Abstract

In order to balance axial mounting stiffness of lithographic projection lenses and the image quality under dynamic working conditions, an easy inverse axial mounting stiffness design method is developed in this article. Imaging quality deterioration at the wafer under different axial vibration levels is analyzed. The desired image quality can be determined according to practical requirements, and axial vibrational tolerance of each lens is solved with the damped least-squares method. Based on adaptive interval adjustment, a binary search algorithm, and the finite element method, the axial mounting stiffness of each lens can be traveled in a large interval, and converges to a moderate numerical solution which makes the axial vibrational amplitude of the lens converge to its axial vibrational tolerance. Model simulation is carried out to validate the effectiveness of the method.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Brunner, “Impact of lens aberrations on optical lithography,” IBM J. Res. Dev. 41, 57–67 (1997).
    [CrossRef]
  2. K. Matsumoto, T. Matsuyama, and S. Hirukawa, “Analysis of imaging performance degradation,” Proc. SPIE 5040, 131–138 (2003).
    [CrossRef]
  3. P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, “Impact of wavefront errors on low k1 processes at extremely high NA,” Proc. SPIE 5040, 119–130 (2003).
    [CrossRef]
  4. P. R. Yoder, Opto-Mechanical Systems Design, 3rd ed. (CRC Press, 2006).
  5. B. Saggin, M. Tarabini, and D. Scaccabarozzi, “Infrared optical element mounting techniques for wide temperature ranges,” Appl. Opt. 49, 542–548 (2010).
    [CrossRef]
  6. J. J. Bacich, “Precision lens mounting,” U.S. patent4,733,945 (29March1988).
  7. A. Ahmad and R. L. Huse, “Mounting for high resolution projection lenses,” U.S. patent4,929,054 (29May1990).
  8. H. Holderer, P. Rummer, and M. Trunz, “Assembly of optical element and mount,” U.S. patent6,229,657 (8May2001).
  9. D. C. Watson and W. T. Novak, “Kinematic lens mounting with distributed support and radial flexure,” U.S. patent6,239,924 (29May2001).
  10. E. Merz and J. Becker, “Optical system, in particular projection-illumination unit used in microlithography,” U.S. patent6,307,688 (23October2001).
  11. T. Schletterer, “Elastic lens holder,” U.S. patent6,560,045 (6May2003).
  12. K. Beck, B. Gellrich, H. Holderer, T. Petasch, C. Roesch, and A. Kohl, “Adjustment arrangement of an optical element,” U.S. patent7,193,794 (20March2007).
  13. C. C. Wu, Z. Chen, and G. R. Tang, “Component tolerance design for minimum quality loss and manufacturing cost,” Comput. Ind. 35, 223–232 (1998).
    [CrossRef]
  14. S. Jin, C. Zheng, K. Yu, and X. Lai, “Tolerance design optimization on cost–quality trade-off using the Shapley value method,” J. Manuf. Syst. 29, 142–150 (2010).
    [CrossRef]
  15. R. Curran, A. Kundu, S. Raghunathan, D. Eakin, and R. McFadden, “Influence of manufacturing tolerance on aircraft direct operating cost (DOC),” J. Mater. Process. Technol. 138, 208–213 (2003).
    [CrossRef]
  16. L. Andolfatto, F. Thiébaut, C. Lartigue, and M. Douilly, “Quality- and cost-driven assembly technique selection and geometrical tolerance allocation for mechanical structure assembly,” J. Manuf. Syst. 33, 103–115 (2014).
    [CrossRef]
  17. J. Meiron, “Damped least-squares method for automatic lens design,” J. Opt. Soc. Am. 55, 1105–1109 (1965).
    [CrossRef]
  18. M. J. Kidger, “Use of the Levenberg–Marquardt (damped least squares) optimization method in lens design,” Opt. Eng. 32, 1731–1739 (1993).
    [CrossRef]
  19. B. B. Chhetri, S. Yang, and T. Shimomura, “Stochastic approach in the efficient design of the direct-binary-search algorithm for hologram synthesis,” Appl. Opt. 39, 5956–5964 (2000).
    [CrossRef]
  20. B. Shen, P. Wang, and R. Menon, “Optimization and analysis of 3D nanostructures for power-density enhancement in ultra-thin photovoltaics under oblique illumination,” Opt. Express 22, A311–A319 (2014).
    [CrossRef]
  21. A. Winman, P. Hansson, and P. Juslin, “Subjective probability intervals: How to reduce overconfidence by interval evaluation,” J. Exp. Psychol. Learn. Mem. Cogn. 30, 1167–1175 (2004).
  22. H. Hayakawa and T. Shibata, “Block-matching-based motion field generation utilizing directional edge displacement,” Comput. Elect. Eng. 36, 617–625 (2010).
    [CrossRef]
  23. Y. Omura, “Projection exposure methods and apparatus, and projection optical systems,” U.S. patent6,864,961 (8March2005).
  24. M. Currie and C. Olson, “Improved optical pulse propagation in water using an evolutionary algorithm,” Opt. Express 19, 10923–10930 (2011).
    [CrossRef]
  25. N. Yamada and T. Ijiro, “Design of wavelength selective concentrator for micro PV/TPV systems using evolutionary algorithm,” Opt. Express 19, 13140–13149 (2011).
    [CrossRef]
  26. C. C. Olson, R. T. Schermer, and F. Bucholtz, “Tailored optical force fields using evolutionary algorithms,” Opt. Express 19, 18543–18557 (2011).
    [CrossRef]
  27. M. Donelli, “Design of broadband metal nanosphere antenna arrays with a hybrid evolutionary algorithm,” Opt. Lett. 38, 401–403 (2013).
    [CrossRef]
  28. X. Zhu, J. Shen, W. Liu, X. Sun, and Y. Wang, “Nonnegative least-squares truncated singular value decomposition to particle size distribution inversion from dynamic light scattering data,” Appl. Opt. 49, 6591–6596 (2010).
    [CrossRef]
  29. C. Mack, Fundamental Principles of Optical Lithography: The Science of Microfabrication (Wiley, 2007).

