Abstract

The superresolution technique is well known for its ability to compress the central diffraction spot to a size that is smaller than the Airy diffraction spot. The radial birefringent filter, which consists of two parallel polarizers and a rotationally symmetric birefringent element, is introduced into the superresolution technology, and the pupil function of it is deduced. It is shown that such a filter can be adapted either for transverse superresolution or for axial superresolution simply by changing the angle between either of the two polarizers and the radial birefringent element. At the same time the superresolution parameters are discussed. The filter is relatively simple in construction as it requires no phase changes, and low-cost replication is possible.

© 2004 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).
  2. D. M. de Juana, J. E. Oti, V. F. Canales, M. P. Cagigal, “Transverse or axial superresolution in a 4π-confocal microscope by phase-only filters,” J. Opt. Soc. Am. A 20, 2172–2178 (2003).
    [CrossRef]
  3. G. Boyer, “New class of axially apodizing filters for confocal scanning microscopy,” J. Opt. Soc. Am. A 19, 584–589 (2002).
    [CrossRef]
  4. T. R. M. Sales, G. M. Morris, “Superresoultion elements for high-density optical storage,” in Joint International Symposiun 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.
  5. G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento, Suppl. 9, 426–435 (1952).
    [CrossRef]
  6. Z. S. Hegedus, V. Sarafis, “Superresolving filters in confocally scanned imaging systems,” J. Opt. Soc. Am. A 3, 1892–1896 (1986).
    [CrossRef]
  7. M. Martinez-Corral, P. Andres, J. Ojeda-Castaneda, G. Saavedra, “Tunable axial superresolution by annular binary filters: application to confocal microcopy,” Opt. Commun. 119, 491–498 (1995).
    [CrossRef]
  8. M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, C. J. R. Sheppard, “Improvement of three-dimensional resolution in confocal scanning microscopy by combination of two pupil filters,” Optik (Stuttgart) 107, 145–148 (1998).
  9. C. J. R. Sheppard, “Leaky annular pupils for improved axial imaging,” Optik (Stuttgart) 99, 32–34 (1995).
  10. M. Gu, T. Tannous, C. J. R. Sheppard, “Effect of an annular pupil on confocal imaging through highly scattering media,” Opt. Lett. 21, 312–314 (1995).
    [CrossRef]
  11. M. Gu, C. J. R. Sheppard, “Confocal fluorescent microscopy with a finite sized circular detector,” J. Opt. Soc. Am. A 9, 643–647 (1992).
    [CrossRef]
  12. M. Martinez-Corral, A. Pons, M. T. Caballero, “Axial apodization in 4π-confocal microscopy by annular binary filters,” J. Opt. Soc. Am. A 19, 1532–1536 (2002).
    [CrossRef]
  13. C. M. Blanca, J. Bewersdorf, S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2000).
    [CrossRef]
  14. A. I. Whiting, A. F. Abouraddy, B. E. A. Saleh, M. C. Teich, J. T. Fourkas, “Polarization-assisted transverse and axial optical superresolution,” Opt. Express 11, 1714–1723 (2003).
    [CrossRef] [PubMed]
  15. J. M. Eggleston, G. Giuliani, R. L. Byer, “Radial intensity filters using radial birefringent elements,” J. Opt. Soc. Am. 71, 1264–1272 (1981).
    [CrossRef]
  16. G. Giuliani, Y. K. Park, R. L. Byer, “The radial birefringent element and its application to laser resonator design,” presented at the Eleventh International Quantum Electronics Conference, Boston, Mass., June 23–26, 1980.
  17. G. Giuliani, Y. K. Park, R. L. Byer, “The radial birefringent element and its application to a Nd:YAG resonator,” Opt. Lett. 5, 491–493 (1980).
    [CrossRef] [PubMed]
  18. T. R. M. Sales, G. M. Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 22, 582–584 (1997).
    [CrossRef] [PubMed]
  19. C. J. R. Sheppard, Z. S. Hegedus, “Axial behavior of pupil plane filters,” J. Opt. Soc. Am. A 5, 643–647 (1988).
    [CrossRef]
  20. K. Bhattacharya, A. K. Chakraborty, A. Ghosh, “Simulation of effects of phase and amplitude coatings on the lens aperture with polarization masks,” J. Opt. Soc. Am. A 11, 586–592 (1994).
    [CrossRef]
  21. S. N. Datta, A. Ghosh, A. K. Chakraborty, “Imaging characteristics of a lens zonally masked by polarizers and retarder,” Optik (Stuttgart) 100, 1–7 (1995).

