Abstract

By introducing a transformed pupil vector into the aberration expansions of an axially symmetric optical system, the aberration coefficients through third order of a pupil decentered off-axis optical system are obtained. Nodal aberration characteristics are revealed only by means of the pupil decentration vector and the aberration coefficients of the axially symmetric system, which shows great convenience since parameters of individual surface such as radius of curvature, decenter as well as the shifted center of the aberration field are not used in the analysis.

©2012 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry

Kevin Thompson
J. Opt. Soc. Am. A 22(7) 1389-1401 (2005)

Interaction of pupil offset and fifth-order nodal aberration field properties in rotationally symmetric telescopes

Haili Hu, Jianjun Liu, and Zhigang Fan
Opt. Express 21(15) 17986-17998 (2013)

Polarization aberrations. 2. Tilted and decentered optical systems

James P. McGuire and Russell A. Chipman
Appl. Opt. 33(22) 5101-5107 (1994)

More Recommended Articles

References

  • View by:
  • Article Order
  • |
  • Year
  • |
  • Author
  • |
  • Publication
  1. R. V. Shack, “Aberration theory, OPTI 514 course notes,” College of Optical Sciences, University of Arizona, Tucson, Arizona.
  2. K. P. Thompson, “Aberration fields in tilted and decentered optical systems,” Ph.D. dissertation (University of Arizona, Tucson, Arizona, 1980).
  3. K. P. Thompson, “Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry,” J. Opt. Soc. Am. A 22(7), 1389–1401 (2005).
    [Crossref] [PubMed]
  4. R. A. Buchroeder, “Tilted component optical systems,” Ph.D. dissertation (University of Arizona, Tucson, Arizona, 1976).
  5. H. H. Hopkins, The Wave Theory of Aberrations (Oxford on Clarendon Press, 1950).
  6. L. B. Moore, A. M. Hvisc, and J. Sasian, “Aberration fields of a combination of plane symmetric systems,” Opt. Express 16(20), 15655–15670 (2008).
    [Crossref] [PubMed]

2008 (1)

2005 (1)

Hvisc, A. M.

Moore, L. B.

Sasian, J.

Thompson, K. P.

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Other (4)

R. V. Shack, “Aberration theory, OPTI 514 course notes,” College of Optical Sciences, University of Arizona, Tucson, Arizona.

K. P. Thompson, “Aberration fields in tilted and decentered optical systems,” Ph.D. dissertation (University of Arizona, Tucson, Arizona, 1980).

R. A. Buchroeder, “Tilted component optical systems,” Ph.D. dissertation (University of Arizona, Tucson, Arizona, 1976).

H. H. Hopkins, The Wave Theory of Aberrations (Oxford on Clarendon Press, 1950).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1 Pupil vector relation before and after pupil decentration.

Download Full Size | PPT Slide | PDF

Fig. 2
Fig. 2 The nodal characteristic of coma field for a pupil decentered optical system: the node lies on the line along the vector direction of pupil decentration.

Download Full Size | PPT Slide | PDF

Fig. 3
Fig. 3 Full field display of a pupil decentered system for third-order coma.

Download Full Size | PPT Slide | PDF

Fig. 4
Fig. 4 Locations of the two nodal points of astigmatism field in a pupil decentered optical system. (a) On the line along the direction of pupil decentration vector. (b) Symmetric about the pupil vector direction line.

Download Full Size | PPT Slide | PDF

Fig. 5
Fig. 5 Full field maps of two pupil decentered systems which correspond to the two different nodal positions as shown in Fig. 4 (a) and (b).

