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基本的三通道相位轮廓测量系统由一台彩色CCD相机和一台DLP投影仪组成,同时,将一个LCD显示屏作为相位标靶与相机和投影仪一起构成投影仪色差建模与校正系统,如图3所示。
由于投影仪色差且离成像中心越远,色差越明显,可以建立色差与位置之间的关系。文中提出了一种新的基于相位标靶的相位测量轮廓术投影色差建模方法,将LCD显示屏作为相位标靶进行分析研究。首先关闭投影仪,由LCD显示屏直接显示条纹, LCD依次显示红、绿、蓝三种颜色的水平正弦条纹和垂直正弦条纹图像,然后由彩色CCD相机分别采集LCD显示的图像,则该图像只包含相机色差。关闭LCD显示屏,打开投影仪,由投影仪向显示屏依次投影相同的图像,此时CCD相机采集的图像包含投影仪色差和相机色差。然后使用四步相移法进行相位折叠,使用最佳三条纹选择方法进行相位展开,计算得到LCD显示的展开相位$ {\varphi }_{lcd\_h\_r} $、$ {\varphi }_{lcd\_v\_r} $和$ {\varphi }_{lcd\_h\_g} $、$ {\varphi }_{lcd\_v\_g} $和$ {\varphi }_{lcd\_h\_b} $、$ {\varphi }_{lcd\_v\_b} $,以及投影仪投影的展开相位$ {\varphi }_{pro\_h\_r} $、$ {\varphi }_{pro\_v\_r} $和$ {\varphi }_{pro\_h\_g} $、$ {\varphi }_{pro\_v\_g} $和$ {\varphi }_{pro\_h\_b} $、$ {\varphi }_{pro\_v\_b} $。然后利用中值滤波的方法去除突起点,拟合为平滑曲面,建立计算出的六组展开相位和相机像素X、Y的数学模型。最后进行理想显示像素点求解以及色差像素模型建立。投影仪色差建模流程图如图4所示。
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由于相机色差的存在,CCD相机采集红、绿、蓝三种通道的同一个像素点的位置也并不重合,需要一个拟合过程来消除相机色差对投影仪色差建模的影响。文中将绿色通道作为理想通道,因此像素点位置与LCD屏显示的绿色条纹相位和投影仪投影的绿色条纹相位的对应关系为理想的对应关系。由于噪声的影响,不可避免计算出的展开有突起点,使用3×3的中值滤波去除明显的粗大误差点。将像素位置作为横纵坐标,拟合展开相位曲面。分别进行一次、二次、三次的曲面拟合,以$ {\phi }_{pro\_h\_g} $为例,拟合结果如表1所示。进行二次曲面拟合的拟合度能达到1,并且均方根误差较小,拟合过程的复杂程度适中。因此,选用二次拟合的方式将红、绿、蓝三颜色通道两个方向的LCD显示条纹展开相位和投影仪投影条纹展开相位拟合为二次曲面。
表 1 拟合结果对比
Table 1. Comparison of fitting results
$ {\varphi }_{pro\_h\_g} $ R-square RMSE Complexity Poly11: 0.9998 1.3860 Simple Poly22: 1 0.5930 Moderate Poly33: 1 0.4819 Complex 拟合出的结果都符合公式(1):
$$ f\left(x,y\right)=p00+p10x+p01y+p20{x}^{2} +p11xy+p02{y}^{2} $$ (1) 式中:x,y表示像素点的位置;f(x, y)表示展开相位的值;p00、p10、p01、p20、p11、p02为拟合出的系数。
为了获取蓝色通道理想的投影仪投影相位值,首先需要拟合蓝色LCD显示像素点,即为在LCD显示蓝色通道中取与绿色相位点的值相同的像素点,该像素点对应的投影仪绿色通道的相位点则为蓝色通道补偿后应投影出的条纹相位。由于LCD显示的蓝色和绿色条纹相位都可以拟合成关于像素点位置的方程,可以将LCD显示的蓝色相位值代入到LCD显示绿色的方程中,计算出在该相位值时像素点的值。计算方程组如公式(2)所示:
$$\left\{\begin{array}{l}{\varphi }_{lcd\_h\_b}= lgh00+xlgh10+ylgh01+\\ \qquad \quad {x}^{2}lgh20+xylgh11+{y}^{2}lgh02\\ {\varphi }_{lcd\_v\_b}=lgv00+xlgv10+ylgv01+\\ \qquad \quad {x}^{2}lgv20+xylgv11+{y}^{2}lgv02\end{array}\right. $$ (2) 其中,$ {\varphi }_{lcd\_h\_b} $和$ {\varphi }_{lcd\_v\_b} $作为已知,lgh和lgv代表已经拟合出的绿色显示水平和垂直方向关于像素点的数学模型的系数。求解出x和y得到理想显示像素。
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根据上一节中计算出的理想显示相位及其对应的理想像素点,将解出的像素点代入到投影仪投影的拟合数学模型中,得到理想的红蓝投影仪投影相位$ {\varphi }_{ideal\_pro\_h\_b} $、$ {\varphi }_{ideal\_pro\_v\_b} $、$ {\varphi }_{ideal\_pro\_h\_r} $、$ {\varphi }_{ideal\_pro\_v\_r} $。新的理想投影仪投影的蓝色和红色相位同样可以拟合成关于整数像素点的新的二元二次数学模型,且拟合度均能达到1。
