Abstract

Optical systems frequently use aspheric surfaces to improve performance. Typically the designer uses a combination of experience and trail and error to decide which surfaces to make aspheric, then the shape of the aspheric surface is optimized as part of the optical system. In this paper, a method of optimally choosing which surfaces are to be made aspheric is developed. This is implemented by allowing the surface number of the asphere to become a variable in the optimization. Imaginary surfaces are used as an intermediary to make the problem continuous for the optimization. The method of implementation and design examples are given.

©2005 Optical Society of America

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References

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  1. A. Osawa, K. Fukuda, and K. Hirata, “Optical design of high-aperture aspherical projection lens”, in Proceedings of 1990 International Lens Design Conference, G. N. Lawrence, ed., Proc. SPIE 1354, 337–343 (1991).
    [Crossref]
  2. L. H. Chen, W. C. Horng, R. H. Chen, and C. C. Lin, “Design and characterization of an aspherical zoom lens for projection TV”, in Proceedings of Projection Displays, M. H. Wu, ed., Proc. SPIE 2407, 80–88 (1995).
    [Crossref]
  3. F. H. Chuang and F. C. Chung, “Design of a projection TV zoom lens with the grin lens and aspherical surface”, in Proceedings of Projection Displays IV, M. H. Wu, ed., Proc. SPIE 3296, 138–148 (1998).
    [Crossref]
  4. W. Ulrich, H. J. Rostalski, and R. M. Hudyma, “The development of dioptric projection lenses for DUV lithography”, in Proceedings of International Optical Design Conference 2002, P. K. Manhart and J. M. Sasian, eds., Proc. SPIE 4832, 158–169 (2002).
    [Crossref]
  5. M. Isshiki, “Global optimization with escape function”, in Proceedings of International Optical Design Conference 1998, L. R. Gardner and K. P. Thompson, eds., Proc. SPIE 3482, 104–109 (1998).
    [Crossref]
  6. A. Yabe, “Global optimization of zoom lenses,” in Proceedings of International Optical Design Conference 1998, L. R. Gardner and K. P. Thompson, eds., Proc. SPIE 3482, 122–125 (1998).
    [Crossref]
  7. I. Ono, S. Kobayashi, and K. Yoshida, “Global and multi-objective optimization for lens design by real-coded genetic algorithms” in Proceedings of International Optical Design Conference 1998, L. R. Gardner and K. P. Thompson, eds., Proc. SPIE 3482, 110–121 (1998).
    [Crossref]
  8. K. E. Moore, “Algorithm for global optimization of optical systems based on genetic competition”, in Proceedings of Optical Design and Analysis Software, R. C. Juergens, ed., Proc. SPIE 3780, 40–47 (1999).
    [Crossref]
  9. Japan Patent, P2004-252119A.

2002 (1)

W. Ulrich, H. J. Rostalski, and R. M. Hudyma, “The development of dioptric projection lenses for DUV lithography”, in Proceedings of International Optical Design Conference 2002, P. K. Manhart and J. M. Sasian, eds., Proc. SPIE 4832, 158–169 (2002).
[Crossref]

1999 (1)

K. E. Moore, “Algorithm for global optimization of optical systems based on genetic competition”, in Proceedings of Optical Design and Analysis Software, R. C. Juergens, ed., Proc. SPIE 3780, 40–47 (1999).
[Crossref]

1998 (4)

F. H. Chuang and F. C. Chung, “Design of a projection TV zoom lens with the grin lens and aspherical surface”, in Proceedings of Projection Displays IV, M. H. Wu, ed., Proc. SPIE 3296, 138–148 (1998).
[Crossref]

M. Isshiki, “Global optimization with escape function”, in Proceedings of International Optical Design Conference 1998, L. R. Gardner and K. P. Thompson, eds., Proc. SPIE 3482, 104–109 (1998).
[Crossref]

A. Yabe, “Global optimization of zoom lenses,” in Proceedings of International Optical Design Conference 1998, L. R. Gardner and K. P. Thompson, eds., Proc. SPIE 3482, 122–125 (1998).
[Crossref]

I. Ono, S. Kobayashi, and K. Yoshida, “Global and multi-objective optimization for lens design by real-coded genetic algorithms” in Proceedings of International Optical Design Conference 1998, L. R. Gardner and K. P. Thompson, eds., Proc. SPIE 3482, 110–121 (1998).
[Crossref]

1995 (1)

L. H. Chen, W. C. Horng, R. H. Chen, and C. C. Lin, “Design and characterization of an aspherical zoom lens for projection TV”, in Proceedings of Projection Displays, M. H. Wu, ed., Proc. SPIE 2407, 80–88 (1995).
[Crossref]

1991 (1)

A. Osawa, K. Fukuda, and K. Hirata, “Optical design of high-aperture aspherical projection lens”, in Proceedings of 1990 International Lens Design Conference, G. N. Lawrence, ed., Proc. SPIE 1354, 337–343 (1991).
[Crossref]

Chen, L. H.