Download Full Size | PPT Slide | PDF

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

W j = ∑ p ∞ ∑ n ∞ ∑ m ∞ ( W klm ) j ( H → ⋅ H → ) p ( ρ → ⋅ ρ → ) n ( H → ⋅ ρ → ) m   , k=2p+m,    l=2n+m ,
ρ → ′ = ρ → + s →  ,
W j = ∑ p ∞ ∑ n ∞ ∑ m ∞ ( W klm ) j ( H → ⋅ H → ) p [ ( ρ → + s → )⋅( ρ → + s → ) ] n [ H → ⋅( ρ → + s → ) ] m   .
W= ∑ j W j   .
W= ∑ j W 020j ( ρ → + s → )⋅( ρ → + s → )+ ∑ j W 111j H → ⋅( ρ → + s → )+ ∑ j W 040j [ ( ρ → + s → )⋅( ρ → + s → ) ] 2                   + ∑ j W 131j [ H → ⋅( ρ → + s → ) ] [ ( ρ → + s → )⋅( ρ → + s → ) ]+ 1 2 ∑ j W 222j [ H → 2 ⋅ ( ρ → + s → ) 2 ]                   + ∑ j W 220 M j ( H → ⋅ H → ) [ ( ρ → + s → )⋅( ρ → + s → ) ]+ ∑ j W 311j ( H → ⋅ H → )[ H → ⋅( ρ → + s → ) ]  ,
W 220 M = W 220 + 1 2 W 222  .
W= W 020 ( ρ → ⋅ ρ → )+2 W 020 ( ρ → ⋅ s → )+ W 020 s 2                   + W 111 ( H → ⋅ ρ → )+ W 111 ( H → ⋅ s → )                   +[ W 040 ( ρ → ⋅ ρ → ) 2 + W 040 s 4 +2 W 040 s → 2 ⋅ ρ → 2 +4 W 040 s 2 ( ρ → ⋅ ρ → )   +4 W 040 ( s → ⋅ ρ → )( ρ → ⋅ ρ → )+4 W 040 s 2 ( s → ⋅ ρ → ) ]                  +[ W 131 ( H → ⋅ ρ → )( ρ → ⋅ ρ → )+2 W 131 s 2 ( H → ⋅ ρ → )+ W 131 ( s → H → ⋅ ρ → 2 ) +2 W 131 ( s → ⋅ H → )( ρ → ⋅ ρ → )+ W 131 s 2 ( s → ⋅ H → )+ W 131 ( s → 2 H → ∗ ⋅ ρ → ) ]                  + 1 2 W 222 ( H → 2 ⋅ ρ → 2 )+ 1 2 W 222 ( H → 2 ⋅ s → 2 )+ W 222 ( H → 2 s → ∗ ⋅ ρ → )                  + W 220 M ( H → ⋅ H → )( ρ → ⋅ ρ → )+ W 220 M s 2 ( H → ⋅ H → )+2 W 220 M ( H → ⋅ H → )( s → ⋅ ρ → )                  + W 311 ( H → ⋅ H → )( H → ⋅ ρ → )+ W 311 ( H → ⋅ H → )( H → ⋅ s → ) ,
W= W 040 ( ρ → ⋅ ρ → ) 2                  +( 4 W 040 s → + W 131 H → )⋅ ρ → ( ρ → ⋅ ρ → )                    +( 1 2 W 222 H → 2 + W 131 s → H → +2 W 040 s → 2 )⋅ ρ → 2                  +[ W 220 M ( H → ⋅ H → )+2 W 131 ( s → ⋅ H → )+( W 020 +4 W 040 s 2    )  ]( ρ → ⋅ ρ → )                  +[ 2 W 020 s →  + W 111 H → +4 W 040 s 2 s → +2 W 131 s 2 H →   + W 131 s → 2 H → ∗    + W 222 H → 2 s → ∗ +2 W 220 M ( H → ⋅ H → ) s → + W 311 ( H → ⋅ H → ) H → ]⋅ ρ →                 +    [ W 020 s 2 + W 111 ( H → ⋅ s → )+ W 040 s 4      + W 131 s 2 ( s → ⋅ H → ) + 1 2 W 222 ( H → 2 ⋅ s → 2   )+ W 220 M s 2 ( H → ⋅ H → )+ W 311 ( H → ⋅ H → )( H → ⋅ s → ) ] .
W=( 4 W 040 s → + W 131 H → )⋅ ρ → ( ρ → ⋅ ρ → )  .
W= W 131 ( H → + 4 W 040 W 131 s → )⋅ ρ → ( ρ → ⋅ ρ → ) .
a → c ≡− 4 W 040 W 131 s →  ,
W= W 131 ( H → − a → c )⋅ ρ → ( ρ → ⋅ ρ → ) .
W=( 1 2 W 222 H → 2 + W 131 s → H → +2 W 040 s → 2 )⋅ ρ → 2  .
W = 1 2 W 222 ( H → 2 + 2 W 131 s → W 222 H → + 4 W 040 s → 2 W 222 )⋅ ρ → 2          = 1 2 W 222 [ ( H → + W 131 s → W 222 ) 2 − ( W 131 2 −4 W 040 W 222 ) s → 2 W 222 2 ]⋅ ρ → 2  .
a → a ≡− W 131 s → W 222  ,
b → a ≡ W 131 2 −4 W 040 W 222 W 222 2 s →  ,
W=     1 2 W 222 [ ( H → − a → a ) 2 − b → a 2 ]⋅ ρ → 2  .
H → = a → a ± b → a  .
W=[ W 220 M ( H → ⋅ H → )+2 W 131 ( s → ⋅ H → )+( W 020 +4 W 040 s 2    )  ]( ρ → ⋅ ρ → )           = W 220 M [ ( H → ⋅ H → )+ 2 W 131 W 220 M ( s → ⋅ H → )+ ( W 020 +4 W 040 s 2    ) W 220 M   ]( ρ → ⋅ ρ → )            = W 220 M [ ( H → + W 131 W 220 M s → )⋅( H → + W 131 W 220 M s → )+ W 020 W 220 M +4 W 040 W 220 M s 2 − W 131 2 s 2 W 220 M 2   ]( ρ → ⋅ ρ → ) .
W=[ 2 W 020 s →  + W 011 H → +4 W 040 s 2 s → +2 W 131 s 2 H →   + W 131 s → 2 H → ∗    + W 222 H → 2 s → ∗ +2 W 220 M ( H → ⋅ H → ) s → + W 311 ( H → ⋅ H → ) H → ]⋅ ρ →  .

Metrics