Abstract

The three-dimensional intensity distribution in the focal region of lenses with filters consisting of arrays of rings is investigated in the paraxial Debye regime. The axial behavior can exhibit a variety of different effects.

© 1998 Optical Society of America

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References

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  1. I. J. Cox, “Increasing the bit-packing density of optical disk systems,” Appl. Opt. 23, 3260–3261 (1984).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  3. T. R. M. Sales, G. M. Morris, “Superresolution elements for high-density optical storage,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 290–292.
  4. H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus and resolution enhancement in optical lithography,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
    [Crossref]
  5. Z. S. Hegedus, “Annular pupil arrays—application to confocal scanning,” Opt. Acta 32, 815–826 (1985).
    [Crossref]
  6. Z. Hegedus, V. Safaris, “Superresolving filters in confocally scanned imaging systems,” J. Opt. Soc. Am. A 3, 1892–1896 (1986).
    [Crossref]
  7. G. Toraldo di Francia, “Supergain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
    [Crossref]
  8. I. J. Cox, C. J. R. Sheppard, T. Wilson, “Reappraisal of arrays of concentric annuli as superresolving filters,” J. Opt. Soc. Am. 72, 1287–1291 (1982).
    [Crossref]
  9. B. J. Thompson, “Diffraction by semitransparent and phase annuli,” J. Opt. Soc. Am. 55(2), 145–149 (1965).
    [Crossref]
  10. C. J. R. Sheppard, Z. A. Hegedus, “Axial behavior of pupil plane filters,” J. Opt. Soc. Am. A 5, 643–647 (1988).
    [Crossref]
  11. C. J. R. Sheppard, “Synthesis of filters for specified axial properties,” J. Mod. Opt. 43(3), 525–536 (1996).
    [Crossref]
  12. C. K. Sieracki, E. W. Hanson, “A leaky annular pupil for improved lateral resolution in confocal fluorescence microscopy,” in Three-Dimensional Microscopy: Image Acquisition and Processing, C. J. Cogswell, K. Carlsson, eds., Proc. SPIE2184, 120–126 (1994).
    [Crossref]
  13. C. J. R. Sheppard, “Leaky annular pupils for improved axial imaging,” Optik 99(1), 32–34 (1995).
  14. M. Martinez-Corral, P. Andrés, E. Silvestre, J. C. Barreiro, “Improvement of three-dimensional resolution in confocal microscopy,” in Second Iberoamerican Meeting on Optics, D. Malacara-Hernandez, S. E. Acosta, R. Rodrı́guez-Vera, Z. Malacara, A. A. Morales, eds., Proc. SPIE2730, 634–638 (1995).
    [Crossref]
  15. D. A. Parthenopoulos, P. M. Rentzepis, “Three-dimensional optical memory,” Science 245, 843–845 (1989).
    [Crossref] [PubMed]
  16. G. Toraldo di Francia, “Nuovo pupille superrisolvente,” Atti Fond. Giorgio Ronchi 7, 366–372 (1952).
  17. R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field—I. Achievement of maximum central irradiance under an energy constraint,” Opt. Acta 27, 857–610 (1980).
  18. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

1996 (1)

C. J. R. Sheppard, “Synthesis of filters for specified axial properties,” J. Mod. Opt. 43(3), 525–536 (1996).
[Crossref]

1995 (1)

C. J. R. Sheppard, “Leaky annular pupils for improved axial imaging,” Optik 99(1), 32–34 (1995).

1991 (1)

H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus and resolution enhancement in optical lithography,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
[Crossref]

1990 (1)

1989 (1)

D. A. Parthenopoulos, P. M. Rentzepis, “Three-dimensional optical memory,” Science 245, 843–845 (1989).
[Crossref] [PubMed]

1988 (1)

1986 (1)

1985 (1)

Z. S. Hegedus, “Annular pupil arrays—application to confocal scanning,” Opt. Acta 32, 815–826 (1985).
[Crossref]

1984 (1)

1982 (1)

1980 (1)

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field—I. Achievement of maximum central irradiance under an energy constraint,” Opt. Acta 27, 857–610 (1980).

1965 (1)

1952 (2)

G. Toraldo di Francia, “Supergain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
[Crossref]

G. Toraldo di Francia, “Nuovo pupille superrisolvente,” Atti Fond. Giorgio Ronchi 7, 366–372 (1952).

Andrés, P.

M. Martinez-Corral, P. Andrés, E. Silvestre, J. C. Barreiro, “Improvement of three-dimensional resolution in confocal microscopy,” in Second Iberoamerican Meeting on Optics, D. Malacara-Hernandez, S. E. Acosta, R. Rodrı́guez-Vera, Z. Malacara, A. A. Morales, eds., Proc. SPIE2730, 634–638 (1995).
[Crossref]

Barreiro, J. C.