理想像素点对应的投影仪投影的蓝色通道和红色通道相位点即为理想的蓝色和红色投影相位,将理想的红色和蓝色投影相位与绿色通道相位差的视为色差,则蓝绿通道的投影仪水平方向和垂直方向的投影仪色差的计算公式为:
$$ {\Delta \mathrm{\varphi }}_{bg\_h}={\varphi }_{ideal\_pro\_h\_b}-{\varphi }_{pro\_h\_g} $$ (3) $$ {\Delta \mathrm{\varphi }}_{bg\_v}={\varphi }_{ideal\_pro\_v\_b}-{\varphi }_{pro\_v\_g} $$ (4) $$ \overrightarrow{{\Delta \varphi }_{bg}}=\left({\Delta \mathrm{\varphi }}_{bg\_h},{\Delta \mathrm{\varphi }}_{bg\_v}\right) $$ (5) 同理,红绿通道的投影仪水平方向和垂直方向的色差的计算公式为:
$$ {\Delta \mathrm{\varphi }}_{rg\_h}={\varphi }_{ideal\_pro\_h\_r}-{\varphi }_{pro\_h\_g} $$ (6) $$ {\Delta \mathrm{\varphi }}_{rg\_v}={\varphi }_{ideal\_pro\_v\_r}-{\varphi }_{pro\_v\_g} $$ (7) $$ \overrightarrow{{\Delta \varphi }_{rg}}=\left({\Delta \mathrm{\varphi }}_{rg\_h},{\Delta \mathrm{\varphi }}_{rg\_v}\right) $$ (8) 由于$ {\varphi }_{ideal\_pro\_h\_b} $、$ {\varphi }_{ideal\_pro\_v\_b} $、$ {\varphi }_{ideal\_pro\_h\_r} $、$ {\varphi }_{ideal\_pro\_v\_r} $和$ {\varphi }_{pro\_h\_g} $、$ {\varphi }_{pro\_v\_g} $都可以拟合成关于像素横纵坐标的二元二次的数学模型,则投影仪投影的理想蓝色通道和红色通道相位减去投影仪投影的绿色通道相位可以建立关于整数像素点的二元二次的数学模型,即投影仪的水平方向和垂直方向的蓝绿色差可以建立一个二元二次的数学模型。同理,水平方向和垂直方向的投影仪红绿色差也可建立二元二次的色差模型。
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由于CCD相机的影响,投影仪色差不能直接通过补偿相机采集的图像进行投影仪色差校正,文中使用生成预补偿条纹的方法进行投影仪色差校正。通过已计算出的投影仪色差生成预补偿条纹,再重新投影到相位标靶上,重新计算投影仪色差,以此验证校正方法的有效性。投影仪色差校正示意图如图5所示。
条纹图的同一像素点经过投影后,色差会导致经红、绿、蓝三种颜色通道的位置差异。提前生成预补偿图像,将红、绿、蓝三种颜色通道的点进行位置偏移,再经过投影仪投影,使投影后的三种颜色通道的点能够汇聚在一点上,从而实现色差校正。
由于计算出的色差数学模型是关于CCD相机像素横纵坐标的数学模型,则每一个CCD相机像素点的红绿色差和蓝绿色差都是已知的。同时,由于计算出的是色差的数学模型,像素点为非整数时的投影仪色差也极易获得。重投影时需要的预补偿条纹应符合投影仪像素,而计算出的投影仪色差模型是基于相机像素的,所以需要转换计算投影仪分辨率下的色差模型。以某一点P为例,将CCD相机分辨率下的P点的像素坐标记为(Pcx, Pcy),转换到投影仪分辨率下,其像素坐标为(Ppx, Ppy),则P点像素在相机分辨率下和投影仪分辨率下的对应关系如公式(9)所示:
$$ \left\{\begin{array}{c}{P}_{px}={P}_{cx}\times {H}_{c}/{H}_{p}\\ {P}_{py}={P}_{cy}\times {V}_{c}⁄{V}_{p}\end{array}\right. $$ (9) 式中:Hc、Vc代表CCD相机的分辨率大小;Hp、Vp代表DLP投影仪的分辨率大小。由于有了相应的色差模型,每一个像素点对应的蓝绿色差和红绿色差都能精准、快速地计算出来,与插值的方法相比,既提高了计算精度,又减少了计算时间,进而提高了测量精度和校正效率。根据色差模型计算出蓝色通道和红色通道理想像素值,再生成符合最佳三条纹和四步相移的预补偿条纹图。
重新投影预补偿条纹即可校正投影仪色差。绿色通道的条纹图像与初投影时相同,继续以2.1节的方法进行色差计算,建立重投影的投影仪蓝绿通道和红绿通道色差模型,最终通过对比初投影时和重投影时的投影仪色差大小,验证基于相位标靶的投影仪色差建模与校正方法研究的有效性。再将预补偿条纹运用到之后的三维测量系统中,以减少投影仪色差对整体测量带来的影响,提高三通道相位测量轮廓术的测量精度。
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文中所需搭建的实验系统如图6所示。基于相位标靶的投影色差建模与方法研究所需的硬件有:一个彩色CCD相机,其型号为ECO424 CVG (SVS-VISTEK);一个LCD显示屏,其型号为CYS-R101;一个DLP投影仪,其型号为CP270 (BenQ)。为保证实验的严谨性,保持实验过程在黑暗环境下进行。
