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工业相机系统由相机壳体、集成电路板(相机运行热源)、支架和镜头组成。集成电路板主要是传感器和主板,当相机运行时,电路板产生的热量在相机部件和环境之间传递导致相机部件温度升高。图1为AVT GT5120工业相机和Nikon 35 mm定焦镜头组成的成像系统主板和传感器在开机之后的温度曲线,温度由相机内置温度传感器测量。在相机通电5 h后,图像传感器升温19 ℃、主板升温16 ℃后趋于稳定。在室温条件下,随着相机成像元件和主板温度的升高,相机内部呈现非均匀温度场,这种非均匀温度场是由相机内部热源与外界环境相互作用产生的结果,主要作用方式是热传导和热对流[19]。通过SolidWorks建立相机三维模型(如图2所示),根据相机器件的升温曲线添加温度载荷,应用有限元分析技术进行该温度场下相机的热应力求解[20-21]。
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文中以AVT GT5120为研究对象,阐述工业相机热致图像坐标漂移模型与补偿方法。首先,为减小计算量并提高计算效率,将相机三维模型中影响较小的几何特征去除,如倒角、圆角和非安装孔。其次,检查模型干涉情况,保证相机模型各零件配合准确。然后,将装配体导入AnsysWorkbench,采用非连续六面体方法对相机三维模型进行网格划分,如图3(a)所示,并添加材料库(材料参数如表1所示)。
表 1 相机各组件材料属性
Table 1. Material properties of camera components
Name Material Young’s
modulus /GPaDensity
/kg·m−3Specific heat
capacity/J·kg−1·℃Thermal conductivity
W·m−1·℃Thermal expansion
coefficient/℃−1Poisson ratio Body Aluminum alloy 71 2770 875 237 2.3×10−5 0.33 Lens tube, top plate Copper alloy 110 8300 385 401 1.8×10−5 0.34 CMOS Monocrystalline Silicon 190 2330 702 124 5.0×10−7 0.064 Lens housing ABS 2 880 1470 0.22 9.0×10−5 0.394 Lens Glass 88 2500 750 1.4 5.8×10−7 0.215 最后,以相机内置温度采集模块所得温度作为热载荷,将热载荷温度梯度添加在成像器件和主板位置,如图3(b)所示。设置热分析总时间22 h,时间增量300 s,相机外表面与空气对流系数
$5{\rm e}- 06\;(\rm W/{{\rm{mm}}}^{2}\cdot$ ℃),对相机进行瞬态热分析,得出相机整体温度场与热流场。将瞬态热分析结果导入瞬态热应力分析,设置相机底面为固定约束,与热分析设置相同的时间步,建立瞬态热应力耦合场。 -
采用间接耦合法对相机进行瞬态热力学分析,通过对相机模型设置相应的温度载荷和对流系数得出相机温度场和热流场,将温度梯度导入瞬态应力场并设置固定约束得出相机变形场。相机在常温20 ℃下工作时,自热达到热平衡状态后,最高温度为35.60 ℃,最低温度为22.75 ℃,温差为12.85 ℃,相机内部呈现非均匀温度场,温度从机身到镜头逐渐降低,温度场分布如图4(a)所示。集成电路板在机身内部,导致机身温度变化幅度最大;镜头接口与机身直接连接且材质为金属,因此热量很容易传到此处引起接口的温升;相机镜头采用机械连接且材质热传导系数小,加上与外界进行热交换,所以温升较小。自热导致相机内部的热流场如图4(b)所示,热量从热源处向镜头和相机四周传递,导致相机各部件产生变形,相机各部件在光路方向产生的变形在镜头处产生累加,导致镜头处的变形量最大,相机整体变形场如图4(c)所示。表2列出了不同温度变化量下,镜头位移、CMOS变形量的仿真数据。可见,随着温度升高,镜头与CMOS在光轴方向上的偏移量逐渐增大,且镜头偏移量大于CMOS偏移量,同时温度变化与变形量变化存在线性关系。CMOS在成像面内的变形量随温度升高逐渐增大,并存在线性关系。CMOS变形场如图4(d)所示,由图中可以看出,CMOS变形包括沿镜头方向的轴向位移以及面内的径向变形。文中通过分析相机组件热变形得出像点漂移的变化规律,进而建立相机像点漂移补偿模型[22]。
表 2 不同温度变化下镜头与CMOS的变形量
Table 2. Deformation of the lens and CMOS under different temperature variation
Temperature
increasement/℃Lens
translation/μmCMOS horizontal
deformation/μmCMOS vertical
deformation/μm0 0.00 0.00 0.00 1 4.28 2.61 2.31 2 9.61 5.25 5.28 3 14.44 7.52 8.02 4 19.76 9.75 10.04 5 24.19 12.61 13.02 6 28.89 15.32 14.89 7 32.58 18.32 17.65 -