2003 (2)

2002 (2)

2000 (1)

C. M. Blanca, J. Bewersdorf, S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2000).
[CrossRef]

1998 (1)

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, C. J. R. Sheppard, “Improvement of three-dimensional resolution in confocal scanning microscopy by combination of two pupil filters,” Optik (Stuttgart) 107, 145–148 (1998).

1997 (1)

1995 (4)

M. Gu, T. Tannous, C. J. R. Sheppard, “Effect of an annular pupil on confocal imaging through highly scattering media,” Opt. Lett. 21, 312–314 (1995).
[CrossRef]

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

M. Martinez-Corral, P. Andres, J. Ojeda-Castaneda, G. Saavedra, “Tunable axial superresolution by annular binary filters: application to confocal microcopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

S. N. Datta, A. Ghosh, A. K. Chakraborty, “Imaging characteristics of a lens zonally masked by polarizers and retarder,” Optik (Stuttgart) 100, 1–7 (1995).

1994 (1)

1992 (1)

1988 (1)

1986 (1)

1981 (1)

1980 (1)

1952 (1)

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

Abouraddy, A. F.

Andres, P.

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, C. J. R. Sheppard, “Improvement of three-dimensional resolution in confocal scanning microscopy by combination of two pupil filters,” Optik (Stuttgart) 107, 145–148 (1998).

M. Martinez-Corral, P. Andres, J. Ojeda-Castaneda, G. Saavedra, “Tunable axial superresolution by annular binary filters: application to confocal microcopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

Bewersdorf, J.

C. M. Blanca, J. Bewersdorf, S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2000).
[CrossRef]

Bhattacharya, K.

Blanca, C. M.

C. M. Blanca, J. Bewersdorf, S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2000).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

Boyer, G.

Byer, R. L.

J. M. Eggleston, G. Giuliani, R. L. Byer, “Radial intensity filters using radial birefringent elements,” J. Opt. Soc. Am. 71, 1264–1272 (1981).
[CrossRef]

G. Giuliani, Y. K. Park, R. L. Byer, “The radial birefringent element and its application to a Nd:YAG resonator,” Opt. Lett. 5, 491–493 (1980).
[CrossRef] [PubMed]

G. Giuliani, Y. K. Park, R. L. Byer, “The radial birefringent element and its application to laser resonator design,” presented at the Eleventh International Quantum Electronics Conference, Boston, Mass., June 23–26, 1980.

Caballero, M. T.

Cagigal, M. P.

Canales, V. F.

Chakraborty, A. K.

S. N. Datta, A. Ghosh, A. K. Chakraborty, “Imaging characteristics of a lens zonally masked by polarizers and retarder,” Optik (Stuttgart) 100, 1–7 (1995).

K. Bhattacharya, A. K. Chakraborty, A. Ghosh, “Simulation of effects of phase and amplitude coatings on the lens aperture with polarization masks,” J. Opt. Soc. Am. A 11, 586–592 (1994).
[CrossRef]

Datta, S. N.

S. N. Datta, A. Ghosh, A. K. Chakraborty, “Imaging characteristics of a lens zonally masked by polarizers and retarder,” Optik (Stuttgart) 100, 1–7 (1995).

de Juana, D. M.

Eggleston, J. M.

Fourkas, J. T.

Ghosh, A.

S. N. Datta, A. Ghosh, A. K. Chakraborty, “Imaging characteristics of a lens zonally masked by polarizers and retarder,” Optik (Stuttgart) 100, 1–7 (1995).

