Abstract

An axial superresolution diffraction theory is developed in a two-photon microfabrication system. This method can improve the axial superresolution of the two-photon microfabrication system. A theoretical analysis of the photosensitive resin is discussed based on the exciting power and the concentration of free radical theory. Simulated results of the two-photon microfabrication verify the method and show that it can provide insight into the microfabrication system.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. W. Gao and M. J. Patasek, "Effects of excited-state absorption on two-photon absorbing materials," Appl. Opt. 45, 2521-2528 (2006).
    [CrossRef] [PubMed]
  2. B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
    [CrossRef]
  3. S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, "Finer features for functional micro devices," Nature 412, 697-698 (2001).
    [CrossRef] [PubMed]
  4. Z. W. Jiang, D. J. Yuan, A. D. Zhu, A. D. Xia, W. H. Huang, J. Chu, R. Chu, and Y. P. Liu, "The development of the two-photon three-dimensional microfabrication technology and the experiment system," Opt. Precision Eng. 3, 234-238 (2003).
  5. Z. W. Jiang, "The analysis of the femtosecond laser two-photon three dimension microfabrication," Ph.D. dissertation (University of Science and Technology of China, 2004).
  6. Z. W. Jiang, D. J. Yuan, R. Guo, Z. Xu, X. Wang, A. D. Xia, and W. H. Huang, "Analysis on the resolution of two-photon three-dimension microfabrication," Microfabrication Technol. 2, 30-36 (2004).
  7. Z. W. Han, Macromolecule Science Tutorial (Trans Huadong Science and Technology University Publications of China, 2001).
  8. H. T. Liu, Y. B. Yan, Q. F. Tan, and G. F.Jin, "Theories for the design of diffractive superresolution elements and limits of optical superresolution," J. Opt. Soc. Am. A 19, 2185-2193 (2002).
    [CrossRef]
  9. H. T. Liu, Y. B. Yan, D. E. Yi, and G. F. Jin, "Theories for the design of a hybrid refractive-diffractive superresolution lens with high numerical aperture," J. Opt. Soc. Am. A 20, 913-924 (2003).
    [CrossRef]
  10. H. T. Liu, "Investigations of design methods of diffractive optical elements to implement optical superresolution," Ph.D. dissertation (Tsinghua University China, 2004).
  11. J. K. Strayer, Linear Programming and Its Application (Springer-Verlag, 1989).
    [CrossRef]
  12. W. X. Xing and J. X. Xie, Modern Optimal Calculation Method (Trans Tsinghua University Publications Beijing, 1999).

2006 (1)

Y. W. Gao and M. J. Patasek, "Effects of excited-state absorption on two-photon absorbing materials," Appl. Opt. 45, 2521-2528 (2006).
[CrossRef] [PubMed]

2004 (1)

Z. W. Jiang, D. J. Yuan, R. Guo, Z. Xu, X. Wang, A. D. Xia, and W. H. Huang, "Analysis on the resolution of two-photon three-dimension microfabrication," Microfabrication Technol. 2, 30-36 (2004).

2003 (2)

H. T. Liu, Y. B. Yan, D. E. Yi, and G. F. Jin, "Theories for the design of a hybrid refractive-diffractive superresolution lens with high numerical aperture," J. Opt. Soc. Am. A 20, 913-924 (2003).
[CrossRef]

Z. W. Jiang, D. J. Yuan, A. D. Zhu, A. D. Xia, W. H. Huang, J. Chu, R. Chu, and Y. P. Liu, "The development of the two-photon three-dimensional microfabrication technology and the experiment system," Opt. Precision Eng. 3, 234-238 (2003).

2002 (1)

H. T. Liu, Y. B. Yan, Q. F. Tan, and G. F.Jin, "Theories for the design of diffractive superresolution elements and limits of optical superresolution," J. Opt. Soc. Am. A 19, 2185-2193 (2002).
[CrossRef]

2001 (1)

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, "Finer features for functional micro devices," Nature 412, 697-698 (2001).
[CrossRef] [PubMed]

1999 (1)

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Ananthavel, S. P.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Barlow, S.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Chu, J.

Z. W. Jiang, D. J. Yuan, A. D. Zhu, A. D. Xia, W. H. Huang, J. Chu, R. Chu, and Y. P. Liu, "The development of the two-photon three-dimensional microfabrication technology and the experiment system," Opt. Precision Eng. 3, 234-238 (2003).

Chu, R.