通过有限元技术分析自热引起的相机变形情况,得出导致像点漂移的两个因素。相机组成器件变形使成像光路发生轴向变化,在物理上表现为成像模型中物距和像距的变化,从而导致成像点向外漂移;CMOS与顶板的热膨胀变形使原始成像范围减小,进而产生像点向内(主点中心)漂移。
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如图5(a)所示,在小孔成像基础上,以相机镜头面和顶板为偏移量采集面分析相机热致变形引起的成像光路变化。通过有限元计算可以得出镜头面和顶板的偏移量,偏移量与机身温度变化关系如图5(b)所示,可以看出,镜头的偏移量
${\delta _{lens}}$ 大于CMOS的偏移量${\delta _{cmos}}$ ,这是由于镜头位于相机传热的最末端,镜头在光轴方向的偏移量${\delta _{lens}}$ 为CMOS偏移、支架偏移和镜头偏移合成量,CMOS偏移量${\delta _{cmos}}$ 为顶板与CMOS偏移合成量。镜头与CMOS偏移量与相机温度变化存在较好的线性关系,对偏移量与机身温度变化量进行线性拟合,计算得出热变形参数为$k_{lens}^{'}$ 和$k_{cmos}^{'}$ :$$k_{lens}^{'} = \frac{{{\delta _{lens}}}}{{\Delta T}}$$ (1) $$k_{cmos}^{'} = \frac{{{\delta _{cmos}}}}{{\Delta T}}$$ (2) 式中:
$\Delta T$ 为机身温度变化量。相机轴向偏移量就是相机成像平面和等效光心的移动,从而引起像距$v$ 及物距$u$ 的变化,如图5(c)所示。可见,相机自热引起镜头和CMOS同时向前移动,从而导致物距
$u$ 减小到$u - {\delta _{lens}}$ ,像距$v$ 增加到$v + {\delta _{lens}} - {\delta _{cmos}}$ 。在针孔模型上分析像点变化关系:$${h^{'}} = {[{(h_x^{'} - {x_0})^2} + {(h_y^{'} - {y_0})^2}]^{\frac{1}{2}}}$$ (3) $$ {h^{''}} = \frac{{u[v + ({\delta _{lens}} - {\delta _{cmos}})]}}{{v(u - {\delta _{lens}})}}{h^{'}} $$ (4) 式中:
$({x_0},{y_0})$ 为主点坐标;$(h_x^{'},h_y^{'})$ 为像点初始坐标,$u$ 为物距;$v$ 为像距;${\delta _{lens}}$ 为镜头的偏移量;${\delta _{cmos}}$ 为CMOS的偏移量;${h^{'}}$ 为初始像点与主点之间的距离,${h^{''}}$ 为像点漂移后与主点之间的距离。如图6(a)所示,像点以主点为中心向四周漂移,每个象限的漂移方向不同,主点位置处的像点坐标不发生变化。以第四象限点为例研究像点漂移情况,如图6(b)所示,像点漂移量
$\Delta {h^{'}}$ 为:$$\Delta {h^{'}} = {h^{''}} - {h^{'}}$$ (5) 联立公式(3)~(5)可得成像光路变化产生的像点漂移量:
$$\Delta {h^{'}} = \frac{{(u + v){\delta _{lens}} - u{\delta _{cmos}}}}{{v(u - {\delta _{lens}})}}{[{(h_x^{'} - {x_0})^2} + {(h_y^{'} - {y_0})^2}]^{\frac{1}{2}}}$$ (6) 像点与主点连线的夹角
$\theta $ 为:$$ \theta = \arctan \frac{{h_y^{'} - {y_0}}}{{h_x^{'} - {x_0}}} $$ (7) 将像点偏移量
$\Delta {h^{'}}$ 在水平和竖直方向上分解,即:$$\Delta h_{_x}^{'} = \frac{{(u + v){\delta _{lens}} - u{\delta _{cmos}}}}{{v(u - {\delta _{lens}})}}{[{(h_x^{'} - {x_0})^2} + {(h_y^{'} - {y_0})^2}]^{\frac{1}{2}}}\cos \theta $$ (8) $$\Delta h_{_y}^{'} = \frac{{(u + v){\delta _{lens}} - u{\delta _{cmos}}}}{{v(u - {\delta _{lens}})}}{[{(h_x^{'} - {x_0})^2} + {(h_y^{'} - {y_0})^2}]^{\frac{1}{2}}}\sin \theta $$ (9) $\Delta h_x^{'}$ 为水平方向像点漂移量,$\Delta h_y^{'}$ 为竖直方向像点漂移量。 -
CMOS受热膨胀导致像点发生径向漂移,CMOS(材质为单晶硅)的热膨胀系数远小于相机机身顶板(材质为铜合金)的热膨胀系数,但由于CMOS与相机顶板固定在一起,顶板热膨胀带动CMOS发生围绕传感器中心的径向变形。CMOS径向膨胀引起的坐标漂移与轴向光路变化产生的漂移具有相反的趋势,成像器件的热膨胀导致成像面扩张,进而造成像点向图像中心漂移,如图7(a)所示。
