Binoculars flat part of the former facing the eye) and the field lens is a double-convex singlet. A reversed Kellner eyepiece was developed in 1975 and in it the field lens is a double concave/ double convex achromatic doublet and the eye lens is a double convex singlet. The reverse Kellner provides 50% more eye relief and works better with small focal ratios as well as having a slightly wider field. Wide field binoculars typically utilize some kind of Erfle configuration, patented in 1921. These have five or six elements in three groups. The groups may be two achromatic doublets with
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