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快速准确处理光斑图像获得xy轴长度差是实现高精度测量厚度的关键,但由于使用激光作为照明光源,图像不可避免受到散斑影响,需针对性设计处理算法。本文中图像处理流程图如图 3所示。
由于探测器采集的图像为彩色,而判断光斑形状只需要亮度信息,因此首先对彩色图像进行灰度化处理,如下式所示:
$ G(i, j) =0.299 r(i, j)+\\ 0.587 g(i, j) +0.114 b(i, j) $
(1) 式中,r(i, j), g(i, j)及b(i, j)分别为(i, j)像素的红色、绿色及蓝色分量,G(i, j)为转化后的灰度数值。进一步对灰度图像进行了二值化操作。由于图像背景较为简单,理论上椭圆光斑外应全部为黑色背景,因此直接使用全局固定阈值寻找光斑位置,如下式所示:
$ B(i, j)=\left\{\begin{array}{l}{255, (G(i, j) \geqslant t)} \\ {0, (G(i, j)<t)}\end{array}\right. $
(2) 式中,t为人工设定的阈值,B(i, j)为二值化后图像。受到激光散斑的影响,光斑之内可能存在空洞,光斑之外可能存在亮斑,为了减小影响,对二值化图像进行了形态学开运算。
$ N=(B \Theta A) \oplus A $
(3) 式中,A为结构元素,Θ及⊕分别为形态学腐蚀及膨胀算子,N为运算后图像,作为后续进一步处理的基础。
虽然形态学开运算能够消除部分较小的散斑亮点,但图像中仍可能存在较大的散斑亮斑,为了避免其影响,需确定光斑是像点还是散斑。使用连通域技术标记每个光斑区域,连通域标记是图像处理领域的经典问题,目前已提出多种快速算法,可参考相关文献,本文中不作具体说明。由于照明光轴与测量光轴同轴,像点的中心位置理论上保持不变,因此,通过比较每个光斑区域的位置与理论位置可确定光斑是否为像点。若图像中不存在与理论位置相符的光斑,表明此时离焦较为严重,待测表面已远离聚焦物点,需通过平移台上下调节光学探头使得聚焦物点靠近待测表面。若存在像点光斑可进行下一步处理。
虽然一般认为存在像散时像点具有椭圆形状,通过使用椭圆曲线拟合光斑边界可确定其xy轴长度,但运算时发现, 一方面光斑形状并非为理想椭圆形,使用椭圆拟合可能引入误差,另一方面实际光斑受散斑影响可能存在空洞,导致边缘出现误差。由于椭圆光斑的xy轴与探测器行列像素之间夹角由柱面镜绕z轴旋转决定,难以确保平行,因此本文中提出直接按照椭圆倾斜角度θ计算光斑的矩形包围盒,其边长即为需要的xy轴长度,由光斑在xy轴两个方向投影的最大长度获得,如下式所示:
$ \left\{\begin{array}{l}{x_{1}=\frac{\max (x \tan \theta-y)-\min (x \tan \theta-y)}{\sqrt{1+\tan ^{2} \theta}}} \\ {y_{1}=\frac{\max (x+y \tan \theta)-\min (x+y \tan \theta)}{\sqrt{1+\tan ^{2} \theta}}} \\ {d_{1}=y_{1}-x_{1}}\end{array}\right. $
(4) 式中,(x, y)为光斑点在图像中的像素位置,xl及yl分别为光斑x及y轴长度,dl为xy轴的长度之差。dl与物点的z轴位置一一对应,可直接根据dl确定厚度。本文中基于ZEMAX模拟仿真了物点不同z轴位置时光斑xy轴的长度差,模拟参量与图 1中一致,结果如图 4所示。可见在两条焦线范围之间,xy轴长度差与物点位置线性相关,因此,获得长度差后通过线性运算可得物点位置。需要注意的是, 模拟只依据几何光学理论,而在焦线附近衍射效应不可忽略,故测量中应尽可能保证光斑位于两条焦线之间。
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本文中使用商用玻璃平片及平凹透镜进行了测试验证,元件如图 5所示。
首先标定了光斑xy轴长度差与物点位置之间的关系。装置中已提供了千分表,标定时只需对于xy平移台表面进行测量,上下移动聚焦物点,并记录不同时刻时的光斑图像及千分表读数,结果如图 6所示。可见与预期一致,物点位置变化时光斑的xy轴长度发生了变化。千分表读数为0mm及0.008mm时光斑xy轴的长度差分别为95pixel及-65pixel,准确厚度可由下式修正获得:
$ T=M+d_{1} / 20 $
(5) 式中,T为修正后厚度,M为千分表读数。经过(5)式修正后厚度数值在上下移动光学探头时应保持不变。
以(5)式为基础,本文中测量了玻璃平片的厚度,测量中直接将玻璃平片放置在xy轴平移台的表面,移动z轴平移台使得聚焦物点移动至待测上表面附近,且光斑位于两条焦线之间,记录经过(5)式修正后厚度,并减去平台表面高度值,可得镜片厚度。测量了平片2×2个位置,相邻两个位置之间距离5mm,每个位置测量5次,结果如表 1所示。
Table 1. Measurement results of glass plate/mm
No. position 1 position 2 position 3 position 4 1 3.010 3.015 3.019 3.008 2 3.009 3.014 3.020 3.008 3 3.009 3.013 3.020 3.006 4 3.010 3.014 3.018 3.006 5 3.011 3.013 3.019 3.007 进一步测量了平凹透镜的中心厚度。将平凹透镜放置在平移台上,使透镜的平面与平移台平面接触,凹面靠近探头。由于凹面顶点与平面的距离最短,因此上表面距离平移台表面的最小距离可认为是透镜的中心厚,测量了中心厚及周围2×2个位置,其中位置1为通过移动xy平移台实时测量最小上表面高度处,其余4个位置偏离顶点,结果如表 2所示。
Table 2. Measurement results of plano-concave lens/mm
No. position 1 position 2 position 3 position 4 position 5 1 2.526 3.102 2.958 2.842 3.056 2 2.524 3.104 2.959 2.844 3.054 3 2.524 3.103 2.960 2.842 3.055 4 2.525 3.104 2.959 2.844 3.054 5 2.525 3.103 2.958 2.844 3.055 表 1及表 2中对于同一位置进行多次测量时, A类不确定度在置信概率95%时均小于2μm,表明系统具有较好的稳定性。进一步分析了测量的B类不确定度,包括理论误差、机械误差及环境影响等3个因素。
(1) 理论误差。体现为需要通过光斑形状准确定位物点位置,而光斑xy轴长度差与物点位置并非为严格的线性关系。由于光斑确定的物点位置范围小于14μm,因此非线性引起的误差极小,可以忽略。
