A Flexible Differential Angle Sensor for Calibration of Linear Scale Gratings with Different Pitches

The accurate evaluation of pitch deviations in scale gratings is essential to ensure the performance of high-precision positioning systems, such as optical encoders and machine tools. Conventional methods, including interferometry and microscopy, provide high resolution but are limited by a restricted measurement range, environmental sensitivity, and poor suitability for in-situ applications. To address these challenges, this paper presents a differential angle sensor that can detect the angles of ±1st-order diffracted beams from a scale grating for pitch deviation calibration of the scale grating. The developed sensor employs a pair of adjustable plane mirrors and a single CMOS image sensor to capture ±1st-order diffracted beams simultaneously. This configuration eliminates the need for multiple detectors and complex symmetric optics, reducing structural complexity while maintaining high sensitivity. More importantly, gratings of different pitches can be accommodated by simple shifts of mirror positions without reconfiguring the optical structure. The method was validated in two stages. First, comparative experiments with a 1.6 µm-pitch grating confirmed that the configuration achieved stability and sensitivity comparable to conventional layouts. Short-range bidirectional scanning and long-range measurements up to 90 mm showed excellent agreement with reference data from a commercial Fizeau interferometer. Second, adaptability tests on a scale grating with a different pitch of 8 µm demonstrated that lateral mirror translation preserved measurement stability and angular sensitivity, confirming the capability to evaluate multiple gratings without structural modification. These results show that the system attains accuracy equivalent to that of interferometric methods while offering significant advantages in simplicity, adaptability, and suitability for in-situ industrial calibration. This paper highlights a practical, cost-effective approach for high-precision evaluation of linear scale gratings.