Reflection Coefficient Estimation of Femtosecond Laser Surface Processing Using Support Vector Regression

An image analysis-based Reflection Coefficient (RC) estimation method of femtosecond laser surface processing for the blackening of X-ray imaging sensor shell is proposed. The Support Vector Regression (SVR) is used for RC computation and both an offline and an online steps are considered in this method. Regarding offline step, the typical laser process parameters are set to perform surface processing and Scanning Electron Microscope (SEM) images are recorded. Then a series of image features are computed and both the computed image features and typical laser parameters are used to train SVR: the training dataset includes the laser line space, laser beam diameter, natural logarithm of laser power divided by laser frequency, and image features of Gray-Level Co-occurrence Matrix (GLCM); the supervising data are laser ablation diameters. As for online step, when SEM image data are recorded after laser processing, the trained SVR is used to predict laser ablation diameter and then the RC can be computed by laser ablation model. Many experiment results have verified the effectiveness of our proposed method, and the RC estimation accuracy can be better than 90.0%.

a kind of noise-sensitive and contrast-low sensor which uses more complex optic elements such as the fiber optic taper or image intensifier [4] to collect the weak X-ray responses from scintillator. To improve its signal response ability, a series of processes and structure design methods have been developed [5], [6]. Recently, the Materials Surface Blackening Process (MSBP) [7] has become one of most important steps for high sensitivity X-ray imaging camera manufacture. The MSBP can restrain the stray light effectively by coating a black light absorption layer on the inner surface of camera shell; then the stray light such as the ambient light or internal reflected light of optic components can be absorbed effectively.
Many research works have been done to achieve the MSBP, such as the electrochemical coating technique [8] or surface coatings method [9], etc. The electrochemical coating technique uses electric energy to induce chemical changes in typical electrolyte and create coatings on the surface of materials. The surface coatings method employs the prepared paint to cover the surface of materials. Clearly, these methods above will meet a series of problems such as the high environment pollution, inflexible operation, low controllability during blackening process, and even the poor blackening quality for complex application. In recent years, the femtosecond laser begins to be used for materials surface blackening [10]. The femtosecond laser can implement materials surface processing by very short-time laser output (10 −15 s), it has high instantaneous power, and it also can focus on a very small spatial area on target. All these merits guarantee its good performance on blackening application. Fig. 1 presents the sketch map of femtosecond laser surface processing. Scanning Electron Microscope (SEM) images of Titanium Alloy (TA) before and after the femtosecond laser ablation are shown. From Fig. 1, the banded metal textures can be observed in TA surface before femtosecond laser processing; while the micro-stripes can be created on materials surface after processing. These micro-stripes will cause rays to experience multi-times reflections and absorptions; and then the materials reflectivity will be reduced. The reflectivity, i.e., Reflection Coefficient (RC) [11] can be used to evaluate the effect of blackening process. Traditionally, the RC can be measured by a spectrometer; however, it will be more convenient if the application of spectrometer can be omitted. Therefore, a SEM analysis-based technique is proposed in this paper. Clearly, This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ the application of SEM imaging data to blackening effect assessment can also improve the measurement stability by using historical accumulated data.
In this paper, a blackening effect estimation, i.e., the RC estimation of femtosecond laser surface processing is proposed. First, the femtosecond laser processing is performed and the laser process parameters [12] are saved. Second, after laser processing, the ablation diameters of femtosecond laser are measured by typical SEM images. The image features of Gray-Level Co-occurrence Matrix (GLCM) [13] are also computed for SEM images. Third, a Support Vector Regression (SVR) [14] is trained by the laser process parameters and GLCM image features above for the laser ablation diameter prediction. Finally, when a new femtosecond laser blackening processing is carried out, the laser ablation diameter can be predicted by the trained SVR; and then the RC can be computed. The main contributions of this paper include: 1) a novel method is proposed to estimate the ablation diameter (i.e., the RC) using the laser process parameters, SEM image features, and SVR. 2) The proposed method extends the measurement of MSBP for camera manufacture.
In the following sections, first, the RC estimation method is proposed. Second, some experiments and discussions are presented. Finally, a conclusion is made. Fig. 2 illustrates the proposed computational flow chart of RC estimation of femtosecond laser surface processing. Since the SVR is used in this paper, its processing flows can be divided into the offline and online steps. Regarding the offline step, a series of blackening processing are performed to accumulate the experiential data. Both the laser process parameters (i.e., the laser line space, laser beam diameter, natural logarithm of laser power divided by laser frequency) and GLCM image features (i.e., the statistical features of GLCM energy, entropy, correlation, and contrast) captured from the SEM are used as the training data. The ablation diameter of femtosecond laser is considered as the supervision data. Then the SVR can be trained. The SVR is considered for our forecasting computation because it has excellent prediction accuracy by just using small amount  of training data. As for the online step, after each blackening processing, the laser ablation diameter will be forecasted by the trained SVR from SEM image; and then the RC can be computed.

