-
PMP相移测量轮廓术具有像素级的测量精度,并且对环境光与物体反射率变化有很强的鲁棒性,但是由于需要投射多幅图像以计算物体相位信息需要花费较多的时间,因此这种方法对物体实时三维形貌测量误差较大[19]。Guan C等人[12]提出的复合光栅投影方法将N幅相移光栅与不同频率的正弦光栅正交相乘后组合得到一帧复合光栅像,如图1所示。
通过投影一帧复合光栅图像到物体表面,CCD获取经物体调制后的变形光栅图像,经过滤波程序,得到N幅携带物体形貌特征的相移变形条纹图,经过相位计算、相位展开和高度映射,重建物体的三维面形。
编码的复合光栅表达式为:
$$I_p^{256}({x^p},{y^p}) \!=\! {\rm{INT}}8\left\{ {C \!+\! D\sum\limits_{n = 1}^N {I_n^p} ({x^p},{y^p})\cos (2{\text{π}} f_n^p{x^p})} \right\}$$ (1) 式中:
${\rm{INT}}\left\{ \bullet \right\}$ 表示8 bit无符号取整算子;$I_n^p({x^p},{y^p})$ 为N幅调制的正弦相移光栅:$$I_n^p({x^p},{y^p}) = A + B\cos (2{\text{π}} f_\varphi ^p{y^p} + 2{\text{π}} n/N)$$ (2) 式中: n=1,2,3.....,N为载频序数;A和B、
$f_\varphi ^p$ 分别为被调制的相移正弦光栅的背景光、对比度和空间频率;$\left( {{x^p},{y^p}} \right)$ 为投影坐标,${y^p}$ 方向为物体高度引起的相位变化方向,与之垂直的${x^p}$ 方向为正交方向;$f_n^p$ 是平行于正交方向的载波频率;C、D为两个常数,由以下公式计算:$$D = ({I_{{{{\rm{max}}}}}} - {I_{{{{\rm{min}}}}}})/\left( \begin{array}{l} ({\rm{max}}\left\{ {\sum\limits_{n = 1}^N {I_n^Pcos(2{\text{π}} f_n^P{x^p})} } \right\} \\ - {\rm{min}}\left\{ {\sum\limits_{n = 1}^N {I_n^Pcos(2{\text{π}} f_n^P{x^p})} } \right\} \\ \end{array} \right)$$ (3) $$C = {I_{{\rm{min}}}} - D{\rm{min}}\left( {\sum\limits_{n = 1}^N {I_n^Pcos(2{\text{π}} f_n^P{x^p})} } \right)$$ (4) $\left[ {{I_{{\rm{min}}}},{I_{{\rm{max}}}}} \right]$ 为与DLP投影强度一致的正交复合光栅的光强范围,通常落在[0,255]灰阶范围内。${\rm{max}}\left\{ \bullet \right\}$ 表示取最大值算子,${\rm{min}}\left\{ \bullet \right\}$ 表示取最小值算子。将光栅$I_p^{256}({x^p},{y^p})$ 投射到被测物体表面后,经过物体反射后CCD拍摄到的变形条纹图为:$$I_{}^{256}(x,y) = r({x^s},{y^s})\left\{ {{\rm{c}} + d\sum\limits_{n = 1}^N {I_n^s} ({x^s},{y^s})\cos (2{\text{π}} f_n^s{x^s})} \right\}$$ (5) 式中:
$r({x^s},{y^s})$ 为物体的反射率;$({x^s},{y^s})$ 代表CCD像素坐标;$I_n^s({x^s},{y^s})$ 为第n帧变形相移条纹图。$$I_n^s({x^s},{y^s}) = a + bcos\left[ {2{\text{π}} f_\varphi ^s{y^s} + \phi ({x^s},{y^s}) + 2{\text{π}} n/N} \right]$$ (6) 通过对变形条纹图快速傅里叶变换得到其频谱,在光栅相移方向设置对应的滤波器滤掉载频,再进行傅里叶逆变换得到。a,b为背景光和对比度,
$\phi ({x^s},{y^s})$ 为物体高度所引起的相位变化值。基于N帧相移变形条纹图计算反应物体高度的相位信息如公式(7)所示:$$\phi ({x^s},{y^s}) = \arctan \left[ {\frac{{\sum\limits_{n = 1}^N {I_n^s} ({x^s},{y^s})\sin (2{\text{π}} n/N)}}{{\sum\limits_{n = 1}^N {I_n^s} ({x^s},{y^s})\cos (2{\text{π}} n/N)}}} \right]$$ (7) 物体相位信息包裹在[-π,π)之间,通过相位展开算法获得连续的相位信息,综合考虑参考面与被测物面信息得到仅受物体高度调制的连续相位
$\psi (x,y)$ ,通过被测物体高度-相位映射关系[20]公式(8)重建物体高度信息。$$\frac{1}{{h(x,y)}} = \alpha (x,y) + \beta (x,y)\frac{1}{{\psi (x,y)}} + \gamma (x,y)\frac{1}{{\psi {{(x,y)}^2}}}$$ (8) 式中:
$\alpha (x,y)$ 、$\beta (x,y)$ 和$\gamma (x,y)$ 均为系统常数,可通过系统标定获得。 -
由于商用DLP的256灰度动态范围的标准限制[17],由OCG测量方法的原理可知,调制进复合光栅的多幅正弦相移光栅共享256个灰阶动态范围而致各幅调制光栅动态范围受到压缩,表达物体面形特征的相位信息受到压缩,引起相位展开环节的展项极点增多,增大解相误差,甚至导致相位断裂而发生物体重建不完整现象。为了解决这一问题,文中提出了一种基于灰度拓展复合光栅的单帧三维测量方法。流程图如图2所示。
首先,设计一个期望具有766灰度动态范围的正交复合光栅图像为:
$$I_p^{766}({x^p},{y^p}) = INT16(C + D\sum\limits_{n = 1}^N {I_n^p} ({x^p},{y^p})\cos (2{\text{π}} f_n^p{x^p}))$$ (9) 有效相位信息为10 bit,N=3,投影常数