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首先对投影仪全局投影进行投影仪色差建模。利用2.1节的方法,以绿色通道作为理想通道,计算投影仪色差的数学模型。以投影仪水平方向色差为横向量,以投影仪垂直方向色差为列向量,绘制投影仪色差矢量图。投影仪蓝绿通道色差矢量图如图7所示。
得到蓝绿通道的色差模型方程式如下:
$$ \begin{split} \Delta bg\_h=& -0.356\;8+0.000\;309\;1x+0.001\;438y-\\ & 0.000\;000\;511\;3{x}^{2}+0.000\;000\;195\;9xy-\\ & 0.000\;000\;301\;7{y}^{2}\\ \Delta bg\_v=& -0.489\;2+0.001\;311x-0.000\;070\;8y+\\ &0.000\;000\;236\;2{x}^{2}+0.000\;000\;259xy-\\ & 0.000\;000\;079\;62{y}^{2} \end{split}$$ (10) 计算出投影仪蓝绿通道的最大色差为0.6090 pixel,平均色差为0.3255 pixel。
投影仪红绿通道色差矢量图如图8所示。
得到红绿通道的色差模型方程式为:
$$\begin{split} \Delta rg\_h=& 0.366\;8-0.001\;104x-0.000\;051\;8y-\\ & 0.000\;000\;054\;05{x}^{2}+0.000\;000\;096\;01xy-\\ & 0.000\;000\;0439\;2{y}^{2}\\ \Delta rg\_v=& 0.474\;8+0.000\;240\;3x-0.002\;065y-\\ & 0.000\;000\;140\;7{x}^{2}-0.000\;000\;236\;7xy-\\ & 0.000\;000\;373\;1{y}^{2}\\[-8pt] \end{split} $$ (11) 计算出投影仪红绿通道的最大色差为0.7225 pixel,平均色差为0.3651 pixel。
色差矢量图中,箭头的指向代表色差的方向,箭头的大小代表色差的大小。由蓝绿通道色差矢量图和红绿色差矢量图可以看出,投影仪越靠近中间的部分色差最小,越靠近四周的部分色差越大。同时,蓝绿通道色差方向与红绿通道色差方向完全相反,投影仪蓝绿通道色差方向由中心指向四周,投影仪红绿通道的色差由四周指向中心,这是由于三种颜色光线波长不同造成的。最终实验结果与理论相符。由于该方法可以得到全局的蓝绿通道色差和红绿通道色差,即使是处于图像最边缘位置的色差也不存在粗大误差的问题,以便于后续对色差进行补偿校正。
下一步对投影仪色差进行校正,文中只针对投影仪色差进行分析研究,在色差建模的过程中,保证了相位标靶与投影仪投影平面的平行,并没有对相机平面和相位标靶之间的位置关系进行确定,因此不能直接将计算出的色差模型的结果补偿到三维测量数据中。文中采用生成与补偿条纹、然后重投影的方法进行投影仪色差校正。经过上述实验可以得到投影仪红色通道和蓝色通道间的色差模型,其结果如公式(10)、(11)所示。利用公式(9)可以将CCD像素坐标系下的投影仪色差转换为投影仪像素坐标系下的投影仪色差模型,生成新的蓝色通道和红色通道的预补偿条纹图像。文中采用最佳三条纹选择方法进行相位计算,因此需要投影三个频率的条纹图。根据色差模型计算出蓝色通道和红色通道理想像素值,生成64、63、56个周期的符合四步相移的预补偿条纹图。新生成的部分条纹图如图9所示。
图 9 预补偿条纹。(a)水平方向蓝色通道预补偿条纹;(b)水平方向红色通道预补偿条纹;(c)垂直方向蓝色通道预补偿条纹;(d)垂直方向红色通道预补偿条纹
Figure 9. Pre-compensated fringes. (a) Horizontal blue channel pre-compensated fringe; (b) Horizontal red channel pre-compensation fringe; (c) Vertical blue channel pre-compensation fringe; (d) Vertical red channel pre-compensation fringe
将预补偿条纹重新投影到LCD显示屏上,再由CCD相机进行采集。重复初投影的方法步骤,计算新的蓝绿通道和红绿通道的投影仪色差,以验证该校正方法的有效性。计算出重投影的投影仪蓝绿通道的最大色差为0.2479 pixel,平均色差为0.1063 pixel。重投影的投影仪红绿通道的最大色差为0.2590 pixel,平均色差为0.1114 pixel。为了直观体现色差校正的效果,如图10所示,对比了预补偿重投影前后的投影仪色差矢量变化。彩色箭头代表补偿前的投影仪色差矢量,黑色箭头代表重投影预补偿条纹后的投影仪色差矢量,可以明显观察到色差有所减小,验证了重投影方法对校正投影仪色差的有效性。
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为了验证利用建立数学测量投影仪色差方法的适用性,文中采用不同的投影仪对该投影仪色差进行建模。新选用的投影仪为实验室中常用的PRO4500数字投影仪, 按照文中所提出的投影仪色差建模的方法步骤进行实验。以绿色通道为基准,分别建立蓝绿通道和红绿通道的色差模型。蓝绿通道水平方向和垂直方向的投影仪色差矢量图如图11所示。