B. Estimation Method of Laser Ablation Diameter
In general, the distribution of single pulse energy of femtosecond laser obeys Gaussian function; its energy distribution can be written by equations (1) and (2) [15]. The diameter of laser ablation region can be estimated by (3). According to Gaussian function, the laser ablation depth in middle position of materials is larger than the depth in edge position of materials; therefore if the laser line spacing is smaller than ablation diameter, the overlap of neighboring ablation tunnel [16] can be observed easily. In that situation, the actual ablation diameter cannot be measured from image directly. Fig. 3 presents the ablation diameter comparison using different laser parameters. Table I shows the laser process parameters of the experiment in Fig. 3. In Fig. 3(a) and (b), because the ablation diameter is larger than  Fig. 3(c) and (d), since the ablation diameter is smaller than laser line spacing (37.16 μm < 40.0 μm), the overlap issue does not happen.
where ϕ h is the laser energy density in edge of effective ablation region; D is the diameter of ablation region; w 0 is the radius of laser spot; P avg is the laser average power; f is the laser repetitive frequency. Clearly, (3) can be deduced from and (2). As a kind of artificial materials, the metal textures mainly come from the repeated forging, folding, and oxidation during manufacture process. From image processing point of view, the image texture feature can represent materials surface character accurately. The GLCM features are one of the best texture definition methods. After the color image is converted into gray one, regarding an image I with a gray level k, its GLCM size should be k × k. Starting from a certain pixel point A with a gray level a, let us define a pixel point B with a gray level b which also has a d-pixel distance from A in direction θ; then the number of pixel intensity pairs a and b with distance d in direction θ is the element of GLCM. The familiar features of GLCM are shown in (4)-(11); they are the energy, entropy, contrast, and correlation. Clearly, the GLCM element can represent the intensity and direction changes of image texture; and its features can also describe the texture change rules.
where P(i, j) is the GLCM element at coordinate (i, j); k is the gray level of image.
Regarding images with the overlap ablation phenomena [17], the ablation diameter can be estimated by the consideration of both the laser process parameters and imaging features of ablation image. Without loss of generality, the corresponding parameters include: the laser process parameters, i.e., the laser line space P lls , laser beam diameter P lbd , and natural logarithm of laser power (P lp ) divided by laser frequency (P lf ) P llpdlf ; the GLCM features, i.e., the mean of energy mP glcm _ ene , variance of energy vP glcm _ ene , mean of entropy mP glcm _ ent , variance of entropy vP glcm _ ent , mean of correlation mP glcm _ cor , variance of correlation vP glcm _ cor , mean of contrast mP glcm _ con ., and variance of contrast vP glcm _ con . The SVR is used to estimate laser ablation diameter; its training vector is [P lls , P lbd , P llpdlf , mP glcm _ ene , vP glcm _ ene , mP glcm _ ent , vP glcm _ ent , mP glcm _ cor , vP glcm _ cor , mP glcm _ con , vP glcm _ con ] 1×11 and its supervising data is the actual ablation diameter of femtosecond laser. Finally, once the surface processing of femtosecond laser is performed, the ablation diameter can be estimated by the trained SVR. The parameters definitions are shown in (12) to (20). The GLCM in 0°, 45°, 90°, and 135°are all used in our model.