Z. W. Jiang, D. J. Yuan, A. D. Zhu, A. D. Xia, W. H. Huang, J. Chu, R. Chu, and Y. P. Liu, "The development of the two-photon three-dimensional microfabrication technology and the experiment system," Opt. Precision Eng. 3, 234-238 (2003).

Cumpston, B. H.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Dyer, D. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Ehrlich, J. E.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Erskine, L. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Gao, Y. W.

Y. W. Gao and M. J. Patasek, "Effects of excited-state absorption on two-photon absorbing materials," Appl. Opt. 45, 2521-2528 (2006).
[CrossRef] [PubMed]

Guo, R.

Z. W. Jiang, D. J. Yuan, R. Guo, Z. Xu, X. Wang, A. D. Xia, and W. H. Huang, "Analysis on the resolution of two-photon three-dimension microfabrication," Microfabrication Technol. 2, 30-36 (2004).

Han, Z. W.

Z. W. Han, Macromolecule Science Tutorial (Trans Huadong Science and Technology University Publications of China, 2001).

Heikal, A. A.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Huang, W. H.

Z. W. Jiang, D. J. Yuan, R. Guo, Z. Xu, X. Wang, A. D. Xia, and W. H. Huang, "Analysis on the resolution of two-photon three-dimension microfabrication," Microfabrication Technol. 2, 30-36 (2004).

Z. W. Jiang, D. J. Yuan, A. D. Zhu, A. D. Xia, W. H. Huang, J. Chu, R. Chu, and Y. P. Liu, "The development of the two-photon three-dimensional microfabrication technology and the experiment system," Opt. Precision Eng. 3, 234-238 (2003).

Jiang, Z. W.

Z. W. Jiang, D. J. Yuan, R. Guo, Z. Xu, X. Wang, A. D. Xia, and W. H. Huang, "Analysis on the resolution of two-photon three-dimension microfabrication," Microfabrication Technol. 2, 30-36 (2004).

Z. W. Jiang, D. J. Yuan, A. D. Zhu, A. D. Xia, W. H. Huang, J. Chu, R. Chu, and Y. P. Liu, "The development of the two-photon three-dimensional microfabrication technology and the experiment system," Opt. Precision Eng. 3, 234-238 (2003).

Z. W. Jiang, "The analysis of the femtosecond laser two-photon three dimension microfabrication," Ph.D. dissertation (University of Science and Technology of China, 2004).

Jin, G. F.

H. T. Liu, Y. B. Yan, D. E. Yi, and G. F. Jin, "Theories for the design of a hybrid refractive-diffractive superresolution lens with high numerical aperture," J. Opt. Soc. Am. A 20, 913-924 (2003).
[CrossRef]

H. T. Liu, Y. B. Yan, Q. F. Tan, and G. F.Jin, "Theories for the design of diffractive superresolution elements and limits of optical superresolution," J. Opt. Soc. Am. A 19, 2185-2193 (2002).
[CrossRef]

Kawata, S.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, "Finer features for functional micro devices," Nature 412, 697-698 (2001).
[CrossRef] [PubMed]

Kuebler, S. M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Lee, I. Y. S.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Liu, H. T.

H. T. Liu, Y. B. Yan, D. E. Yi, and G. F. Jin, "Theories for the design of a hybrid refractive-diffractive superresolution lens with high numerical aperture," J. Opt. Soc. Am. A 20, 913-924 (2003).
[CrossRef]

H. T. Liu, Y. B. Yan, Q. F. Tan, and G. F.Jin, "Theories for the design of diffractive superresolution elements and limits of optical superresolution," J. Opt. Soc. Am. A 19, 2185-2193 (2002).
[CrossRef]

H. T. Liu, "Investigations of design methods of diffractive optical elements to implement optical superresolution," Ph.D. dissertation (Tsinghua University China, 2004).

Liu, Y. P.

Z. W. Jiang, D. J. Yuan, A. D. Zhu, A. D. Xia, W. H. Huang, J. Chu, R. Chu, and Y. P. Liu, "The development of the two-photon three-dimensional microfabrication technology and the experiment system," Opt. Precision Eng. 3, 234-238 (2003).

Marder, S. R.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Maughon, D. M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Patasek, M. J.

Y. W. Gao and M. J. Patasek, "Effects of excited-state absorption on two-photon absorbing materials," Appl. Opt. 45, 2521-2528 (2006).
[CrossRef] [PubMed]

Perry, J. W.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Qin, J.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Rockel, H.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Rumi, M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Strayer, J. K.