2014 (2)

L. Andolfatto, F. Thiébaut, C. Lartigue, and M. Douilly, “Quality- and cost-driven assembly technique selection and geometrical tolerance allocation for mechanical structure assembly,” J. Manuf. Syst. 33, 103–115 (2014).
[CrossRef]

B. Shen, P. Wang, and R. Menon, “Optimization and analysis of 3D nanostructures for power-density enhancement in ultra-thin photovoltaics under oblique illumination,” Opt. Express 22, A311–A319 (2014).
[CrossRef]

2013 (1)

2011 (3)

2010 (4)

B. Saggin, M. Tarabini, and D. Scaccabarozzi, “Infrared optical element mounting techniques for wide temperature ranges,” Appl. Opt. 49, 542–548 (2010).
[CrossRef]

X. Zhu, J. Shen, W. Liu, X. Sun, and Y. Wang, “Nonnegative least-squares truncated singular value decomposition to particle size distribution inversion from dynamic light scattering data,” Appl. Opt. 49, 6591–6596 (2010).
[CrossRef]

H. Hayakawa and T. Shibata, “Block-matching-based motion field generation utilizing directional edge displacement,” Comput. Elect. Eng. 36, 617–625 (2010).
[CrossRef]

S. Jin, C. Zheng, K. Yu, and X. Lai, “Tolerance design optimization on cost–quality trade-off using the Shapley value method,” J. Manuf. Syst. 29, 142–150 (2010).
[CrossRef]

2004 (1)

A. Winman, P. Hansson, and P. Juslin, “Subjective probability intervals: How to reduce overconfidence by interval evaluation,” J. Exp. Psychol. Learn. Mem. Cogn. 30, 1167–1175 (2004).

2003 (3)

R. Curran, A. Kundu, S. Raghunathan, D. Eakin, and R. McFadden, “Influence of manufacturing tolerance on aircraft direct operating cost (DOC),” J. Mater. Process. Technol. 138, 208–213 (2003).
[CrossRef]

K. Matsumoto, T. Matsuyama, and S. Hirukawa, “Analysis of imaging performance degradation,” Proc. SPIE 5040, 131–138 (2003).
[CrossRef]

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, “Impact of wavefront errors on low k1 processes at extremely high NA,” Proc. SPIE 5040, 119–130 (2003).
[CrossRef]

2000 (1)

1998 (1)

C. C. Wu, Z. Chen, and G. R. Tang, “Component tolerance design for minimum quality loss and manufacturing cost,” Comput. Ind. 35, 223–232 (1998).
[CrossRef]

1997 (1)

T. Brunner, “Impact of lens aberrations on optical lithography,” IBM J. Res. Dev. 41, 57–67 (1997).
[CrossRef]

1993 (1)

M. J. Kidger, “Use of the Levenberg–Marquardt (damped least squares) optimization method in lens design,” Opt. Eng. 32, 1731–1739 (1993).
[CrossRef]

1965 (1)

Ahmad, A.

