## 5 Conclusions  
In this study, DIC and AE were combined to obtain the deformation information of red sandstone under uniaxial compression. The second-order STS-DIC algorithm was developed for measuring strongly heterogeneous deformation fields and was used to calculate the deformation field during the deformation localization stage of the rock specimens. The experimental results for the deformation field and AE were used to analyze the evolution of the rock deformation localization.  
First, the evolution of the deformation field during rock deformation localization was analyzed in detail by using second-order STS-DIC and AE. In the deformation localization process, many small deformation concentration regions were observed; some eventually connected to form DLBs, but others stopped developing. The evolution of the DLB was crucial to the rock's mechanical behavior. The DLB fully developed before the peak stress was reached. After the peak stress, macro-cracks appeared at the DLB, which led to rock instability and failure. The failure mode of the rock specimen was consistent with the final state of the DLB. Second, the evolution of the DLB was analyzed. When the deformation localization was initiated, the length of the DLB increased continuously, but the width increased only when the length reached a certain value. The sliding rate had a significant effect on the length of the DLB formed by shear deformation. However, the opening rate had a greater influence on the length and width of the DLB formed by tensile deformation. The sliding rate and opening had a significant influence on the AE counts.  
This study mainly focused on the deformation localization of rock and had several deficiencies. For the analysis on rock deformation characteristics, the relationship between the initiation of the deformation localization and the stress level (i.e., the competition mechanism among DLBs) needs to be studied in more detail. The characteristics of instability and failure also need to be studied in more detail. To realize instability failure analysis, highly accurate DIC algorithms need to be developed for measuring discontinuous deformation fields. Higher-performance measurement systems need to be developed, such as an adaptive image acquisition system for different deformation states (e.g., low-frequency acquisition during early loading, medium-frequency acquisition during the deformation localization, and high-frequency acquisition during instability).  
Conceptualization, Y.S. and T.X.; methodology, T.X. and H.Z.; software, H.Z. and T.X.; writing--original draft, T.X.; writing--review and editing, H.Z. and Y.S.; funding acquisition, T.X. and H.Z. All authors have read and agreed to the published version of the manuscript.  
This study was supported by the National Natural Science Foundation of China (Grant Nos. 12302243 and 12072323), Natural Science Foundation of Zhejiang Province (Grant No. LZ22A020006).  
Figure 9: Correlation between the relative displacement rate and the AE counts.  
Data Availability StatementRestrictions apply to the datasets. The datasets presented in this article are not readily available due to technical/time limitations. Requests to access the datasets should be directed to first author.  
The authors declare no conflicts of interest.