J. K. Strayer, Linear Programming and Its Application (Springer-Verlag, 1989).
[CrossRef]

Sun, H.-B.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, "Finer features for functional micro devices," Nature 412, 697-698 (2001).
[CrossRef] [PubMed]

Takada, K.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, "Finer features for functional micro devices," Nature 412, 697-698 (2001).
[CrossRef] [PubMed]

Tan, Q. F.

H. T. Liu, Y. B. Yan, Q. F. Tan, and G. F.Jin, "Theories for the design of diffractive superresolution elements and limits of optical superresolution," J. Opt. Soc. Am. A 19, 2185-2193 (2002).
[CrossRef]

Tanaka, T.

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, "Finer features for functional micro devices," Nature 412, 697-698 (2001).
[CrossRef] [PubMed]

Wang, X.

Z. W. Jiang, D. J. Yuan, R. Guo, Z. Xu, X. Wang, A. D. Xia, and W. H. Huang, "Analysis on the resolution of two-photon three-dimension microfabrication," Microfabrication Technol. 2, 30-36 (2004).

Wu, X. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

Xia, A. D.

Z. W. Jiang, D. J. Yuan, R. Guo, Z. Xu, X. Wang, A. D. Xia, and W. H. Huang, "Analysis on the resolution of two-photon three-dimension microfabrication," Microfabrication Technol. 2, 30-36 (2004).

Z. W. Jiang, D. J. Yuan, A. D. Zhu, A. D. Xia, W. H. Huang, J. Chu, R. Chu, and Y. P. Liu, "The development of the two-photon three-dimensional microfabrication technology and the experiment system," Opt. Precision Eng. 3, 234-238 (2003).

Xie, J. X.

W. X. Xing and J. X. Xie, Modern Optimal Calculation Method (Trans Tsinghua University Publications Beijing, 1999).

Xing, W. X.

W. X. Xing and J. X. Xie, Modern Optimal Calculation Method (Trans Tsinghua University Publications Beijing, 1999).

Xu, Z.

Z. W. Jiang, D. J. Yuan, R. Guo, Z. Xu, X. Wang, A. D. Xia, and W. H. Huang, "Analysis on the resolution of two-photon three-dimension microfabrication," Microfabrication Technol. 2, 30-36 (2004).

Yan, Y. B.

H. T. Liu, Y. B. Yan, D. E. Yi, and G. F. Jin, "Theories for the design of a hybrid refractive-diffractive superresolution lens with high numerical aperture," J. Opt. Soc. Am. A 20, 913-924 (2003).
[CrossRef]

H. T. Liu, Y. B. Yan, Q. F. Tan, and G. F.Jin, "Theories for the design of diffractive superresolution elements and limits of optical superresolution," J. Opt. Soc. Am. A 19, 2185-2193 (2002).
[CrossRef]

Yi, D. E.

H. T. Liu, Y. B. Yan, D. E. Yi, and G. F. Jin, "Theories for the design of a hybrid refractive-diffractive superresolution lens with high numerical aperture," J. Opt. Soc. Am. A 20, 913-924 (2003).
[CrossRef]

Yuan, D. J.

Z. W. Jiang, D. J. Yuan, R. Guo, Z. Xu, X. Wang, A. D. Xia, and W. H. Huang, "Analysis on the resolution of two-photon three-dimension microfabrication," Microfabrication Technol. 2, 30-36 (2004).

Z. W. Jiang, D. J. Yuan, A. D. Zhu, A. D. Xia, W. H. Huang, J. Chu, R. Chu, and Y. P. Liu, "The development of the two-photon three-dimensional microfabrication technology and the experiment system," Opt. Precision Eng. 3, 234-238 (2003).

Zhu, A. D.

Z. W. Jiang, D. J. Yuan, A. D. Zhu, A. D. Xia, W. H. Huang, J. Chu, R. Chu, and Y. P. Liu, "The development of the two-photon three-dimensional microfabrication technology and the experiment system," Opt. Precision Eng. 3, 234-238 (2003).

Appl. Opt. (1)

Y. W. Gao and M. J. Patasek, "Effects of excited-state absorption on two-photon absorbing materials," Appl. Opt. 45, 2521-2528 (2006).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

H. T. Liu, Y. B. Yan, D. E. Yi, and G. F. Jin, "Theories for the design of a hybrid refractive-diffractive superresolution lens with high numerical aperture," J. Opt. Soc. Am. A 20, 913-924 (2003).
[CrossRef]

J. Opt. Soc. Am. A (1)

H. T. Liu, Y. B. Yan, Q. F. Tan, and G. F.Jin, "Theories for the design of diffractive superresolution elements and limits of optical superresolution," J. Opt. Soc. Am. A 19, 2185-2193 (2002).
[CrossRef]

Microfabrication Technol. (1)

Z. W. Jiang, D. J. Yuan, R. Guo, Z. Xu, X. Wang, A. D. Xia, and W. H. Huang, "Analysis on the resolution of two-photon three-dimension microfabrication," Microfabrication Technol. 2, 30-36 (2004).

