Buchdahl dispersion model for gradient index glass families

Optical elements which are made out of macro gradient refractive material are represented by lines, as opposed to points, on the glass map (n d Vs. v d diagram). Thus, optical designers need account for gradient dispersion as well as gradient index. A dispersion model for the material must be readily available and optical design programs must be capable of defining and maintaining this relationship before and during optimization, simplifying user input and confining the material to walk a well defined path on the glass map. Thinking in terms of lines on the glass map for arbitrary glass families yields a simple dispersion model based on least squares fitting of Buchdahl coefficients. This paper introduces the concept of glass lines and outlines a technique to construct a dispersion model for any contiguous family of gradient refractive material.