Automatic classification of true and false laser-induced damage in large aperture optics

Abstract. An automatic classification method based on machine learning is proposed to distinguish between true and false laser-induced damage in large aperture optics. First, far-field light intensity distributions are calculated via numerical calculations based on both the finite-difference time-domain and the Fourier optical angle spectrum theory for Maxwell’s equations. The feature vectors are presented to describe the possible damage sites, which include true and false damage sites. Finally, a kernel-based extreme learning machine is used for automatic recognition of the true sites and false sites. The method studied in this paper achieves good recognition of false damage, which includes a variety of types, especially attachment-type false damage, which has rarely been studied before.


Introduction
A final optics assembly (FOA) is located at the output end of an inertial confinement fusion (ICF) experimental device. There are 48 FOAs in the Shenguang-III (SG-III) laser facility, each containing nine large aperture optics, the aperture size of which is 430 mm × 430 mm. Laser-induced damage is easily generated under 351-nm high-power laser irradiation. [1][2][3] When the number of damaged sites increases to a certain magnitude, these sites modulate the high-power UV lasers in ICF experiments, thereby significantly affecting the beam quality. [4][5][6][7] The best way to rapidly and efficiently detect and track the damage on an FOA surface is to design an online imaging system for observing tiny defects in the center of the target chamber. From the literature published in recent years, there are mainly two research teams in the field of damage online detection in ICF experiments for large aperture optics: the Lawrence Livermore National Laboratory (LLNL) and the China Academy of Engineering Physics (CAEP). Each team has developed its own experimental version of the final optics damage inspection (FODI) system, namely, the NIF FODI developed for the United States National Ignition Facility (NIF) by LLNL scientists 8,9 and the SG-III FODI we developed for the SG-III laser facility at the CAEP. 10 In general, FODI is an online imaging system based on machine vision for rapidly observing laser-induced damage. With edge illumination technology in the dark field, FODI captures images of the damage on an FOA surface and obtains the damage information by image processing. LLNL scientists have conducted much meaningful research in this field. Kegelmeyer et al. 11 used the local area signal-to-noise ratio (LASNR) algorithm to process FODI images to obtain all possible damage sites; these sites are also called candidate sites or LASNR markers. The FOA damage condition can be roughly obtained using these LASNR markers. However, due to the presence of stray light, a significant amount of noise is present in FODI images in addition to true damage, as shown in Fig. 1(b), which is referred to as false damage. 6,12,13 These candidate sites can generally be divided into these categories: damage site, hardware reflection (HR), damaged CCD pixels (DC), reflection of a damage site (RD), and attachments (Att). 14 Damage sites are also called true damage sites or true sites, and the others are called false damage sites or false sites. How to accurately remove all kinds of false damage while retaining the true damage is a hot and challenging topic in the present research. Abdulla et al. conducted machine learning of an ensemble of decision trees to identify HR-type false sites from LASNR markers with very high accuracy (99.8%, 10-fold crossvalidation). After the removal of HR-type sites, the remaining false sites (Abdulla et al. 15 referred to them as being of the unknown type, here abbreviated as UN-type) and true sites were mixed together. DC-type false sites are caused by radiation or thermal noise generated by long-term operation in a vacuum environment and generally appear as randomly distributed isolated pixels with high gray values. These DC can be easily identified via machine learning or other pattern recognition methods. To save time for later machine learning classifications, we have identified these pixels in the data-preprocessing step and removed them from the FODI image. RD-type false sites are also easy to identify and will be discussed in Sec. 2.1. Att-type false sites are more similar to true sites than any other types of false site when observed by the naked eye. The traditional machine learning methods often struggle to identify them, and almost no related studies exist in the field of damage online inspection. To solve this problem, we establish our FODI detection system in the SG-III laser facility and present a new solution for the classification of true and false sites. Limited by the size of the workspace, the SG-III FODI system is smaller than the NIF FODI system, as shown in Fig. 1(a); its size is 0.35 m. The SG-III FODI system obtains online images in a vacuum target chamber, in which the distance between the FOA and FODI camera usually ranges from 3.7 to 5.1 m. This system can detect damage larger than 100 μm with a sizing accuracy of at most AE15% and damage ranging from 50 to 100 μm with a sizing accuracy of at most AE30%. For convenience of description, FODI is herein used to refer to SG-III FODI unless specified as NIF FODI.
The goal is to combine all false sites together as one type, identifying and removing all of them simultaneously rather than identifying only one false site type or leaving other false site types to be mistaken for true sites. The categories, causes, and solutions of the candidate sites are summarized in Table 1. To propose a new solution, we analyze the optical principles of the generation of false damage and true damage and the differences in the optical features of their images generated by a CCD. The simulation and experiment reveal that the light leakage caused by edge illumination forms stray light, which is an important factor of the appearing of HRtype, RD-type, and Att-type false sites in FODI images. As shown in Fig. 1(b), the illuminated border on the adjacent optics, the unmarked white strip, and the large bright spot are all false sites. In this work, the greatest challenge is to identify Att-type false sites. To effectively distinguish them, this paper analyzes their scattering and imaging features. Since a scratch is a lengthened pit, we need to analyze only the luminous characteristics of a pit. The true damage sites are shown in Fig. 1(b), e.g., sites B and E. Finally, we use machine learning to perform high-accuracy classification experiments on false and true damage.  When the single MLD light power is 1.579 W, the power P i injected into the optic is 2 × 1.579 W. The data corresponding to the incident light power on each position monitor (P left , P right , P front , P back , P up , and P down ), the total power radiated outward [P o , as shown in Eq. (1)], and the fraction of leakage power (P o ∕P i ) are shown in Table 2.
E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 3 2 6 ; 7 5 2 The data presented in Table 2 show that the power of leaked light accounts for nearly 1/4 of the luminous power of the two MLDs. This leaked light interferes with FODI imaging. In the FOA presented in Fig. 3, two damage sites are shown: pit types A and B on optic1 and optic2. In addition, a fused silica particle of Att-type C is shown in optic2. The FODI system uses time-division-multiplexingindependent edge illumination technology; thus, if the inspected optic is optic2, only the MLDs on the optic2 edge illumination light source are turned on, whereas the MLDs on the others optics are turned off. Stray light leaked from optic2 will be reflected onto the final inner metal wall or adjacent optics3; A and C may also be illuminated by this stray light. Although A represents true damage on optic1, it is false damage for optic2 in the FODI image. For this false damage, which Spaeth et al. 14 called the reflection of a damage site (RD-type false site), we can adjust the FODI camera lens so that its imaging is blurry and easy to distinguish using a machine learning classifier. For the case of C, if the contact area between C and the optic surface is small and no extraneous stray light exists, C will not appear in the FODI image. When extraneous stray light irradiates C, an Att-type false site will appear in the FODI image of optic2.