C、D的计算以获得最优的被测物的深度信息 $\left[ {{I_{{\rm{min}}}},{I_{{\rm{max}}}}} \right]$ 落在[0,765]之间。$$D = 765/\left( \begin{array}{l} (\max\left\{ {\sum\limits_{n = 1}^N {I_n^Pcos(2{\text{π}} f_n^P{x^p})} } \right\} - \\ \min\left\{ {\sum\limits_{n = 1}^N {I_n^Pcos(2{\text{π}} f_n^P{x^p})} } \right\} \end{array} \right)$$ (10) $$C = - D\min\left( {\sum\limits_{n = 1}^N {I_n^Pcos(2{\text{π}} f_n^P{x^p})} } \right)$$ (11) 虽然理论设计的OCGGE具有766灰阶动态范围,但是由于商用DLP的标准限制其只能投射256灰阶动态范围的光栅图像,如果直接将设计的具有766灰阶动态范围的复合光栅投射到被测物体表面,DLP将自动压缩其灰阶范围在[0,255]范围内,难以达到灰阶拓展的目的。如果直接投影256灰阶动态范围的复合光栅图像
$I_p^{256}({x^p},{y^p})$ ,设置CCD的曝光时间为DLP刷新周期的3 m倍,获得的灰度值为:$$ F\left( {x,y} \right) = 3m*I_p^{256}({x^p},{y^p})\;\;\;m = 1,2,3.... $$ (12) 采集到的最大灰阶个数为255×1+1=256个,即只能增大对应点整体亮度而不能达到增大灰阶动态范围的目的。由时分复用原理可知,如果将正交复合光栅图像均匀拆分为3幅图像并依次投影,调整CCD积分时间为三幅图像投影周期的m倍,采集得到图像灰度值为:
$$ {F^e}\left( {x,y} \right) = m*\sum\limits_{i = 1}^N {I_p^{256}(x_i^p,y_i^p)} \;\;\;m = 1,2,3\ldots $$ (13) 采集到的最大灰阶个数为255×3+1=766个,因此正交复合光栅
$I_p^{766}$ 拆分为3幅具有256动态范围的正交复合光栅图像需满足以下要求:$$\left\{ \begin{aligned} & I_p^{766} = I_1^{256}+I_2^{256}+ I_3^{256}\\ & \left| {I_i^{256} - I_j^{256}} \right| \le 1\;i = 1,2,3;\;j = 1,2,3 \end{aligned} \right.$$ (14) 如果直接依次投射所拆分的三幅复合条纹图,每幅图像投射需要较长时间,且各幅图像投射时间会因程序指令差异而导致不一致,采集图像一方面会因设置CCD曝光时间较长而过饱和失真,另一方面会因不同图像投射时间的差异性而使不同时刻采集的图像灰度存在差异,导致图像采集的不稳定。为此,提出了将三幅静态图像依次连续地加载进视频,用重复视频播放投影替换传统静态图像投影,这样一方面使CCD曝光时间显著缩短以确保采集的变形条纹图不致饱和失真,另一方面会因视频刷新帧率的稳定而确保图像采集的稳定。为了进一步量化分析,设视频中每帧图像的播放周期为
${t_0}$ ,完成三帧条纹投影的完整周期为$t = 3{t_0}$ ,如果调整CCD的曝光时间为t的整数m倍即${T_{{\rm{CCD}}}} = mt$ ,这样无需考虑DLP与CCD同步,只要选择10 bit及以上的CCD即可采集到动态范围为[0,755]的组合变形条纹图。此时采集到的组合变形条纹表达式可表示为:
$$I^{766}(x,y) = r({x^e},{y^e})({{c}} + d\sum\limits_{n = 1}^N {I_n^{\rm{e}}} ({x^e},{y^e})\cos (2{\text{π}} f_n^e{x^e}))$$ (15) 通过傅里叶变换后通过选择恰当的滤波器滤波得到三帧变形相移条纹图像:
$$I_n^e({x^e},{y^e}) = {{a}} + bcos[2{\text{π}} f_\varphi ^e{y^e} + \phi ({x^e},{y^e}) + 2{\text{π}} n/N]$$ (16) 物体相位信息
$\phi ({x^e},{y^e})$ 同理可通过公式(7)计算得到,经相位展开与相位-高度映射算法即可重建被测物体的三维面形。
Single-shot 3D measurement using grayscale expanded composited grating
-
摘要:
提出了一种基于灰度拓展的单帧正交复合光栅三维测量方法。由于受商用DLP最大灰阶动态范围256的标准限制,单帧复合光栅中的多张调制光栅共享256灰阶动态范围导致其对比度变小,其表征的三维物体的相位信息被压缩,解相过程出现相位断裂现象,测量误差增大。采用时分复用原理,将一具有766灰阶的正交复合光栅拆分为三幅不同的具有256灰阶的条纹图。依次序加载进循环播放的视频中投射至待测物体表面,当用曝光时间为3倍视频刷新周期的整数倍10 bit CCD采集时,就可采集到具有766灰阶动态范围的变形复合光栅像。通过滤波和灰度校准等计算后,物体的三维面形能够完整而精确的重建。经仿真和实验验证,所提方法打破了DLP256灰度投影的限制,有效提高了相移变形条纹的动态范围,增大了被测物体细节信息,避免了相位展开环节相位断裂而引起物体面形重构不完整的现象。
Abstract:A single-shot 3D shape measurement using orthogonal composited grating based on grayscale expanding (OCGGE) was proposed. In the traditional orthogonal composited grating (OCG) profilometry, the modulated gratings in the orthogonal composited grating must share the same grayscale level since the maximal grayscale dynamic range of commercial Digital Light Processing (DLP) is limited in 256, that results in some phenomenon increasing the measuring error, including the weakened contrast of the modulated grating, the compressed phase information and the broken phase during the process of phase unwrapping. Based on the principle of time division multiplexing, one orthogonal composited grating was