图 11 投影仪蓝绿通道色差矢量图
Figure 11. Chromatic aberration vector diagram of projector blue and green channels
得到PRO4500投影仪蓝绿通道色差模型的方程式为:
$$ \begin{split} \Delta bg\_h=& -0.158\;8+0.000\;078\;87x+0.000\;694\;5y\\ &{x}^{2}+0.000\;000\;275\;4xy-0.000\;000\;248{y}^{2}\\ \Delta bg\_v=& -0.285\;0+0.000\;683\;8x+0.000\;020\;06y+\\ &0.000\;000\;341\;3{x}^{2}+0.000\;000\;021\;93xy-\\ & 0.000\;000\;060\;18{y}^{2}\\[-8pt] \end{split} $$ (12) 经计算,投影仪蓝绿通道最大色差为0.3459 pixel,平均色差为0.1844 pixel。
红绿通道水平方向和垂直方向的投影仪色差矢量图如图12所示。
图 12 投影仪红绿通道色差矢量图
Figure 12. Chromatic aberration vector diagram of projector red and green channels
得到PRO4500投影仪红绿通道色差模型的方程式为:
$$ \begin{split} \Delta rg\_h=&0.159\;3+0.000\;164\;2x-0.000\;751\;8y\\ & 0.000\;000\;067\;52{x}^{2}-0.000\;000\;297\;9xy-\\ & 0.000\;000\;0133\;7{y}^{2}-\\ \Delta rg\_v=& 0.286\;1-0.000\;783\;6x-0.000\;104\;5y-\\ & 0.000\;000\;245\;4{x}^{2}+0.000\;000\;211\;1xy-\\ & 0.000\;000\;019\;26{y}^{2} \end{split} $$ (13) 经计算,投影仪红绿通道最大色差为0.3814 pixel,平均色差为0.1951 pixel。由于PRO4500投影仪通常为实验专用投影仪,精度较高,相较于之前的CP270 (BenQ)商业投影仪来说色差较小,实验结果符合预期。
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预补偿前后的彩色条纹进行光学三维测量,验证预补偿前后光学系统的测量精度。实验系统可以保证投影仪投影的条纹能覆盖台阶表面,同时,相机采集视场能采集到台阶表面的全部信息。
校正投影仪色差前后恢复的台阶的三维形貌如图13所示。
图 13 投影仪色差校正前后台阶三维形貌。(a)校正前的台阶三维形貌;(b)校正后的台阶三维形貌
Figure 13. 3D topography of steps before and after chromatic aberration correction of projector. (a) 3D morphology of the step before correction; (b) 3D morphology of the step after correction
可以看出,相较于校正色差前的恢复效果,校正投影仪色差后恢复的台阶的三维形貌更平滑,噪声更少。为了进一步验证文中提出的基于相位标靶的投影色差建模方法的有效性,再使用PRO4500投影仪进行台阶间距测量实验,得到的校正前后的台阶三维形貌图如图14所示。可以看出,校正投影仪色差后,整体的测量精度有了进一步提高。
图 14 PRO4500投影仪色差校正前后台阶三维形貌。(a) 校正前的台阶三维图;(b) 校正后的台阶三维图
Figure 14. 3D topography of step before and after chromatic aberration correction of PRO4500 projector. (a) 3D morphology of the step before correction; (b) 3D morphology of the step after correction
为了定量评价校正前后的精度,对台阶间的间距进行了对比。使用三坐标测量仪测量实验台阶相邻台阶面的高度,并以该结果作为标准值,三坐标测量仪的型号为 Zeiss Contura-G2,当环境温度范围为18~22 ℃时,长度测量误差为 1.5+L/350 m,扫描误差为 2 μm。选择第二、三、四级台阶间距进行测量计算,投影三次相同的条纹到台阶表面并采集变形条纹图像,计算三组数据,对测量出的三组台阶间距取平均值,作为利用该条纹测量台阶间距的测量值。对比台阶间距的标准值与校正不同型号投影仪色差前后的数据。不同的台阶间距数据如表2所示。
从表2中可以得出,校正投影仪色差前的三个台阶间距的平均误差为0.489 mm,校正投影仪色差后的三个台阶间距的平均误差为0.038 mm。校正PRO4500投影仪色差前的三个台阶间距的平均误差为0.051 mm,校正PRO4500投影仪色差后的三个台阶间距的平均误差为0.025 mm。对比校正CP270投影仪和PRO4500投影仪色差前后的精度误差,可以得出文中提出的基于相位标靶的投影色差建模与校正方法能够较好地提升相位轮廓测量术中的投影质量,提升精度较差的商业投影仪的测量精度,使其能够达到实验所需的效果;对于本身精度较高的投影仪来说,该方法能够进一步提高测量精度。