Far-Field Light Intensity Features of True and Att-Type False Damage
For optic2, our experimental results indicate that the pit depth h is approximately one-fifth the lateral diameter d.
Assuming that the damage section of the pit is a smooth arc or a burr arc, fused silica debris attachments are divided  19,20 The far-field intensity distributions at the FODI camera lens of pit, Att 1 , and Att 2 are simulated using the FDTD method in different illumination modes. The light intensity distributions at the CCD surface are calculated using the Fourier optic AST. [20][21][22] The intensity distribution curves for the smooth-shaped pit, Att 1 , and Att 2 are shown in Fig. 5. The light intensity distribution curves for the burrshaped pit, Att 1 , and Att 2 are shown in Fig. 6.
Suppose that the maximum light intensity value of the CCD in Figs. 5(b), 5(d), 6(b), and 6(d) is v max , v 1 ¼ 0.1v max , and v 2 ¼ 0.9v max , L is the total interval length along the x-axis, L 1 is the interval length of the light intensity value greater than v 1 , and L 2 is the interval length of the light intensity value greater than v 2 . We refer to the light intensity illuminated only with S as the signal light intensity and the light intensity illuminated with S and N as the mixed light intensity. An examination of Figs. 5(b), 5(d), 6(b), and 6(d) shows that the light intensity distributions of the pit and attachments differ, especially at the CCD surface, and that this difference can be represented by a series of features defined as follows: (1) effective light interval ratio [z ð1Þ ],   Figure 7 shows that due to the presence of stray light N, the mixed light intensity is higher than the corresponding signal light intensity. The noise light intensity can be obtained by subtracting the signal light intensity from the mixed light intensity. We suppose that a baseline exists in Fig. 7 and that the curve above the baseline can cause the CCD pixels to produce photoelectric induction. In the  case of illumination with S or S + N, the interval of pit above the baseline is always longer than that of Att 1 and Att 2 . This means that a pit can form a larger spot on a CCD than attachments when they have the same size. For the curves above the baseline, the curve of pit is higher than that of Att 1 and Att 2 . This means that a pit can form a brighter spot on a CCD than attachments when they have the same size. In other words, the difference in z ð1Þ between the pit and attachments will result in different bright spot sizes on the CCD, the difference in z ð2Þ between the pit and attachments will result in different sums of the pixel gray values of the spot signal on the CCD, and so on. A comparison of these features ½z ð1Þ ; : : : ; z ð12Þ for the burr-shaped pit, Att 1 , and Att 2 in the optical simulation is shown in Table 3.

