Research On Astigmatism Law And Correction Method Of Plane Equal Periodic Grating Virtual Image

Grating is an important and widely used optical element,in addition to the effects of dispersion and spectral separation,it also has the function of selfimaging and imaging of general objects.However,astigmatism problems generally exist in planar grating imaging systems,which seriously affect the imaging quality.In general,the virtual image formed by a plane isoperimetric grating on an object has astigmatism,and the astigmatism can be eliminated only when its diffracted light is at the minimum deflection angle.This article will study and solve the common basic problem of this type of grating imaging systemastigmatism from the perspective of digital image processing.First,in this paper,the imaging principle of grating imaging system and several kinds of aberrations in optical system are analyzed.On this basis,the degradation model is studied,and an image restoration method based on image processing is proposed,that is,image convolution restoration is used to achieve astigmatism.Compared with traditional optical systems that achieve astigmatism elimination through optical design,image restoration has a unique advantage.In addition,this paper also analyzes the commonly used point spread function(PSF)extraction methods,and uses the edge method to extract the PSF.Secondly,this paper focuses on the optimization of edge fitting function and the construction of point diffusion function model of grating imaging system.Two improvement methods are proposed for the edge-fitting problem: First,for images with large astigmatism,the traditional edge-fitting function cannot be fitted effectively,and a method of edge-fitting based on Boltzmann function is proposed to improve the edge-fitting accuracy,thereby improving the accuracy of subsequent PSF extraction;Second,for the selection of initial parameters for fitting,a large number of experiments were carried out to determine the appropriate initial parameters to improve the efficiency of the fitting,and finally the PSF model of the grating imaging system was given,and the double angle of incidence was constructed as the independent variable The curvilinear PSF model reveals the spatial distribution of the PSF of the grating imaging system.Finally,in this paper,the Lucy-Richardson algorithm is used for image restoration.The experimental results show that after using this method to restore raster images with different degrees of astigmatism,for some images with small astigmatism,the Grayscale Mean Gradient(GMG)improvement is above 22%,and the Structural Similarity(SSIM)improvement is above 72%;For some pictures,the GMG improvement is above 60.2%,and the SSIM improvement is above 66.5%.At the same time,comparing the restoration effects of different fitting functions,this method is significantly better than similar methods for images with large astigmatism,the established PSF model is also conducive to the understanding of the characteristics of grating imaging system,provides a new method and approach for the image restoration of this type of imaging system,and lays a theoretical foundation for the study of grating astigmatic problem and provides a solution.