Analysis of Refractive Index Distributions in Cylindrical, Graded-Index Glass Rods (GRIN Rods) Used as Image Relays

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.