An Heuristic Solution for the Arbitrary Index Distribution and Ray-Trajectory-Angular-Frequency Aberration Linkage

Abstract

The applied gradient index optics is 25 years old today. And almost all the time the long-thin-GRIN-rod-lenses with good imaging capability being the most dramatic examples of GRIN systems were a challenge for fabrication, investigation and actual design. It is well known that the ion-exchange diffusion technology yields the best results in achieving smooth, controllable and reproducible refractive index distributions. But even in that case we can not avoid some discrepancies of actual index distributions from the ideal or prescribed ones. For actual design these discrepancies are to be accurately measured and characterized, and it must be pointed out, that for the low numerical aperture GRIN rod lenses with the index difference of about 0.003 we are dealing with discrepancies of the order of 0.00005 in marginal areas of the rod and even less in the main paraxial area.