Tracing rays through graded-index media: a new method

Anurag Sharma; D. Vizia Kumar; A. K. Ghatak

doi:10.1364/AO.21.000984

Applied Optics
Vol. 21,
Issue 6,
pp. 984-987
(1982)
•https://doi.org/10.1364/AO.21.000984

Tracing rays through graded-index media: a new method

Anurag Sharma, D. Vizia Kumar, and A. K. Ghatak

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Anurag Sharma, D. Vizia Kumar, and A. K. Ghatak, "Tracing rays through graded-index media: a new method," Appl. Opt. 21, 984-987 (1982)

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Abstract

A new method for tracing rays through graded-index media is presented. The method essentially consists of transforming the ray equation into a convenient form and solving the resulting equation using a standard numerical technique. A detailed comparison of this method with existing methods has also been made, and it is shown that for obtaining a desired accuracy this method requires much less computational effort.

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Equations (20)

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Δt	Fractional error at z = 1
0.05	6 × 10⁻¹⁰
0.10	8 × 10⁻⁹
0.20	1 × 10⁻⁷
0.25	4 × 10⁻⁶

f/No.	f/6.3
Focal length	10
Thickness	0.45
Curvature of front surface	0.36
Curvature of back surface	0.184623
Maximum field angle	25.5°
Distance of entrance pupil from first surface	3.65

Aberration	Singlet with N₂ = 0.0	Singlet with N₂ = 0.0042
Spherical aberration	0.249	0.138
Meridional coma	0.029	0.138
Astigmatism	−0.199	0.150
Petzval curvature	−1.409	−0.550
Distortion	6.1%	5.8%

Lens radius	1
Thickness	0.5
Gradient index	N₀ = 1.5
	N₁ = −0.05
	N₂ = 4.036 × 10⁻⁵
Focal length	20.0557
Back focus	19.8888
Aperture	f/10
Maximum field angle	14°
Distance of entrance pupil from the first surface	−8.031

Aberration	Third-order	Total
Spherical aberration	0.0	0.00034
Meridional coma	0.022	0.0185
Astigmatism	0.0	0.2273
Petzval curvature	−0.523	−0.5607
Distortion	0.6%	0.52%

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Applied Optics