在不同象限的成像点具有不同的漂移方向,以第四象限为例分析成像器件膨胀导致的像点漂移,如图7(b)所示。根据铜合金底板的膨胀系数
${k}_{cmos}= $ $ 1.8\;\rm e-05/^\circ {\rm{C}}$ 计算像点漂移量为:$$\Delta {h^{''}} = {k_{cmos}}{h^{'}}\Delta T$$ (10) 进一步将成像器件膨胀引起的像点漂移量在水平方向和竖直方向上分解:
$$\Delta h_x^{''} = {k_{cmos}}{h^{'}}\Delta T\cos \theta $$ (11) $$\Delta h_y^{''} = {k_{cmos}}{h^{'}}\Delta T\sin \theta $$ (12) 联合公式(1)、(2)、(8)、(9)、(11)、(12)可以得出温度变化引起像点在水平和竖直方向的漂移量为:
$$\begin{split} \Delta {h_x} =& \left[\frac{{(u + v + v{k_{cmos}}\Delta T)k_{lens}^{'} - u(k_{cmos}^{'} + v{k_{cmos}})}}{{v(u - k_{lens}^{'}\Delta T)}}\right]\times\\ &{[{(h_x^{'} - {x_0})^2} + {(h_y^{'} - {y_0})^2})^{\frac{1}{2}}}]\Delta T\cos \theta \end{split}$$ (13) $$\begin{split} \Delta {h_y} =& \left[\frac{{(u + v + v{k_{cmos}}\Delta T)k_{lens}^{'} - u(k_{cmos}^{'} + v{k_{cmos}})}}{{v(u - k_{lens}^{'}\Delta T)}}\right]\times\\ &{[{(h_x^{'} - {x_0})^2} + {(h_y^{'} - {y_0})^2})^{\frac{1}{2}}}]\Delta T\sin \theta \end{split} $$ (14) 其他象限像点坐标漂移也可以通过相同的方式分析获得。
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拍摄对象为带回光反射标记点的陶瓷板,如图8(a)所示固定在光学平台上。拍摄相机为AVT Prosilica GT5120红外相机,分辨率为
$5\;120 \times 5\;120$ pixel,像元尺寸为4.5 μm×4.5 μm,搭配尼克尔AF 35 mm定焦镜头,如图8(b)所示固定在光学平台上。使用红外光源照明陶瓷板,令回光反射标记点成像更清晰。相机与陶瓷板相距1.5 m,并且使相机光轴近似垂直于陶瓷平面。相机内部有两个温度传感器,可以检测相机主板和CMOS温度,测量精度为0.1 ℃。同时,在相机机身、陶瓷板处额外放置测温仪,测量并记录相机和陶瓷板的温度变化,测量精度为0.1 ℃。设计图像采集软件控制相机每5 min采集一次图像,通过灰度重心法求取回光反射标记点的图像坐标,并实时保存图像坐标和采集时刻的温度。相机主板、CMOS传感器、机身与标定板温度变化如图8(c)所示,CMOS与主板的温度在开机5 h后达到平衡,机身温度变化因热传导过程缓慢而存在延时性。为减小环境温度与光照变化对实验的影响,实验中使用幕布将实验环境封闭,实验环境及标定板的温度变化只有±0.2 ℃。根据陶瓷材料热膨胀系数得出其最大热膨胀量为0.2 μm,引起的像点漂移量为0.001 pixel,对实验结果造成的影响可以忽略不计。
考虑靠近图像边缘成像点漂移效果明显,图像中心像素坐标为(2560, 2560),选取图像边缘的成像点对模型准确性进行分析。根据公式(13)~(14)计算得出相机自热引起的像点漂移量,对初始像点坐标漂移量进行补偿,将补偿后像点的坐标同实测坐标进行比较评价模型的准确性,结果如图9所示。
图 9 自热状态下各象限点补偿后坐标值与实验测量值的结果对比
Figure 9. In the self-heating state, the coordinate value of each quadrant point after compensation is compared with the experimental measurement value
通过对比实验可以看出,经过该模型补偿后的像点坐标同其实测坐标有很强的相关性,进而验证了像点漂移补偿模型的有效性。同时,从实验测量结果可以看出,以开机时刻像点坐标为基准,相机自热导致像点产生
$0.4 \sim 0.6$ pixel漂移量。以升温后目标点坐标实测结果为真值,将像点漂移模型仿真结果与实验测量结果作差处理,可以得出像点漂移补偿模型误差,误差绝对值统计结果如表3所示。表 3 像点漂移补偿模型误差
Table 3. Pixel drift compensation model error
