一种基于背景校正的2+1相移算法
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摘要
由于投影仪与相机普遍存在的伽马非线性效应,变形条纹图直流项与背景图光强分布并不相等,会引入测量误差.本文在传统2+1相移算法中引入背景校正,以所捕获的背景图光强分布为模板,采用最小二乘原理逼近变形条纹图的直流项,能有效提高测量精度.所提2+1相移算法中两帧相移正弦光栅的相移量不再固定为π/2,可任意,算法更灵活.实验结果验证了该算法的有效性和实用性.
Due to the gamma nonlinear effects of the projectors and cameras,the Direct Current(DC)component of the deformed fringe pattern and the intensity distribution of background image are not equal,so measurement errors are introduced.This paper introduces a background image correction method in the traditional 2+1 phase-shifting algorithm.The intensity distribution of the captured background image is used as a template,and the DC component of the deformed fringe pattern is approximated by the least squares principle,which can effectively improve the measurement accuracy.And the phase shift of the 2 phase-shifting sinusoidal gratings is no longer fixed to beπ/2 in the new 2+1 phase-shifting algorithm,the algorithm is more flexible.The experimental results verify the effectiveness and practicability of the algorithm.
Due to the gamma nonlinear effects of the projectors and cameras,the Direct Current(DC)component of the deformed fringe pattern and the intensity distribution of background image are not equal,so measurement errors are introduced.This paper introduces a background image correction method in the traditional 2+1 phase-shifting algorithm.The intensity distribution of the captured background image is used as a template,and the DC component of the deformed fringe pattern is approximated by the least squares principle,which can effectively improve the measurement accuracy.And the phase shift of the 2 phase-shifting sinusoidal gratings is no longer fixed to beπ/2 in the new 2+1 phase-shifting algorithm,the algorithm is more flexible.The experimental results verify the effectiveness and practicability of the algorithm.
引文
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[14]WANG Y,JIANG C,ZHANG S.Double-pattern triangular pulse width modulation technique for high-accuracy highspeed 3Dshape measurement[J].Optics Express,2017,25(24):30177-30188.
[15]WIZINOWICH P L.Phase shifting interferometry in the presence of vibration:a new algorithm and system[J].Applied Optics,1990,29(22):3271-3297.
[16]ZHANG S,YAU S T.High-speed three-dimensional shape measurement using a modified two-plus-one phase-shifting algorithm[J].Optical Engineering,2007,46(11):113603.
[17]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.
[18]WANG X,FANG S P,ZHU X D.Weighted least-squares phase unwrapping algorithm based on a non-interfering image of an object[J].Applied Optics,2017,56(15):4543-4550.
[2]ZUO C,FENG S J,HUANG L,et al.Phase shifting algorithms for fringe projection profilometry:a review[J].Optics and Lasers in Engineering,2018,109:23-59.
[3]TAKEDA M,MOTOH K.Fourier transform profilometry for the automatic measurement of 3-D object shapes[J].Applied Optics,1983,22(24):3977-3982.
[4]LI B W,LIU Z P,ZHANG S.Motion-induced error reduction by combining Fourier transform profilometry with phaseshifting profilometry[J].Optics Express,2016,24(20):23289-23303.
[5]SRINIVASAN V,LIU H C,HALIOUA M.Automated phase-measuring profilometry of 3D diffuse objects[J].Applied Optics,1984,23(18):3105-3108.
[6]ZHU L,CAO Y P,HE D W,et al.Grayscale imbalance correction in real-time phase measuring profilometry[J].Optics Communications,2016,376:72-80.
[7]ZHAI Ai-ping,CAO Yi-ping,HE Yu-hang,et al.3D measurement with orthogonal composite structure light based on two-plus-one phase-shifting algorithm[J].Chinese Journal of Lasers,2012,39(2):0208003.翟爱平,曹益平,何宇航,等.基于“2+1”相移算法的正交复合光三维测量方法[J].中国激光,2012,39(2):0208003.
[8]HU Y,CHEN Q,ZHANG Y Z,et al.Dynamic microscopic 3Dshape measurement based on marker-embedded Fourier transform profilometry[J].Applied Optics,2018,57(4):772-780.
[9]ZHANG G M,TANG H W,ZHONG K,et al.High-speed FPGA-based phase measuring profilometry architecture[J]Optics Express,2017,25(9):10553-10564.
[10]MA M X,CAO Y P,HE D W,et al.Grayscale imbalance correcting method based on fringe normalization in RGBtricolor real-time three-dimensional measurement[J].Optical Engineering,2016,55(3):034102.
[11]ZHANG Xiao-xuan,WANG Yue-min,HUANG Shu-jun,et al.A two-step phase-shifting algorithm for phase calculation[J].Acta Photonica Sinica,2017,46(3):0311005.张晓璇,王月敏,黄淑君,等.一种两步相移相位解算方法[J].光子学报,2017,46(3):0311005.
[12]TAO T Y,CHEN Q,DA J,et al.Real-time 3-D shape measurement with composite phase-shifting fringes and multiview system[J].Optics Express,2016,24(18):20253-20269.
[13]LI Bao-shun,CAI Qing-qing,BAO Ya-ping,et al.Two-step phase-shifting algorithm by the use of half angle of phase[J].Acta Photonica Sinica,2014,43(11):1110002.李宝顺,蔡青青,包亚萍,等.采用相位半角的两步相移法[J].光子学报,2014,43(11):1110002.
[14]WANG Y,JIANG C,ZHANG S.Double-pattern triangular pulse width modulation technique for high-accuracy highspeed 3Dshape measurement[J].Optics Express,2017,25(24):30177-30188.
[15]WIZINOWICH P L.Phase shifting interferometry in the presence of vibration:a new algorithm and system[J].Applied Optics,1990,29(22):3271-3297.
[16]ZHANG S,YAU S T.High-speed three-dimensional shape measurement using a modified two-plus-one phase-shifting algorithm[J].Optical Engineering,2007,46(11):113603.
[17]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.
[18]WANG X,FANG S P,ZHU X D.Weighted least-squares phase unwrapping algorithm based on a non-interfering image of an object[J].Applied Optics,2017,56(15):4543-4550.