M. Martinez-Corral, P. Andrés, E. Silvestre, J. C. Barreiro, “Improvement of three-dimensional resolution in confocal microscopy,” in Second Iberoamerican Meeting on Optics, D. Malacara-Hernandez, S. E. Acosta, R. Rodrı́guez-Vera, Z. Malacara, A. A. Morales, eds., Proc. SPIE2730, 634–638 (1995).
[Crossref]

Boivin, A.

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field—I. Achievement of maximum central irradiance under an energy constraint,” Opt. Acta 27, 857–610 (1980).

Boivin, R.

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field—I. Achievement of maximum central irradiance under an energy constraint,” Opt. Acta 27, 857–610 (1980).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

Cox, I. J.

Fujii, H.

Fukuda, H.

H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus and resolution enhancement in optical lithography,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
[Crossref]

Hanson, E. W.

C. K. Sieracki, E. W. Hanson, “A leaky annular pupil for improved lateral resolution in confocal fluorescence microscopy,” in Three-Dimensional Microscopy: Image Acquisition and Processing, C. J. Cogswell, K. Carlsson, eds., Proc. SPIE2184, 120–126 (1994).
[Crossref]

Hegedus, Z.

Hegedus, Z. A.

Hegedus, Z. S.

Z. S. Hegedus, “Annular pupil arrays—application to confocal scanning,” Opt. Acta 32, 815–826 (1985).
[Crossref]

Hirose, Y.

Kubota, K.

Martinez-Corral, M.

M. Martinez-Corral, P. Andrés, E. Silvestre, J. C. Barreiro, “Improvement of three-dimensional resolution in confocal microscopy,” in Second Iberoamerican Meeting on Optics, D. Malacara-Hernandez, S. E. Acosta, R. Rodrı́guez-Vera, Z. Malacara, A. A. Morales, eds., Proc. SPIE2730, 634–638 (1995).
[Crossref]

Morris, G. M.

T. R. M. Sales, G. M. Morris, “Superresolution elements for high-density optical storage,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 290–292.

Okazaki, S.

H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus and resolution enhancement in optical lithography,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
[Crossref]

Parthenopoulos, D. A.

D. A. Parthenopoulos, P. M. Rentzepis, “Three-dimensional optical memory,” Science 245, 843–845 (1989).
[Crossref] [PubMed]

Rentzepis, P. M.

D. A. Parthenopoulos, P. M. Rentzepis, “Three-dimensional optical memory,” Science 245, 843–845 (1989).
[Crossref] [PubMed]

Safaris, V.

Sales, T. R. M.

T. R. M. Sales, G. M. Morris, “Superresolution elements for high-density optical storage,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 290–292.

Sheppard, C. J. R.

C. J. R. Sheppard, “Synthesis of filters for specified axial properties,” J. Mod. Opt. 43(3), 525–536 (1996).
[Crossref]

C. J. R. Sheppard, “Leaky annular pupils for improved axial imaging,” Optik 99(1), 32–34 (1995).

C. J. R. Sheppard, Z. A. Hegedus, “Axial behavior of pupil plane filters,” J. Opt. Soc. Am. A 5, 643–647 (1988).
[Crossref]

I. J. Cox, C. J. R. Sheppard, T. Wilson, “Reappraisal of arrays of concentric annuli as superresolving filters,” J. Opt. Soc. Am. 72, 1287–1291 (1982).
[Crossref]

Sieracki, C. K.

C. K. Sieracki, E. W. Hanson, “A leaky annular pupil for improved lateral resolution in confocal fluorescence microscopy,” in Three-Dimensional Microscopy: Image Acquisition and Processing, C. J. Cogswell, K. Carlsson, eds., Proc. SPIE2184, 120–126 (1994).
[Crossref]

Silvestre, E.

M. Martinez-Corral, P. Andrés, E. Silvestre, J. C. Barreiro, “Improvement of three-dimensional resolution in confocal microscopy,” in Second Iberoamerican Meeting on Optics, D. Malacara-Hernandez, S. E. Acosta, R. Rodrı́guez-Vera, Z. Malacara, A. A. Morales, eds., Proc. SPIE2730, 634–638 (1995).
[Crossref]

Terasawa, T.

H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus and resolution enhancement in optical lithography,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
[Crossref]

Thompson, B. J.

Toraldo di Francia, G.

