基于级联支持向量机的飞秒激光烧蚀光斑分类 
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Objective Femtosecond laser micromachining technology has excellent three-dimensional (3D) processing capabilities and provides significant advantages in the production of experimental materials with complex 3D structural features. However, the continuous improvement of ablation efficiency and accuracy is still an eternal topic. The femtosecond laser ablation of monocrystalline silicon is accompanied by the luminescence phenomenon derived from the plasma. During the movement of the three-degree-of-freedom motion control platform in 3D space, the plasma spot produces different forms, particularly during the reciprocating ablation process in the X direction, and two distinct spot forms appear. The trailing direction of the light spot is the upper and lower left when moving forward and backward, respectively. The optimized cascaded support vector machine (SVM) classifier is used to accurately classify and analyze the light spot and can explore the ablation efficiency and accuracy in different ablation directions.
Methods First, the SVM classifier uses the feature of the spot centroid to classify the light spots at the first level. Then, we introduce the means of upper and lower peer lines and obtain two types of light spots. One type is correctly classified into the corresponding ablation direction, called the R light spot, which includes the first-level UP light spot (the trailing direction is the upper left) and first-level DN spot (the trailing direction is the lower left). The other type is incorrectly classified into the opposite ablation direction, called the E spot. Next, the first-level DN spot is superimposed, and the average value is calculated to obtain the average spot. To further obtain the standard model to maximize the similarity of each first-level DN spot, the mean spot is placed into a generative adversarial network (GAN) for training and generation. Compared with random noise, the use of average light spots can reduce the number of training and produce a final generated image more similar to the standard model. Finally, SSIM is used to calculate the similarity between the E spot and standard model, and the E spot is classified using the second-level SVM to generate the second-level UP and DN. Combining the E spot with the first-level UP and DN spots, the final classification result is achieved.
Results and Discussions Using this method, the classification accuracy is 100% under the processing power of 10 mW. In the entire ablation cycle, 34 spots are produced corresponding to the two trailing directions in the two ablation directions. Under 20 mW, the classification accuracy is also 100%. Each half of the ablation cycle produces 33 light spots in the same trailing direction. The deviation is the classification result under 50 mW, and its accuracy is 98.5%. There should be 66 light spots in the same motion state every half cycle; in the second half cycle, one light spot is not correctly classified in the classification result. In the entire time series, only two spots are misclassified, which is close to 100%, and the classification effect is significantly improved. To verify the accuracy of the cascaded SVM classifier in the classification of different states of light spots generated under different ablation directions, three classification methods of histogram of oriented gradient (HOG)-SVM, local binary mode (LBP)-SVM, and Gaussian pyramid (GP)-SVM are compared. Among them, HOG is constructed by calculating and counting the histogram of the gradient direction of the local area of the image operating on the image local grid unit and maintaining good invariance of the image deformation. LBP is an operator that can effectively measure and extract local texture information of an image. It has significant advantages such as nonrotational deformation and gray invariance. GP downsamples the image to obtain partial information of the image. Compared with the traditional HOG-SVM, LBP-SVM, and GP-SVM classification methods, the classification accuracy of the cascaded SVM classifier is increased by 5 to 9 percentage points, 12 to 16 percentage points and 9.0 to 15.5 percentage points 10, 20, and 50 mW, respectively. The cascaded SVM classifier delivers nearly 100% classification accuracy for the spot when using each level of processing power, which has obvious advantages.
Conclusions To classify the different forms of light spots in the femtosecond laser ablation process of single crystal silicon, an optimized cascaded SVM classifier is used. First, the first-level classification is performed based on the spot centroid feature. Then, the standard model is established by generating confrontation GAN. Next, the second-level SVM classification is performed using the structural similarity SSIM of the misclassified spot and the standard model. The classification results are remarkable. A better understanding of the movement state of the light spots can aid further exploration of the law of ablation. It has an indelible effect on the improvement of ablation efficiency and accuracy.