A. Ahmad and R. L. Huse, “Mounting for high resolution projection lenses,” U.S. patent4,929,054 (29May1990).

Andolfatto, L.

L. Andolfatto, F. Thiébaut, C. Lartigue, and M. Douilly, “Quality- and cost-driven assembly technique selection and geometrical tolerance allocation for mechanical structure assembly,” J. Manuf. Syst. 33, 103–115 (2014).
[CrossRef]

Bacich, J. J.

J. J. Bacich, “Precision lens mounting,” U.S. patent4,733,945 (29March1988).

Beck, K.

K. Beck, B. Gellrich, H. Holderer, T. Petasch, C. Roesch, and A. Kohl, “Adjustment arrangement of an optical element,” U.S. patent7,193,794 (20March2007).

Becker, J.

E. Merz and J. Becker, “Optical system, in particular projection-illumination unit used in microlithography,” U.S. patent6,307,688 (23October2001).

Brunner, T.

T. Brunner, “Impact of lens aberrations on optical lithography,” IBM J. Res. Dev. 41, 57–67 (1997).
[CrossRef]

Bucholtz, F.

Chen, Z.

C. C. Wu, Z. Chen, and G. R. Tang, “Component tolerance design for minimum quality loss and manufacturing cost,” Comput. Ind. 35, 223–232 (1998).
[CrossRef]

Chhetri, B. B.

Curran, R.

R. Curran, A. Kundu, S. Raghunathan, D. Eakin, and R. McFadden, “Influence of manufacturing tolerance on aircraft direct operating cost (DOC),” J. Mater. Process. Technol. 138, 208–213 (2003).
[CrossRef]

Currie, M.

Donelli, M.

Douilly, M.

L. Andolfatto, F. Thiébaut, C. Lartigue, and M. Douilly, “Quality- and cost-driven assembly technique selection and geometrical tolerance allocation for mechanical structure assembly,” J. Manuf. Syst. 33, 103–115 (2014).
[CrossRef]

Eakin, D.

R. Curran, A. Kundu, S. Raghunathan, D. Eakin, and R. McFadden, “Influence of manufacturing tolerance on aircraft direct operating cost (DOC),” J. Mater. Process. Technol. 138, 208–213 (2003).
[CrossRef]

Flagello, D. G.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, “Impact of wavefront errors on low k1 processes at extremely high NA,” Proc. SPIE 5040, 119–130 (2003).
[CrossRef]

Garreis, R. B.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, “Impact of wavefront errors on low k1 processes at extremely high NA,” Proc. SPIE 5040, 119–130 (2003).
[CrossRef]

Gellrich, B.

K. Beck, B. Gellrich, H. Holderer, T. Petasch, C. Roesch, and A. Kohl, “Adjustment arrangement of an optical element,” U.S. patent7,193,794 (20March2007).

Goehnermeier, A.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, “Impact of wavefront errors on low k1 processes at extremely high NA,” Proc. SPIE 5040, 119–130 (2003).
[CrossRef]

Graeupner, P.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, “Impact of wavefront errors on low k1 processes at extremely high NA,” Proc. SPIE 5040, 119–130 (2003).
[CrossRef]

Hansson, P.

A. Winman, P. Hansson, and P. Juslin, “Subjective probability intervals: How to reduce overconfidence by interval evaluation,” J. Exp. Psychol. Learn. Mem. Cogn. 30, 1167–1175 (2004).

Hayakawa, H.

H. Hayakawa and T. Shibata, “Block-matching-based motion field generation utilizing directional edge displacement,” Comput. Elect. Eng. 36, 617–625 (2010).
[CrossRef]

Heil, T.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, “Impact of wavefront errors on low k1 processes at extremely high NA,” Proc. SPIE 5040, 119–130 (2003).
[CrossRef]

Hirukawa, S.

