. By using the proposed method to reconstruct several height-known flat planes, the maximum mean absolute error(MAE) is decreased from 0.48 mm to 0.06 mm and the maximum root-mean-square error(RMSE) is decreased from 0.55 mm to 0.07 mm.
A full-field compensation method for nonlinear phase error is proposed. By measuring the reference plane for multiple times, the accuracy of phase unwrapping on the reference plane can be efficiently improved. An expected phase plane approaching to the ideal values can be extracted from these multiple measured phases on the reference plane. This expected phase plane can be used to detect the nonlinear phase error. When reconstructing the measured object, the nonlinear phase error can be directly searched in the look-up table with the unwrapped phase of the object, then the full-field unwrapping phase of the object be compensated. By using the proposed method to reconstruct several height-known flat planes, the maximum mean absolute error(MAE) is decreased from 0.48 mm to 0.06 mm and the maximum root-mean-square error(RMSE) is decreased from 0.55 mm to 0.07 mm.
引文
[1] Chen F, Su X Y, Xiang L Q. Analysis and identification of phase error in phase measuring profilometry[J]. Optics Express, 2010, 18(11): 11300-11307.
[2] Xu X F, Cao Y P, Peng K. Pixel matching method in on-line three-dimensional measurement based on phase prediction[J]. Acta Optica Sinica, 2016, 36(6): 0612005. 许幸芬, 曹益平, 彭旷. 基于相位预测的在线三维测量像素匹配方法[J]. 光学学报, 2016, 36(6): 0612005.
[3] Lu P, Sun C K, Wang P. Fringe projection phase-to-height mapping model and its calibration method[J]. Acta Optica Sinica, 2018, 38(2): 0212004. 陆鹏, 孙长库, 王鹏. 条纹投影相位高度转换映射模型及其标定方法[J]. 光学学报, 2018, 38(2): 0212004.
[4] Xu W, Chen X B, Xi J T. A method of phase error compensation for structural light measurement[J]. Acta Optica Sinica, 2011, 31(3): 0312008. 许伟, 陈晓波, 习俊通. 结构光测量相位波动误差补偿方法研究[J]. 光学学报, 2011, 31(3): 0312008.
[5] Zhang S. Comparative study on passive and active projector nonlinear Gamma calibration[J]. Applied Optics, 2015, 54(13): 3834-3841.
[6] Zhong L J, Cao Y P. An on-line phase measuring profilometry with phase-shifting perpendicular to moving direction of measured object[J]. Acta Optica Sinica, 2009, 29(2): 417-420. 钟立俊, 曹益平. 相移正交物体运动方向的在线相位测量轮廓术[J]. 光学学报, 2009, 29(2): 417-420.
[7] Peng K, Cao Y P, Wu Y C, et al. On-line three-dimensional measurement method based on low modulation feature[J]. Chinese Journal of Lasers, 2013, 40(7): 0708006. 彭旷, 曹益平, 武迎春, 等. 基于低调制度特征的在线三维测量方法[J]. 中国激光, 2013, 40(7): 0708006.
[8] Bian X T, Cheng J, Zuo F, et al. A method of 3D shape measurement based on alignment grating projection[J]. Laser & Optoelectronics Progress, 2017, 54(1): 011202. 边心田, 程菊, 左芬, 等. 基于光栅预校正的三维面形测量方法[J]. 激光与光电子学进展, 2017, 54(1): 011202.
[9] Lü F X, Xing S, Guo H W. Self-correction of projector nonlinearity in phase-shifting fringe projection profilometry[J]. Applied Optics, 2017, 56(25): 7204-7216.
[10] Zhang S, Yau S T. Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector[J]. Applied Optics, 2007, 46(1): 36-43.
[11] Li Z W, Wang C J, Shi Y S, et al. High precision phase error compensation algorithm for structural light measurement[J]. Acta Optica Sinica, 2008, 28(8): 1527-1532. 李中伟, 王从军, 史玉升, 等. 结构光测量中的高精度相位误差补偿算法[J]. 光学学报, 2008, 28(8): 1527-1532.
[12] Ma S, Quan C, Zhu R, et al. Investigation of phase error correction for digital sinusoidal phase-shifting fringe projection profilometry[J]. Optics and Lasers in Engineering, 2012, 50(8): 1107-1118.
[13] Cai Z W, Liu X L, Jiang H, et al. Flexible phase error compensation based on Hilbert transform in phase shifting profilometry[J]. Optics Express, 2015, 23(19): 25171-25181.