designed with 766 gray level and was spited into three different fringe patterns with 256 grayscales, then loaded these patterns in sequence to edit a video. When this video was played and projected onto the measured object continuously, by setting the exposure time as an integer times of the 3 times of the frame refresh cycle of the video for a 10bit CCD, a deformed pattern with 766 grayscales could be obtained. After the filtering and grayscale calibration, the object could be reconstructed accurately and completely. Both simulation and experiment results prove that the proposed method can break the limit of 256 grayscale projection and increase the dynamic range of the phase-shifting deformed patterns efficiently. And it can also enrich the detailed information of the measured object and avoid the incomplete surface reconstruction caused by phase break.
-
图 3 OCG和OCGGE方法的实验对比。(a),(f)OCG与OCGGE的变形条纹图;(b),(g)OCG和OCGGE方法的频谱分布;(c),(d),(e)OCG方法从滤波器1,2,3中提取的变形相移条纹图在第512列的截面图;(h),(i),(j)OCGGE方法从滤波器4,5,6中提取的变形相移条纹图在第512列的截面图;(k)OCG的重建结果;(l)图3(k)中虚线框的局部放大图;(m)OCGGE方法的重建结果
Figure 3. Experimental contrast between OCG and OCGGE. (a), (f) Deformed pattern of OCG and OCGGE; (b), (g) spectrum distribution of OCG and OCGGE; (c), (d), (e) OCG cutaway views at column 512 of the deformed phase shifting fringe patterns extracting from filter1, filter2, filter3; (h), (i), (j) OCGGE cutaway views at column 512 of the deformed phase shifting fringe patterns extracting from filter4, filter5, filter6; (k) reconstructed result of OCG; (l) zoom in on the dashed box from Fig.3(k); (m) reconstructed result of OCGGE
图 4 OCG, OCGGE和PMP方法实验结果对比。(a)被测物体;(b)OCGGE方法所获取的变形条纹图;(c)OCGGE方法重建的三维面形;(d)三种方法在第476列的剖面图;(e)图4(d)中短划线框的局部放大图;(f)图4(d)中方点线框的局部放大图
Figure 4. Comparison results between OCG, OCGGE and PMP. (a) Measured object; (b) deformed pattern of OCGGE; (c) reconstructed result with OCGGE; (d) cutaway view at column 476 with OCG, OCGGE and PMP; (e) magnified view of the dashed box from Fig. 4(d); (f) magnified view of the point line box from Fig. 4(d)
-
[1] Gao Peng, Wen Kai, Sun Xueying, et al. Review of resolution enhancement technologies in quantitative phase microscopy [J]. Infrared and Laser Engineering, 2019, 48(6): 0603007. (in Chinese) doi: 10.3788/IRLA201948.0603007 [2] Zhang Wenhui, Cao Liangcai, Jin Guofan. Review on high resolution and large field of view digital holography [J]. Infrared and Laser Engineering, 2019, 48(6): 0603008. (in Chinese) doi: 10.3788/IRLA201948.0603008 [3] Zhang Lei, Liu Dong, Shi Tu, et al. Optical free-form surfaces testing techonlogies [J]. Chinese Optics, 2017, 10(3): 283−299. (in Chinese) doi: 10.3788/co.20171003.0283 [4] 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. doi: 10.1016/j.optlaseng.2018.04.019 [5] Shang Wanqi, Zhang Wenxi, Wu Zhou, et al. Three-dimensional measurement system based on full-field heterodyne interferometry [J]. Optics and Precision Engineering, 2017, 46(3): 