K. Matsumoto, T. Matsuyama, and S. Hirukawa, “Analysis of imaging performance degradation,” Proc. SPIE 5040, 131–138 (2003).
[CrossRef]

Holderer, H.

H. Holderer, P. Rummer, and M. Trunz, “Assembly of optical element and mount,” U.S. patent6,229,657 (8May2001).

K. Beck, B. Gellrich, H. Holderer, T. Petasch, C. Roesch, and A. Kohl, “Adjustment arrangement of an optical element,” U.S. patent7,193,794 (20March2007).

Huse, R. L.

A. Ahmad and R. L. Huse, “Mounting for high resolution projection lenses,” U.S. patent4,929,054 (29May1990).

Ijiro, T.

Jin, S.

S. Jin, C. Zheng, K. Yu, and X. Lai, “Tolerance design optimization on cost–quality trade-off using the Shapley value method,” J. Manuf. Syst. 29, 142–150 (2010).
[CrossRef]

Juslin, P.

A. Winman, P. Hansson, and P. Juslin, “Subjective probability intervals: How to reduce overconfidence by interval evaluation,” J. Exp. Psychol. Learn. Mem. Cogn. 30, 1167–1175 (2004).

Kidger, M. J.

M. J. Kidger, “Use of the Levenberg–Marquardt (damped least squares) optimization method in lens design,” Opt. Eng. 32, 1731–1739 (1993).
[CrossRef]

Kohl, A.

K. Beck, B. Gellrich, H. Holderer, T. Petasch, C. Roesch, and A. Kohl, “Adjustment arrangement of an optical element,” U.S. patent7,193,794 (20March2007).

Kundu, A.

R. Curran, A. Kundu, S. Raghunathan, D. Eakin, and R. McFadden, “Influence of manufacturing tolerance on aircraft direct operating cost (DOC),” J. Mater. Process. Technol. 138, 208–213 (2003).
[CrossRef]

Lai, X.

S. Jin, C. Zheng, K. Yu, and X. Lai, “Tolerance design optimization on cost–quality trade-off using the Shapley value method,” J. Manuf. Syst. 29, 142–150 (2010).
[CrossRef]

Lartigue, C.

L. Andolfatto, F. Thiébaut, C. Lartigue, and M. Douilly, “Quality- and cost-driven assembly technique selection and geometrical tolerance allocation for mechanical structure assembly,” J. Manuf. Syst. 33, 103–115 (2014).
[CrossRef]

Liu, W.

Lowisch, M.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, “Impact of wavefront errors on low k1 processes at extremely high NA,” Proc. SPIE 5040, 119–130 (2003).
[CrossRef]

Mack, C.

C. Mack, Fundamental Principles of Optical Lithography: The Science of Microfabrication (Wiley, 2007).

Matsumoto, K.

K. Matsumoto, T. Matsuyama, and S. Hirukawa, “Analysis of imaging performance degradation,” Proc. SPIE 5040, 131–138 (2003).
[CrossRef]

Matsuyama, T.

K. Matsumoto, T. Matsuyama, and S. Hirukawa, “Analysis of imaging performance degradation,” Proc. SPIE 5040, 131–138 (2003).
[CrossRef]

McFadden, R.

R. Curran, A. Kundu, S. Raghunathan, D. Eakin, and R. McFadden, “Influence of manufacturing tolerance on aircraft direct operating cost (DOC),” J. Mater. Process. Technol. 138, 208–213 (2003).
[CrossRef]

Meiron, J.

Menon, R.

Merz, E.

E. Merz and J. Becker, “Optical system, in particular projection-illumination unit used in microlithography,” U.S. patent6,307,688 (23October2001).

Novak, W. T.

D. C. Watson and W. T. Novak, “Kinematic lens mounting with distributed support and radial flexure,” U.S. patent6,239,924 (29May2001).

Olson, C.

Olson, C. C.

Omura, Y.

Y. Omura, “Projection exposure methods and apparatus, and projection optical systems,” U.S. patent6,864,961 (8March2005).

Petasch, T.

K. Beck, B. Gellrich, H. Holderer, T. Petasch, C. Roesch, and A. Kohl, “Adjustment arrangement of an optical element,” U.S. patent7,193,794 (20March2007).

