Ray tracing through gradient-index media: recent improvements

Sead Dorić

doi:10.1364/AO.29.004026

Applied Optics
Vol. 29,
Issue 28,
pp. 4026-4029
(1990)
•https://doi.org/10.1364/AO.29.004026

Ray tracing through gradient-index media: recent improvements

Sead Dorić

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Sead Dorić, "Ray tracing through gradient-index media: recent improvements," Appl. Opt. 29, 4026-4029 (1990)

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Abstract

A general ray tracing algorithm for gradient-index media that treats various refractive index distributions in a unified manner has been developed by implementing the concept of isoindicial surfaces, position variables, and cubic splines. A novel and simpler algorithm for optical path length calculations is also presented.

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Name of distribution	Shape of isoindicial surfaces	Position variable	$\frac{\partial p}{\partial x}$	$\frac{\partial p}{\partial y}$	$\frac{\partial p}{\partial z}$	Paraxial value of position variable
Plane	Parallel plane	p=z	0	0	1	z
Cylindrical	Coaxial cylinders	p²=x² + y²	x/p	y/p	0	0
Spherical	Concentric spheres	p²=x²+y²+z²	x/p	y/p	z/p	\|z\|
Spheroidal	Coaxial concentric spheroids	p²=x² + y² + (z/z₀)²	x/p	y/p	z/p	\|z/z₀\|
Ellipsoidala	Triaxial ellipsoids	$p^{2} = {(\frac{x}{x_{0}})}^{2} + {(\frac{y}{y_{0}})}^{2} + {(\frac{z}{z_{0}})}^{2}$	x/(x₀p)	y/(y₀p)	z/(z₀p)	\|z/z₀\|
Paraboloidalb	Coaxial equivalent paraboloids	p=z − c(x² + y²)/2	−cx	−cy	1	z
Conicalc	Coaxial cones with a common vertex	$p^{2} = \frac{x^{2} + y^{2}}{{(1 - z / 1)}^{2}}$	$\frac{x}{p {(1 - z / 1)}^{2}}$	$\frac{y}{p (1 - z / 1)}$	$\frac{p}{1 - z}$	0

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Applied Optics