Abstract

In a recent paper [J. Opt. Soc. Am. A 21, 832 (2004)], aberration functions that are a complete, orthogonal, and normalized set over a weighted spherical pupil were developed. The results apply to electromagnetic, aplanatic, or paraboloidal mirror systems. An equation in this paper is corrected. Further work has led to a general aberration function that is also presented.

© 2004 Optical Society of America

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References

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  1. C. J. R. Sheppard, “Orthogonal aberration functions for high-aperture optical systems,” J. Opt. Soc. Am. A 21, 832–838 (2004).
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Equations (14)

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F 0 F 1 F 2 F 3 0 G 1 G 2 G 3 0 0 H 2 H 3 0 0 0   b 0 b 1 b n = const . × 0 0 0 1 ,
Φ nm = A nm ( b n c n + b n - 1 c n - 1 + + b 0 ) ( 1 - c 2 ) m sin   m ϕ .
A nm 2 = f 0 b n 2 F 2 n + 2 b n b n - 1 F 2 n - 1 + + b 0 2 F 0 ,
= 1 , m = 0 ,
= 2 , m 0 .
Φ nm = A pm 1 c c 2 c n F 0 m F m 1 F 2 m F nm F 1 m F 2 m F n - 1 , m F 2 n - 1 , m .
Φ 0 m = A 0 m sin m   θ   sin   m ϕ ,
A 0 m 2 = f 0 F 0 m .
Φ 1 m = A 1 m ( F 0 m cos   θ - F 1 m ) sin m   θ   sin   m ϕ ,
A 1 m 2 = f 0 F 0 m G 1 m .
Φ 2 m = A 2 m [ G 1 m cos 2   θ - G 2 m cos   θ + ( F 1 m F 3 m - F 2 m 2 ) ] sin m   θ   sin   m ϕ ,
A 2 m 2 = f 0 G 1 m H 2 m .
Φ 3 m = A 3 m H 2 m cos 3   θ - H 3 m cos 2   θ + F 0 m F 1 m F 2 m F 1 m F 2 m F 3 m F 2 m F 3 m F 4 m cos   θ - F 1 m F 2 m F 3 m F 2 m F 3 m F 4 m F 3 m F 4 m F 5 m sin m   θ   sin   m ϕ ,
A 3 m 2 = f 0 H 2 m J 3 m ,

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