[14] Liu C, Gai S Y, Da F P. Sub-regional phase error compensation for structural light measurement[J]. Chinese Journal of Lasers, 2018, 45(6): 0604002. 刘超, 盖绍彦, 达飞鹏. 结构光测量中分区域相位误差补偿方法研究[J]. 中国激光, 2018, 45(6): 0604002.
[15] Xiao Y S, Cao Y P, Wu Y C, et al. Gamma nonlinearity correction based on Fourier spectrum analysis for phase measuring profilometry[J]. Acta Optica Sinica, 2012, 32(12): 1212004. 肖焱山, 曹益平, 武迎春, 等. 基于傅里叶频谱分析的相位测量轮廓术系统Gamma非线性校正方法[J]. 光学学报, 2012, 32(12): 1212004.
[16] Liu K, Wang Y C, Lau D L, et al. Gamma model and its analysis for phase measuring profilometry[J]. Journal of the Optical Society of America A, 2010, 27(3): 553-562.
[17] Zhou P, Liu X R, He Y, et al. Phase error analysis and compensation considering ambient light for phase measuring profilometry[J]. Optics and Lasers in Engineering, 2014, 55: 99-104.
[18] Hoang T, Pan B, Nguyen D, et al. Generic Gamma correction for accuracy enhancement in fringe-projection profilometry[J]. Optics Letters, 2010, 35(12): 1992-1994.
[19] Xiao Y S, Cao Y P, Wu Y C, et al. Single orthogonal sinusoidal grating for Gamma correction in digital projection phase measuring profilometry[J]. Optical Engineering, 2013, 52(5): 053605.
[20] Li Y, Cao Y P, Huang Z F, et al. A three dimensional on-line measurement method based on five unequal steps phase shifting[J]. Optics Communications, 2012, 285(21/22): 4285-4289.
[21] Srinivasan V, Liu H C, Halioua M. Automated phase-measuring profilometry of 3-D diffuse objects[J]. Applied Optics, 1984, 23(18): 3105-3108.
[22] Chen Y T, Cao Y P, Chen C, et al. Phase measurement profilometry based on binary gratings with unequal duty cycle[J]. Acta Optica Sinica, 2018, 38(8): 0815021. 陈雨婷, 曹益平, 陈澄, 等. 基于不等占空比二元光栅的相位测量轮廓术[J]. 光学学报, 2018, 38(8): 0815021.
[23] Su X Y. Phase unwrapping techniques for 3D shape measurement[J]. Proceedings of SPIE, 1996, 2866: 460-465.
[24] Li W S, Su L K, Su X Y. Phase-measuring profilometry in big scale measurement[J]. Acta Optica Sinica, 2000, 20(6): 792-796. 李万松, 苏礼坤, 苏显渝. 相位检测面形术在大尺度三维面形测量中的应用[J]. 光学学报, 2000, 20(6): 792-796.
[2] Xu X F, Cao Y P, Peng K. Pixel matching method in on-line three-dimensional measurement based on phase prediction[J]. Acta Optica Sinica, 2016, 36(6): 0612005. 许幸芬, 曹益平, 彭旷. 基于相位预测的在线三维测量像素匹配方法[J]. 光学学报, 2016, 36(6): 0612005.
[3] Lu P, Sun C K, Wang P. Fringe projection phase-to-height mapping model and its calibration method[J]. Acta Optica Sinica, 2018, 38(2): 0212004. 陆鹏, 孙长库, 王鹏. 条纹投影相位高度转换映射模型及其标定方法[J]. 光学学报, 2018, 38(2): 0212004.
[4] Xu W, Chen X B, Xi J T. A method of phase error compensation for structural light measurement[J]. Acta Optica Sinica, 2011, 31(3): 0312008. 许伟, 陈晓波, 习俊通. 结构光测量相位波动误差补偿方法研究[J]. 光学学报, 2011, 31(3): 0312008.
[5] Zhang S. Comparative study on passive and active projector nonlinear Gamma calibration[J]. Applied Optics, 2015, 54(13): 3834-3841.
[6] Zhong L J, Cao Y P. An on-line phase measuring profilometry with phase-shifting perpendicular to moving direction of measured object[J]. Acta Optica Sinica, 2009, 29(2): 417-420. 钟立俊, 曹益平. 相移正交物体运动方向的在线相位测量轮廓术[J]. 光学学报, 2009, 29(2): 417-420.