Raghunathan, S.

R. Curran, A. Kundu, S. Raghunathan, D. Eakin, and R. McFadden, “Influence of manufacturing tolerance on aircraft direct operating cost (DOC),” J. Mater. Process. Technol. 138, 208–213 (2003).
[CrossRef]

Roesch, C.

K. Beck, B. Gellrich, H. Holderer, T. Petasch, C. Roesch, and A. Kohl, “Adjustment arrangement of an optical element,” U.S. patent7,193,794 (20March2007).

Rummer, P.

H. Holderer, P. Rummer, and M. Trunz, “Assembly of optical element and mount,” U.S. patent6,229,657 (8May2001).

Saggin, B.

Scaccabarozzi, D.

Schermer, R. T.

Schletterer, T.

T. Schletterer, “Elastic lens holder,” U.S. patent6,560,045 (6May2003).

Shen, B.

Shen, J.

Shibata, T.

H. Hayakawa and T. Shibata, “Block-matching-based motion field generation utilizing directional edge displacement,” Comput. Elect. Eng. 36, 617–625 (2010).
[CrossRef]

Shimomura, T.

Sun, X.

Tang, G. R.

C. C. Wu, Z. Chen, and G. R. Tang, “Component tolerance design for minimum quality loss and manufacturing cost,” Comput. Ind. 35, 223–232 (1998).
[CrossRef]

Tarabini, M.

Thiébaut, F.

L. Andolfatto, F. Thiébaut, C. Lartigue, and M. Douilly, “Quality- and cost-driven assembly technique selection and geometrical tolerance allocation for mechanical structure assembly,” J. Manuf. Syst. 33, 103–115 (2014).
[CrossRef]

Trunz, M.

H. Holderer, P. Rummer, and M. Trunz, “Assembly of optical element and mount,” U.S. patent6,229,657 (8May2001).

Wang, P.

Wang, Y.

Watson, D. C.

D. C. Watson and W. T. Novak, “Kinematic lens mounting with distributed support and radial flexure,” U.S. patent6,239,924 (29May2001).

Winman, A.

A. Winman, P. Hansson, and P. Juslin, “Subjective probability intervals: How to reduce overconfidence by interval evaluation,” J. Exp. Psychol. Learn. Mem. Cogn. 30, 1167–1175 (2004).

Wu, C. C.

C. C. Wu, Z. Chen, and G. R. Tang, “Component tolerance design for minimum quality loss and manufacturing cost,” Comput. Ind. 35, 223–232 (1998).
[CrossRef]

Yamada, N.

Yang, S.

Yoder, P. R.

P. R. Yoder, Opto-Mechanical Systems Design, 3rd ed. (CRC Press, 2006).

Yu, K.

S. Jin, C. Zheng, K. Yu, and X. Lai, “Tolerance design optimization on cost–quality trade-off using the Shapley value method,” J. Manuf. Syst. 29, 142–150 (2010).
[CrossRef]

Zheng, C.

S. Jin, C. Zheng, K. Yu, and X. Lai, “Tolerance design optimization on cost–quality trade-off using the Shapley value method,” J. Manuf. Syst. 29, 142–150 (2010).
[CrossRef]

Zhu, X.

Appl. Opt. (3)

Comput. Elect. Eng. (1)

H. Hayakawa and T. Shibata, “Block-matching-based motion field generation utilizing directional edge displacement,” Comput. Elect. Eng. 36, 617–625 (2010).
[CrossRef]

Comput. Ind. (1)

C. C. Wu, Z. Chen, and G. R. Tang, “Component tolerance design for minimum quality loss and manufacturing cost,” Comput. Ind. 35, 223–232 (1998).
[CrossRef]

IBM J. Res. Dev. (1)

T. Brunner, “Impact of lens aberrations on optical lithography,” IBM J. Res. Dev. 41, 57–67 (1997).
[CrossRef]

J. Exp. Psychol. Learn. Mem. Cogn. (1)

A. Winman, P. Hansson, and P. Juslin, “Subjective probability intervals: How to reduce overconfidence by interval evaluation,” J. Exp. Psychol. Learn. Mem. Cogn. 30, 1167–1175 (2004).