C. Computational Method of RC
In many cases, the effect of femtosecond laser only occurs on the surface of material; its effect on interior is not apparent. Thus, the femtosecond laser can realize a kind of fine ablation, which is suitable for MSBP. During the process of ablation, when the temperatures of electrons and lattice reach the metal melting value, the irradiated part turns into thermal plasma and evaporates outward; the metal appears ablation phenomenon and forms pits. The fine sputtered particles will be deposited in and around pits. From the perspective of microstructure, the RC of materials is not only related to the properties of oxide layer formed by laser ablation, but also related to the microstructure of ablation stripes (see Fig. 1). For example, the angle between the groove formed by the stripe and incident light will determine the direction and times of light reflection. Therefore, to estimate RC by analyzing the groove (image texture) and imaging intensity (oxidation degree) of material surface after laser treatment has its meaning. (21) to (23) illustrate the relationship between ablation diameter and RC [18], [19], [20].
where F n is the laser ablation threshold; ρ is the material density (kg/cm 3 ); D T is the heat diffusivity (m 2 /s); τ P is the pulse duration (ns); Ω vap is the material heat of vaporization (J/g); α b is the material absorption coefficient (1/m); R is the material reflectance coefficient; D is the ablation diameter (cm); r 0 is the laser beam radius (cm); I 0 is the maximum value of laser energy density (J/cm 2 ).

III. EXPERIMENTS AND DISCUSSIONS
The practical surface processing experiments of femtosecond laser were performed, and a series of simulation experiments were also carried out on our PC (2.4 GHz, 8.0 GB RAM) by Python 3. 8. 0 to test the correctness of proposed algorithm.

A. Data Source
A femtosecond laser device (Pharos, Light Conversion Ltd., Lithuania) was used to carry out the materials surface processing experiment toward the Stainless Steel (SS) and TA. In this experiment, only the image data with ablation overlap phenomenon were recorded. The main compositions of SS and TA are shown in Tables II and III. Fig. 4(a) and (b) present the SEM (SolidSpec-3700i, Daojin, Japan) imaging results of SS and TA, respectively. Table IV illustrates the process parameter samples of femtosecond laser. In Fig. 4, the images with 500  Table IV. Some ablation phenomena can be observed in Fig. 4. For example, the oxidation degree will increase (the image looks darker) when the laser power is improved; and the sputter pits can be observed if the laser frequency is enlarged. Therefore, it is necessary to estimate the ablation effect by analyzing both the laser process parameters and image features.

B. Evaluations of RC Estimation Methods
Seven computational methods are designed to estimate the ablation diameter, and then the RC can be calculated.
1) Method 1: The polynomial fitting technique is considered in Method 1. The linear weighted function is used here. (24) presents its computational method. Table V shows the fitting results of (24). The fitting experiment data amount is 60. Clearly, in this experiment the orders of magnitude of laser processing parameters and GLCM image features are totally different. For example, the values of P lls and P lbd are large than 10, the value of P llpdlf is between −6.0 to 0.0, and the values of GLCM features are between 0.0 and 1.0. As a result, the fitting effect may be limited. An error index is defined in (25). If this prediction error is less than 5.0% of true value, the predicted result is determined to be correct in this experiment.
where k 1,i (i = 1, 2, …, 11) is the weight; D T is the true value; D P is the prediction value.
2) Method 2: Another polynomial fitting technique is considered in Method 2. Equation (26) shows its computational method, 60 fitting data is used and Table VI present its fitting result. Because the values of P lls and P lbd are much larger than GLCM features, the negative two powers are used to decrease the values of P lls and P lbd ; and the three power is considered to increase the value of P llpdlf . In this experiment, since all the variables have the similar order of magnitude, its fitting effect may be better than the results of Method 1.

3) Method 3:
The polynomial fitting technique is used again in Method 3. Unlike Method 2, the values of P lls , P lbd , and P llpdlf are decreased further. (27) presents its computational method, the same 60 data in Methods 1 and 2 are used to estimate the parameters of (27). The fitting results are shown in Table VII. Clearly, the order of magnitudes of all variables have the close values, thus its fitting effect may be good.

