After gaining an insight into the performance and limitations of NVG, the autofocus operating process can be more accurately developed. Referring to the document of basic structure [
2], the image quality of NVG relies on the electromagnetic spectrum signals detected by the enlarged image intensifier. The electro-optic system of the image intensifier is an important component. This component significantly affects resolution and light amplification. However, this component is subject to damage under strong light or high-humidity environments, and the general architectural diagram of the image intensifier is as shown in
Figure 1 [
2]. As the image intensifier will affect aviator’s safety, image intensifier detection has become a standardized process. The current aviator’s nighttime NVG test bench (TS-3895A/UV) [
3] can provide the nighttime low-light environment required for NVG calibration. However, the test bench itself is unable to automatically adjust the NVG focal length. In addition to the drawback of needing to observe NVG eyepiece images by human eye before manually adjusting nighttime NVG focal length, human factors may lead to inaccurate test results. Therefore, this project intends to use a direct current (DC) servo driver to promote the focal knob of NVG to achieve the purpose of adjusting focus and acquiring quantitative value of rotation angle. For the configuration and design, refer to the document [
1]. At present the autofocusing methods can be divided into active autofocusing and passive autofocusing [
4]. Active autofocusing involves installing external infrared or other tools to measure distance between camera lens and target. Passive autofocusing, on the other hand, involves calculating sharpness information of a single image obtained from the camera. After calculating the sharpness of multiple images, the sharpness curve is acquired. The peak value of the sharpness curve is the best focal distance. Since this case proposes to adjust focus via image information of NVG, the passive autofocusing method was adopted. The key to the application of this method lies in whether effective sharpness points can be calculated through image information. Light luminance is the key affecting the passive autofocusing system. In previous studies, many types of sharpness computing methods were compared [
5] to determine merits and drawbacks, which were applied in NVG’s autofocusing [
1]. In passive autofocusing, regardless of sharpness computing method, the subsequent image intensifier display on the screen undergoes defect testing, all of which are independent processes. Jian and Peng proposed autofocusing process for NVGs [
1], which uses gradient-based variable step search and variation of normalized gray-level as the main method for accomplishing autofocus. Wang et al. [
6] suggested the application of a robust principal component analysis method in multifocus image fusion. Additionally, an increasing number of related themes have undergone research [
7], and low-rank matrix and sparse matrix themes aroused the study interest. Therefore, further development and application in NGV autofocusing and image fusion to aid in identifying NVG equipment availability were explored.
The configuration of the mechanism comprises an NVG testing autofocusing system that includes a platform, motor, mechanism, and camera, as shown in
Figure 2, as well as the multifocus problem caused by the inaccuracy between lens and NVG, as shown in
Figure 3. This study adopted the image fusion method to resolve multifocus problems. Targeting how to correctly fuse images to ensure results presenting better information representativeness compared to any single input image is also an important topic in image fusion [
7]. So far, a large quantity of image fusion techniques have been proposed. Among them, wavelet transport-based image fusion is a popular subject of research [
8,
9] because it can maintain precision of spectrum while increasing and improving accuracy of the space. When using wavelet decomposition, if only a few decomposition stages are used, the fused image’s accuracy of space will be poorer. On the contrary, if too many decomposition stages are used, spatial similarity between the fused image and the original will be poorer [
10]. Among those fusion methods, structure-aware image fusion [
11] and image fusion in the discrete cosine transform (DCT) domain [
12,
13] are quite classic methods and widely used in various fields [
14,
15]. The following discusses wavelet-based image fusion in recent years. Vanmali et al. [
16] proposed a quantitative measure using structural dissimilarity to measure the ringing artifacts. Ganasala and Prasad [
17] especially focused on poor contrast and high-computational complexity issues of fusion outcomes. Seal and Panigrahy [
18] focused on translation-invariant à trous wavelet transform and fractal dimension using a differential box counting method. Hassan et al. [
19] implemented image fusion methods that are combined with wavelet transform and the learning ability of artificial neural networks. In recent years, deep learning networks have also been used to execute image fusion [
20,
21,
22]. In general, deep learning networks’ fusion quality depend on the sample characteristics at the time of data training. Image fusion based on low-rank matrix and sparse matrix characteristics has been a popular topic in recent years. Maqsood and Javed [
23] proposed a multimodal image fusion scheme, which was based on two-scale image decomposition and sparse representation. This technology mainly uses the edge information of the sparse matrix for fusion. Ma et al. [
24] proposed a multifocus image fusion method, mainly established in one fusion rule of sparse coefficients, which is based on the optimum theory and solved by the orthogonal matching pursuit method. Wang and Bai [
25] proposed a novel strategy on the low frequency fusion assisted through sparse representation. Wang [
26] proposed a novel fusion method based on sparse representation and non-subsampled contourlet transform, and used some indicators to prove the fusion result was excellent. Fu et al. [
27] proposed a multifocus image fusion method through distributed compressed sensing (DCS). This method is mainly considered the high-frequency images’ information. The final result was using visual and quantitative metric evaluations to analyze the results of the fusion. Among all the methods for decomposing data into low-rank matrix and sparse matrix, the most classic is robust principal component analysis (RPCA). There have been quite extensive expansion and application of RPCA, where RPCA via the principal component pursuit (PCP) method has been used to reduce the amount of calculation, with numerous extensions and expansions [
28], including stable principal component pursuit (SPCP) [
28], quantization based principal component pursuit (QPCP) [
29], block based principal component pursuit (BPCP) [
30], and local principal component pursuit (LPCP) [
31]. Additionally, other methods for solving low-rank matrix and sparse matrix also include the subspace tracking series method [
32], matrix completion series method [
33], and nonnegative matrix factorization series method [
34]. Of the discussions on these various methods, so far, studies have provided different pros to decompose matrices [
28,
35,
36]. This study attempts to fuse the images of different focal distances by decomposing low-rank matrix and sparse matrix, not only taking into consideration decomposition and recombination of a single image [
37,
38] but also considering simultaneously decomposing and fusing more than two images [
6,
7] and even expanding to multiple images. Among those studies to date, there has not yet been a correct image fusion rating standard, and different fields result in different conclusions. Nevertheless, the rating standard currently provides evidential fusion results and field applicability related studies [
39,
40,
41]. Thus, the indicators provided in the study by Liu [
42] et al. were adopted to carry out fusion rating. The program for fusion rating standard used is provided by the website below:
https://github.com/zhengliu6699/imageFusionMetrics, which discusses feasibility of applying deep semi- nonnegative matrix factorization (NMF) model [
34] method in autofocusing and image fusion.