Abstract

A two-mode adjustable superresolving filter based on a birefringent filter is proposed. This kind of filter has superresolution in two modes of adjustment. One is rotation of the binary pupil filter on the optical axis of the system and the other is the tilt of the filter away from the pupil plane on axis parallel or perpendicular to the optical axis of the crystal. The filters act as complex amplitude filters in the former mode, and as pure phase filters in the latter. By analyzing two superresolving parameters, we obtain the optimal design parameters that ensure a large field of view, a large superresolving range, and a high setting accuracy. This kind of filter can provide more flexibility in practical applications.

© 2006 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  2. Z. S. Hegedus and V. Safaris, "Superresolving filters in confocally scanned imaging systems," J. Opt. Soc. Am. A 3, 1892-1896 (1986).
    [CrossRef]
  3. D. M. de Juana, J. E. Oti, V. F. Canales, and M. P. Cagigal, "Transverse or axial superresolution in a 4Pi-confocal microscope by phase-only filters," J. Opt. Soc. Am. A 20, 2172-2178 (2003).
    [CrossRef]
  4. G. Boyer, "New class of axially apodizing filters for confocal scanning microscopy," J. Opt. Soc. Am. A 19, 584-589 (2002).
  5. T. R. M. Sales and 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, 1996), pp. 290-292.
  6. H. Fukuda, T. Terasawa, and S. Okazaki, "Spatial filtering for depth of focus and resolution enhancement in optical lithography," J. Vac. Sci. Technol. B 9, 3113-3116 (1991).
    [CrossRef]
  7. G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento Suppl. 9, 426-435 (1952).
    [CrossRef]
  8. M. Martinez-Corral, P. Andres, J. Ojeda-Castaneda, and G. Saavedra, "Adjustable axial superresolution by annular binary filters: application to confocal microcopy," Opt. Commun. 119, 491-498 (1995).
    [CrossRef]
  9. M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and 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).
  10. C. J. R. Sheppard, "Leaky annular pupils for improved axial imaging," Optik (Stuttgart) 99, 32-34 (1995).
  11. M. Gu, T. Tannous, and C. J. R. Sheppard, "Effect of an annular pupil on confocal imaging through highly scattering media," Opt. Lett. 21, 312-314 (1996).
    [CrossRef] [PubMed]
  12. M. Gu and C. J. R. Sheppard, "Confocal fluorescent microscopy with a finite sized circular detector," J. Opt. Soc. Am. A 9, 151-153(1992).
    [CrossRef]
  13. M. Yun, L. Liu, J. Sun, and D. Liu, "Transverse or axial superresolution with radial birefringent filter," J. Opt. Soc. Am. A 21, 1869-1874 (2004).
    [CrossRef]
  14. S. Zhou and C. Zhou, "Discrete continuous-phase superresolving filters," Opt. Lett. 29, 2746-2748 (2004).
    [CrossRef] [PubMed]
  15. F. Xiao, J. Yuan, G. Wang, and Z. Xu, "Tunable phase-only optical filters with a uniaxial crystal," Appl. Opt. 43, 3415-3419 (2004).
    [CrossRef] [PubMed]
  16. A. I. Whiting, A. F. Abouraddy, B. E. A. Saleh, M. C. Teich, and J. T. Fourkas, "Polarization-assisted transverse and axial optical superresolution," Opt. Express 11, 1714-1723 (2003).
    [CrossRef] [PubMed]
  17. C. J. R. Sheppard and Z. S. Hegedus, "Axial behavior of pupil-plane filters," J. Opt. Soc. Am. A 5, 643-647 (1988).
    [CrossRef]
  18. J. M. Eggleston, G. Giuliani, and R. L. Byer, "Radial intensity filters using radial birefringent elements," J. Opt. Soc. Am. 71, 1264-1272 (1981).
    [CrossRef]

2004

M. Yun, L. Liu, J. Sun, and D. Liu, "Transverse or axial superresolution with radial birefringent filter," J. Opt. Soc. Am. A 21, 1869-1874 (2004).
[CrossRef]

S. Zhou and C. Zhou, "Discrete continuous-phase superresolving filters," Opt. Lett. 29, 2746-2748 (2004).
[CrossRef] [PubMed]

F. Xiao, J. Yuan, G. Wang, and Z. Xu, "Tunable phase-only optical filters with a uniaxial crystal," Appl. Opt. 43, 3415-3419 (2004).
[CrossRef] [PubMed]

2003

A. I. Whiting, A. F. Abouraddy, B. E. A. Saleh, M. C. Teich, and J. T. Fourkas, "Polarization-assisted transverse and axial optical superresolution," Opt. Express 11, 1714-1723 (2003).
[CrossRef] [PubMed]

D. M. de Juana, J. E. Oti, V. F. Canales, and M. P. Cagigal, "Transverse or axial superresolution in a 4Pi-confocal microscope by phase-only filters," J. Opt. Soc. Am. A 20, 2172-2178 (2003).
[CrossRef]

2002

G. Boyer, "New class of axially apodizing filters for confocal scanning microscopy," J. Opt. Soc. Am. A 19, 584-589 (2002).

