A Method Of Three-dimensional Angle Errors Measurement Based On Non-diffracting Beams And Moire Fringes

With the development of modern industry,the requirement of the motion accuracy of components is increasing,measuring the motion errors(including straightness error and angle error)of the working stage plays an important role in ensuring processing precision.Non-diffracting beam(NDB)has the features of great concentration in central spot,and constant intensity distribution of central spot in transmission process.Combined with moire fringe technique for its high sensitivity to small displacement,a method of three-dimensional angle error measurement is put forward.The main research contents are as follows:Firstly,based on the theory of NDB and its interference theory,the formation mechanism and characteristics of moire fringes are analyzed.According to the Fresnel diffraction formula,the diffraction intensity of an axicon is obtained,combined with interference theory,mathematical model of moire fringes of two NDBs is derived,the relationship of the number of moire fringes and the distance between spots center is given.Comparing with moire fringe of common circular grating,it is verified that the moire fringe of NDB can accurately detect small displacement error.Secondly,the measuring light path is designed,the error measurement formula is also deduced using space vector algorithm.Two CCDs are adopted in the measurement for comparison,for the NDB patterns of different CCDs,the variation of centre positions of whom are substituted into calculation to figure out three-dimensional angle errors(pitch,yaw,roll),ZMAX software is used for numerical simulation,simulated results agree well with theoretical results,which confirms the rationality of the theoretical model.Thirdly,in consideration of the characteristics of the moire fringe pattern,the corresponding image processing algorithm is designed to extract information of the moire fringe.By image enhancement,image contrast is progressed,and low-pass filtering is also applied to eliminate high frequency components and noise of the image.Substantially,clear contour of moire fringes can be obtained by binarization and smoothing process,then transform the image to polar coordinate,the number of moire fringes can be counted by multiple interval scanning method from the gray value alternation of moire fringe image in a circle.Finally,the verification experiment is carried out,the final results are calculated by the error measurement formula and the image processing algorithm,the measurement error is not more than 0.05 degrees in the range of 1 degree,which show that the proposed method can accurately measure the three-dimensional angle error.