True and Att-Type False Damage in an FODI Image
In the SG-III laser facility damage inspection experiment, Att 1 and Att 2 are attributed to Att-type false damage; they are also UN-type false sites, as mentioned in the introduction. An FODI system is used to collect the images under the same illumination conditions and with a pit and an attachment located on the same optic surface. The pit and attachment are ∼100 μm in size, and their images are shown in Fig. 8. An FODI image is usually considered to be the superposition of a signal image and a noise image. The signal image can be obtained by processing an FODI image using a Gaussian high-pass filter, whereas the noise image can be obtained by processing FODI images using a Gaussian low-pass filter. 10,11 According to the 12 feature parameters of the light intensity distribution on the CCD surface in the simulation formed by pit, Att 1 , and Att 2 , we present the 12 parameters that correspond to the former parameters for describing true and false damage in the experimental FODI images: (1) Table 3.
Under constant illumination conditions, the differences in the pit and attachment in an FODI image can be characterized by ½x ð1Þ ; : : : ; x ð14Þ , that is, we can use 14 features to distinguish between false sites and true sites with an appropriate mathematical model. Because the SG-III FODI system uses  edge illumination technology, it is affected by the inhomogeneity of the light field distribution within the optics. Using TracePro simulations, we can obtain the internal light intensity distribution, as shown in Fig. 9. When the same shape flaw is located at different locations on the optic surface, the scattered light energy generally appears to be different, which causes variations in the light energy scattered to the CCD; therefore, images with different brightness values are generated. To express differences in the imaging caused by this uneven illumination, image coordinates ðX; YÞ should be added, with x ð15Þ ¼ X and x ð16Þ ¼ Y, and a total of 16 features constitute the feature vector x i ¼ ½x

