光学学报, 2011, 31 (4): 0412011, 网络出版: 2020-06-18   

用泽尼克多项式消除三维轮廓术中的条纹载频

Carrier Removal Method in Fringe Projection Profilometry Using Zernike Polynomials
作者单位
四川大学电子信息学院光电科学技术系, 四川 成都 610065
摘要
在基于条纹投影的三维轮廓术中,投影条纹不可避免地会引入载频分量。同时实际成像系统又存在畸变等光学像差,导致载频分量不再是线性分布,只有准确消除载频成分后,才能还原待测物体的三维形貌。提出了一种运用泽尼克多项式拟合消除载频的方法,用参考平面区域数据点的相位值和泽尼克多项式值,拟合得到整幅图像的载频相位分布,从整体的相位中减去载频相位,获得由物体高度调制的相位分布。对理想变形条纹和有畸变变形条纹的载频消除过程分别进行了模拟实验,并与现有方法的结果进行了对比,验证了该方法的有效性。实物实验也表明该方法可以有效地消除载频,减小重建误差,且其算法简单,只需单帧图像即可消除载频,有望在动态三维面形测量中得到应用。
Abstract
In three-dimentional (3D) profilometry based on fringe projection, projected fringe patterns will introduce carrier phases into the overall phase distribution. In an actual imaging system, optical aberration will result in nonlinear carrier, so the nonlinear carrier must be removed accurately to get the phase distribution modulated by the object. A new carrier removal method using Zernike polynomials fitting is proposed. The carrier phases can be obtained by Zernike polynomials fitting using data points on reference area. By subtracting the carrier phases from the overall phase distribution, the object height-related phases can be obtained. Simulation experiments are performed to evaluate the performance of the method for two deformed fringe patterns with and without image aberration. The experimental results show that the method can effectively remove the carrier, and reduce the reconstruction error. And this method has simple algorithm, needs only one image and can be used in the applications which require least time consumption.
参考文献

[1] . Fourier transform profilometry for the automatic measurement of 3-D object shapes[J]. Appl. Opt., 1983, 22(24): 3977-3982.

[2] . Srinivasan, H. C. Liu, M. Halioua. Automated phase-measuring profilometry of 3-D diffuse objects[J]. Appl. Opt., 1984, 23(18): 3105-3108.

[3] . Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry[J]. J. Opt. Soc. Am., 1982, 72(1): 156-160.

[4] . . Removal of carrier frequency in phase-shifting techniques[J]. Optics and Lasers in Engineering, 1998, 30(1): 107-115.

[5] . Carrier phase component removal: a generalized least-squares approach[J]. J. Opt. Soc. Am. A, 2006, 23(2): 435-443.

[6] . Quan, C. J. Tay, L. J. Chen. A study on carrier-removal techniques in fringe projection profilometry[J]. Optics & Laser Technology, 2007, 39(6): 1155-1161.

[7] 侯溪, 伍凡, 杨力 等. 中心遮拦干涉图的圆泽尼克拟合对计算赛德尔像差的影响分析[J]. 光学学报, 2006, 26(1): 54~60

    Hou Xi, Wu Fan, Yang Li et al.. Effect of central obscuration interferograms fitted with Zernike circle polynomials on calculating Seidel aberrations [J]. Acta Optica Sinaca, 2006, 26(1): 54~60

[8] 唐玉科, 何小海, 陶青川. 基于泽尼克多项式的显微镜点扩展函数研究[J]. 光学学报, 2009, 29(1): 169~175

    Tang Yuke, He Xiaohai, Tao Qingchuan. Research on the point spread function of microscope based on the Zernike polynomials [J]. Acta Optica Sinaca, 2009, 29(1): 169~175

[9] James C. Wyant. Applied Optics and Optical Engineering, Vol. XI [M]. Riverport: Academic Press, 1992

[10] . 应用泽尼克多项式自由曲面的成像物镜设计[J]. 浙江大学学报(工学版), 2008, 42(12): 2202-2206.

    . . Design of reflective lens with Zernike polynomial free form surfaces[J]. J. Zhejiang University (Engineering Science), 2008, 42(12): 2202-2206.

[11] 江旻珊, 周传清, 任秋实. 两种可变形反射镜泽尼克系数的生成误差分析[J]. 光学学报, 2009, 29(s1): 396~398

    Jiang Minshan, Zhou Chuanqing, Ren Qiushi. Zernike generation analysis of two deformable mirrors [J]. Acta Optica Sinaca, 2009, 29(s1): 396~398

[12] 叶红卫, 李新阳, 鲜浩 等. 光学系统的Zernike像差与光束质量β因子的关系[J]. 中国激光, 2009, 36(6): 1420~1427

    Ye Hongwei, Li Xinyang, Xian Hao et al.. Relationship between Zernike wavefront errors and beam quality factor β for optics system [J]. Chinese J. Lasers, 2009, 36(6): 1420~1427

[13] . 用Zernike自由曲面设计弯曲屏幕超薄投影系统[J]. 浙江大学学报(工学版), 2009, 43(8): 1428-1432.

    . . Design of ultra-thin projection system with curved screen based on Zernike free-form surfaces[J]. J. Zhejiang University (Engineering Science), 2009, 43(8): 1428-1432.

[14] 莫卫东. 数字平面检测系统误差和精度评价方法的研究[J]. 光学学报, 2003, 23(7): 879~883

    Mo Weidong. Error and precision evaluation of a system for inspecting surface of optical plane [J]. Acta Optica Sinaca, 2003, 23(7): 879~883

[15] 刘元坤, 苏显渝, 吴庆阳. 基于傅里叶条纹分析的多摄像机标定方法[J]. 光子学报, 2007, 36(9): 1734~1737

    Liu Yuankun, Su Xianyu, Wu Qingyang. Multi-camera calibration by FTP technique [J]. Acta Photonica Sinica, 2007, 36(9): 1734~1737

吴志云, 张启灿. 用泽尼克多项式消除三维轮廓术中的条纹载频[J]. 光学学报, 2011, 31(4): 0412011. Wu Zhiyun, Zhang Qican. Carrier Removal Method in Fringe Projection Profilometry Using Zernike Polynomials[J]. Acta Optica Sinica, 2011, 31(4): 0412011.

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