1 引言
由于飞秒激光微加工技术具备卓越的三维加工能力,因此在制作具有复杂三维结构特征的实验材料时具有显著优势,然而不断提高烧蚀效率和精度仍是一个亘古不变的话题。
飞秒激光烧蚀单晶硅的过程中,采集到的序列光斑图像与烧蚀效果有直接关系。三自由度运动控制平台在沿着X方向往复移动的过程中,每一个烧蚀周期的光斑都会呈现两种不同的运动状态,此时需对光斑进行精准分类。对光斑的形态特征进行分析能够进一步探究加工规律,进而提高烧蚀效率与精度。
在机器学习中,支持向量机(SVM)[1-3]的监督学习模型与相关的学习算法可以用于数据分类和回归分析。SVM其是一种二类分类模型[4],基本模型定义为特征空间上间隔最大的线性分类器,学习策略便是间隔的最大化,最终可转化为一个凸二次规划问题的求解。SVM在很多诸如文本分类、图像分类、生物序列分析、生物数据挖掘和手写字符识别等领域有很多的应用范围。
HOG特征[5]、LBP特征[6]、Haar特征[7]、SIFT特征[8]、SURF特征[9]、PCA特征[10]和LDA特征[11]等常与SVM分类器结合,广泛应用于图像识别与分类等。图像的特征描述子[12]不仅应该具有很强的不变性,还应该具有很强的可区分性。Wang等[6]使用HOG特征对SVM分类器进行了训练和优化,可以对油棕树进行精确计数。Kumar等[7]提出了一种新的自动实时FED(Facial Expression Detection)算法,该算法使用径向基函数对Haar小波进行变换用于特征提取,并将RBF-SVM(Radial Basis Function-SVM)用于分类。Sirajudeen等[13]基于多尺度LBP和SVM分类器对糖尿病患者的病变视网膜进行了有效的概率多标记病变分类。综上可知,国内外的研究在此领域都取得了不错的成果。
结合多种分类方式的经验,本文提出优化的级联SVM分类方法,其中第一级SVM分类方法结合质心特征,第二级SVM分类方法结合结构相似性(SSIM)[14],通过生成对抗网络(GAN)[15]生成标准模型。将所提方法与传统方法进行比较,精度有大幅度的提升。
2 飞秒激光烧蚀平台
飞秒激光广泛应用于微加工领域,使用高能量的激光束烧蚀样品可以获得各种微尺度结构。实验中的烧蚀样品为P型掺杂(硼)单晶硅片,通过三自由度运动控制平台的移动来完成对单晶硅在三维空间的烧蚀。飞秒激光脉冲沿着Z方向垂直于硅片进行微结构的深度方向烧蚀。三自由度运动控制平台沿着X方向往复一次为一个烧蚀周期,每半个烧蚀周期沿着Y方向步进2 μm,按此规律完成X-Y平面的烧蚀。飞秒激光烧蚀平台如
在飞秒激光烧蚀单晶硅的过程中,伴随着离子体的发光,使用CCD(Charge Coupled Device)相机来采集序列光斑图像。由于三自由度运动控制平台沿着X方向往复移动并对单晶硅进行烧蚀,此时光斑呈现两种运动状态。沿着X轴正向移动,光斑的拖尾方向为左上,沿着X轴反向移动,光斑的拖尾方向为左下[16]。对不同加工参数下的光斑图像进行精准分类研究,有助于把握其烧蚀规律,对烧蚀深度的探究可以起到推动作用。
图 2. 光斑在不同功率下的两种形态。(a)10 mW;(b)20 mW;(c)50 mW
Fig. 2. Two forms of light spot at different powers. (a) 10 mW;(b) 20 mW;(c) 50 mW
3 光斑分类
虽然不同的烧蚀方向对应的光斑呈现不同的运动状态,但是加工设备存在的误差和周围环境的影响会导致光斑不稳定,而且光斑非常小,灰度级较低,因此较难判读并区分光斑的运动状态。于是,采用优化的级联SVM分类器对光斑进行分类。首先一级SVM分类器利用光斑的质心特征进行初次分类,得到一类是被正确地分类到相对应的运动状态,称为R光斑,其中包括一级拖尾方向为左上(UP)的光斑和一级拖尾方向为左下(DN)的光斑,另一类被错误分类,称为E光斑;然后通过GAN生成代表两种光斑的标准模型;最后通过各个光斑与标准模型之间的相似特征进行二级SVM分类。整体的操作流程如
3.1 一级质心特征SVM分类
SVM[17]是从瓦普尼克(Vapnik)的统计学习理论发展而来的,主要是对小样本数据进行学习、分类和预测的一种方法,其基本模型是在特征空间上找到最佳的分离超平面,使得训练集上正、负样本间隔最大。
一级SVM分类器,如
图 4. 序列光斑在不同功率下的质心位置。(a)10 mW;(b)20 mW;(c)50 mW