1998

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and 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).

1996

1995

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, and G. Saavedra, "Adjustable axial superresolution by annular binary filters: application to confocal microcopy," Opt. Commun. 119, 491-498 (1995).
[CrossRef]

1992

M. Gu and C. J. R. Sheppard, "Confocal fluorescent microscopy with a finite sized circular detector," J. Opt. Soc. Am. A 9, 151-153(1992).
[CrossRef]

1991

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

1988

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

1986

1981

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

1952

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

Abouraddy, A. F.

A. I. Whiting, A. F. Abouraddy, B. E. A. Saleh, M. C. Teich, and J. T. Fourkas, "Polarization-assisted transverse and axial optical superresolution," Opt. Express 11, 1714-1723 (2003).
[CrossRef] [PubMed]

Andres, P.

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and 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, and G. Saavedra, "Adjustable axial superresolution by annular binary filters: application to confocal microcopy," Opt. Commun. 119, 491-498 (1995).
[CrossRef]

Born, M.

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

Boyer, G.

G. Boyer, "New class of axially apodizing filters for confocal scanning microscopy," J. Opt. Soc. Am. A 19, 584-589 (2002).

Byer, R. L.

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

Cagigal, M. P.

Canales, V. F.

de Juana, D. M.

Eggleston, J. M.

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

Fourkas, J. T.

A. I. Whiting, A. F. Abouraddy, B. E. A. Saleh, M. C. Teich, and J. T. Fourkas, "Polarization-assisted transverse and axial optical superresolution," Opt. Express 11, 1714-1723 (2003).
[CrossRef] [PubMed]

Fukuda, H.

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

Giuliani, G.

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

Gu, M.

M. Gu, T. Tannous, and C. J. R. Sheppard, "Effect of an annular pupil on confocal imaging through highly scattering media," Opt. Lett. 21, 312-314 (1996).
[CrossRef] [PubMed]

M. Gu and C. J. R. Sheppard, "Confocal fluorescent microscopy with a finite sized circular detector," J. Opt. Soc. Am. A 9, 151-153(1992).
[CrossRef]

Hegedus, Z. S.

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

Z. S. Hegedus and V. Safaris, "Superresolving filters in confocally scanned imaging systems," J. Opt. Soc. Am. A 3, 1892-1896 (1986).
[CrossRef]

Liu, D.

Liu, L.

Martinez-Corral, M.

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and 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, and G. Saavedra, "Adjustable axial superresolution by annular binary filters: application to confocal microcopy," Opt. Commun. 119, 491-498 (1995).
[CrossRef]

Morris, G. M.

T. R. M. Sales and 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, 1996), pp. 290-292.

Ojeda-Castaneda, J.

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

Okazaki, S.

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

Oti, J. E.

Saavedra, G.

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

Safaris, V.

Saleh, B. E. A.

A. I. Whiting, A. F. Abouraddy, B. E. A. Saleh, M. C. Teich, and J. T. Fourkas, "Polarization-assisted transverse and axial optical superresolution," Opt. Express 11, 1714-1723 (2003).
[CrossRef] [PubMed]

Sales, T. R. M.

T. R. M. Sales and 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, 1996), pp. 290-292.

Sheppard, C. J. R.

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and 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. Gu, T. Tannous, and C. J. R. Sheppard, "Effect of an annular pupil on confocal imaging through highly scattering media," Opt. Lett. 21, 312-314 (1996).
[CrossRef] [PubMed]

Sheppard, C. J. R.

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

M. Gu and C. J. R. Sheppard, "Confocal fluorescent microscopy with a finite sized circular detector," J. Opt. Soc. Am. A 9, 151-153(1992).
[CrossRef]

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

Sun, J.

Tannous, T.

Teich, M. C.

A. I. Whiting, A. F. Abouraddy, B. E. A. Saleh, M. C. Teich, and J. T. Fourkas, "Polarization-assisted transverse and axial optical superresolution," Opt. Express 11, 1714-1723 (2003).
[CrossRef] [PubMed]

Terasawa, T.

H. Fukuda, T. Terasawa, and 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.

F. Xiao, J. Yuan, G. Wang, and Z. Xu, "Tunable phase-only optical filters with a uniaxial crystal," Appl. Opt. 43, 3415-3419 (2004).
[CrossRef] [PubMed]

Whiting, A. I.

A. I. Whiting, A. F. Abouraddy, B. E. A. Saleh, M. C. Teich, and J. T. Fourkas, "Polarization-assisted transverse and axial optical superresolution," Opt. Express 11, 1714-1723 (2003).
[CrossRef] [PubMed]

Wolf, E.

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

Xiao, F.

F. Xiao, J. Yuan, G. Wang, and Z. Xu, "Tunable phase-only optical filters with a uniaxial crystal," Appl. Opt. 43, 3415-3419 (2004).
[CrossRef] [PubMed]

Xu, Z.

