Abstract

It has recently been shown that the coefficients that specify the aspheric departure from a spherical surface in high NA lithographic lenses routinely require more significant digits than are available in even double precision computers when they are described as part of a power series in aperture-squared. The Q-type aspheric description has been introduced to solve this problem. An important by-product of this new surface description is that it allows the slope of a surface to be directly constrained during optimization. Results show that Q-type aspheric surfaces that are optimized with slope constraints are not only more testable, an original motivation, but, they can also lead to solutions that are less sensitive to assembly induced misalignments for lithographic quality lenses. Specifically, for a representative NA 0.75 lens, the sensitivity to tilt and decenter is reduced by more than 3X, resulting in significantly higher lens performance in-use.

© 2011 OSA

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References

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  1. E. Abbe, “Lens system,” U.S. Patent 697,959 (Apr. 1902).
  2. G. W. Forbes, “Robust, efficient computational methods for axially symmetric optical aspheres,” Opt. Express 18(19), 19700–19712 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-19700 .
    [CrossRef] [PubMed]
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    [CrossRef]
  6. G. W. Forbes, “Manufacturability estimates for optical aspheres,” Opt. Express 19(10), 9923–9941 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-10-9923 .
    [CrossRef] [PubMed]
  7. D. Stephenson, “Improving asphere manufacturability using Forbes polynomials,” in Proceedings of the SPIE OptiFab, TD07–38 (2011).
  8. Y. Omura, “Projection exposure methods and apparatus, and projection optical systems,” U.S. Patent 6,606,144 Bl (Aug. 2003).
  9. T. G. Kuper and J. R. Rogers, “Automatic determination of optimal aspheric placement,” in International Optical Design Conference, Technical Digest (CD) (Optical Society of America, 2010), paper IThB3. http://www.opticsinfobase.org/abstract.cfm?URI=IODC-2010-IThB3 .
  10. J. R. Rogers, “Using global synthesis to find tolerance-insensitive design forms,” in International Optical Design Conference, Technical Digest (CD) (Optical Society of America, 2006), paper TuA4. http://www.opticsinfobase.org/abstract.cfm?URI=IODC-2006-TuA4 .
  11. P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J, 62930J-10 (2006).
    [CrossRef]
  12. J. E. Greivenkamp, A. E. Lowman, and R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35(10), 2962–2969 (1996).
    [CrossRef]
  13. Optical Research Associates, “Release Notes CODE V 10.3 ALPHA” (2010).

2011

2010

2007

2006

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J, 62930J-10 (2006).
[CrossRef]

1996

J. E. Greivenkamp, A. E. Lowman, and R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35(10), 2962–2969 (1996).
[CrossRef]

1986

J. Kross, F. W. Oertmann, and R. Schuhmann, “On aspherics in optical systems,” Proc. SPIE 655, 300–309 (1986).

1954

A. B. Bhatia, E. Wolf, and M. Born, “On the circle polynomials of Zernike and related orthogonal sets,” Proc. Camb. Philos. Soc. 50(1), 40–48 (1954).
[CrossRef]

Bhatia, A. B.

A. B. Bhatia, E. Wolf, and M. Born, “On the circle polynomials of Zernike and related orthogonal sets,” Proc. Camb. Philos. Soc. 50(1), 40–48 (1954).
[CrossRef]

Born, M.

A. B. Bhatia, E. Wolf, and M. Born, “On the circle polynomials of Zernike and related orthogonal sets,” Proc. Camb. Philos. Soc. 50(1), 40–48 (1954).
[CrossRef]

DeVries, G.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J, 62930J-10 (2006).
[CrossRef]

Fleig, J.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J, 62930J-10 (2006).
[CrossRef]

Forbes, G.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J, 62930J-10 (2006).
[CrossRef]

Forbes, G. W.

Greivenkamp, J. E.

J. E. Greivenkamp, A. E. Lowman, and R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35(10), 2962–2969 (1996).
[CrossRef]

Kross, J.

