Abstract

A novel method of fabricating phase-only optical filters that is based on the properties of a uniaxial crystal is proposed. With these optical filters, the phase differences are tunable among the different filter zones. Many focal patterns can be obtained if these optical filters are placed in front of a lens; furthermore, these optical filters can also be used to make up for the distortions in fabrications in which they were used only as untunable optical filters.

© 2004 Optical Society of America

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References

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  1. T. R. M. Sales, G. M. Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 22, 582–584 (1997).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. 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]
  6. G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
    [CrossRef]
  7. C. J. R. Sheppard, “The use of lenses with annular aperture in scanning optical microscopy,” Optik 48, 329–334 (1977).
  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. 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, 587–610 (1980).
    [CrossRef]
  10. T. R. M. Sales, G. M. Morris, “Diffractive superresolution elements,” J. Opt. Soc. Am. A 14, 1637–1646 (1997).
    [CrossRef]
  11. T. R. M. Sales, G. M. Morris, “Axial superresolution with phase-only pupil filters,” Opt. Commun. 156, 227–230 (1998).
    [CrossRef]
  12. J. A. Davis, J. C. Escalera, J. Campos, A. Marquez, J. Yzuel, “Programmable axial apodizing and hyperresolving amplitude filters with a liquid-crystal spatial light modulator,” Opt. Lett. 24, 628–630 (1999).
    [CrossRef]
  13. T. H. Barnes, T. Eiju, K. Matusda, N. Ooyama, “Phase-only modulation using a twisted nematic liquid crystal television,” Appl. Opt. 28, 4845–4850 (1989).
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  14. K. Zhao, X. Zhong, Optics, 2nd ed. (Peking University Press, Peking, 1996), pp. 165–179.
  15. M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).

1999 (1)

1998 (1)

T. R. M. Sales, G. M. Morris, “Axial superresolution with phase-only pupil filters,” Opt. Commun. 156, 227–230 (1998).
[CrossRef]

1997 (3)

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)

1986 (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, 587–610 (1980).
[CrossRef]

1977 (1)

C. J. R. Sheppard, “The use of lenses with annular aperture in scanning optical microscopy,” Optik 48, 329–334 (1977).

1952 (1)

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

Barnes, T. H.

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, 587–610 (1980).
[CrossRef]

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, 587–610 (1980).
[CrossRef]

Campos, J.

Cox, I. J.

Davis, J. A.

Ding, Z.

Eiju, T.

Escalera, J. C.

Fan, Z.

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]

Gu, M.

Z. Ding, G. Wang, M. Gu, Z. Wang, Z. Fan, “Superresolution with an apodization film in a confocal setup,” Appl. Opt. 36, 360–363 (1997).
[CrossRef] [PubMed]

M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).

Hegedus, Z.

Hirose, Y.

Kubota, K.

Marquez, A.

Matusda, K.

Morris, G. M.

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]

Ooyama, N.

Safaris, V.

Sales, T. R. M.

Sheppard, C. J. R.

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]

C. J. R. Sheppard, “The use of lenses with annular aperture in scanning optical microscopy,” Optik 48, 329–334 (1977).

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]

Toraldo di Francia, G.

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

Wang, G.

Wang, Z.

Wilson, T.

Yamanaka, Y.

Yzuel, J.

Zhao, K.

K. Zhao, X. Zhong, Optics, 2nd ed. (Peking University Press, Peking, 1996), pp. 165–179.

Zhong, X.

K. Zhao, X. Zhong, Optics, 2nd ed. (Peking University Press, Peking, 1996), pp. 165–179.

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

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, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
[CrossRef]

Opt. Acta (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, 587–610 (1980).
[CrossRef]

Opt. Commun. (1)

T. R. M. Sales, G. M. Morris, “Axial superresolution with phase-only pupil filters,” Opt. Commun. 156, 227–230 (1998).
[CrossRef]

Opt. Lett. (2)

Optik (1)

C. J. R. Sheppard, “The use of lenses with annular aperture in scanning optical microscopy,” Optik 48, 329–334 (1977).

Other (2)

K. Zhao, X. Zhong, Optics, 2nd ed. (Peking University Press, Peking, 1996), pp. 165–179.

M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).

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Figures (8)

Fig. 1
Fig. 1

Sketch map of a TPOPF system used in the microscope. The incident light is polarized by the polarizer in the y direction. The simplest pupil filter is used to modulate the wave front, which contains only an isotropic material zone and a uniaxial crystal zone; a and r are the radius of the inner and the outer zone, respectively, and h is the thickness of the pupil filter. The angle regulator controls the phase difference of the two zones.

Fig. 2
Fig. 2

Plot of the refractive index of extraordinary light versus θ. The refractive index varies from 1.54425 to 1.55336 when θ increases from 0 to π/2 in quartz; the wavelength of the incident beam is λ = 589 nm.

Fig. 3
Fig. 3

Phase delay of extraordinary light versus θ is shown in quartz. The thickness of the quartz is 1.00 mm, and the wavelength of the incident beam is 589 nm.

Fig. 4
Fig. 4

Geometric relationships obtained when the uniaxial crystal is rotated along the y axis. θ is the rotation angle. The dashed-dotted line is the optical axis of the uniaxial crystal that is in the xy plane.

Fig. 5
Fig. 5

Two-zone pupil filter. The inner zone is made of quartz; its radius and thickness are a and 1.00 mm, respectively. The outer ring is made of glass (K9, with refractive index 1.1536), and its thickness is the same as that of the quartz. The outer radius of the glass is r.

Fig. 6
Fig. 6

Phase difference of the quartz zone and the glass zone is shown near θ = 0 rad, where the initial angle ϕ is set to zero.

Fig. 7
Fig. 7

Lateral focal patterns for three phase differences: 0.9π, 1.2π, and 1.5π. The Airy disk pattern (thin solid curve) is also plotted. In (a) all curves are normalized to the central intensity of the Airy disk pattern; in (b) every curve is normalized to its own central intensity.

Fig. 8
Fig. 8

Axial focal patterns for three phase differences: 0.9π, 1.2π, and 1.5π. The Airy disk pattern (the thin solid curve) is also plotted. All curves are normalized to the central intensity of the Airy disk pattern.

Equations (6)

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

neθ=cos2 θno2+sin2 θne21/2,
na sin θ=neϕ+ϑsin ϑ,
φ=kneϕ+ϑlcos ϑ,
δh=1cos ϑsinθ-ϑ.
Uv, 0=2 01 PρJ0vρρdρ,
U0, u=01 Pρexpjuρ2/2ρdρ,

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