(2) 机械误差。成因较为复杂,分为3个方面:(a)系统需通过千分表测量探头的位置,因此千分表的测量精度直接决定了最终结果的精度,需保证确保千分表的垂直度以防止其倾斜导致测量数值偏大;(b)当测量双凸透镜的中心厚度时,若XY平移台表面与水平面存在一定角度,则可能导致双凸透镜受到重力影响倾斜,导致测量结果出现误差,因此需保证XY平移台表面与水平面平行;(c)若待测量双凸透镜重心不位于光轴,则即使放置于水平面仍然可能倾斜,因此,对下表面为凸面的元件需确保其加工质量能够满足测量要求。
(3) 环境影响。装置的使用环境包括温度、振动及杂散光会对测量结果造成影响。温度变化导致千分表受热胀冷缩影响测量出现误差。振动导致光斑抖动,难以准确测量。杂散光影响拍摄图像背景强度,若强度过大可能使图像处理失败,无法获得光斑xy轴长度。因此需在恒温环境及防震工作台上进行测量,同时需避免杂散光过强。
以上分析表明,通过精密装配及保证使用环境,能够确保B类不确定度可以忽略,因此最终测量不确定度主要由A类不确定度组成,在置信概率95%时小于2μm,可满足一般光学加工企业的要求。
基于像散的光学元件厚度非接触测量研究
Non-contact thickness measurement of optical elements based on astigmatism
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摘要: 为了解决光学工厂低成本高精度检测光学元件厚度的实际问题, 采用像散法厚度测量技术搭建了测量系统, 并进行了理论分析和实验验证。该系统通过柱面镜引入像散形成长宽比与厚度相关的椭圆光斑, 基于实时图像处理获得元件厚度, 具有较高的测量效率, 最后使用商用玻璃平片及平凹透镜进行了测量实验。结果表明, 该系统测量不确定度在置信概率95%时小于2μm, 中心厚测量范围为25mm, 能够满足目前一般加工公差要求; 该装置操作简单、精度高、成本低, 可用于测量透明及不透明材料, 适用范围较广。该装置为企业提供了一种低成本、非接触、高精度的厚度测量方案, 适合中小型光学加工企业使用, 具有广阔的应用前景。Abstract: In order to measure thickness of optical elements with low cost and high precision in optical factories, astigmatism thickness measurement technology was used to build the measurement system. Theoretical analysis and experimental verification were carried out. In this system, astigmatism was introduced into cylindrical mirror to form elliptical spot with thickness-dependent aspect ratio. The thickness of components was obtained based on real-time image processing with high measuring efficiency. Finally, measurement experiments were carried out with commercial glass plates and concave lenses. The results show that measurement uncertainty of the system is less than 2μm when confidence probability is 95%. Measuring range of center thickness is 25mm and it can meet current general processing tolerance requirements. The device has the advantages of simple operation, high accuracy and low cost. It can be used to measure transparent and opaque materials with a wide range of application. The device provides a low-cost, non-contact and high-precision thickness measurement scheme for enterprises and is suitable for small and medium-sized optical processing enterprises. It has broad application prospects.
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Figure 1. Schematic of thickness measurement based on astigmatism
a—focusing point at the sample surface b—focusing point below the sample surface c—focusing point above the sample surface d—spot shape at the detection plane in Fig. 1a e—spot shape at the detection plane in Fig. 1b f—spot shape at the detection plane in Fig. 1c
Table 1. Measurement results of glass plate/mm
No. position 1 position 2 position 3 position 4 1 3.010 3.015 3.019 3.008 2 3.009 3.014 3.020 3.008 3 3.009 3.013 3.020 3.006 4 3.010 3.014 3.018 3.006 5 3.011 3.013 3.019 3.007 Table 2. Measurement results of plano-concave lens/mm
No. position 1 position 2 position 3 position 4 position 5 1 2.526 3.102 2.958 2.842 3.056 2 2.524 3.104 2.959 2.844 3.054 3 2.524 3.103 2.960 2.842 3.055 4 2.525 3.104 2.959 2.844 3.054 5 2.525 3.103 2.958 2.844 3.055 -
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