As high-precision and ultra-precision structural components are widely applied in high-end precision manufacturing, biomedicine, aerospace, and other high-end fields, their quality inspection becomes particularly critical. White light interferometry and confocal microscopy are the most widely employed in micro-nano detection, and the first measurement step is to focus on the surface of the measured sample. As the core of the focusing process, the performance of focusing evaluation functions directly affects the focusing accuracy. Therefore, it is of great theoretical significance and engineering value to study the focusing evaluation algorithm of anti-light intensity, anti-reflectivity unevenness, and high resolution to improve microscopic measurement accuracy. At present, methods for focusing evaluation are mainly image sharpness evaluation algorithms, which can be divided into three categories according to the principle of different algorithms. The first category is based on the gray value of images, which is mainly judged by calculating the gray value or gray gradient of the images. However, in the axial micro-step scanning of microscopic measurement, the gray difference between adjacent images is subtle, which can easily cause misjudgment of the focal plane. The second is the evaluation method based on the machine learning model. This kind of method mainly realizes the ambiguity judgment of images by training the network model. Although better performance in the public dataset can be realized, it is limited by the image type of the training set and network model framework in practical application. The third is the method based on the calculation of image quality, the most representative of which is the double fuzzy theory of images. The first blur is camera defocused blur, and the second is artificially added blur. The reference image is constructed by artificially blurring the image to be detected, and then the difference between the images to be detected and their blurred images are calculated to realize the clarity evaluation of the images to be detected. However, the existing methods are based on specific image boundary or gray distribution under macroscopic measurement conditions, and they are subjective and lack positioning and quantification of axial positions. In microscopic measurement, the surface texture of the tested sample is more complex, and its different and irregular edge directions make the traditional boundary judgment method easy to fail. Additionally, it is more sensitive to illumination intensity changes, uneven illumination distribution, and changes in sample surface reflectivity. Therefore, we propose a microscopic image focusing evaluation method with anti-light intensity, anti-reflectivity unevenness, and sub-micron accuracy.

Based on the principle of imaging technology, we design a microscopic image focusing evaluation method based on double blur. To address the problems in existing methods, we adopt the combination of image spatial domain and image frequency domain information and employ the local variance to calculate the difference between an original image and its blurred image. As a result, the problem that previous focusing evaluation methods are insensitive to illumination intensity changes, uneven illumination distribution, and changes in sample surface reflectivity is solved. With an aim at the selection of artificially blurred standard deviation, the concept of effective standard deviation is proposed, and the range of effective standard deviation is determined through theoretical and experimental analysis. DB-FEM includes the following steps. The first is to obtain the axial scanning image of the microscopic imaging device. In the second step, the obtained axial scanning image is artificially blurred by the Gaussian kernel function with a known standard deviation. The third step is to calculate the difference between the spatial edge information and the Haar wavelet frequency domain information of the image and its blurred image by local variance. The difference degree includes spatial edge, low-frequency texture, and high-frequency edge. The fourth step is to multiply all the differences to get the focus evaluation curve based on the difference and complete the focus evaluation.

The experimental results show that the proposed microscopic focusing evaluation algorithm based on double blur has an excellent focusing evaluation ability. At the focal plane of ±0.5 μm, the DB-FEM′ axial resolution is better than 0.3 μm. The axial resolution of DB-FEM is better than 0.2 μm during leaving the focal plane ±0.5 μm (Fig. 10). In the experiment of illumination amplitude variation, compared with other focusing evaluation methods, the DB-FEM has a performance improvement of more than three orders of magnitude in clarity ratio, an improvement of one to two orders of magnitude in peak sensitivity, and certain multiple improvements in steepness (Fig. 11 and Table 1). In the uneven reflectivity experiment, the sensitivity ratio of DB-FEM is at least three orders of magnitude higher than that of Sobel, SML, SMD, SMD2, DCT, Robert, Energy, and Brenner, and the peak sensitivity value is 2.18, 1.90, 2.28, 2.27, 1.88, 2.17, 2.15, and 1.71 higher than that of Sobel, SML, SMD, SMD2, DCT, Robert, Energy, and Brenner, respectively. The steepness values are 0.29, 0.34, 0.35, and 0.37 higher than that of the SML, DCT, Energy, and Brenner respectively [Fig. 14(a), Table 2]. In the double focal plane experiment, DB-FEM has better axial positioning ability and convergence than other focusing evaluation algorithms [Fig. 14(b)].

In this paper, a double blur micro-images focusing evaluation method (DB-FEM) based on double blur theory is proposed, which is resistant to light intensity, uneven reflectance, and submicron precision. The concept of artificially fuzzy effective standard deviation is studied, and a better value is found through the theory and experiments. The experimental results of plane mirrors and piezoelectric ceramics show that the axial resolution of this method is better than 0.3 μm under the condition of 20×/0.65 objective lens. The sharpness ratio, peak sensitivity, and steepness of the focusing evaluation can be increased to vary degrees on the traditional focusing evaluation method under different illumination amplitude conditions and uneven reflectivity conditions. Under the same curve threshold, the full width at half maximum of the proposed method is less than that of the compared focus evaluation method. In addition, in the complex focusing environment with double focusing surfaces, DB-FEM can well determine the focusing positions of two different indications, which plays a significant role in advancing the development of high-precision microscopic measurement systems.