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SAGI sensors are measurement feedback devices that operate based on the optical principle of gratings. Grating scales are frequently used in the closed-loop servo systems of CNC machine tools and can be used to detect linear or angular displacement. The measurement output signal is a digital pulse, characterized by a large detection range, high detection accuracy, and fast response speed. For example, in CNC machine tools, they are often used to detect the coordinates of tools and workpieces to observe and track tool path errors, thereby compensating for tool motion errors. Depending on the manufacturing method and optical principle, grating scales are divided into transmission gratings and