基于Boltzmann函数刃边拟合的光栅成像系统点扩展函数模型  

Point Spread Function Model of Grating Imaging System Based on Boltzmann Function Edge Fitting

作　　者：卢泉[1] 张泽昊 张卫平[2] 刘诣荣 Lu Quan;Zhang Zehao;Zhang Weiping;Liu Yirong(School of Electrical Engineering,Guangxi University,Nanning,Guangxi 530004,China;School of Physical Science and Technology,Guangxi University,Nanning,Guangxi 530004,China)

机构地区：[1]广西大学电气工程学院,广西南宁530004 [2]广西大学物理科学与工程技术学院,广西南宁530004

出　　处：《光学学报》2020年第14期26-33,共8页Acta Optica Sinica

基　　金：国家自然科学基金(61167001)。

摘　　要：为了提高平面光栅成像系统的点扩展函数(PSF)提取准确度,构建PSF模型,提出一种基于Boltzmann函数的刃边函数拟合方法。构建以入射角为自变量的双曲线型变化PSF模型,揭示了光栅成像系统PSF的分布规律。最后,采用Lucy-Richardson算法对不同模糊程度的图像进行复原,并对复原后的图像进行质量评价,其中灰度平均梯度(GMG)提升均在60.2%以上,结构相似度(SSIM)提升均在66.5%以上。对比不同拟合方法的复原效果,结果表明,所提方法在对像差较大的图像进行复原时,效果明显优于其他同类方法,建立的PSF模型也可以准确地表现光栅成像系统的特性。To improve the accuracy of the point spread function(PSF)extraction of planar grating imaging systems and develop PSF models,a fitting method of edge spread function based on the Boltzmann function is proposed.A hyperbolic PSF model with the incident angle as the independent variable is constructed,and then the PSF distribution rules of the grating imaging systems are obtained.Finally,the Lucy-Richardson algorithm is employed to restore images with different degrees of blur,and the quality of the restored images is evaluated.A grayscale mean gradient(GMG)improvement of above 60.2%and structural similarity(SSIM)improvement of above 66.5%are obtained.In a comparison with the restoration effects of different fitting methods,the proposed method shows better image restoration for large aberrations than other similar methods.The developed PSF model can also accurately represent the characteristics of grating imaging systems.

关 键 词：光栅 光栅成像 刃边函数拟合 Boltzmann函数 点扩展函数模型 图像复原 

分 类 号：O439[机械工程—光学工程]