G. Toraldo di Francia, “Supergain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
[Crossref]

G. Toraldo di Francia, “Nuovo pupille superrisolvente,” Atti Fond. Giorgio Ronchi 7, 366–372 (1952).

Wilson, T.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

Yamanaka, Y.

Appl. Opt. (2)

Atti Fond. Giorgio Ronchi (1)

G. Toraldo di Francia, “Nuovo pupille superrisolvente,” Atti Fond. Giorgio Ronchi 7, 366–372 (1952).

J. Mod. Opt. (1)

C. J. R. Sheppard, “Synthesis of filters for specified axial properties,” J. Mod. Opt. 43(3), 525–536 (1996).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

J. Vac. Sci. Technol. B (1)

H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus and resolution enhancement in optical lithography,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
[Crossref]

Nuovo Cimento Suppl. (1)

G. Toraldo di Francia, “Supergain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
[Crossref]

Opt. Acta (2)

Z. S. Hegedus, “Annular pupil arrays—application to confocal scanning,” Opt. Acta 32, 815–826 (1985).
[Crossref]

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field—I. Achievement of maximum central irradiance under an energy constraint,” Opt. Acta 27, 857–610 (1980).

Optik (1)

C. J. R. Sheppard, “Leaky annular pupils for improved axial imaging,” Optik 99(1), 32–34 (1995).

Science (1)

D. A. Parthenopoulos, P. M. Rentzepis, “Three-dimensional optical memory,” Science 245, 843–845 (1989).
[Crossref] [PubMed]

Other (4)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

M. Martinez-Corral, P. Andrés, E. Silvestre, J. C. Barreiro, “Improvement of three-dimensional resolution in confocal microscopy,” in Second Iberoamerican Meeting on Optics, D. Malacara-Hernandez, S. E. Acosta, R. Rodrı́guez-Vera, Z. Malacara, A. A. Morales, eds., Proc. SPIE2730, 634–638 (1995).
[Crossref]

C. K. Sieracki, E. W. Hanson, “A leaky annular pupil for improved lateral resolution in confocal fluorescence microscopy,” in Three-Dimensional Microscopy: Image Acquisition and Processing, C. J. Cogswell, K. Carlsson, eds., Proc. SPIE2184, 120–126 (1994).
[Crossref]

T. R. M. Sales, G. M. Morris, “Superresolution elements for high-density optical storage,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 290–292.

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Figures (5)

Fig. 1
Fig. 1

Axial variation in intensity for filters: (a) 1, (b) 2, (c) 3, (d) 4, (e) 5.

Fig. 2
Fig. 2

Axial variation in intensity for small values of u for filters: (a) 1, (b) 2, (c) 3, (d) 4, and (e) 5. The intensity variation for an unobstructed pupil is shown as a dashed curve.

Fig. 3
Fig. 3

Contours of equal intensity for a meridional plane for filters: (a) 1, (b) 2, (c) 3, (d) 4, and (e) 5. The zeros in the focal plane are indicated by arrows.

Fig. 4
Fig. 4

Transverse intensity variation for filter 2 in the plane u=22. An identical variation is produced for u=-22, suggesting the use as a bifocal lens.

Fig. 5
Fig. 5

Axial variation in intensity for a confocal system using (a) filter 3 and (b) filter 5, together with an unobstructed pupil. The variation for a confocal system with two unobstructed pupils is shown as a dashed curve.

Tables (1)

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Table 1 Properties of the Five Filters

Equations (21)

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vi=2πri sin α/λ.
t=(r/a)2,
In=01Q(t)tndt,
t¯=I1/I0,t2¯=I2/I0.
GT=(2t¯)1/2,GA=(12t2¯-(t¯)2)1/2.
U(v, u)=01Q(t)J0(vt)exp-12iutdt,
v=2πr sin α/λ,
u=8πz sin2(α/2)/λ.
Ul(v, u)=(l-1)/nl/nJ0(vt)exp-12iutdt.
U(v, u)=l=1nklUl(v, u)=k·U(v, u),
Ul(0, 0)=1n,
U(0, 0)=1nl=1nkl=1,
l=1nkl=n.
Ul(v, 0)=ln2J1(vl/n)vl/n-l-1n2J1(v(l-1)/n)(v(l-1)/n),
Ul(v, 0)=l=1n(kl-kl+1) ln2J1(vl/n)vl/n,
kl+1=0.
U(0, u)=1nexpiu4n sin(u/4n)u/4nl=1nkl exp-iul2n.
t¯=12n2l=1n(2l-1)kl,
t2¯=13n3l=1n(3l2-3l+1)kl,
S=1/kmax2,
E=1nl=1n kl2kmax2,

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