Abstract

We define a new class of aberration, skew aberration, which is a component of polarization aberration. Skew aberration is an intrinsic rotation of polarization states due to the geometric transformation of local coordinates, independent of coatings and interface polarization. Skew aberration in a radially symmetric system has the form of a circular retardance tilt plus coma aberration. Skew aberration causes undesired polarization distribution in the exit pupil. We demonstrate statistics on skew aberration of 2383 optical systems described in Code V’s U.S. patent library [Code V Version 10.3 (Synopsys, 2011), pp. 22–24]; the mean skew aberration is 0.89° and the standard deviation is 1.37°. The maximum skew aberration found is 17.45° and the minimum is 11.33°. U.S. patent 2,896,506, which has ±7.01° of skew aberration, is analyzed in detail. Skew aberration should be of concern in microlithography optics and other high NA and large field of view optical systems.

© 2011 Optical Society of America

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References

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  1. H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, 1950).
  2. E. Sklar, J. Opt. Soc. Am. 65, 1520 (1975).
    [CrossRef]
  3. J. P. Mills and B. J. Thompson, J. Opt. Soc. Am. A 3, 694(1986).
    [CrossRef]
  4. J. P. Mills and B. J. Thompson, J. Opt. Soc. Am. A 3, 704(1986).
    [CrossRef]
  5. R. A. Chipman, Proc. SPIE 0891, 10 (1988).
  6. G. Yun, S. McClain, and R. A. Chipman, Appl. Opt. 50, 2866 (2011).
    [CrossRef] [PubMed]
  7. Code V Version 10.3 (Synopsys, 2011), pp. 22–24.
  8. H. Azuma, “High aperture wide-angle objective lens,” U.S. patent 2,896,506 (July 28, 1959).
  9. M. Mansuripur, Appl. Opt. 30, 3154 (1991).
    [CrossRef] [PubMed]
  10. J. P. McGuire and R. A. Chipman, J. Opt. Soc. Am. A 7, 1614 (1990).
    [CrossRef]
  11. J. Ruoff and M. Totzeck, J. Micro/Nanolithogr. MEMS MOEMS 8, 031404 (2009).
    [CrossRef]

2011 (1)

2009 (1)

J. Ruoff and M. Totzeck, J. Micro/Nanolithogr. MEMS MOEMS 8, 031404 (2009).
[CrossRef]

1991 (1)

1990 (1)

1988 (1)

R. A. Chipman, Proc. SPIE 0891, 10 (1988).

1986 (2)

1975 (1)

Appl. Opt. (2)

J. Micro/Nanolithogr. MEMS MOEMS (1)

J. Ruoff and M. Totzeck, J. Micro/Nanolithogr. MEMS MOEMS 8, 031404 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Proc. SPIE (1)

R. A. Chipman, Proc. SPIE 0891, 10 (1988).

Other (3)

Code V Version 10.3 (Synopsys, 2011), pp. 22–24.

H. Azuma, “High aperture wide-angle objective lens,” U.S. patent 2,896,506 (July 28, 1959).

H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, 1950).

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Figures (5)

Fig. 1
Fig. 1

(a) Double-pole grid of reference vectors on a unit sphere viewed along the chief ray’s propagation vector and (b) oblique view.

Fig. 2
Fig. 2

Optical system layout of U.S. patent 2,896,506 from Code V’s library has seven lenses. The system is defined with three field angles.

Fig. 3
Fig. 3

(a) Skew aberration of a ray grid with 32 ° field angle is evaluated at the exit pupil of U.S. patent 2,896,506. The maximum skew aberration is + 7.01 ° and the minimum is 7.01 ° (ray A). Both extremes occur from skew rays at the edge of the pupil. (b) Horizontal cross section [indicated in orange dashed line in part (a)] of the skew aberration exit pupil map has zero skew aberration for the center ray, which is the chief ray.

Fig. 4
Fig. 4

Skew ray A’s skew aberration contribution from each lens surface sums to 7.01 ° through the system.

Fig. 5
Fig. 5

Histogram of the maximum skew aberration evaluated for 2383 nonreflecting optical systems in Code V’s library of patented lenses.

Equations (8)

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g In , i k In , i , g Exit , i k Exit , i .
g C = k In , C × k Exit , C ,
g In , i = R ( θ In , i , axis In , i ) g C , g Exit , i = R ( θ Exit , i , axis Exit , i ) g C ,
1 A 2 ( A 2 B + ( 1 B ) D 2 F [ ( 1 B ) D G ] D [ ( 1 B ) C + H ] F [ ( 1 B ) D + L ] A 2 B + ( 1 B ) F 2 C [ ( 1 B ) F H ] D [ ( 1 B ) C L ] C [ ( 1 B ) F + G ] A 2 B + ( 1 B ) C 2 ) ,
{ G , H , L } = A 1 B 2 C 2 + F 2 { A 2 F 2 , A 2 C 2 , A 2 D 2 } .
1 A ( A 2 ( k x , j 1 k x , j ) 2 B C B A 2 ( k y , j 1 k y , j ) 2 D C D A 2 ( k z , j 1 k z , j ) 2 ) ,
Q Total , i = j = Exit In Q j = Q Exit Q j Q 1 Q In .
g Exit , i = Q Total , i g In , i .

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