5) Method 5:
The SVR is used again in Method 5. The training data of SVR include the laser process parameter, i.e., P lls , P lbd , and P llpdlf , and some new image features. The Local Binary Pattern (LBP) image features are computed to the original image, and the Principal Component Analysis (PCA) is used to implement the dimensionality reduction [22]. Finally, after PCA computation, only 8 LBP features are left; and then all the 11 features, i.e., 3 laser process parameters above and 8 LBP features, are used to train SVR. The RBF kernel function is employed here. The same training data, test data, and error judgment method in Method 4 are used in this experiment.
6) Method 6: The AlexNet with transfer learning mechanism [23] is used in Method 6. For the AlexNet, the original training data set adopts the ImageNet2012 to accomplish the pre-training. The ImageNet2012 dataset is divided into 1000 categories, including 1.2 million training images, 50 thousand verification images, and 1 million and 50 thousand test images. We migrate the AlexNet model parameters trained on ImageNet2012 to the new data set for network training, fix the parameters of first five convolution layers, corresponding pooling layer, and three fully connected layers, use the random initialization for other parameters, and replace the last layer with the regression layer to train the new data set. Finally the same training data, test data, and error judgment method in Method 4 are used for AlexNet. 7) Method 7: Method 7 is our proposed method. The SVR is used to predict ablation diameter. The training data vector of SVR is [P lls , P lbd , P llpdlf , mP glcm _ ene , vP glcm _ ene , mP glcm _ ent , vP glcm _ ent , mP glcm _ cor , vP glcm _ cor , mP glcm _ con , vP glcm _ con ] 1×11 ; and the supervising data is the true value of ablation diameter. The RBF kernel function is considered here again. The same training data, test data, and error judgment method in Method 4 are used here.   RC estimation accuracy using different SVR kernel functions; and the RBF can get the best result. The similar results can be found in Methods 4 and 5. Furthermore, we have tested different design methods, including various polynomial fitting models and training features of SVR, however the prediction performances of them are poor; as a result, only 7 methods above are mentioned in this paper. Fig. 5 presents the prediction result comparison of ablation diameter: (a) and (b) are the results of SS and TA, respectively. Table IX shows the parameters of laser ablation model. Tables X and XI present RC and running time comparisons of SS and TA. From Fig. 5, Tables X and XI, first, Method 1 cannot get ideal prediction result which may come from the fact that the values of laser parameters and GLCM features have large difference. Second, regarding the polynomial fitting technique, Method 3 can get better result for SS while Method 2 can achieve better performance for TA. This result may come from the fact that the textures of TA look more significant than those of SS after laser processing. Third, Methods 4 and 5 cannot get good results than Method 7 which may come from the improper training data design and organization. Fourth, Method 6 cannot have good result which may be explained that the effect of pre-training of AlexNet is limited and the training data amount is too small. Finally, Method 7 can get a comparable good result for our application currently.

