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

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References

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  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).

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Figures (5)

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

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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.

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

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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.

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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).

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Equations (20)

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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 →  .

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