F. Xiao, J. Yuan, G. Wang, and Z. Xu, "Tunable phase-only optical filters with a uniaxial crystal," Appl. Opt. 43, 3415-3419 (2004).
[CrossRef] [PubMed]

Yuan, J.

F. Xiao, J. Yuan, G. Wang, and Z. Xu, "Tunable phase-only optical filters with a uniaxial crystal," Appl. Opt. 43, 3415-3419 (2004).
[CrossRef] [PubMed]

Yun, M.

Zapata-Rodriguez, C. J.

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and 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).

Zhou, C.

S. Zhou and C. Zhou, "Discrete continuous-phase superresolving filters," Opt. Lett. 29, 2746-2748 (2004).
[CrossRef] [PubMed]

Zhou, S.

S. Zhou and C. Zhou, "Discrete continuous-phase superresolving filters," Opt. Lett. 29, 2746-2748 (2004).
[CrossRef] [PubMed]

Appl. Opt.

F. Xiao, J. Yuan, G. Wang, and Z. Xu, "Tunable phase-only optical filters with a uniaxial crystal," Appl. Opt. 43, 3415-3419 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

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

J. Opt. Soc. Am. A

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

M. Gu and C. J. R. Sheppard, "Confocal fluorescent microscopy with a finite sized circular detector," J. Opt. Soc. Am. A 9, 151-153(1992).
[CrossRef]

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

H. Fukuda, T. Terasawa, and 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

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

Opt. Commun.

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

Opt. Express

A. I. Whiting, A. F. Abouraddy, B. E. A. Saleh, M. C. Teich, and J. T. Fourkas, "Polarization-assisted transverse and axial optical superresolution," Opt. Express 11, 1714-1723 (2003).
[CrossRef] [PubMed]

Opt. Lett.

S. Zhou and C. Zhou, "Discrete continuous-phase superresolving filters," Opt. Lett. 29, 2746-2748 (2004).
[CrossRef] [PubMed]

Opt. Lett.

Optik

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and 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).

Other

G. Boyer, "New class of axially apodizing filters for confocal scanning microscopy," J. Opt. Soc. Am. A 19, 584-589 (2002).

T. R. M. Sales and 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, 1996), pp. 290-292.

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

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Figures (5)

Fig. 1
Fig. 1

Sketch of (a) a DMASF and (b) a BPF: oz is the optical axis, ε is the relative radius of the crystal zone, and ↔ represents the direction of the optical axis of the crystal. The hollow arrows indicate the operation in use: 1, rotation in the RLA mode; 2, 3, the permissible tilt directions in the TTA mode; p and q, the axes on which the BPF tilts.

Fig. 2
Fig. 2

Dependence of (a) S and (b) G on rotation angle θ in the RLA for different thicknesses of the BPF denoted by ( 2 m - 1 ). (a) ( 2 m - 1 ) = 16.5 , 17 , 18 , 19 , 21 , 21.5 , 22 , 23 , 25 , and  25.5 , respectively; (b) ( 2 m - 1 ) = 17 , 19 , 21 , 23 ,    and   25 .

Fig. 3
Fig. 3

Dependence of (a) S and (b) G on tilting angle i in TTA for different thicknesses [characterized by ( 2 m - 1 )] of BPF for ( 2 m - 1 ) = 17 , 19 , 21 , 23 ,     and  25 , respectively.

Fig. 4
Fig. 4

(a), (b) Transverse and (c) axial intensity for different superresolved patterns in the RLA mode. The rotation angles have values of 0 ° , 15 ° , 30 ° ,   and  45 ° , respectively. (a), (c) normalized to the airy pattern; (b) normalized to the intensity distribution itself.

Fig. 5
Fig. 5

(a), (b) Transverse and (c) axial intensity for different superresolved patterns in the TTA mode. The tilting angles have values of 0 ° , 1 ° , 2 ° , 3 ° ,   and  3.8 ° , respectively. (a), (c) normalized to the airy pattern; (b) normalized to the intensity distribution itself.

Equations (11)

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

U ( ν , u ) = 2 0 1 P ( ρ ) J 0 ( ν ρ ) exp ( j u ρ 2 / 2 ) ρ .
ν = k r sin α ,
u = 4 k z sin 2 ( α / 2 ) ,
U ( ν , 0 ) = 2 0 1 P ( ρ ) J 0 ( ν ρ ) ρ ,
U ( 0 , u ) = 2 0 1 P ( ρ ) exp ( j u ρ 2 / 2 ) ρ dρ.
T ( ρ ) = cos 2 [ δ 0 2 ] sin 2 2 θ + cos 2 2 θ,
l = ( 2 m 1 ) λ / ( 2 Δ n ),
δ = 2 π Δ n λ l cos β ,
P ( ρ ) = { 1 T e i δ ( 1 > ρ > ε ) ( 0 < ρ ε ) ,
I = U U * ,
n = n e 1 + ( n o 2 - n e 2 ) cos 2 Φ 0 sin 2 α n o 2 n e 2 ,

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