Nature (2)

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. M. Maughon, J. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization imitators for three-dimensional optical data storage and microfabrication," Nature 398, 51-54 (1999).
[CrossRef]

S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, "Finer features for functional micro devices," Nature 412, 697-698 (2001).
[CrossRef] [PubMed]

Opt. Precision Eng. (1)

Z. W. Jiang, D. J. Yuan, A. D. Zhu, A. D. Xia, W. H. Huang, J. Chu, R. Chu, and Y. P. Liu, "The development of the two-photon three-dimensional microfabrication technology and the experiment system," Opt. Precision Eng. 3, 234-238 (2003).

Other (5)

Z. W. Jiang, "The analysis of the femtosecond laser two-photon three dimension microfabrication," Ph.D. dissertation (University of Science and Technology of China, 2004).

H. T. Liu, "Investigations of design methods of diffractive optical elements to implement optical superresolution," Ph.D. dissertation (Tsinghua University China, 2004).

J. K. Strayer, Linear Programming and Its Application (Springer-Verlag, 1989).
[CrossRef]

W. X. Xing and J. X. Xie, Modern Optimal Calculation Method (Trans Tsinghua University Publications Beijing, 1999).

Z. W. Han, Macromolecule Science Tutorial (Trans Huadong Science and Technology University Publications of China, 2001).

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 (5)

Fig. 1
Fig. 1

Comparison between single-photon and two-photon methods of microfabrication.

Fig. 2
Fig. 2

Block diagram of two-photon microfabrication.

Fig. 3
Fig. 3

Performances of (a) radial coordinate and (b) axial coordinate.

Fig. 4
Fig. 4

Structure of the optimized DSE.

Fig. 5
Fig. 5

PSF intensity of the axial coordinate.

Tables (1)

Tables Icon

Table 1 Superresolution of Two-Photon Microfabrication

Equations (28)

