IMPROVEMENTS IN THE COMPUTATION OF REFRACTIVE-INDEX PROFILES FOR THE GENERALIZED LUNEBURG LENS

The generalized Luneburg lens problem has been reexamined with the aim of optimizing the methods for computing the Luneburg integral, which determines the refractive-index distribution of spherically symmetric inhomogeneous lenses. As a result, substantial modifications have been introduced into the already known series representation of this integral, and a novel series solution has been derived that is rapidly converging for short focal distances. Both representations are provided with simple formulas for quick estimation of the truncation error. Additionally, two approximate solutions to the Luneburg integral are proposed, which, at a minimum time expense, offer a computation accuracy of better than 10(-7), independently of the magnitude of the focal length involved.