| In ultra-precision measuring instruments,the linear stage is often the key component,whose main function is to drive the probe or the tested sample to achieve cross-scale scanning.It is inevitable that there are some defects in the manufacturing and installation process of the linear stage,which may lead to multi-degrees-offreedom motion error during the movement.The motion error is coupled in the measurement result,which greatly reduces the measurement accuracy of the instrument.Therefore,the measurement and separation of motion error is of great research value for the realization of ultra-precision measurement.In this paper,the motion error of a linear stage is taken as the research object.Aiming at the high-precision,multi-degree-of-freedom measurement and separation requirements of the motion error,a three-degree-of-freedom(3-DOF)motion error measurement system(film interferometer)is developed based on the principle of film interference,which is capable of measuring linear motion error(horizontal straightness error)and angular motion error(yaw error and roll error)at the same time.The film interferometer has been applied to the coordinate measuring machine(CMM)to separate the motion error.The main contents of this paper are as follows:(1)Theoretical analysis of motion error separation based on film interference.According to the calculation of the optical path difference between the two coherent beams,the mathematical model between the phase shift of the interferogram and the horizontal straightness error is derived.Combined with the geometric relationship,the measurement principle of yaw error and roll error is further explained.Finally,in order to realize the miniaturization and modularization of the system,the two-point method is adopted as the solution of motion error separation.(2)Design of film interferometer and phase analysis algorithm.According to the overall scheme and expected indicators,the hardware selection is carried out and the construction of the optical measurement system is completed.On the basis of the hardware,phase analysis algorithms based on edge fitting and connected domain extraction are proposed respectively,the better solution is determined by comparing the advantages and disadvantages.In addition,a phase recognition algorithm is developed to track the rolling of the corresponding fringe,and then obtain the phase shift information of the two interferograms.(3)Verification of the measurement and separation capability of motion error.A confocal sensor and a laser interferometer are used to calibrate the unknown parameters,and based on their measurement results,the motion error measurement capability of the film interferometer is analyzed through comparative experiments.The experimental results show that the linear and angular motion error measurement accuracy of the film interferometer is ±0.03 μm and ±0.08",respectively.After that,the film interferometer is installed on the bottom of the three-dimensional topography measurement system,and a sets of step(obtained by grinding the standard gauge blocks with known thickness)height measurement experiments are carried out to evaluate its motion error separation capability.The experimental results show that the system can effectively restore the three-dimensional topography of the steps above 10μm,and the relative error of the height measurement result is within 1.7%. |
