Double-Gauss lens objective lens by adding a meniscus lens to its single convex and concave lens design. Alvan Clark and Bausch & Lomb further refined the design in 1888 by taking two of these lenses and placing them back to back making a "double Gauss" with indifferent photographic results. Current double Gauss lenses can be traced back to an 1895 improved design, when Paul Rudolph of Carl Zeiss Jena thickened the interior negative menisci and converted to them to cemented doublets of two elements of equal refraction but differing dispersion in the "Zeiss Planar" of 1896 to correct for chromatic aberration. It
Luneburg lens one side, and formula_14 only on the other: The parameter formula_19 is a constant for any given ray, but differs between rays passing at different distances from the centre of the lens. For rays passing through the centre, it is zero. In some special cases, such as for Maxwell's fish-eye, this first order equation can be further integrated to give a formula for formula_14 as a function or formula_13. In general it provides the relative rates of change of formula_14 and formula_13, which may be integrated numerically to follow the path of the ray through the lens. Luneburg lens A