表 2 校正投影仪色差前后台阶间距测量值(单位:mm)
Table 2. Measurement value of step spacing before and after correcting projector chromatic aberration (Unit: mm)
Projector model Step spacing Standard value Before correction After correction Pre-correction error Corrected error CP270 Step surface
2-313.258 13.732 13.308 0.474 0.050 Step surface
3-418.422 17.918 18.447 −0.504 0.025 PRO4500 Step surface
2-313.258 13.317 13.220 0.059 −0.038 Step surface
3-418.422 18.465 18.411 0.043 −0.011
Projection chromatic aberration modeling and correction of phase measurement profilometry based on phase target
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摘要: 光学三维测量中的三通道相位测量轮廓术具有高精度、易识别、自动化程度高等优点,在科学研究和工程应用中获得了广泛的关注。在三通道相位测量轮廓术中,投影仪不同通道间的色差成为影响测量精度的关键因素。针对该问题,文中开展了基于相位标靶的相位测量轮廓术投影色差建模与校正研究。提出了将带有全息投影膜的液晶显示屏(Liquid Crystal Display, LCD)当作相位标靶对投影色差建模与校正的方法。通过LCD显示条纹与投影仪投射条纹的相位,计算投影仪色差并建立其数学模型。然后通过预补偿的方法实现投影仪三通道投射色差的校正,进行实验验证校正前后对相位测量轮廓术精度的影响。实验结果表明,文中所提方法的校正效果为蓝绿通道的平均色差由0.3255 pixel校正为0.1063 pixel,红绿通道的平均色差由0.3651 pixel校正为0.1114 pixel。该方法可为三通道相位测量轮廓术提升投影质量。实测台阶的平均误差从0.489 mm减少到0.038 mm。实验结果验证了投影仪色差建模与校正方法的有效性,提升了三通道相位测量轮廓术的整体测量精度。与已有方法相比,可以有效避免相机误差带来的影响,大大缩短计算时间,能够适用于不同型号的投影仪色差测量与校正。Abstract:
Objective Due to the advantages of high precision, easy recognition and high degree of automation, the three-channel phase measurement profilometry in optical three-dimensional measurement has gained increasing attention in both scientific research and engineering applications. For three-channel phase measurement profilometry, the chromatic aberration between projector channels is the key factor affecting the measurement accuracy. Most of the existing chromatic aberration correction methods of projectors regard projectors as "reverse cameras". Therefore, the accuracy of correction results will be dependent on the imaging quality of the camera. Moreover, the existing chromatic aberration measurement and correction methods still have shortcomings, so it is significant to improve the measurement accuracy of the system. Therefore, this study carries out the research on the projection chromatic aberration modeling and correction of phase target-based phase measurement profilometry. Methods In this paper, the projection chromatic aberration modeling and correction method using the LCD screen with holographic projection film as the phase