J. Manuf. Syst. (2)

L. Andolfatto, F. Thiébaut, C. Lartigue, and M. Douilly, “Quality- and cost-driven assembly technique selection and geometrical tolerance allocation for mechanical structure assembly,” J. Manuf. Syst. 33, 103–115 (2014).
[CrossRef]

S. Jin, C. Zheng, K. Yu, and X. Lai, “Tolerance design optimization on cost–quality trade-off using the Shapley value method,” J. Manuf. Syst. 29, 142–150 (2010).
[CrossRef]

J. Mater. Process. Technol. (1)

R. Curran, A. Kundu, S. Raghunathan, D. Eakin, and R. McFadden, “Influence of manufacturing tolerance on aircraft direct operating cost (DOC),” J. Mater. Process. Technol. 138, 208–213 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

M. J. Kidger, “Use of the Levenberg–Marquardt (damped least squares) optimization method in lens design,” Opt. Eng. 32, 1731–1739 (1993).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Proc. SPIE (2)

K. Matsumoto, T. Matsuyama, and S. Hirukawa, “Analysis of imaging performance degradation,” Proc. SPIE 5040, 131–138 (2003).
[CrossRef]

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, “Impact of wavefront errors on low k1 processes at extremely high NA,” Proc. SPIE 5040, 119–130 (2003).
[CrossRef]

Other (10)

P. R. Yoder, Opto-Mechanical Systems Design, 3rd ed. (CRC Press, 2006).

J. J. Bacich, “Precision lens mounting,” U.S. patent4,733,945 (29March1988).

A. Ahmad and R. L. Huse, “Mounting for high resolution projection lenses,” U.S. patent4,929,054 (29May1990).

H. Holderer, P. Rummer, and M. Trunz, “Assembly of optical element and mount,” U.S. patent6,229,657 (8May2001).

D. C. Watson and W. T. Novak, “Kinematic lens mounting with distributed support and radial flexure,” U.S. patent6,239,924 (29May2001).

E. Merz and J. Becker, “Optical system, in particular projection-illumination unit used in microlithography,” U.S. patent6,307,688 (23October2001).

T. Schletterer, “Elastic lens holder,” U.S. patent6,560,045 (6May2003).

K. Beck, B. Gellrich, H. Holderer, T. Petasch, C. Roesch, and A. Kohl, “Adjustment arrangement of an optical element,” U.S. patent7,193,794 (20March2007).

C. Mack, Fundamental Principles of Optical Lithography: The Science of Microfabrication (Wiley, 2007).

Y. Omura, “Projection exposure methods and apparatus, and projection optical systems,” U.S. patent6,864,961 (8March2005).

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 (6)

Fig. 1.
Fig. 1.

Schematic of compliant mounting manners. (a) Compliant manners of objective and lenses. (b) Compliant means from [7]. (c) Compliant means from [11]. (d) Compliant means from [12].

Fig. 2.
Fig. 2.

Model illustration. (a) Projection optical system [23]. (b) Axial APSD specification.

Fig. 3.
Fig. 3.

Flow chart of inverse axial stiffness design procedure.

Fig. 4.
Fig. 4.

Random vibration analysis of the projection objective with ANSYS Academic Research 15.0. (a) FE model of the projection objective. (b) One 3σ displacements solution of random vibration analysis.

Fig. 5.
Fig. 5.

Evaluation of image quality. (a) Mask. (b) Dipole. (c) Image quality at best focal plane. (d) Image at ±30nm axially offset from the best focal plane. (e) Image at ±100nm axially offset from the best focal plane. (f) Image at ±200nm axially offset from the best focal plane.

Fig. 6.
Fig. 6.

Design results of the axial tolerances for lenses and their related axial mounting stiffness.

Equations (9)

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

MinimizeKn(n=1,2,320),
Subject toΔFΔFdesired,
AΔXdesired=ΔFdesired,
Ψ(ΔXdesired)=(AΔXdesiredΔFdesired)+p2ΔXdesiredTΔXdesired,
Min{Ψ(ΔXdesired)}.
(ATA+p2I)ΔXdesired=ATΔFdesired,
ΔXdesired=(ATA+p2I)1ATΔFdesired.
ΔXdesired=V{(ΣTΣ+p2I)1ΣT}UTΔFdesired,
DOF=k2λNA2,

Metrics