Investigation and Calibration of Error Compensation Methods for Linear Image-Type Angular Displacement Measurement

Angular displacement measurement based on image recognition methods is an increasingly popular approach to absolute displacement measurement. Employing multiple, collaborative image sensors can significantly reduce measurement errors when determining angular displacement. However, limited installation space restricts the number of sensors that can be utilized, and residual errors persist even when numerous sensors are employed. We propose an error correction method based on nonlinear fitting of multiple harmonic components to enhance measurement accuracy. This article begins by elucidating the principles of image-type displacement measurement, then analyzing the harmonic errors inherent to such measurement results. Subsequently, we introduce a method for correcting angular displacement measurement errors based on nonlinear fitting of multiple harmonic components. We validate this method through experimentation. The results indicate that our error correction method can improve measurement accuracy from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$510.97"$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.82"$ </tex-math></inline-formula> with a code disk diameter of 87 mm when using only one reading head, suggesting that our method is effective. This work may offer a sound technical basis for the advancement of miniaturized and high-precision angular displacement measurement technology.