target is proposed (Fig.3). Firstly, the unfolded phase of LCD display fringes and projector projection fringes are calculated respectively. Next, binary fitting on display phase and projection phase are carried out. The green channel is regarded as an ideal channel, and the ideal pixel values of red and blue channels is calculated. Then the ideal pixel is substituted into the projection equation, and the ideal phases of the red and blue channels are obtained. Thus, the mathematical model of the chromatic aberration of the projector is established. Finally, the pre-compensation of projection fringes is implemented with the established chromatic aberration model(Fig.5). Then, the pre-compensated fringes are projected in three channels, so that the chromatic aberration of the projector is corrected. Results and Discussions The experimental results demonstrated the performance of the proposed method. The average chromatic aberration of the blue and green channels is corrected from 0.325 5 pixel to 0.106 3 pixel. The average chromatic aberration of the red and green channels is corrected from 0.365 1 pixel to 0.111 4 pixel (Fig.10). This method can effectively improve the projection quality for three-channel phase measurement profilometry. The average error of the measured step is reduced from 0.489 mm to 0.038 mm (Tab.2). The experimental results verified the effectiveness of the chromatic aberration modeling and correction method of projector. This method can improve the overall measurement accuracy of three-channel phase measurement profilometry. Compared with the existing methods, the proposed method can be calibrated to avoid the impact of camera errors and effectively shorten the calculation time. Moreover, this method can be applied to the measurement and correction of different projector chromatic aberration. Conclusions A phase-measurement contouring chromatic aberration modeling method using an LCD display as a phase target is designed and calibrated for study. This method eliminated the coupling error of the camera while measuring and calibrating the projector chromatic aberration, and enabled measurement of the projector chromatic aberration at global pixel points, while using mathematical modeling to model the projector chromatic aberration in a chromatic way to shorten the calculation time. By measuring the 3D shape of the actual object for accuracy