Abstract

We propose a high-speed, parallel system for lens aberration measurement employing a confocal optical setup. This method uses a non-interferometric, conventional confocal axial response to determine the spherical aberration coefficient of a confocal objective. The aberration coefficients are successfully calculated from the intensity axial response by employing a neural network. It is estimated that the system can find out the aberration coefficients of 10,000 microlenses in 20 seconds of measurement and 1 second of calculation time. Our experimental results also demonstrate the practicality of this system.

©2002 Optical Society of America

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References

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  1. H. J. Matthews, D. K. Hamilton, and C. J. R. Sheppard, “Aberration Measurement by Confocal Interferometry,” J. Mod. Opt. 36, 233–250 (1989).
    [Crossref]
  2. H. Zhouand, M. Guand, and C. J. R. Sheppard, “Investigation of Aberration Measurement in Confocal Microscopy,” J. Mod. Opt. 42, 627–638 (1995).
    [Crossref]
  3. H. Zhouand and C. J. R. Sheppard, “Aberration measurement in confocal microscopy: phase retrieval from a single intensity measurement,” J. Mod. Opt. 44, 1553–1561 (1997).
    [Crossref]
  4. Hans J. Tiziani and Hans-Martin Uhde, “Three dimensional analysis by a microlens-array confocal arrangement,” Appl. Opt. 33, 567–572 (1994).
    [Crossref] [PubMed]
  5. H. J. Tiziani, R. Achi, R. N. Kramer, and L. Wiegers, “Theoretical analysis of confocal microscopy with microlenses,” Appl. Opt. 35, 120–125 (1996).
    [Crossref] [PubMed]
  6. H. J. Tiziani, T. Haist, and S. Reuter, “Optical inspection and characterization of microoptics using confocal microscopy,” Opt. and Laser Eng. 36, 403–415 (2001).
    [Crossref]
  7. T. R. Corle, C.-H. Chouand, and G. S. Kino, “Depth Response of Confocal Optical Microscopes,” Opt. Lett. 11, 770–772 (1986).
    [Crossref] [PubMed]
  8. T. Wilson and A. R. Carlini, “The Effect of Aberrations on the Axial Response of Confocal Imaging System,” J. Microscopy 154243–256 (1989).
    [Crossref]
  9. Joseph M. Geary and Phil Peterson, “Spherical aberration: a possible new measurement technique,” Opt. Eng. 25286–291 (1986).
  10. Qian Gong and Smiley S. Hsu, “Aberration measurement using axial intensity,” Opt. Eng. 331176–1186 (1994).
    [Crossref]
  11. Todd K. Barrett and David G. Sandler, “Artificial neural network for determination of Hubble Space Telescope aberration from stellar images,” Appl. Opt. 32, 1720–1727 (1993)
    [Crossref] [PubMed]
  12. Tae-Seok Yang and Jun Ho Oh, “Identification of primary aberrations on a lateral shearing inter-ferogram of optical components using neural network,” Opt. Eng. 40, 2771–2779 (2001).
    [Crossref]
  13. Developed at University of Stuttgart, Maintained at University of Tubingen, “Stuttgart Neural Network Simulator,” http://www-ra.informatik.uni-tuebingen.de/SNNS/
  14. D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representation by back-propagation errors,” Nature 323, 583–586 (1986).
    [Crossref]

2001 (2)

H. J. Tiziani, T. Haist, and S. Reuter, “Optical inspection and characterization of microoptics using confocal microscopy,” Opt. and Laser Eng. 36, 403–415 (2001).
[Crossref]

Tae-Seok Yang and Jun Ho Oh, “Identification of primary aberrations on a lateral shearing inter-ferogram of optical components using neural network,” Opt. Eng. 40, 2771–2779 (2001).
[Crossref]

1997 (1)

H. Zhouand and C. J. R. Sheppard, “Aberration measurement in confocal microscopy: phase retrieval from a single intensity measurement,” J. Mod. Opt. 44, 1553–1561 (1997).
[Crossref]

1996 (1)

1995 (1)

H. Zhouand, M. Guand, and C. J. R. Sheppard, “Investigation of Aberration Measurement in Confocal Microscopy,” J. Mod. Opt. 42, 627–638 (1995).
[Crossref]

1994 (2)

1993 (1)

1989 (2)

H. J. Matthews, D. K. Hamilton, and C. J. R. Sheppard, “Aberration Measurement by Confocal Interferometry,” J. Mod. Opt. 36, 233–250 (1989).
[Crossref]

T. Wilson and A. R. Carlini, “The Effect of Aberrations on the Axial Response of Confocal Imaging System,” J. Microscopy 154243–256 (1989).
[Crossref]

1986 (3)

Joseph M. Geary and Phil Peterson, “Spherical aberration: a possible new measurement technique,” Opt. Eng. 25286–291 (1986).

