Theory of fifth-order aberration of graded-index media*

In the present paper we have given the theory of the fifth-order aberrations of rotationally symmetric optical systems. Explicit formulas have been derived for the aberrations of an inhomogeneous medium. We have used these formulas to make an explicit evaluation of the variation of aberrations of meridional and skew rays with the angle of injection of the ray with the z axis. The results have been compared with those obtained by numerically solving the ray equation. We have also shown that for the values of parameters found in experimentally prepared graded-index media the fifth-order contribution is significant and must be taken into consideration while calculating the image patterns formed by these media.