Michael E. Harrigan

Some first-order properties of radial gradient lenses compared to homogeneous lenses

A radial gradient rod is shown to be paraxially equivalent to three air-spaced thin lenses. Formulas for calculating the powers and spacings are given, and some ray traces are compared. The effective aperture stop and entrance pupil are derived.

The Y−Ӯ diagram for radial gradient systems

The properties of the Y-? diagram as applied to radial gradient lens systems are developed. It is shown that the diagram consists of elliptical arcs, which are circular arcs for certain conditions. The effects of pupil and object shifts are discussed as well as the effects of scaling the pupil size. It is shown how the constructional parameters of the system are read from the diagram. Finally, for the purpose of design, it is shown how one may obtain the Y-? diagram of a system which satisfies a certain set of design constraints.

Use of the Y−Ӯ diagram in GRIN rod design

The Y-? diagram of Delano is applied to the design of gradient-index rods and is used to explain GRIN rod vignetting. Several detailed design examples are given which show how to use the diagram for GRIN rods. The Y-? diagram is a particularly useful tool to explore potential solutions involving diameter constraints and equips one with a rapid nonalgebraic investigation method.