D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representation by back-propagation errors,” Nature 323, 583–586 (1986).
[Crossref]

T. R. Corle, C.-H. Chouand, and G. S. Kino, “Depth Response of Confocal Optical Microscopes,” Opt. Lett. 11, 770–772 (1986).
[Crossref] [PubMed]

Achi, R.

Barrett, Todd K.

Carlini, A. R.

T. Wilson and A. R. Carlini, “The Effect of Aberrations on the Axial Response of Confocal Imaging System,” J. Microscopy 154243–256 (1989).
[Crossref]

Chouand, C.-H.

Corle, T. R.

Geary, Joseph M.

Joseph M. Geary and Phil Peterson, “Spherical aberration: a possible new measurement technique,” Opt. Eng. 25286–291 (1986).

Gong, Qian

Qian Gong and Smiley S. Hsu, “Aberration measurement using axial intensity,” Opt. Eng. 331176–1186 (1994).
[Crossref]

Guand, M.

H. Zhouand, M. Guand, and C. J. R. Sheppard, “Investigation of Aberration Measurement in Confocal Microscopy,” J. Mod. Opt. 42, 627–638 (1995).
[Crossref]

Haist, T.

H. J. Tiziani, T. Haist, and S. Reuter, “Optical inspection and characterization of microoptics using confocal microscopy,” Opt. and Laser Eng. 36, 403–415 (2001).
[Crossref]

Hamilton, D. K.

H. J. Matthews, D. K. Hamilton, and C. J. R. Sheppard, “Aberration Measurement by Confocal Interferometry,” J. Mod. Opt. 36, 233–250 (1989).
[Crossref]

Hinton, G. E.

D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representation by back-propagation errors,” Nature 323, 583–586 (1986).
[Crossref]

Ho Oh, Jun

Tae-Seok Yang and Jun Ho Oh, “Identification of primary aberrations on a lateral shearing inter-ferogram of optical components using neural network,” Opt. Eng. 40, 2771–2779 (2001).
[Crossref]

Hsu, Smiley S.

Qian Gong and Smiley S. Hsu, “Aberration measurement using axial intensity,” Opt. Eng. 331176–1186 (1994).
[Crossref]

Kino, G. S.

Kramer, R. N.

Matthews, H. J.

H. J. Matthews, D. K. Hamilton, and C. J. R. Sheppard, “Aberration Measurement by Confocal Interferometry,” J. Mod. Opt. 36, 233–250 (1989).
[Crossref]

Peterson, Phil

Joseph M. Geary and Phil Peterson, “Spherical aberration: a possible new measurement technique,” Opt. Eng. 25286–291 (1986).

Reuter, S.

H. J. Tiziani, T. Haist, and S. Reuter, “Optical inspection and characterization of microoptics using confocal microscopy,” Opt. and Laser Eng. 36, 403–415 (2001).
[Crossref]

Rumelhart, D. E.

D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representation by back-propagation errors,” Nature 323, 583–586 (1986).
[Crossref]

Sandler, David G.

Sheppard, C. J. R.

H. Zhouand and C. J. R. Sheppard, “Aberration measurement in confocal microscopy: phase retrieval from a single intensity measurement,” J. Mod. Opt. 44, 1553–1561 (1997).
[Crossref]

H. Zhouand, M. Guand, and C. J. R. Sheppard, “Investigation of Aberration Measurement in Confocal Microscopy,” J. Mod. Opt. 42, 627–638 (1995).
[Crossref]

H. J. Matthews, D. K. Hamilton, and C. J. R. Sheppard, “Aberration Measurement by Confocal Interferometry,” J. Mod. Opt. 36, 233–250 (1989).
[Crossref]

Tiziani, H. J.

H. J. Tiziani, T. Haist, and S. Reuter, “Optical inspection and characterization of microoptics using confocal microscopy,” Opt. and Laser Eng. 36, 403–415 (2001).
[Crossref]

H. J. Tiziani, R. Achi, R. N. Kramer, and L. Wiegers, “Theoretical analysis of confocal microscopy with microlenses,” Appl. Opt. 35, 120–125 (1996).
[Crossref] [PubMed]

Tiziani, Hans J.

Uhde, Hans-Martin

Wiegers, L.

Williams, R. J.

D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representation by back-propagation errors,” Nature 323, 583–586 (1986).
[Crossref]

Wilson, T.

