Research On Positioning Error Measurement Of 2D Precision Stages Based On Image Registration

Two-dimensional(2D)precision stages are widely applied in the precision and ultra-precision manufacturing and measurement fields,and its motion accuracy determines the accuracy of manufacturing and measurement.Positioning error is a primary performance indicator of stages,so it is critical to calibrate it.Among the existing measurement methods of the positioning error,the optics methods have the highest accuracy,but the measurement instrument is expensive;most of vision methods require a specialized artifact to provide identifiable features,for example a plane artifact with a grid of markers.The application of image registration methods has been a hot research topic in recent years,which can be roughly divided into two categories: image grayscale-based(or called autocorrelation)and image feature-based.Researchers have applied the image autocorrelation methods to measure the positioning error of stages.These methods no longer rely on a specialized artifact.However,they were not suitable for large-scale measurement due to the limitation of the FOV of a camera.This paper attempts to apply a feature-based image registration method to measure the positioning error of stages.In this paper,we propose a positioning error measurement method based on image registration for 2D precision stages.For the limitation that the vision methods require the artifacts with a grid feature,the proposed method uses an arbitrary texture plane without markers to measure the positioning error,which uses image feature points to characterize the inherent characteristics of the texture plane.The texture plane is tiled on the 2D stage,and a camera obtains the sequence images of the texture plane.Then the current position of the stage can be obtained by pairwise registration between adjacent images,thus the positioning error can be calculated from the registration results,and make the measurement range not limited by the FOV of the camera.In the image registration process,the proposed method uses the scale invariant feature transform method(SIFT)to extract the image feature points,then uses the random sample consensus method(RANSAC)to remove the mismatched feature point pairs and calculate the registration matrix of adjacent images.By comparing with multiple feature point extraction methods,the SIFT method has the best accuracy in the measurement of positioning error.In the comparative experiment,it was also found that the image registration would lead to the accumulation of measurement error.For the error accumulation problem,a bundle adjustment method is used to globally optimise the positioning error,and a sparse LM algorithm is used to quickly solve the objective function of optimisation.A computer simulation with artificial imaging noise showed that the optimization of positioning error was effective,by providing a maximum measurement error of 0.3 ?m over a 40 mm range.The proposed method relies on the accurate calibration of the camera.A camera calibration method is proposed based on the existing laboratory conditions and image registration.In the camera calibration,the calculation is accelerated by merging camera parameters.A real experiment with the 2D precision stage of a coordinate measuring machine showed that the method can achieve high-accuracy measurement,by providing a maximum measurement error of 3.23 ?m and uncertainty of 1.31 ?m over a 100 mm range.Based on image registration,the proposed method uses a texture plane to measure the positioning error,which gets rid of the limitations of specialized artifact and the FOV of camera.Moreover,the measurement process is simple and convenient.