PARAXIAL-OPTICS FORMULAS FOR SYSTEMS CONTAINING GRADIENT-INDEX ELEMENTS

This paper considers the ray path in media with a radial refractive-in dex distribution in the paraxial approximation. Formulas are derived f or calculating the path of the zeroth ray through a complex system con sisting of gradient-index media divided by spheres. Expressions are de rived for the Abbe and Lagrange-Helmholtz invariants as applied to the given case. It is shown that the Lagrange-Helmholtz invariant does no t change its form in going to radial gradient-index media. Formulas ar e presented for calculating the principal quantities for a single grad ient-index lens in air.