Fig. 4. Centroid coordinates of sequential spots at different powers. (a) 10 mW; (b) 20 mW; (c) 50 mW
从
式中:w为超平面的法向量;b为截距。SVM[19]就是使这个超平面和离其最近的质心点之间的距离尽可能大,这样有利于将分布在两个范围内的质心点明确分离出来。根据质心特征得到的一级SVM分类结果如
图 5. 不同功率下的一级SVM分类结果。(a)10 mW;(b)20 mW;(c)50 mW
Fig. 5. First-level SVM classification results under different powers. (a) 10 mW; (b) 20 mW; (c) 50 mW
若分类结果为1,则表示此光斑质心点分布在较高的范围内,也就是此光斑拖尾方向为左上。若分类结果为0,则表示此光斑质心点分布在较低的范围内,对应的拖尾方向为左下。
光斑的不稳定性和质心提取存在的误差,导致一些光斑被错误分类。理想状态下,三自由度运动控制平台沿着X方向往复移动,每半个烧蚀周期所对应的光斑数量应相同的,也就是每半个烧蚀周期下1和0的分类结果是相同的。根据这一特征,引入上下对等线的方式将被错误分类的光斑提取出来。上下对等线的方式如
一级分类结果:10 mW功率下的分类精度为93%,20 mW功率下的分类精度为91%,50 mW功率下的分类精度为86.5%。
3.2 基于GAN-SSIM的二级SVM分类
采用上下对等线的方式对被错误分类的E光斑进行粗提取,因相邻两个半周期之间转换的几个光斑不易精确地区分出来,于是再使用如
1)在R光斑中,将拖尾方向为左上的光斑挑选出来,称其为一级UP光斑,将拖尾方向为左下的光斑称为一级DN光斑。将所有一级DN光斑图像进行叠加后取平均,表达式为
式中:g(x,y)为光斑在(x,y)处的灰度值。得到的均值光斑如
2)将均值光斑通过GAN生成一个标准模型,使其与每个一级DN光斑的相似度尽可能最大,并将其作为DN类光斑的代表。
GAN[20-25]的主要灵感源于博弈论中零和博弈的思想,应用到深度学习神经网络上就是通过生成网络G(Generator)和判别网络D(Discriminator)不断博弈,进而使G学习到数据的分布,如果应用到图片生成上,则训练完成后,G可以从一段随机数中生成逼真的图像。
G是一个生成式的网络,其接收一个随机的噪声(随机数),通过这个噪声来生成图像。D是一个判别网络,判别一张图像是不是“真实的”,其输入是一张生成图像和一张真实图像,输出的数值代表生成图像为真实图像的概率,如果概率值为1,就代
训练过程中,G的目标就是尽量生成真实的图像以欺骗D,而D的目标就是尽量辨别出G生成的假图像和真实图像,这样G和D就构成了一个动态的“博弈过程”,最终的平衡点即纳什均衡点[26]。
两个博弈优化过程可表示为
式中:Pdata(l)为真实数据的概率期望值;Pk(k)为生成数据的概率期望值;l为训练数据;k为生成数据。由随机噪声生成图像,这个过程需要训练很多次才能成形。实验采用
由此生成的标准模型不仅减少了GAN的训练次数,而且对于DN类光斑来说,标准模型也比均值图像更为优质。不同功率下DN类光斑的标准模型如
图 7. 不同功率下的标准模型。(a)10 mW;(b)20 mW;(c)50 mW
Fig. 7. Standard models at different powers. (a) 10 mW; (b) 20 mW; (c) 50 mW
3)求取一级分类过程中被错误分类的E光斑与标准模型的SSIM,以此作为二级SVM分类器的数据源并对E光斑进行二次分类,如
SSIM是一种衡量两幅图像相似度的指标,该指标由德州大学奥斯丁分校的图像和视频工程实验室(Laboratory for Image and Video Engineering)[27]提出。对图像的亮度、对比度和结构进行计算,表达式为
式中:μX和μY分别为图像X和Y的均值;σX和σY分别为图像X和Y的标准差;σXY为图像X和Y的协方差;C1、C2和C3为常数,是为了避免分母为0而维持稳定,通常取C1=
最后的SSIM指数为
当设定C3=C2/2时,可以将(7)式改写成更简单的形式,即
SSIM指数从图像组成的角度将结构信息定义为,独立于亮度和对比度的反映场景中物体结构的属性,并将失真建模为亮度、对比度和结构三个不同因素的组合。使用均值作为亮度的估计,标准差作为对比度的估计,协方差作为结构相似程度的度量。
