A Novel Self-Correction Method for Linear Displacement Measurement Based on 2-D Synthesis Mechanism

Abstract

With increased range, the accuracy of longer-range linear displacement measurement is difficult to guarantee. According to the analysis, it is inevitable that there will be a certain margin between the direction of the calibration grating and the direction of the reading head, which will impact the longer-range linear displacement measurement. In order to eliminate this measurement error, a self-correction method based on 2-D synthesis is herein proposed. First, we describe the principle of absolute linear displacement measurement based on image recognition. Then, the error model is established, which caused by the included angle between the calibration grating and the reading head. Third, a method is proposed for obtaining the vertical offset of the calibration grating by using the vertical image sensor. Finally, we reach an error self-correction method based on 2-D synthesis. In order to test the feasibility of the proposed method, a linear displacement measuring device with a range of 200 mm was developed. After experiment, the maximum absolute error was reduced from 4.34 to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.03~\mu \text{m}$ </tex-math></inline-formula> with the proposed error correction in the long range of 200 mm. The proposed algorithm does not depend on the assembly and installation position, and can realize self-correction of errors. So the method could lay the groundwork for improving larger range linear displacement measurement technology.