Wafer Surface Defect Detection Based on Background ...

From Formulas (2), (3), (8), and (9), the peak spacing (Δu&#;, Δv&#;) of the 1D spectral signal is almost equal to the period (Δx, Δy) of the original image. The most common method for obtaining the peak value is to perform a secondary derivative on the sequence signal. However, defects and secondary texture elements will cause interference peaks. Before performing a secondary derivative on the 1D spectral signal, it is necessary to apply a filter to eliminate outliers. After the main peak values are obtained, the average value of the spacing between peaks is extracted as the image period.

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where Δx refers to the period in the direction of the row in the original image, Δy refers to the period in the direction of the column in the original image, Δu refers to the spacing of the peaks in the direction of the row in the spectral image, and Δv refers to the spacing of the peaks in the direction of the column in the spectral image. The peak value of the Fourier spectrum will be affected by the existence of noise, defect, and secondary texture, and directly calculating the peak spacing will lead to inaccurate period calculation. Therefore, this study selects the areas near the central column and central row in the spectral image to make gray projection, thereby forming two 1D vectors:

where W and H refer to the width and height of the image, respectively; f(x,y) refers to the original image; and F(u,v) refers to the spectral image. The spectral image of a is shown in b. It describes the frequency and amplitude distribution information of the image texture. Specifically, there is a relationship between the spacing of periodic peaks in the spatial domain, and the spacing of peaks in the frequency domain, as shown below:

The common texture period measurement methods include the spectral analysis method, autocorrelation method, and gray-level co-occurrence matrix method. Regarding the image as a 2D signal, the spectral analysis method positions the peak value and extracts the texture period in the frequency-domain spectrum. However, this method is vulnerable to the interference of defect components and secondary texture elements, and so it is difficult to accurately measure the texture period. With the autocorrelation method, an autocorrelation function is used to describe the autocorrelation degree of an image in two directions, namely row and column. Period measurement is then performed in accordance with the position where the peak value of the autocorrelation function appears. This method requires the image to have good autocorrelation; otherwise, it is easy to have a certain range of deviation. The gray-level co-occurrence matrix describes the image texture information through the probability that a certain gray-level structure appears repeatedly in the image. This method is used to obtain the spatial correlation of the image by extracting its texture structure. Nevertheless, there are some problems, such as a large amount of computation and frequent loss of information, which lead to inaccurate period calculation.

2.2.2. Reconstruction of Background Image

The background image can be reconstructed on the basis of the period features of the wafer image. The period features of the wafer image refer to the periodic structural parameters of the image, including texture number, texture period, and texture uniformity. Among them, texture period is equal to the period of the image (Δx, Δy); the number of textures distributed horizontally is nx = floor(W/Δx); the number of textures distributed longitudinally is ny = floor(H/Δy). The wafer image can be divided into multiple repeated substructure images by texture period and texture number. Through the random sampling and superimposed averaging of substructure images, the approximate defect-free substructure image can be obtained. Then, a complete wafer image can be reconstructed through tiling the substructure image in accordance with the texture period and the texture number. However, this operation requires high accuracy of the texture period and accurate positioning of all substructure images. Otherwise, a large number of false defects will be generated in the defect extraction stage. Therefore, the template matching method is required to position and calibrate the substructure image. Nevertheless, the traditional template matching method has some problems, such as dislocated matching and low accuracy. A local template matching method in the mode of sliding window, which can effectively solve the problem with dislocated matching and improve the matching accuracy, is proposed in this paper. The substructure image is taken as the matching template, and the sliding window is set to be the matching region. The sliding window should include a complete substructure image, but it should not be too large to avoid redundant calculations. In this study, the width of the sliding window is set to be 1.2 times of the width of the period, and the height of the window is 1.2 times the height of the period. The horizontal sliding distance of the sliding window is set to a single time of the period width, and the longitudinal sliding distance is set to a single time of the period height. The sliding window starts to move from the upper left of the image to be measured. The matching template just needs to match in the sliding window.

shows the schematics of different template matching algorithms. a provides a schematic of the traditional matching algorithms. The template keeps moving in the image and calculates the similarity, with a large matching area. However, the matching targets are arranged periodically in the period image. There is only one target to be matched in one local area. Therefore, there are more redundant calculations in the matching of period images by traditional matching algorithms. The improved matching algorithm in this paper is shown in b. The image to be matched is divided into many matching areas by the sliding window. The template image only needs to be matched in the local range, which greatly reduces the irrelevant matching area and thus improves the phenomenon of dislocated matching.

To improve the matching accuracy, the Sobel edge detection algorithm is used to extract the template image and shape information in the area to be matched, and to perform matching and positioning on the basis of shape features, taking cosine similarity [22] as the measurement criterion:

S(x,y)=px,y&#;T||px,y||×||T||,

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(10)

where T refers to the shape feature vector of the template image; px,y refers to the shape feature vector of the area to be matched; S(x,y) refers to the similarity between the template image and the area to be matched. The matching point with the highest similarity in the sliding window is selected to compare with the given threshold. If it is greater than the given threshold, then this point will be added to the matching point set. The threshold value determines the positioning accuracy of the matching, and directly affects the quality of the reconstructed image. Given an extremely low threshold value, the poor matching result will be tolerated, which leads to a substantial substructure image offset and further produces false defects. shows the matching scores of the sample image. It can be seen from the scores that images without defects have a high matching score, with a minimum value of 0.. Therefore, the threshold should not be less than 0.9. It is set to 0.9 in this study. On the basis of the coordinates in the matching point set, multiple substructure images can be extracted from the wafer image. Then, they are superposed and averaged to further obtain the substructure image with accurate registration. Owing to the interference of defects, the matching results may be missing in some areas. In this study, the least square method is used to fit point sets to obtain the fitted lines in the two directions, namely row and column. The intersection of the two lines can be used as the matching result in the missing area. Finally, the substructure image is tiled in accordance with the period features and matching coordinate point sets to reconstruct the background image for subsequent processing.

In the process of industrial production, the surface defect detection of products is a problem that every production enterprise needs to pay attention to. With the rapid development of the electronic industry, some enterprises that produce industrial parts are constantly increasing the output of industrial parts, so the efficiency of traditional manual detection is becoming lower and lower, which can not meet the needs of today's enterprises. Nowadays, machine vision equipment has become a popular equipment in today's industrial industry, and surface defect detection is widely used in various industries. At present, it has also been favored by the majority of enterprises.

The so-called surface defect detection is actually a kind of detection technology based on machine vision to complete a series of detection work, in which the surface defect detection mainly includes transmission, image acquisition, image processing and control execution modules, and can detect the surface appearance defects of objects online, such as scratches, spots, color differences and other defects. It helps enterprises to save production costs and improve product quality.

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