L. H. Chen, W. C. Horng, R. H. Chen, and C. C. Lin, “Design and characterization of an aspherical zoom lens for projection TV”, in Proceedings of Projection Displays, M. H. Wu, ed., Proc. SPIE 2407, 80–88 (1995).
[Crossref]

Chen, R. H.

L. H. Chen, W. C. Horng, R. H. Chen, and C. C. Lin, “Design and characterization of an aspherical zoom lens for projection TV”, in Proceedings of Projection Displays, M. H. Wu, ed., Proc. SPIE 2407, 80–88 (1995).
[Crossref]

Chuang, F. H.

F. H. Chuang and F. C. Chung, “Design of a projection TV zoom lens with the grin lens and aspherical surface”, in Proceedings of Projection Displays IV, M. H. Wu, ed., Proc. SPIE 3296, 138–148 (1998).
[Crossref]

Chung, F. C.

F. H. Chuang and F. C. Chung, “Design of a projection TV zoom lens with the grin lens and aspherical surface”, in Proceedings of Projection Displays IV, M. H. Wu, ed., Proc. SPIE 3296, 138–148 (1998).
[Crossref]

Fukuda, K.

A. Osawa, K. Fukuda, and K. Hirata, “Optical design of high-aperture aspherical projection lens”, in Proceedings of 1990 International Lens Design Conference, G. N. Lawrence, ed., Proc. SPIE 1354, 337–343 (1991).
[Crossref]

Hirata, K.

A. Osawa, K. Fukuda, and K. Hirata, “Optical design of high-aperture aspherical projection lens”, in Proceedings of 1990 International Lens Design Conference, G. N. Lawrence, ed., Proc. SPIE 1354, 337–343 (1991).
[Crossref]

Horng, W. C.

L. H. Chen, W. C. Horng, R. H. Chen, and C. C. Lin, “Design and characterization of an aspherical zoom lens for projection TV”, in Proceedings of Projection Displays, M. H. Wu, ed., Proc. SPIE 2407, 80–88 (1995).
[Crossref]

Hudyma, R. M.

W. Ulrich, H. J. Rostalski, and R. M. Hudyma, “The development of dioptric projection lenses for DUV lithography”, in Proceedings of International Optical Design Conference 2002, P. K. Manhart and J. M. Sasian, eds., Proc. SPIE 4832, 158–169 (2002).
[Crossref]

Isshiki, M.

M. Isshiki, “Global optimization with escape function”, in Proceedings of International Optical Design Conference 1998, L. R. Gardner and K. P. Thompson, eds., Proc. SPIE 3482, 104–109 (1998).
[Crossref]

Kobayashi, S.

I. Ono, S. Kobayashi, and K. Yoshida, “Global and multi-objective optimization for lens design by real-coded genetic algorithms” in Proceedings of International Optical Design Conference 1998, L. R. Gardner and K. P. Thompson, eds., Proc. SPIE 3482, 110–121 (1998).
[Crossref]

Lin, C. C.

L. H. Chen, W. C. Horng, R. H. Chen, and C. C. Lin, “Design and characterization of an aspherical zoom lens for projection TV”, in Proceedings of Projection Displays, M. H. Wu, ed., Proc. SPIE 2407, 80–88 (1995).
[Crossref]

Moore, K. E.

K. E. Moore, “Algorithm for global optimization of optical systems based on genetic competition”, in Proceedings of Optical Design and Analysis Software, R. C. Juergens, ed., Proc. SPIE 3780, 40–47 (1999).
[Crossref]

Ono, I.

I. Ono, S. Kobayashi, and K. Yoshida, “Global and multi-objective optimization for lens design by real-coded genetic algorithms” in Proceedings of International Optical Design Conference 1998, L. R. Gardner and K. P. Thompson, eds., Proc. SPIE 3482, 110–121 (1998).
[Crossref]

Osawa, A.

A. Osawa, K. Fukuda, and K. Hirata, “Optical design of high-aperture aspherical projection lens”, in Proceedings of 1990 International Lens Design Conference, G. N. Lawrence, ed., Proc. SPIE 1354, 337–343 (1991).
[Crossref]

Rostalski, H. J.

W. Ulrich, H. J. Rostalski, and R. M. Hudyma, “The development of dioptric projection lenses for DUV lithography”, in Proceedings of International Optical Design Conference 2002, P. K. Manhart and J. M. Sasian, eds., Proc. SPIE 4832, 158–169 (2002).
[Crossref]

Ulrich, W.

W. Ulrich, H. J. Rostalski, and R. M. Hudyma, “The development of dioptric projection lenses for DUV lithography”, in Proceedings of International Optical Design Conference 2002, P. K. Manhart and J. M. Sasian, eds., Proc. SPIE 4832, 158–169 (2002).
[Crossref]

Yabe, A.

