Error-correct arithmetic for angular displacement measurement with single linear image detector

Abstract. This paper proposes a grating eccentricity error correction technique for high-precision angular measurement via image processing. We first built a mathematical model of grating eccentricity error, then we established an error-correct arithmetic based on the least square method. We tested the proposed method to find that it yields a standard error deviation of only 6.33″, compared to the uncorrected standard error deviation of 22.33″. This method is based on a single detector, which is inexpensive and performs well. The results presented here may provide a theoretical and technological foundation for further research on small-size, high-resolution photographic rotary encoders.

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