T. Wilson and A. R. Carlini, “The Effect of Aberrations on the Axial Response of Confocal Imaging System,” J. Microscopy 154243–256 (1989).
[Crossref]

Yang, Tae-Seok

Tae-Seok Yang and Jun Ho Oh, “Identification of primary aberrations on a lateral shearing inter-ferogram of optical components using neural network,” Opt. Eng. 40, 2771–2779 (2001).
[Crossref]

Zhouand, H.

H. Zhouand and C. J. R. Sheppard, “Aberration measurement in confocal microscopy: phase retrieval from a single intensity measurement,” J. Mod. Opt. 44, 1553–1561 (1997).
[Crossref]

H. Zhouand, M. Guand, and C. J. R. Sheppard, “Investigation of Aberration Measurement in Confocal Microscopy,” J. Mod. Opt. 42, 627–638 (1995).
[Crossref]

Appl. Opt. (3)

J. Microscopy (1)

T. Wilson and A. R. Carlini, “The Effect of Aberrations on the Axial Response of Confocal Imaging System,” J. Microscopy 154243–256 (1989).
[Crossref]

J. Mod. Opt. (3)

H. J. Matthews, D. K. Hamilton, and C. J. R. Sheppard, “Aberration Measurement by Confocal Interferometry,” J. Mod. Opt. 36, 233–250 (1989).
[Crossref]

H. Zhouand, M. Guand, and C. J. R. Sheppard, “Investigation of Aberration Measurement in Confocal Microscopy,” J. Mod. Opt. 42, 627–638 (1995).
[Crossref]

H. Zhouand and C. J. R. Sheppard, “Aberration measurement in confocal microscopy: phase retrieval from a single intensity measurement,” J. Mod. Opt. 44, 1553–1561 (1997).
[Crossref]

Nature (1)

D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representation by back-propagation errors,” Nature 323, 583–586 (1986).
[Crossref]

Opt. and Laser Eng. (1)

H. J. Tiziani, T. Haist, and S. Reuter, “Optical inspection and characterization of microoptics using confocal microscopy,” Opt. and Laser Eng. 36, 403–415 (2001).
[Crossref]

Opt. Eng. (3)

Joseph M. Geary and Phil Peterson, “Spherical aberration: a possible new measurement technique,” Opt. Eng. 25286–291 (1986).

Qian Gong and Smiley S. Hsu, “Aberration measurement using axial intensity,” Opt. Eng. 331176–1186 (1994).
[Crossref]

Tae-Seok Yang and Jun Ho Oh, “Identification of primary aberrations on a lateral shearing inter-ferogram of optical components using neural network,” Opt. Eng. 40, 2771–2779 (2001).
[Crossref]

Opt. Lett. (1)

Other (1)

Developed at University of Stuttgart, Maintained at University of Tubingen, “Stuttgart Neural Network Simulator,” http://www-ra.informatik.uni-tuebingen.de/SNNS/

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic diagram of the confocal setup employed to measure the axial intensity response, where FT lens is a Fourier transform lens, Mag. lens is a magnification lens, and BS is a beam splitter. The pupils of the microlenses are imaged on the CCD camera, and the reference mirror is driven axially by a stepping motor. The response includes the aberration information of the objective. (b) One example of axial intensity response.

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Fig. 2.
Fig. 2. The schema of a neural network for determining aberration coefficient from confocal intensity-axial-response.

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Fig. 3.
Fig. 3. Estimated spherical aberration coefficients. The lateral axis and the height axis respectively represent designed aberration coefficients and estimated coefficients. ×, ∗, and o respectively denote the results from trained, untrained, and experimental axial responses. The solid line represents an ideal estimation.

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Fig. 4.
Fig. 4. The learning curve of the neural network. The learning process can clearly be classified into four processes.

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Fig. 5.
Fig. 5. Various activities of the weight in different processes, in the second and third phases. The weight matrices are aligned as the same as Fig. 2, V is the weight matrix between the input and the hidden layer, and W is the weight matrix between the hidden and the output layer. The horizontal axis of V represents the ID of input neurons i, and vertical axes of V and W represent the ID of hidden neurons j.

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Equations (6)

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

H j = f ( ∑ i l V i , j I i )
O = f ( ∑ j m W j H j )
W j n + 1 = W j n + α ( O n − T ) O n ( 1 − O n ) H j n
V i , j n + 1 = V i , j n + α ( O n − T ) O n ( 1 − O n ) W j n H j n ( 1 − H j n )
τ = L ( M + N ) δ m + [ L ( M − 1 ) + N ( L − 1 ) ] δ a
τ ′ = ( 2 M + NL + LM + 1 ) δ m + ( LM − NL + N − L + 3 M ) δ a .

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