K. Bhattacharya, A. K. Chakraborty, A. Ghosh, “Simulation of effects of phase and amplitude coatings on the lens aperture with polarization masks,” J. Opt. Soc. Am. A 11, 586–592 (1994).
[CrossRef]

Giuliani, G.

J. M. Eggleston, G. Giuliani, R. L. Byer, “Radial intensity filters using radial birefringent elements,” J. Opt. Soc. Am. 71, 1264–1272 (1981).
[CrossRef]

G. Giuliani, Y. K. Park, R. L. Byer, “The radial birefringent element and its application to a Nd:YAG resonator,” Opt. Lett. 5, 491–493 (1980).
[CrossRef] [PubMed]

G. Giuliani, Y. K. Park, R. L. Byer, “The radial birefringent element and its application to laser resonator design,” presented at the Eleventh International Quantum Electronics Conference, Boston, Mass., June 23–26, 1980.

Gu, M.

Hegedus, Z. S.

Hell, S. W.

C. M. Blanca, J. Bewersdorf, S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2000).
[CrossRef]

Martinez-Corral, M.

M. Martinez-Corral, A. Pons, M. T. Caballero, “Axial apodization in 4π-confocal microscopy by annular binary filters,” J. Opt. Soc. Am. A 19, 1532–1536 (2002).
[CrossRef]

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, C. J. R. Sheppard, “Improvement of three-dimensional resolution in confocal scanning microscopy by combination of two pupil filters,” Optik (Stuttgart) 107, 145–148 (1998).

M. Martinez-Corral, P. Andres, J. Ojeda-Castaneda, G. Saavedra, “Tunable axial superresolution by annular binary filters: application to confocal microcopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

Morris, G. M.

T. R. M. Sales, G. M. Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 22, 582–584 (1997).
[CrossRef] [PubMed]

T. R. M. Sales, G. M. Morris, “Superresoultion elements for high-density optical storage,” in Joint International Symposiun 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.

Ojeda-Castaneda, J.

M. Martinez-Corral, P. Andres, J. Ojeda-Castaneda, G. Saavedra, “Tunable axial superresolution by annular binary filters: application to confocal microcopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

Oti, J. E.

Park, Y. K.

G. Giuliani, Y. K. Park, R. L. Byer, “The radial birefringent element and its application to a Nd:YAG resonator,” Opt. Lett. 5, 491–493 (1980).
[CrossRef] [PubMed]

G. Giuliani, Y. K. Park, R. L. Byer, “The radial birefringent element and its application to laser resonator design,” presented at the Eleventh International Quantum Electronics Conference, Boston, Mass., June 23–26, 1980.

Pons, A.

Saavedra, G.

M. Martinez-Corral, P. Andres, J. Ojeda-Castaneda, G. Saavedra, “Tunable axial superresolution by annular binary filters: application to confocal microcopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

Saleh, B. E. A.

Sales, T. R. M.

T. R. M. Sales, G. M. Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 22, 582–584 (1997).
[CrossRef] [PubMed]

T. R. M. Sales, G. M. Morris, “Superresoultion elements for high-density optical storage,” in Joint International Symposiun 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.

Sarafis, V.

Sheppard, C. J. R.

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, C. J. R. Sheppard, “Improvement of three-dimensional resolution in confocal scanning microscopy by combination of two pupil filters,” Optik (Stuttgart) 107, 145–148 (1998).

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

M. Gu, T. Tannous, C. J. R. Sheppard, “Effect of an annular pupil on confocal imaging through highly scattering media,” Opt. Lett. 21, 312–314 (1995).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Confocal fluorescent microscopy with a finite sized circular detector,” J. Opt. Soc. Am. A 9, 643–647 (1992).
[CrossRef]

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

Tannous, T.

Teich, M. C.

Toraldo di Francia, G.

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

Whiting, A. I.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

Zapata-Rodriguez, C. J.

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, C. J. R. Sheppard, “Improvement of three-dimensional resolution in confocal scanning microscopy by combination of two pupil filters,” Optik (Stuttgart) 107, 145–148 (1998).

