Catadioptric system with a gradient-index corrector plate

Duncan T. Moore

doi:10.1364/JOSA.67.001143

Catadioptric system with a gradient-index corrector plate

Duncan T. Moore

Journal of the Optical Society of America
Vol. 67,
Issue 9,
pp. 1143-1146
(1977)
•https://doi.org/10.1364/JOSA.67.001143

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Duncan T. Moore, "Catadioptric system with a gradient-index corrector plate," J. Opt. Soc. Am. 67, 1143-1146 (1977)

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History
- Original Manuscript: February 21, 1977
- Published: September 1, 1977

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Abstract

Sands showed the equivalence of the third-order aspheric surface contribution of the aberration polynomial to the third-order inhomogenous surface contribution. This fact is exemplified by the substitution of an axial gradient for the aspheric surface of the Schmidt corrector plate. It is shown that a gradient-index corrector plate system is limited in its off-axis performance by fifth-order oblique spherical aberration just as the conventional Schmidt system is.

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Equations (22)

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Relative aperture of neutral zone	0	0. 707	0. 866
Fourth–order aspheric coefficient	$\frac{1}{16 f^{3}}$	$\frac{1}{16 f^{3}}$	$\frac{1}{16 f^{3}}$
Curvature of surface	$\frac{- 1}{64 f f #^{2}}$	$\frac{- 2}{64 f f #^{2}}$	$\frac{- 3}{64 f f #^{2}}$
Transverse axial chromatic	$\frac{f}{2049 f #^{3}}$	$\frac{f}{4096 f #^{3}}$	$\frac{f}{8192 f #^{3}}$

	Ordinary surface contribution	Inhomogeneous surface contribution	Transfer contribution
Plate	−0. 000 012	+ 0. 015 006	0. 000 000
Primary	−0. 014 832	0. 0	0. 0
Total σ₁ = + 0. 000 168

N₀₁	N₀₂	First curvature	Second curvature	Spot radius (μm)
0. 0	0. 051055	0. 007474	0. 006907	4
−0. 01	0. 047119	0. 007543	0. 007123	4
−0. 02	0. 045695	0. 007484	0. 007197	4
−0. 03	0. 044550	0. 007438	0. 007283	4
−0. 04	0. 043666	0. 007405	0. 007380	3
−0. 05	0. 043031	0. 007382	0. 007490	2
0. 01	0. 050928	0. 007697	0. 007007	6
0. 05	0. 064139	0. 008135	0. 006855	10
N₀₃	N₀₂

−0. 005	0. 056769	0. 007686	0. 007002	4
0. 0	0. 051055	0. 007474	0. 006907	0
−0. 005	0. 046471	0. 007222	0. 006670	4
N₀₄	N₀₂

−0. 001	0. 052588	0. 007540	0. 006963	8
−0. 0005	0. 051811	0. 007568	0. 006936	5
+ 0. 0005	0. 050320	0. 007440	0. 006878	2
+ 0. 001	0. 049608	0. 007405	0. 006848	3

Relative aperture of neutral zone	0	0. 707	0. 866
Fourth–order aspheric coefficient	$\frac{1}{16 f^{3}}$	$\frac{1}{16 f^{3}}$	$\frac{1}{16 f^{3}}$
Curvature of surface	$\frac{- 1}{64 f f #^{2}}$	$\frac{- 2}{64 f f #^{2}}$	$\frac{- 3}{64 f f #^{2}}$
Transverse axial chromatic	$\frac{f}{2049 f #^{3}}$	$\frac{f}{4096 f #^{3}}$	$\frac{f}{8192 f #^{3}}$

	Ordinary surface contribution	Inhomogeneous surface contribution	Transfer contribution
Plate	−0. 000 012	+ 0. 015 006	0. 000 000
Primary	−0. 014 832	0. 0	0. 0
Total σ₁ = + 0. 000 168

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