A. Yabe, “Global optimization of zoom lenses,” in Proceedings of International Optical Design Conference 1998, L. R. Gardner and K. P. Thompson, eds., Proc. SPIE 3482, 122–125 (1998).
[Crossref]

Yoshida, K.

I. Ono, S. Kobayashi, and K. Yoshida, “Global and multi-objective optimization for lens design by real-coded genetic algorithms” in Proceedings of International Optical Design Conference 1998, L. R. Gardner and K. P. Thompson, eds., Proc. SPIE 3482, 110–121 (1998).
[Crossref]

Proc. SPIE (8)

A. Osawa, K. Fukuda, and K. Hirata, “Optical design of high-aperture aspherical projection lens”, in Proceedings of 1990 International Lens Design Conference, G. N. Lawrence, ed., Proc. SPIE 1354, 337–343 (1991).
[Crossref]

L. H. Chen, W. C. Horng, R. H. Chen, and C. C. Lin, “Design and characterization of an aspherical zoom lens for projection TV”, in Proceedings of Projection Displays, M. H. Wu, ed., Proc. SPIE 2407, 80–88 (1995).
[Crossref]

F. H. Chuang and F. C. Chung, “Design of a projection TV zoom lens with the grin lens and aspherical surface”, in Proceedings of Projection Displays IV, M. H. Wu, ed., Proc. SPIE 3296, 138–148 (1998).
[Crossref]

W. Ulrich, H. J. Rostalski, and R. M. Hudyma, “The development of dioptric projection lenses for DUV lithography”, in Proceedings of International Optical Design Conference 2002, P. K. Manhart and J. M. Sasian, eds., Proc. SPIE 4832, 158–169 (2002).
[Crossref]

M. Isshiki, “Global optimization with escape function”, in Proceedings of International Optical Design Conference 1998, L. R. Gardner and K. P. Thompson, eds., Proc. SPIE 3482, 104–109 (1998).
[Crossref]

A. Yabe, “Global optimization of zoom lenses,” in Proceedings of International Optical Design Conference 1998, L. R. Gardner and K. P. Thompson, eds., Proc. SPIE 3482, 122–125 (1998).
[Crossref]

I. Ono, S. Kobayashi, and K. Yoshida, “Global and multi-objective optimization for lens design by real-coded genetic algorithms” in Proceedings of International Optical Design Conference 1998, L. R. Gardner and K. P. Thompson, eds., Proc. SPIE 3482, 110–121 (1998).
[Crossref]

K. E. Moore, “Algorithm for global optimization of optical systems based on genetic competition”, in Proceedings of Optical Design and Analysis Software, R. C. Juergens, ed., Proc. SPIE 3780, 40–47 (1999).
[Crossref]

Other (1)

Japan Patent, P2004-252119A.

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Figures (13)

Fig. 1.
Fig. 1. Thin glass layer after the sphere on the rear side of the glass.

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Fig. 2.
Fig. 2. Thin glass layer before the sphere on the front side of the glass.

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Fig. 3.
Fig. 3. Thin air layer before the sphere on the rear side of the glass.

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Fig. 4.
Fig. 4. Thin air layer after the sphere on the front side of the glass.

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Fig. 5.
Fig. 5. Starting point of the examples.

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Fig. 6.
Fig. 6. Merit function values for the different position of aspherics.

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Fig. 7.
Fig. 7. Real surface number for each solution with 1 aspherics.

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Fig. 8.
Fig. 8. Merit function value of each solution with 1 aspherics.

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Fig. 9.
Fig. 9. Solution for FNO=1.8 and the tangent of the field of view =0.28.

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Fig. 10.
Fig. 10. Real surface numbers for each solution with 4 aspherics.

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Fig. 11.
Fig. 11. Merit function value of each solution with 4 aspherics.

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Fig. 12.
Fig. 12. Solution for FNO=1.5 and the tangent of the field of view =0.33.

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Fig. 13.
Fig. 13. Solutions for ArF microlithography lens

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Tables (4)

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Table 1. Lens data of Fig. 1

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Table 2. Lens data of Fig. 2

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Table 3. Lens data of Fig. 3

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Table 4. Lens data of Fig. 4

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Equations (14)

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

C = b C k + a C k + 1
N = b N k + a N k + 1 ′
z 1 ( x , y ) = az ( x , y )
z 2 ( x , y ) = − bz ( x , y )
z 1 ( x , y ) = − az ( x , y )
z 2 ( x , y ) = bz ( x , y )
z 1 ( x , y ) − z 2 ( x , y ) = z ( x , y )
z 1 ( x , y ) − z 2 ( x , y ) = − z ( x , y )
a ( 0 ) = 0
a ( 1 ) = 1
a ( r ) = r
a ′ ( 0 ) = 0
a ′ ( 1 ) = 0
a ( r ) = ( 1 − cos ⁡ ( π r ) ) 2

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