comparison experiments and comparing the accuracy error before and after correcting the chromatic aberration of CP270 projector and PRO4500 projector, it can be concluded that the projection chromatic aberration modeling and correction study based on phase target proposed in this paper can better improve the projection quality in phase contour measurement and enhance the measurement accuracy of commercial projectors with poor accuracy. For the projectors with low accuracy, the method of correcting chromatic aberration in this paper can greatly improve the measurement accuracy of projectors. For the projectors with high accuracy, the proposed projector chromatic aberration modeling and correction method can further improve the measurement accuracy. -
图 9 预补偿条纹。(a)水平方向蓝色通道预补偿条纹;(b)水平方向红色通道预补偿条纹;(c)垂直方向蓝色通道预补偿条纹;(d)垂直方向红色通道预补偿条纹
Figure 9. Pre-compensated fringes. (a) Horizontal blue channel pre-compensated fringe; (b) Horizontal red channel pre-compensation fringe; (c) Vertical blue channel pre-compensation fringe; (d) Vertical red channel pre-compensation fringe
表 1 拟合结果对比
Table 1. Comparison of fitting results
$ {\varphi }_{pro\_h\_g} $ R-square RMSE Complexity Poly11: 0.9998 1.3860 Simple Poly22: 1 0.5930 Moderate Poly33: 1 0.4819 Complex 表 2 校正投影仪色差前后台阶间距测量值(单位:mm)
Table 2. Measurement value of step spacing before and after correcting projector chromatic aberration (Unit: mm)
Projector model Step spacing Standard value Before correction After correction Pre-correction error Corrected error CP270 Step surface
2-313.258 13.732 13.308 0.474 0.050 Step surface
3-418.422 17.918 18.447 −0.504 0.025 PRO4500 Step surface
2-313.258 13.317 13.220 0.059 −0.038 Step surface
3-418.422 18.465 18.411 0.043 −0.011 -
[1] Dai M L, Yang F J, Liu C. A dual-frequency fringe projection three-dimensional shape measurement system using a DLP 3D projector [J]. Optics Communications, 2017, 382: 294-301. doi: 10.1016/j.optcom.2016.08.004 [2] Yang L X, Xie X, Zhu L Q, et al. Review of electronic speckle pattern interferometry (ESPI) for three-dimensional displacement measurement [J]. Chinese Journal of Mechanical, 2014, 27(1): 1-13. doi: 10.3901/CJME.2014.01.001 [3] 白雪飞, 张宗华. 基于彩色条纹投影术的三维形貌测量[J]. 