First quadrant error/pixel Second quadrant error/pixel Third quadrant error/pixel Fourth quadrant error/pixel Minimum Max Minimum Max Minimum Max Minimum Max Horizontal coordinate value 0.00 0.09 0.00 0.12 0.00 0.12 0.00 0.13 Vertical coordinate value 0.00 0.10 0.00 0.20 0.00 0.15 0.00 0.16 可以看出,通过温度补偿模型进行补偿后,可以将温度升高导致的像点漂移从
$0.4 \sim 0.6$ pixel降低到$0.1 \sim 0.2$ pixel,验证了文中提出的像点漂移补偿模型的有效性。 -
工程上通过对相机进行隔热设计减少相机温度变化对成像系统的影响[22]。文中设计制作了一套温控系统,如图10(a)所示,温控系统使用隔热材料隔绝相机与外界之间的热传导,同时使用固定在上层的导热片将多余热量导出,实验证明相机自热状态下,温控装置将相机主板和传感器温度控制在±0.1 ℃,有效抑制相机自热温度变化对成像系统的影响。
在相似实验条件下,将相机放在温控系统内部,如图10(b)所示,同样记录相机开机后目标点图像坐标变化。对比热控设计方案与温度补偿模型对于像点漂移的抑制或补偿效果,四个象限像点漂移误差绝对值的统计结果如表4所示。
表 4 热控装置方法与像点漂移补偿方法对比
Table 4. Comparison of thermal control device method and image point drift compensation method
First quadrant
error/pixelSecond quadrant
error/pixelThird quadrant
error/pixelFourth quadrant
error/pixelMinimum Max Minimum Max Minimum Max Minimum Max Thermal control device method 0.00 0.20 0.01 0.17 0.02 0.13 0.01 0.15 Image point drift compensation method 0.00 0.10 0.00 0.20 0.01 0.15 0.00 0.16 可以看出,两种方案对像点漂移抑制效果非常接近,也进一步证明温度补偿模型的正确性。考虑到热控装置结构复杂、质量大、成本高的缺点,文中提出的温度补偿模型具有明显的优越性。
Model and compensation method of image point drift caused by self-heating of industrial camera
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摘要: 为减小视觉测量中温度对工业相机像点坐标的影响,对相机自热引起的像点漂移进行研究,提出一种针对工业相机热致像点漂移补偿方法。通过Ansys Workbench对工业相机模型进行有限元仿真分析,得出工业相机自热会引起成像光路变化和传感器膨胀变化,定量分析光路变化与传感器膨胀对像点坐标的影响,建立图像像点漂移补偿模型。大量实验表明,利用模型补偿后的像点漂移误差从
$0.4 \! \sim \! 0.6$ pixel降低到$0.1\! \sim \! 0.2$ pixel,与采用硬件热控方式达到的像点漂移抑制效果相当。但是相对于热控装置,使用模型进行补偿的方法具有结构简单、成本低的明显优势。该研究提出的温度补偿模型为减小视觉测量中相机自热导致的像点漂移误差提供了理论依据。Abstract: In order to reduce the influence of temperature on the image point coordinates of industrial cameras in visual measurement, the image point drift caused by the self-heating of the camera was studied, and a compensation method for the thermal image point drift of industrial cameras was proposed. The finite element simulation analysis of the industrial camera model through Ansys Workbench shows that the self-heating of the industrial camera will cause the imaging optical path change and sensor expansion change, quantitatively the influence of the optical path change and sensor expansion on the image point coordinates was analyzed, and the image point drift compensation model was