Rawson E G, Herriott D R, McKenna J
Appl Opt. 1970 Mar 1;9(3):753-9. doi: 10.1364/AO.9.000753.
Cylindrical transparent media whose refractive index decreases with increasing cylinder radius have been investigated in connection with coherent light propagation in gas waveguides. Recently, graded index glass rods (trade named SELFOC rods) have been used as imaging devices. We report here on a geometrical optical study of graded index systems used for relaying images at unit magnification. We have found that two index distributions previously studied result in large image aberrations when the presence of skew rays is taken into account. We have derived an index distribution which is "ideal" for helical skew rays. Using ray tracing methods we have examined image aberrations for various index distributions and for various rod geometries. We find that (1) no one refractive index distribution can be "ideal" for both meridional and skew rays, (2) image resolution is generally low, reaching about 1000 spots per field, and (3) the optimal index distribution varies with the ratio of rod length to radius and the relative aperture and is intermediate between the helically ideal and the meridionally ideal distributions.
折射率随圆柱半径增加而减小的圆柱形透明介质已结合气体波导中的相干光传播进行了研究。最近，渐变折射率玻璃棒（商品名为自聚焦棒）已被用作成像装置。我们在此报告对用于以单位放大率中继图像的渐变折射率系统的几何光学研究。我们发现，当考虑到斜光线的存在时，先前研究的两种折射率分布会导致较大的像差。我们推导了一种对螺旋斜光线“理想”的折射率分布。使用光线追迹方法，我们研究了各种折射率分布和各种棒几何形状的像差。我们发现：（1）没有一种折射率分布对子午光线和斜光线都是“理想”的；（2）图像分辨率通常较低，每场约达到1000个光斑；（3）最佳折射率分布随棒长与半径之比以及相对孔径而变化，且介于螺旋理想分布和子午理想分布之间。