J. Kross, F. W. Oertmann, and R. Schuhmann, “On aspherics in optical systems,” Proc. SPIE 655, 300–309 (1986).

Lowman, A. E.

J. E. Greivenkamp, A. E. Lowman, and R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35(10), 2962–2969 (1996).
[CrossRef]

Miladinovic, D.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J, 62930J-10 (2006).
[CrossRef]

Murphy, P.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J, 62930J-10 (2006).
[CrossRef]

O'Donohue, S.

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J, 62930J-10 (2006).
[CrossRef]

Oertmann, F. W.

J. Kross, F. W. Oertmann, and R. Schuhmann, “On aspherics in optical systems,” Proc. SPIE 655, 300–309 (1986).

Palum, R. J.

J. E. Greivenkamp, A. E. Lowman, and R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35(10), 2962–2969 (1996).
[CrossRef]

Schuhmann, R.

J. Kross, F. W. Oertmann, and R. Schuhmann, “On aspherics in optical systems,” Proc. SPIE 655, 300–309 (1986).

Wolf, E.

A. B. Bhatia, E. Wolf, and M. Born, “On the circle polynomials of Zernike and related orthogonal sets,” Proc. Camb. Philos. Soc. 50(1), 40–48 (1954).
[CrossRef]

Opt. Eng.

J. E. Greivenkamp, A. E. Lowman, and R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35(10), 2962–2969 (1996).
[CrossRef]

Opt. Express

Proc. Camb. Philos. Soc.

A. B. Bhatia, E. Wolf, and M. Born, “On the circle polynomials of Zernike and related orthogonal sets,” Proc. Camb. Philos. Soc. 50(1), 40–48 (1954).
[CrossRef]

Proc. SPIE

J. Kross, F. W. Oertmann, and R. Schuhmann, “On aspherics in optical systems,” Proc. SPIE 655, 300–309 (1986).

P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J, 62930J-10 (2006).
[CrossRef]

Other

E. Abbe, “Lens system,” U.S. Patent 697,959 (Apr. 1902).

Optical Research Associates, “Release Notes CODE V 10.3 ALPHA” (2010).

D. Stephenson, “Improving asphere manufacturability using Forbes polynomials,” in Proceedings of the SPIE OptiFab, TD07–38 (2011).

Y. Omura, “Projection exposure methods and apparatus, and projection optical systems,” U.S. Patent 6,606,144 Bl (Aug. 2003).

T. G. Kuper and J. R. Rogers, “Automatic determination of optimal aspheric placement,” in International Optical Design Conference, Technical Digest (CD) (Optical Society of America, 2010), paper IThB3. http://www.opticsinfobase.org/abstract.cfm?URI=IODC-2010-IThB3 .

J. R. Rogers, “Using global synthesis to find tolerance-insensitive design forms,” in International Optical Design Conference, Technical Digest (CD) (Optical Society of America, 2006), paper TuA4. http://www.opticsinfobase.org/abstract.cfm?URI=IODC-2006-TuA4 .

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Figures (2)

Fig. 1
Fig. 1

A typical lens layout from the solution set.

Fig. 2
Fig. 2

Changes of RMS wavefront for each tolerance terms. (a-b) Barrel Beta Tilt (BTX 0.01 mrad). (c-d) Barrel Alpha Tilt (BTY 0. 01 mrad). (e-f) Element X-decenter (DSX 2 μm). (g-h) Element Y-decenter (DSY 2 μm). Two columns show the worst field for Q-type without slope constraints and Q-type with slope constraints, respectively.

Tables (4)

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Table 1 Lens Design Specifications

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Table 2 Comparison of Aspheric Departure (μm)

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Table 3 Comparisons of Maximum RMS Slope (Fringes/mm)

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Table 4 Compensator Range of Movement

Equations (1)

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z ( ρ ) = c ρ 2 1 + 1 c 2 ρ 2 + 1 1 c 2 ρ 2 { u 2 ( 1 u 2 ) m = 0 M a m Q m ( u 2 ) }

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