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Area of Science:

Optical physics
Geometrical optics
Materials science

Background:

Graded index (GRIN) rods, like SELFOC rods, are used in optics.
These rods have a refractive index that changes with radial distance.
Applications include coherent light propagation and imaging.

Purpose of the Study:

To perform a geometrical optical study of GRIN systems for unit magnification image relay.
To analyze image aberrations in GRIN rods, considering both meridional and skew rays.
To identify optimal refractive index distributions for improved imaging performance.

Main Methods:

Geometrical optical analysis.
Derivation of an "ideal" index distribution for helical skew rays.
Ray tracing simulations for various index profiles and rod geometries.

Main Results:

Previously studied index distributions yield significant aberrations with skew rays.
An index distribution ideal for helical skew rays was derived.
No single refractive index profile is ideal for both meridional and skew rays.
Image resolution is limited, approximately 1000 spots per field.
Optimal index distribution is dependent on rod geometry (length-to-radius ratio) and relative aperture.

Conclusions:

Image relay using GRIN rods is limited by aberrations, particularly from skew rays.
The ideal refractive index profile is a compromise between meridional and helical ray requirements.
Performance optimization requires careful consideration of rod dimensions and optical parameters.