[7] Peng K, Cao Y P, Wu Y C, et al. On-line three-dimensional measurement method based on low modulation feature[J]. Chinese Journal of Lasers, 2013, 40(7): 0708006. 彭旷, 曹益平, 武迎春, 等. 基于低调制度特征的在线三维测量方法[J]. 中国激光, 2013, 40(7): 0708006.
[8] Bian X T, Cheng J, Zuo F, et al. A method of 3D shape measurement based on alignment grating projection[J]. Laser & Optoelectronics Progress, 2017, 54(1): 011202. 边心田, 程菊, 左芬, 等. 基于光栅预校正的三维面形测量方法[J]. 激光与光电子学进展, 2017, 54(1): 011202.
[9] Lü F X, Xing S, Guo H W. Self-correction of projector nonlinearity in phase-shifting fringe projection profilometry[J]. Applied Optics, 2017, 56(25): 7204-7216.
[10] Zhang S, Yau S T. Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector[J]. Applied Optics, 2007, 46(1): 36-43.
[11] Li Z W, Wang C J, Shi Y S, et al. High precision phase error compensation algorithm for structural light measurement[J]. Acta Optica Sinica, 2008, 28(8): 1527-1532. 李中伟, 王从军, 史玉升, 等. 结构光测量中的高精度相位误差补偿算法[J]. 光学学报, 2008, 28(8): 1527-1532.
[12] Ma S, Quan C, Zhu R, et al. Investigation of phase error correction for digital sinusoidal phase-shifting fringe projection profilometry[J]. Optics and Lasers in Engineering, 2012, 50(8): 1107-1118.
[13] Cai Z W, Liu X L, Jiang H, et al. Flexible phase error compensation based on Hilbert transform in phase shifting profilometry[J]. Optics Express, 2015, 23(19): 25171-25181.
[14] Liu C, Gai S Y, Da F P. Sub-regional phase error compensation for structural light measurement[J]. Chinese Journal of Lasers, 2018, 45(6): 0604002. 刘超, 盖绍彦, 达飞鹏. 结构光测量中分区域相位误差补偿方法研究[J]. 中国激光, 2018, 45(6): 0604002.
[15] Xiao Y S, Cao Y P, Wu Y C, et al. Gamma nonlinearity correction based on Fourier spectrum analysis for phase measuring profilometry[J]. Acta Optica Sinica, 2012, 32(12): 1212004. 肖焱山, 曹益平, 武迎春, 等. 基于傅里叶频谱分析的相位测量轮廓术系统Gamma非线性校正方法[J]. 光学学报, 2012, 32(12): 1212004.
[16] Liu K, Wang Y C, Lau D L, et al. Gamma model and its analysis for phase measuring profilometry[J]. Journal of the Optical Society of America A, 2010, 27(3): 553-562.
[17] Zhou P, Liu X R, He Y, et al. Phase error analysis and compensation considering ambient light for phase measuring profilometry[J]. Optics and Lasers in Engineering, 2014, 55: 99-104.
[18] Hoang T, Pan B, Nguyen D, et al. Generic Gamma correction for accuracy enhancement in fringe-projection profilometry[J]. Optics Letters, 2010, 35(12): 1992-1994.
[19] Xiao Y S, Cao Y P, Wu Y C, et al. Single orthogonal sinusoidal grating for Gamma correction in digital projection phase measuring profilometry[J]. Optical Engineering, 2013, 52(5): 053605.
[20] Li Y, Cao Y P, Huang Z F, et al. A three dimensional on-line measurement method based on five unequal steps phase shifting[J]. Optics Communications, 2012, 285(21/22): 4285-4289.
[21] Srinivasan V, Liu H C, Halioua M. Automated phase-measuring profilometry of 3-D diffuse objects[J]. Applied Optics, 1984, 23(18): 3105-3108.
[22] Chen Y T, Cao Y P, Chen C, et al. Phase measurement profilometry based on binary gratings with unequal duty cycle[J]. Acta Optica Sinica, 2018, 38(8): 0815021. 陈雨婷, 曹益平, 陈澄, 等. 基于不等占空比二元光栅的相位测量轮廓术[J]. 光学学报, 2018, 38(8): 0815021.
[23] Su X Y. Phase unwrapping techniques for 3D shape measurement[J]. Proceedings of SPIE, 1996, 2866: 460-465.
[24] Li W S, Su L K, Su X Y. Phase-measuring profilometry in big scale measurement[J]. Acta Optica Sinica, 2000, 20(6): 792-796. 李万松, 苏礼坤, 苏显渝. 相位检测面形术在大尺度三维面形测量中的应用[J]. 光学学报, 2000, 20(6): 792-796.