Abstract

We present a new method with which to binarize pupil filters designed to control the three-dimensional irradiance distribution in the focal volume of an optical system. The method is based on a one-dimensional iterative algorithm, which results in efficient use of computation time and in simple, easy to fabricate binary filters. An acceptable degree of resemblance between the point-spread function of the annular binary filter and that of its gray-tone counterpart is obtained.

© 2001 Optical Society of America

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References

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  1. P. Jacquinot and B. Rozien-Dossier, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. III.
  2. D. Zalvidea and E. E. Sicre, Appl. Opt. 37, 3623 (1998).
    [CrossRef]
  3. M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodríguez, and M. Kowalczyk, Opt. Commun. 165, 267 (1999).
    [CrossRef]
  4. J. B. Pawley, ed., Handbook of Biological Confocal Microscopy (Plenum, New York, 1995).
  5. M. A. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, Opt. Lett. 25, 245 (2000).
    [CrossRef]
  6. M. Martínez-Corral, M. Kowalczyk, C. J. Zapata-Rodríguez, and P. Andrés, Appl. Opt. 37, 6914 (1998).
    [CrossRef]
  7. S. Grill and E. H. K. Stelzer, J. Opt. Soc. Am. A 16, 2658 (1999).
    [CrossRef]
  8. C. J. R. Sheppard, Opt. Lett. 24, 505 (1999).
    [CrossRef]
  9. M. Broja, F. Wyrowski, and O. Bringdahl, Opt. Commun. 69, 205 (1989).
    [CrossRef]
  10. R. Ulichney, Digital Halftoning (MIT Press, Cambridge, Mass., 1987).
  11. T. Peter, F. Wyrowski, and O. Bringdahl, J. Mod. Opt. 40, 591 (1993).
    [CrossRef]
  12. T. Cichocki, M. Martínez-Corral, M. Kowalczyk, and P. Andrés, J. Mod. Opt. 45, 227 (1998).
    [CrossRef]
  13. H. Arsenault and A. Boivin, J. Appl. Phys. 38, 3988 (1967).
    [CrossRef]
  14. J. E. A. Landgrave and L. R. Berriel-Valdos, J. Opt. Soc. Am. A 14, 2962 (1997).
    [CrossRef]
  15. J. A. Davis, J. C. Escalera, J. Campos, A. Marquez, M. J. Yzuel, and C. Iemmi, Opt. Lett. 24, 628 (1999).
    [CrossRef]
  16. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), Chap.  8.

2000

1999

1998

1997

1993

T. Peter, F. Wyrowski, and O. Bringdahl, J. Mod. Opt. 40, 591 (1993).
[CrossRef]

1989

M. Broja, F. Wyrowski, and O. Bringdahl, Opt. Commun. 69, 205 (1989).
[CrossRef]

1967

H. Arsenault and A. Boivin, J. Appl. Phys. 38, 3988 (1967).
[CrossRef]

Andrés, P.

M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodríguez, and M. Kowalczyk, Opt. Commun. 165, 267 (1999).
[CrossRef]

M. Martínez-Corral, M. Kowalczyk, C. J. Zapata-Rodríguez, and P. Andrés, Appl. Opt. 37, 6914 (1998).
[CrossRef]

T. Cichocki, M. Martínez-Corral, M. Kowalczyk, and P. Andrés, J. Mod. Opt. 45, 227 (1998).
[CrossRef]

Arsenault, H.

H. Arsenault and A. Boivin, J. Appl. Phys. 38, 3988 (1967).
[CrossRef]

Berriel-Valdos, L. R.

Boivin, A.

H. Arsenault and A. Boivin, J. Appl. Phys. 38, 3988 (1967).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), Chap.  8.

Bringdahl, O.

T. Peter, F. Wyrowski, and O. Bringdahl, J. Mod. Opt. 40, 591 (1993).
[CrossRef]

M. Broja, F. Wyrowski, and O. Bringdahl, Opt. Commun. 69, 205 (1989).
[CrossRef]

Broja, M.

M. Broja, F. Wyrowski, and O. Bringdahl, Opt. Commun. 69, 205 (1989).
[CrossRef]

Campos, J.

Cichocki, T.

T. Cichocki, M. Martínez-Corral, M. Kowalczyk, and P. Andrés, J. Mod. Opt. 45, 227 (1998).
[CrossRef]

Davis, J. A.