Automatic Classification Method and Experimental Results
Machine learning is an effective method for managing complex classification problems. In this paper, we use the kernelbased extreme learning machine (K-ELM) to solve the automatic classification problem for true and false damage. [23][24][25] The K-ELM is a fast learning algorithm for single-hiddenlayer neural networks, and compared with traditional machine learning methods, such as the error backpropagation neural network (BPNN) and support vector machine (SVM), it has the advantage of being able to perform rapid learning and to obtain highly accurate results. 26,27 The K-ELM classification model we used in this paper is as follows: Kðx; x 1 Þ . . .
Here, Kðx; x i Þ is the kernel function, x ¼ ½x ð1Þ ; : : : ; x ð16Þ is the input sample site to be classified, x i ¼ ½x The machine learning classification process for the identification of true or false damage is shown in Fig. 10.
The K-ELM is a supervised learning method. The training data consist of a set of samples, with each sample being a pair consisting of a feature vector x i and a class label y i (also called the type of site). We match the FODI offline image to the FODI online image to complete the collection of samples. Detailed steps, as well as an example of our experiment, are as follows: Step 1: Collect the FODI online image of an inspected optic vacuum isolator, mark all possible damage sites using the LASNR algorithm, as shown in Fig. 11(a), and characterize these markers with a feature vector x i . We refer to these sites as online sites. Step 2: Remove the inspected optic vacuum isolator from the SG-III laser facility and place it in a nondisturbing light environment after cleaning the attachments on its surface. Use the FODI offline system to collect an offline image, and mark all sites (referred to as offline sites) using the LASNR algorithm, as shown in Fig. 11(b). Since the attachments have been cleaned away, Att-type false sites do not appear in Fig. 11(b). HR-type false sites are also not generated in the offline image in the nondisturbing light environment; hence, all the offline sites can be considered to be true damage sites.
Step 3: Perform a geometric transformation to match the offline sites to the online sites. The sites in the FODI online image that can be matched with offline sites represent true damage sites; the other sites in the FODI online image that cannot be matched with offline sites represent false damage sites. As shown in Fig. 12, after matching, we obtain false sample sites and true sample sites. Moreover, let y i ¼ 1 for the i'th true online site and y i ¼ −1 for the i'th false online sites; thus, all online sites can be recorded as T ¼ fðx i ; y i Þjx i ∈ R 16 ; y i ¼ AE1; i ¼ 1; : : : ; Pg.
We randomly divide the sample T into two parts: T train and T test . The training data set is T train ¼ fðx i ; y i Þjx i ∈ R 16 ; y i ¼ AE1; i ¼ 1; : : : ; Mg, and the testing data set is T test ¼ fðx i ; y i Þjx i ∈ R 16 ; y i ¼ AE1; i ¼ 1; : : : ; Ng; here, M ¼ N ¼ P∕2.
Step 4: Use the K-ELM to conduct learning on the training data set T train . Then, optimize the parameters ðC; γÞ, as shown in Fig. 13.
Step 5: Use the K-ELM classifier with the optimized parameters ðC Ã ; γ Ã Þ after training to verify the classification accuracy rate on the testing data set T test . The testing accuracy rate R is expressed as follows: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 3 2 6 ; 9 1 R ¼  Here, N TtoT is the number of true sites accurately classified, N FtoF is the number of false sites accurately classified, and N is the number of testing data sets.
We wrote our codes using the Halcon software (MVTec Software GmbH, Munich, Germany) to perform the above steps. In our training and testing samples, which include true sites and all types of false sites, the damage size range is 50 to 1200 μm. As shown in Table 4, the testing accuracy rate of the K-ELM with 16 features and the optimized parameters ðC Ã ; γ Ã Þ is verified on the testing data set.  Fig. 11(a). (d) Enlarged view of the green frame in Fig. 11(b).  Table 4 (T: true sites, F: false sites).

Discussion
Overall, the results in Table 4 show that the testing accuracy rate of the K-ELM is the highest among these classifiers. From the perspective of training speed, the speed of the K-ELM is the fastest, which is due to the structure and characteristics of the algorithm, regarding which this paper offers no further discussion. The rapid training speed helps to reduce the time required to obtain the optimal classifiers. From the perspective of testing speed, the speed of the K-ELM is only slightly lower than that of the SVM and higher than that of all other classifiers. The rapid testing speed has important practical significance in terms of practical application. Further analysis shows that because the testing accuracy rate of EDT2 is higher than that of EDT1, the 16 features presented in this paper are more effective in characterizing the difference between true and false damage. Thus, it is meaningful to analyze the optical principle of true and false damage. In addition, choosing the appropriate classifier can further improve the classification accuracy, as well as help to reduce the training time and testing time.

Conclusions
This paper presents an automatic classification method for the identification of true and false damage sites in an FODI online image, and it solves the problem of false damage interference, especially from Att-type false damage, which cannot be identified by the human eye and regarding which the previous literature in the field of damage online inspection makes little reference. This method accurately aligns the FODI system inspection results with the FOA damage condition, thereby improving authenticity and credibility. First, stray light caused by edge illumination is an important factor of the generation of false damage sites, as determined by the Monte Carlo ray-tracing method. Second, the FDTD and Fourier optic AST for Maxwell's equations are used to analyze the far-field light intensity characteristics of the pit and attachments, and the multiparameter-characterized differences in light intensity distributions on CCD surfaces are analyzed theoretically. The multiparameter-characterized differences provide a key theoretical basis for selecting features in machine learning. Finally, the K-ELM model is used to realize intelligent classification of true and false damage sites based on feature vectors consisting of multiple parameters. The experimental results show that the 16 features proposed in this paper can improve the classification accuracy of true and false damage sites, including false damage site types such as HR, DC, RD, and Att. In the field of damage online inspection, the K-ELM model is also more suitable for the classification of true and false sites than the existing methods. The accuracy rate of the K-ELM classifier is 97.46% for the testing data set, for which the damage size range is 50 to 1200 μm, and its calculation speed is relatively good, thus meeting the technical requirements for the FODI online system.