网格基任向偏导实现及层析应用  

A New Technique to Calculate Partial Derivative in Random Direction on Micro-grid Frame Being Applied to Tomography

作　　者：宋一中[1,2] 赵志敏[1] 

机构地区：[1]南京航空航天大学理学院,南京210016 [2]德州学院物理系,山东德州253000

出　　处：《光子学报》2008年第11期2231-2233,共3页Acta Photonica Sinica

基　　金：国家自然科学基金(60678031);中国博士后科学基金(20060400930);江苏省博士后基金(0602040B)资助

摘　　要：将光线偏折方程中的任向偏导转化为数值差分形式,并应用于层析线性运算.网格化待测场,将微分待测场的每一正方形网格及相应折射率近似为曲面底的正圆锥体,圆锥体顶端的折射率值对应该网格的折射率,在底面的投影对应网格的中心.假设紧邻三网格中心间的折射率分布共平面,在一个网格宽度内将偏导转化成数值差分形式.结果发现:基于上述近似和假设,可以将任意探测光线相关的偏导转化为数值差分形式,将非线性偏导方程转化为线性差分方程,建立层析方程.于是,偏折角可以作为投影直接重建.The random-direction partial derivatives in refraction equation were transformed into numerical differences in reference frames for tomography, and the nonlinear refraction equations were transformed into linear reconstructive equations. The diagnosed field was divided into tiny foursquare grids. Each grid and its relative refractive index were approximated to a correct cone with an irregular bottom. The peak of the cone corresponded to the refractive index of the grid, and its geometrical projection to the bottom located the grid center. With the approximation, the space partial increment calculation was much simplified at any grid, in any direction, and to any detecting ray. It was assumed that the refractive index distribution should be coplanar in the zone between three grid centers of the three close-adjacent grids. Here,the zone was a space triangle deriving from connecting the close-adjacent grid centers with straight lines. With the assumption,the refractive index partial increment could be calculated with a numerical difference function of close-adjacent grid refractive indexes. With the approximation and assumption,the partial derivative was transformed into numerical difference in a grid width. And based on the approximation and assumption, partial derivative related to any detecting ray could be transformed into numerical difference. Nonlinear refraction equations could be transformed into linear reconstructive equations. The deflection angles can be applied to reconstruction.directly as projections.

关 键 词：层析 折射率 投影 偏导 差分 

分 类 号：O241[理学—计算数学]