Escalera, J. C.

Grill, S.

Iemmi, C.

Jacquinot, P.

P. Jacquinot and B. Rozien-Dossier, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. III.

Juskaitis, R.

Kowalczyk, M.

M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodríguez, and M. Kowalczyk, Opt. Commun. 165, 267 (1999).
[CrossRef]

T. Cichocki, M. Martínez-Corral, M. Kowalczyk, and P. Andrés, J. Mod. Opt. 45, 227 (1998).
[CrossRef]

M. Martínez-Corral, M. Kowalczyk, C. J. Zapata-Rodríguez, and P. Andrés, Appl. Opt. 37, 6914 (1998).
[CrossRef]

Laczik, Z. J.

Landgrave, J. E. A.

Marquez, A.

Martínez-Corral, M.

M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodríguez, and M. Kowalczyk, Opt. Commun. 165, 267 (1999).
[CrossRef]

T. Cichocki, M. Martínez-Corral, M. Kowalczyk, and P. Andrés, J. Mod. Opt. 45, 227 (1998).
[CrossRef]

M. Martínez-Corral, M. Kowalczyk, C. J. Zapata-Rodríguez, and P. Andrés, Appl. Opt. 37, 6914 (1998).
[CrossRef]

Neil, M. A. A.

Peter, T.

T. Peter, F. Wyrowski, and O. Bringdahl, J. Mod. Opt. 40, 591 (1993).
[CrossRef]

Rozien-Dossier, B.

P. Jacquinot and B. Rozien-Dossier, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. III.

Sarafis, V.

Sheppard, C. J. R.

Sicre, E. E.

Stelzer, E. H. K.

Ulichney, R.

R. Ulichney, Digital Halftoning (MIT Press, Cambridge, Mass., 1987).

Wilson, T.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), Chap.  8.

Wyrowski, F.

T. Peter, F. Wyrowski, and O. Bringdahl, J. Mod. Opt. 40, 591 (1993).
[CrossRef]

M. Broja, F. Wyrowski, and O. Bringdahl, Opt. Commun. 69, 205 (1989).
[CrossRef]

Yzuel, M. J.

Zalvidea, D.

Zapata-Rodríguez, C. J.

M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodríguez, and M. Kowalczyk, Opt. Commun. 165, 267 (1999).
[CrossRef]

M. Martínez-Corral, M. Kowalczyk, C. J. Zapata-Rodríguez, and P. Andrés, Appl. Opt. 37, 6914 (1998).
[CrossRef]

Appl. Opt.

J. Appl. Phys.

H. Arsenault and A. Boivin, J. Appl. Phys. 38, 3988 (1967).
[CrossRef]

J. Mod. Opt.

T. Peter, F. Wyrowski, and O. Bringdahl, J. Mod. Opt. 40, 591 (1993).
[CrossRef]

T. Cichocki, M. Martínez-Corral, M. Kowalczyk, and P. Andrés, J. Mod. Opt. 45, 227 (1998).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodríguez, and M. Kowalczyk, Opt. Commun. 165, 267 (1999).
[CrossRef]

M. Broja, F. Wyrowski, and O. Bringdahl, Opt. Commun. 69, 205 (1989).
[CrossRef]

Opt. Lett.

Other

R. Ulichney, Digital Halftoning (MIT Press, Cambridge, Mass., 1987).

J. B. Pawley, ed., Handbook of Biological Confocal Microscopy (Plenum, New York, 1995).

P. Jacquinot and B. Rozien-Dossier, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. III.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), Chap.  8.

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Figures (3)

Fig. 1
Fig. 1

Binary filters obtained by use of a 1D IFTA for M=33: (a) parabolic filter, (b) Gaussian filter. Dashed curves, amplitude transmittance of the gray-tone filters.

Fig. 2
Fig. 2

Contours of constant normalized irradiance in the meridian plane corresponding to (a) a parabolic filter, (b) the binary version.

Fig. 3
Fig. 3

Contour of constant normalized irradiance in the meridian plane corresponding to (a) a Gaussian filter, (b) the binary version.

Equations (3)

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hu,v=2π01tρexp-i2πuρ2J0vρρdρ.
hu,v=12πm=-+hm,0hCu-m,v,
hu,0=π-0.50.5qμexp-i2πuμdμ.

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