仪器仪表学报, 2017, 38(8): 1912-1925. doi: 10.3969/j.issn.0254-3087.2017.08.009 Bai X F, Zhang Z H. 3D shape measurement based on colour fringe projection techniques [J]. Chinese Journal of Scientific Instrument, 2017, 38(8): 1912-1925. (in Chinese) doi: 10.3969/j.issn.0254-3087.2017.08.009 [4] Zuo C, Feng S, 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] Huang J H, Xue Q, Wang Z, et al. Analysis and compensation for lateral chromatic aberration in a color coding structured light 3D measurement system [J]. Sensors, 2016, 16(9): 1426. doi: 10.3390/s16091426 [6] Mallon J, Whelan P F. Calibration and removal of lateral chromatic aberration in images [J]. Pattern Recognition Letters, 2007, 28: 125-135. doi: 10.1016/j.patrec.2006.06.013 [7] Korneliussen J T, Hirakawa K. Camera processing with chromatic aberration [J]. IEEE Transactions on Image Processing, 2014, 23(10): 4539-4552. doi: 10.1109/TIP.2014.2350911 [8] Pagès J, Collewetb C, Forest J, et al. Optimised De Bruijn patterns for one-shot shape acquisition [J]. Image and Vision Computing, 2005, 23(8): 707-712. doi: 10.1016/j.imavis.2005.05.007 [9] Li W G, Duan S J. Color calibration and correction applying linear interpolation technique for color fringe projection system [J]. Optik, 2016, 127(4): 2074-2082. doi: 10.1016/j.ijleo.2015.11.093 [10] Sun P P, Xue Q, Ji W, et al. Analysis and compensation of lateral chromatic aberration of structured light 3D measurement system [J]. Optics Communications, 2021, 488(25): 126871. [11] Zhang Z H, Towers C, Towers D. Compensating lateral chromatic aberration of a color fringe projection system for shape metrology [J]. Optics and Lasers in Engineering, 2010, 48(2): 159-165. doi: 10.1016/j.optlaseng.2009.04.010 [12] Li Z, Shi Y, Wang C, et al. Accurate calibration method for a structured light system [J]. Optical Engineering, 2008, 47(5): 525-534. [13] Li B W, Song Z. Structured light system calibration method with optimal fringe angle [J]. Applied Optics, 2014, 53(33): 7942-7950. doi: 10.1364/AO.53.007942 [14] Huang S, Xie L, Wang Z, et al. Accurate projector calibration method by using an optical coaxial camera [J]. Applied Optics, 2015, 54(4): 789-795. doi: 10.1364/AO.54.000789 [15] Xue Q, Wang Z, Huang J, et al. A two-level space-time color-coding method for 3D measurements using structured light [J]. Measurement Science and Technology, 2015, 26(11): 115204. doi: 10.1088/0957-0233/26/11/115204 [16] Zhang X, Zhu L. Projector calibration from the camera image point of view [J]. Optical Engineering, 2009, 48(11): 117208. doi: 10.1117/1.3265551