三种功率下,E光斑与DN光斑标准模型的SSIM如
图 8. E光斑在不同功率下的SSIM值。(a)10 mW;(b)20 mW;(c)50 mW
Fig. 8. SSIM values of E spot at different powers. (a)10 mW; (b) 20 mW; (c) 50 mW
基于GAN+SSIM对E光斑进行二级SVM分类,得到二级UP光斑和二级DN光斑。
3.3 合并分类结果
采用级联SVM分类器对光斑进行分类,将二级UP和DN光斑与一级UP和DN光斑结合,分类结果如
图 9. 级联SVM在不同功率下的分类结果。(a)10 mW;(b)20 mW;(c)50 mW
Fig. 9. Cascade SVM classification results at different powers. (a) 10 mW; (b) 20 mW; (c) 50 mW
从
4 分类结果对比分析
为了验证级联SVM分类器对不同烧蚀方向产生不同状态的光斑的分类准确性,将HOG-SVM、LBP-SVM和GP-SVM三种分类方法与所提方法进行对比。其中HOG特征是通过计算和统计图像局部区域的梯度方向直方图来构成的,在图像的局部方格单元上对图像的形变能够保持很好的不变性;LBP特征能够有效地度量和提取图像的局部纹理信息,具有旋转不变性和灰度不变性等显著优点;GP特征对图像进行下采样处理,可以获取图像部分信息。将三种特征描述特征分别与SVM结合并对光斑进行分类。在同一加工功率和同一时间序列下,对比分析4种方法的分类结果及分类精度,结果如
从
图 10. 10 mW功率下不同方法的分类结果。(a)HOG-SVM方法;(b)LBP-SVM方法;(c)GP-SVM方法;(d)4种方法的精度对比曲线
Fig. 10. Classification results of different methods at 10 mW power. (a) HOG-SVM method; (b) LBP-SVM method; (c) GP-SVM method; (d) accuracy comparison curves of four methods
表 1. 不同法的分类精度
Table 1. Classification accuracy of different methods
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图 11. 20 mW功率下不同方法的分类结果。(a)HOG-SVM方法;(b)LBP-SVM方法;(c)GP-SVM方法;(d)4种方法的精度对比曲线
Fig. 11. Classification results of different methods at 20 mW power. (a) HOG-SVM method; (b) LBP-SVM method; (c) GP-SVM method; (d) accuracy comparison curves of four methods
图 12. 50 mW功率下不同方法的分类结果。(a)HOG-SVM方法;(b)LBP-SVM方法;(c)GP-SVM方法;(d)4种方法的精度对比曲线
Fig. 12. Classification results of different methods at 50 mW power. (a) HOG-SVM method; (b) LBP-SVM method; (c) GP-SVM method; (d) accuracy comparison curves of four methods
从
5 结论
为了对飞秒激光烧蚀单晶硅过程中不同形态的光斑进行分类,采用优化的级联SVM分类器。首先通过光斑质心特征进行一级分类,然后经过GAN生成标准模型,利用被错误分类的光斑与标准模型之间的SSIM特征进行二级SVM分类。实验结果表明,在10 mW和20 mW的加工功率下,分类精度高达100%,在50 mW的加工功率下,分类精度达到98.5%,也接近100%,这对光斑的运动状态有更大的把握,能够进一步探究烧蚀规律,对烧蚀效率与烧蚀精度的提高起到不可磨灭的作用。
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