established. A large number of experiments have shown that the image point drift error compensated by the model is reduced from 0.4-0.6 pixel to 0.1-0.2 pixel, which is equivalent to the image point drift suppression effect achieved by hardware thermal control. However, compared with the thermal control device, the method of using the model for compensation has obvious advantages of simple structure and low cost. The temperature compensation model proposed in this research provides a theoretical basis for reducing the image point drift error caused by the self-heating of the camera in the visual measurement. -
表 1 相机各组件材料属性
Table 1. Material properties of camera components
Name Material Young’s
modulus /GPaDensity
/kg·m−3Specific heat
capacity/J·kg−1·℃Thermal conductivity
W·m−1·℃Thermal expansion
coefficient/℃−1Poisson ratio Body Aluminum alloy 71 2770 875 237 2.3×10−5 0.33 Lens tube, top plate Copper alloy 110 8300 385 401 1.8×10−5 0.34 CMOS Monocrystalline Silicon 190 2330 702 124 5.0×10−7 0.064 Lens housing ABS 2 880 1470 0.22 9.0×10−5 0.394 Lens Glass 88 2500 750 1.4 5.8×10−7 0.215 表 2 不同温度变化下镜头与CMOS的变形量
Table 2. Deformation of the lens and CMOS under different temperature variation
Temperature
increasement/℃Lens
translation/μmCMOS horizontal
deformation/μmCMOS vertical
deformation/μm0 0.00 0.00 0.00 1 4.28 2.61 2.31 2 9.61 5.25 5.28 3 14.44 7.52 8.02 4 19.76 9.75 10.04 5 24.19 12.61 13.02 6 28.89 15.32 14.89 7 32.58 18.32 17.65 表 3 像点漂移补偿模型误差
Table 3. Pixel drift compensation model error
First quadrant error/pixel Second quadrant error/pixel Third quadrant error/pixel Fourth quadrant error/pixel Minimum Max Minimum Max Minimum Max Minimum Max Horizontal coordinate value 0.00 0.09 0.00 0.12 0.00 0.12 0.00 0.13 Vertical coordinate value 0.00 0.10 0.00 0.20 0.00 0.15 0.00 0.16 表 4 热控装置方法与像点漂移补偿方法对比
Table 4. Comparison of thermal control device method and image point drift compensation method
First quadrant
error/pixelSecond quadrant
error/pixelThird quadrant
error/pixelFourth quadrant
error/pixelMinimum Max Minimum Max Minimum Max Minimum Max Thermal control device method 0.00 0.20 0.01 0.17 0.02 0.13 0.01 0.15 Image point drift compensation method 0.00 0.10 0.00 0.20 0.01 0.15 0.00 0.16 -
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