C. Discussions
The femtosecond laser blackening process has broad application prospects in camera manufacture or other micro materials researches [24]- [25]. Fig. 6 presents the application examples of the Intensified Complementary Metal-oxide-Semiconductor (ICMOS) camera. In Fig. 6, (a) is a photo of an ICMOS camera, (b) illustrates the mass produced products of fiber optic taper coupling ICMOS module. The physical phenomenon of laser incident on the surface of matter can be attributed to thermal and mechanical effects [26]. It mainly includes the reflection, absorption, and energy conversion of matter to laser. The femtosecond laser can produce many densely arranged cavities and cylindrical convex structures on the surface of metal materials, and the depths of these structures are about 1.0 μm∼5.0 μm. These structures can consume the energy of incident light and reduce the reflectivity. Thus it is necessary to estimate RC to evaluate surface processing effect of femtosecond laser. Fig. 7 presents the blackening effects of SS and TA, and their image samples with 50 or 10000 times magnification. In Fig. 7(a) and (b) are the blackening results (i.e., the visible light camera images) with 50 times magnification of SS and TA, respectively; (c) and (d) are the results (i.e., the SEM images) with 10000 times magnification of SS and TA, respectively. From Fig. 7, if the process parameters of femtosecond laser are proper, the blackening effect will be acceptable. In this study, only the images with 500 times magnification are used in our research. If the magnification is too small, the texture information of metal surface cannot be observed clearly; on the contrary, if the magnification is too large (see Fig. 7(c) and (d)), the ablation diameter cannot be identified from the image accurately too [27]. In future, the RC estimation using the fine stripe will be considered in our model.
The robust GLCM features [28] are used in our model. Compared with other image features, the GLCM features have good computing effect for textures with large period and stripe type; especially they are suitable for modeling and characterization of materials surface morphology after femtosecond laser processing. Both the data standardization treatment and data normalization step are needed for our data preprocessing. (28) and (29) are the corresponding computational methods. The data standardization is used when calculating the GLCM and the data normalization is employed when inputting data for SVR. Clearly, the data standardization can improve the data generalization ability and prevent overfitting phenomenon; and the data normalization can limit the data into a certain range, so as to eliminate the adverse effects caused by the singular sample data.
where X and F are the input data; Y and T are the output data; the definitions of mean(·) and var(·) can be found in equations (12)- (20); and the functions min(·) and max(·) compute the minimum and maximum values of data, respectively. Both the polynomial fitting technique and the machine learning method are investigated to predict the ablation diameter (i.e., RC) of femtosecond laser. Although it is easy to build a relationship between the image feature and the ablation diameter by the machine learning tool; however, both the laser character and the materials attribution can influence the laser surface processing effect; as a result, some laser parameters and image features are all used for ablation diameter forecasting in this study. The ablation diameter prediction only uses the image features (without laser parameter factors) is unreliable. When designing the prediction method, because the microstructure of materials surface has diversity, the polynomial fitting effect is limited according to our experiment. Regarding the machine learning method, it also does not mean the higher the image feature dimension, the better the calculation effect. For example, Methods 4 and 7 can illustrate that result.
Our proposed method has a certain practical value, and it has the possibility to develop a system for application to improve the product quality. First, in the system modeling stage, we can control the femtosecond laser output to obtain the SEM images with different ablation effects, and calculate the image features, so as to repeatedly obtain the training data set of SVR; and then we use the laser parameters and image features proposed in this paper to train SVR. Second, in the application stage of system, after we carry out femtosecond laser for surface treatment, the SEM images can be collected; if there is no obvious overlap of ablation tunnel, the trained SVR can be used to predict RC. Third, the product quality data package can be formed according to RC prediction results to judge whether the products are qualified or unqualified. To improve the automation level of system, both the femtosecond laser and SEM can be installed into an integrated device (see [12]).
The proposed method at least has three merits. First, it has high level of intelligence. The SVR method is considered in the proposed method, which can solve the problems of the complex thermal effect and random surface appearance of materials. Second, its processing effect is stable. Since lots of historical data are encapsulated into this model, its computational effect will be increased dramatically with the accumulation of experiment data. Third, it has good scalability. Like the Graph Pad Prism tool [29], many image features and computational methods of laser process parameters can be researched in this proposed model; and other machine learning tools, such as the deep learning network [30] can also be designed in our next research step. Clearly, the proposed method also has some drawbacks. For example, currently the accumulated data are limited, and the model generalization is still can be improved. In future, more data will be collected and other machine learning methods will be studied.

IV. CONCLUSION
A RC estimation of femtosecond laser surface processing is developed. The machine learning method is proposed in this method and both an offline and an online computations are used. Regarding the offline step, a SVR is trained to predict the laser ablation diameter. The laser line space, laser beam diameter, natural logarithm of laser power divided by laser frequency, and some image features of GLCM are all used to train the SVR. As for the online step, after the implementation of laser surface processing, the ablation diameter can be estimated by the trained SVR and then the RC can be computed by the laser ablation model. The proposed method is suitable for the femtosecond laser processing image with the overlap phenomenon and can achieve a convenient engineering application. In future, more image features and machine learning methods will be designed to improve the estimation accuracy of RC in our method.