中文摘要：

基于衍射光栅完全电导率积分理论,通过变换光栅方程给出了任意衍射级次Littrow设置下衍射波矢的镜像方程,用此方程和幂级数性质简化了代表核函数的无穷级数,提出将其表示为一个对称性级数与一个等比级数之和的方法.通过与未做简化的积分法比较,从数值计算角度指出了此方法具有缩短计算时间和提高收敛性的特性.推广结果表明,在偏Litrrow设置下仍然可以通过幂级数性质提高收敛性.

英文摘要：

On the base of perfect conductivity integral theory of diffraction gratings,after transforming the grating equation,the image equation of diffraction wave vector in Littrow mounting is given. Using the equation and in view of the power function property,the infinite series,which represents the kernel function,is transformed into the sum of a symmetrical series and a geometrical series. Compared with the primary integral method,from the view of numerical calculation,the new kernel function can reduce the computing time and improve the convergence. The extension results show that the power function character can improve convergence in the deviated Littrow mounting.