# Online Deformation Measurement of Laser Repair Substrate Based on Orthogonal Sampling Moire
## 1 Introduction  
Laser repair based on the principle of direct energy deposition (DED) is a branch of metal additive manufacturing technology that has wide application potential in the aerospace, automobile and ship industries [1]. Compared with traditional repair technologies (welding, thermal spraying, etc.), laser repair has many advantages such as small heat affected zone on the component, little warpage and distortion of the substrate, and excellent metallurgical bonding between the cladding material and the substrate [2].  
During laser repair, a molten pool is formed on the surface of the substrate using a high-power laser beam as the heat source. Simultaneously, metal powder is introduced into the molten pool through a synchronous powder feeding system. Due to the high temperature, the surface of the substrate and metal powder melt together and generate metallurgical bonding [3]. By moving the laser beam, the molten pool moves back and forth on the surface of the substrate, which makes the temperature of the repaired component change dynamically, leading to a complex thermal history. Available results have shown that the thermal history of a component has a significant influence on the homogeneity of the microstructure and final mechanical properties of the components [4, 5, 6]. Therefore,online deformation measurement during the repair process is essential for understanding the evolution mechanism of stress and deformation in laser repair [7].  
As a new optical measurement method, the sampling moire proposed by [PERSON] can realize phase analyses using a single grating image by digital phase-shifting [8]. It has been proven that the sampling moire method has the advantages of a simple operation and low requirement for specimen grating frequency. Therefore, sampling moire has been popularized and applied in the fields of real-time deformation measurement of materials and structures in different scales [9; 10; 11; 12; 13]. However, extreme environments such as ultra-high temperature, strong laser radiation and metal powder splashing exist during laser repair, which make impacts on the imaging process [14], bringing great challenges for the measurement of sampling moire method.  
In order to enable the application of sampling moire in laser repair environment, in this paper, an online deformation measurement system based on orthogonal sampling moire is developed, which is applied to measure the deformation field of the substrate during laser repair. In the measurement, laser repair is performed on a cantilever beam substrate, the size of which is properly designed to make the deformation within the measurement range of sampling moire. Then, high temperature resistant grating is etched on the side surface of the cantilever by laser milling. Grating images are recorded by an optical imaging system, in which a group of filter components are designed to obtain images with high signal-to-noise ratio. Finally, the deformation field of the substrate during laser repair is calculated with the orthogonal sampling moire method. The result shows that the scanning path in the repair process has a significant influence on the distribution of residual deformation, which offers a reference for optimizing the parameters of laser repair performed in the repair process.