Seidel aberration coefficients for radial gradient -index lenses

Short and accurate analytic formulas for the Seidel coefficients of gradient-index lenses with arbitrary radial refractive-index distributions have been obtained. Starting from analytic ray-tracing formulas, we have developed a technique for decomposing the two components of the transverse aberration of an arbitrary skew ray in surface and inhomogeneous transfer contributions and a technique for shortening the large expressions for the third-order terms resulting from the transfer contributions. Unlike previously known derivation methods, our method delivers simple algebraic expressions for '111 Seidel coefficients.