Appl. Phys. Lett. (1)

C. M. Blanca, J. Bewersdorf, S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (7)

Nuovo Cimento, Suppl. (1)

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

Opt. Commun. (1)

M. Martinez-Corral, P. Andres, J. Ojeda-Castaneda, G. Saavedra, “Tunable axial superresolution by annular binary filters: application to confocal microcopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Optik (Stuttgart) (3)

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, C. J. R. Sheppard, “Improvement of three-dimensional resolution in confocal scanning microscopy by combination of two pupil filters,” Optik (Stuttgart) 107, 145–148 (1998).

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

S. N. Datta, A. Ghosh, A. K. Chakraborty, “Imaging characteristics of a lens zonally masked by polarizers and retarder,” Optik (Stuttgart) 100, 1–7 (1995).

Other (3)

G. Giuliani, Y. K. Park, R. L. Byer, “The radial birefringent element and its application to laser resonator design,” presented at the Eleventh International Quantum Electronics Conference, Boston, Mass., June 23–26, 1980.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

T. R. M. Sales, G. M. Morris, “Superresoultion elements for high-density optical storage,” in Joint International Symposiun 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 (7)

Fig. 1
Fig. 1

System for the superresolution; L is lens, SF is superresolved filter, OP is observation plane.  

Fig. 2
Fig. 2

RBF and RBE; R, d0, and ρ0 are the curvature, center thickness, and radial distance of the RBE, respectively.

Fig. 3
Fig. 3

Transverse superresolution parameters (a) G and (b) S.

Fig. 4
Fig. 4

Normalized (a) transverse and (b) axial intensity for the RBF (solid curve) with θ=π/4 compared with clear pupil (dotted curve).

Fig. 5
Fig. 5

Images of (a) the Airy spot and (b) the superresolution pattern.

Fig. 6
Fig. 6

Axial superresolution parameters (a) G and (b) S.

Fig. 7
Fig. 7

Normalized (a) transverse and (b) axial intensity for the RBF (solid curve) with θ=π/2 compared with clear pupil (dotted curve).

Equations (25)

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

U(v, u)=201P(ρ)J0(vρ)exp-iuρ22ρdρ.
v=kr sin α,
u=4kz sin2α2,
U(v, 0)=201P(ρ)J0(vρ)ρdρ,
U(0, u)=201P(ρ)exp-iuρ22ρdρ.
U(0, u)=01Q(t)exp-iut2dt.
δ(ρ)=2πΔnλ d(ρ),
d(ρ)=d0-R[1-(1-ρ2/R2)1/2].
d(ρ)=d0+ρ2/2R,
L=cosδ(ρ)2+i sinδ(ρ)2cos 2θi sinδ(ρ)2sin 2θi sinδ(ρ)2sin 2θcosδ(ρ)2-i sinδ(ρ)2cos 2θ  .
Ao=PLPAi=acosδ(ρ)2+i sinδ(ρ)2cos 2θ10.
P(ρ)=acosδ(ρ)2+i sinδ(ρ)2cos 2θ.
T(ρ)=a2cos2δ(ρ)2sin2 2θ+cos2 2θ.
d0=(2m-1) λ2Δn,m=1,2,3,
dρ0=d0+λ2Δn.
R-(R2-ρ02)1/2=dρ0-d0=λ2Δn.
R=Δnρ02λ+λ4Δn.
d0=5.673mm,dρ0=5.788mm,
R=218.15mm.
δ(ρ)=2πΔnλd0+ρ22R=17.450π5.673+ρ2436.3,
P(ρ, θ)=acos8.725π5.673+ρ2436.3+i sin8.725π5.673+ρ2436.3cos 2θ.
U(v, θ)=20ρ0P(ρ, θ)J0(vρ)ρdρ,
U(θ, u)=20ρ0P(ρ, θ)expiuρ22ρdρ,
It=U(v, θ)U*(v, θ),
Ia=U(u, θ)U*(u, θ).

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