Design Method and Error Analysis of 3d Metrology System in Accordance with the Abbe Principle

Abstract

In high-precision measurement and machining, the accuracy is crucial. To avoid errors caused by mechanical structures, the metrology system is required to conform to the Abbe principle. The Abbe principle can be easily met by one-dimensional (1D) mechanical systems but not by 2D and 3D ones. By analyzing the characteristics of the Abbe principle in 3D measurement space, this paper presents a 3D metrology system design method obeying the Abbe principle. The method greatly reduces the first-order Abbe errors by reducing the Abbe offsets and structurally avoids the effect caused by 21 geometric errors. To prove the rationality of the method, a 3D metrology system model is established for error analysis. For the error sources generated in the 3D metrology system, a new error-compensation model is proposed to further improve the accuracy. This method has great significance for designing ultraprecision 3D systems and error compensation.

Keywords: Abbe principle, Geometric error, 3D metrology system, Error analysis