251−259. (in Chinese) [6] Chen Chao, Yu Yanqin, Huang Shujun, et al. 3D small-field imaging system [J]. Infrared and Laser Engineering, 2016, 45(8): 0824002. (in Chinese) doi: 10.3788/IRLA201645.0824002 [7] Wang Z Z, Yang Y M. Single-shot three- dimensional reconstruction based on structured light line pattern [J]. Optics and Lasers in Engineering, 2018, 106: 10−16. doi: 10.1016/j.optlaseng.2018.02.002 [8] Wu Yingchun, Cao Yiping, Xiao Yanshan. On-line three-dimensional inspection using randomly phase-shifting fringe based on least-square iteration [J]. Optics and Precision Engineering, 2014, 22(5): 1347−1353. (in Chinese) doi: 10.3788/OPE.20142205.1347 [9] Zhang Z H. Review of single-shot 3D shape measurement by phase calculation-fringe projection techniques [J]. Optics and Lasers in Engineering, 2012, 50(8): 1097−1106. doi: 10.1016/j.optlaseng.2012.01.007 [10] Wang Jianhua, Yang Yanxi. Double N-step phase-shifting profilometry using color-encoded grating projection [J]. Chinese Optics, 2019, 12(3): 616−626. (in Chinese) doi: 10.3788/co.20191203.0616 [11] Takeda M. Fourier transform profilometry for the automatic measurement of 3-D object shapes [J]. Appl Opt, 1983: 22. [12] Guan C, Hassebrook L G, Lau D L. Composite structured light pattern for three-dimensional video [J]. Optics Express, 2003, 11(5): 406−417. doi: 10.1364/OE.11.000406 [13] He Yuhang, Cao Yiping, Zhai Aiping. A 3-D measurement method with orthogonal composite light based on fringe contrast and background calibration [J]. Acta Optica Sinica, 2010, 30(11): 3191−3196. (in Chinese) doi: 10.3788/AOS20103011.3191 [14] Zhai Aiping, Cao Yiping, He Yuhang. 3D measurement with orthogonal composite structure light based on two-plus-one phase-shifting algorithm [J]. Chinese Journal of Lasers, 2012, 39(2): 147−152. (in Chinese) [15] He Y H, Cao Y P. Shifted-phase calibration for a 3-D shape measurement system based on orthogonal composite grating projection [J]. Optik, 2011, 122(19): 1730−1734. doi: 10.1016/j.ijleo.2010.10.033 [16] He D W, Cao Y P, He D G, et al. Optimized design of composite grating in real-time three-dimensional shape measurement [J]. Optik, 2015, 126(21): 2781−2787. doi: 10.1016/j.ijleo.2015.07.003 [17] Zhang Lizhen, Cao Yiping, Fu Guangkai, et al. Application of grayscale expansion for accuracy improvement in phase-measuring profilometry [J]. Displays, 2019, 59: 28−34. doi: 10.1016/j.displa.2019.06.001 [18] Cao Yiping, Su XianYu, Chen Wenjing, et al. Effect on the phase measuring profilometer to the spatio-temporal characteristic of DMD [J]. Optical Technique, 2004, 30(2): 157−160. (in Chinese) [19] Wang Z Z. Robust measurement of the diffuse surface by phase shift profilometry [J]. Journal of Optics, 2014, 16(10). [20] Ma Q N, Cao Y P, Chen C, et al. Intrinsic feature revelation of phase-to-height mapping in phase measuring profilometry [J]. Optics & Laser Technology, 2018, 108: 46−52.
计量
- 文章访问数: 464
- HTML全文浏览量: 225
- 被引次数: 0