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

I ( r 2 , z ) = ( 2 π λ f ) 2 | 0 R u ( r 1 ) exp ( i π r 1 2 λ z f 2 ) J 0 ( 2 π r 1 r 2 λ f ) r 1 d r 1 | 2 ,
I ( η , μ ) = 4 | 0 1 U ( ρ ) exp ( i 2 π μ ρ 2 ) J 0 ( x J η ρ ) ρ d ρ | 2 ,
max U ( ρ ) I ( 0 , 0 ) ,
I ( 0 , ± μ 1 ) / I ( 0 , 0 ) α A ,
I ( 0 , ± μ j ) / I ( 0 , 0 ) K A ,
j = 2 , 3 ,  ,  N A , 0 < μ 1 < μ j < μ j + 1 ,
| U ( ρ ) | 1 ,
max { A ( ρ ) , B ( ρ ) } { [ 0 1 A ( ρ ) ρ d ρ ] 2 + [ 0 1 B ( ρ ) ρ d ρ ] 2 } ,
[ 0 1 A ( ρ ) cos ( 2 π μ j ρ 2 ) ρ d ρ 0 1 B ( ρ ) sin ( 2 π μ j ρ 2 ) ρ d ρ ] 2 + [ 0 1 B ( ρ ) cos ( 2 π μ j ρ 2 ) ρ d ρ + 0 1 A ( ρ ) sin ( 2 π μ j ρ 2 ) ρ d ρ ] 2 ω j { [ 0 1 A ( ρ ) ρ d ρ ] 2 + [ 0 1 B ( ρ ) ρ d ρ ] 2 } ,
[ 0 1 A ( ρ ) cos ( 2 π μ j ρ 2 ) ρ d ρ + 0 1 B ( ρ ) sin ( 2 π μ j ρ 2 ) ρ d ρ ] 2 + [ 0 1 B ( ρ ) cos ( 2 π μ j ρ 2 ) ρ d ρ 0 1 A ( ρ ) sin ( 2 π μ j ρ 2 ) ρ d ρ ] 2 ω j { [ 0 1 A ( ρ ) ρ d ρ ] 2 + [ 0 1 B ( ρ ) ρ d ρ ] 2 } ,
A ( ρ ) 2 + B ( ρ ) 2 1 ,
ϕ 0 = n π + arctan { 0 1 [ A 0 ( ρ ) B 0 ( ρ ) ] ρ d ρ 0 1 [ A 0 ( ρ ) + B 0 ( ρ ) ] ρ d ρ } ;
min { A ( ρ ) , B ( ρ ) } 0 1 A ( ρ ) ρ d ρ ,
0 1 A ( ρ ) ρ d ρ = 0 1 B ( ρ ) ρ d ρ ,
[ 0 1 A ( ρ ) cos ( 2 π μ j ρ 2 ) ρ d ρ 0 1 B ( ρ ) sin ( 2 π μ j ρ 2 ) ρ d ρ ] 2 + [ 0 1 B ( ρ ) cos ( 2 π μ j ρ 2 ) ρ d ρ + 0 1 A ( ρ ) sin ( 2 π μ j ρ 2 ) ρ d ρ ] 2 ω j { [ 0 1 A ( ρ ) ρ d ρ ] 2 + [ 0 1 B ( ρ ) ρ d ρ ] 2 } ,
[ 0 1 A ( ρ ) cos ( 2 π μ j ρ 2 ) ρ d ρ + 0 1 B ( ρ ) sin ( 2 π μ j ρ 2 ) ρ d ρ ] 2 + [ 0 1 B ( ρ ) cos ( 2 π μ j ρ 2 ) ρ d ρ 0 1 A ( ρ ) sin ( 2 π μ j ρ 2 ) ρ d ρ ] 2 ω j { [ 0 1 A ( ρ ) ρ d ρ ] 2 + [ 0 1 B ( ρ ) ρ d ρ ] 2 } ,
A ( ρ ) 2 + B ( ρ ) 2 1.
min { A ( ρ ) , B ( ρ ) } 0 1 A ( ρ ) ρ d ρ ,
[ 0 1 A ( ρ ) cos ( 2 π μ j ρ 2 ) ρ d ρ ] 2 + [ 0 1 A ( ρ ) sin ( 2 π μ j ρ 2 ) ρ d ρ ] 2 ω j [ 0 1 A ( ρ ) ρ d ρ ] 2 ,
1 / 2 A ( ρ ) 1 / 2 ,
B ( ρ ) = A ( ρ ) .
( 1 ) m [ 0 1 A ( ρ ) cos ( 2 π μ j ρ 2 ) ρ d ρ ] cos γ ( p ) + ( 1 ) n [ 0 1 A ( ρ ) sin ( 2 π μ j ρ 2 ) ρ d ρ ] sin γ ( p ) ω j [ 0 1 A ( ρ ) ρ d ρ ] cos π 4 P m , n { 1 , 2 } , p = 1 , , P ,
min { A k , B k } k = 1 K A k ( ρ k 2 ρ k 1 2 ) ,
( 1 ) m { k = 1 K A k [ sin ( 2 π μ j ρ k 2 ) sin ( 2 π μ j ρ k 1 2 ) ] / ( 2 π μ j ) } × cos γ ( p ) + ( 1 ) n { k = 1 K A k [ cos ( 2 π μ j ρ k 2 ) cos ( 2 π μ j ρ k 1 2 ) ] / ( 2 π μ j ) } sin γ ( p ) ω j [ k = 1 K A k ( ρ k 2 ρ k 1 2 ) ] cos π 4 P m , n { 1 , 2 } , p = 1 , , P ,
1 / 2 A k 1 / 2 , k = 1 , 2 , K ,
B k = A k , k = 1 , 2 , K .
R 1 i = ρ i b R , i = 1 , 2 , N b .
I ( r 2 , z ) = ( 2 π λ f ) 2 | 0 R u ( r 1 ) exp ( i π r 1 2 λ × z f 2 ) J 0 ( 2 π r 1 r 2 λ f ) r 1 d r 1 = ( 2 π λ f ) 2 | 0 R 11 exp ( i π r 1 2 λ × z f 2 ) J 0 ( 2 π r 1 r 2 λ f ) r 1 d r 1 R 11 R 12 exp ( i π r 1 2 λ × z f 2 ) J 0 ( 2 π r 1 r 2 λ f ) r 1 d r 1 + + ( 1 ) N b + 1 R 1 ( N b 1 ) R 1 B b exp ( i π r 1 2 λ × z f 2 ) J 0 ( 2 π r 1 r 2 λ f ) r 1 d r 1 | 2 .

Metrics