Abstract

Many applications can benefit from the use of pupil filters for controlling the light intensity distribution near the focus of an optical system. Most of the design methods for such filters are based on a second-order expansion of the Point Spread Function (PSF). Here, we present a new procedure for designing radially-symmetric pupil filters. It is more precise than previous procedures as it considers the exact expression of the PSF, expanded as a function of first-order Bessel functions. Furthermore, this new method presents other advantages: the height of the side lobes can be easily controlled, it allows the design of amplitude-only, phase-only or hybrid filters, and the coefficients of the PSF expansion can be directly related to filter parameters. Finally, our procedure allows the design of filters with very different behaviours and optimal performance.

© 2006 Optical Society of America

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  1. G. Boyer, "New class of axially apodizing filters for confocal scanning microscopy," J. Opt. Soc. Am A 19584-589 (2002).
    [CrossRef]
  2. M. Martínez-Corral, P. Andrés, C.J. Zapata-Rodríguez and M. Kowalczyk, "Three-dimensional superresolution by annular binary filtres," Opt.Commun. 165, 267-278 (1999).
    [CrossRef]
  3. M.T. Caballero, P. Andrés, A. Pons, J. Lancis and M. Martínez-Corral, "Axial resolution in two-color excitation fluorescence microscopy by phase-only apodization," Opt.Commun. 246, 313-321 (2005).
    [CrossRef]
  4. 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]
  5. <jrn>. X. Zhao, C. Li and H. Ruan, "A new approach for improving transverse superresolution in optical data storage," Opt. Eng. 44, 125202 1-4 (2005).</jrn>
    [CrossRef]
  6. S. Pereira and A.S. van de Nes, "Superresolution by means of polarisation, phase and amplitude pupil masks," Opt.Commun. 234, 119-124 (2004).
    [CrossRef]
  7. V.F. Canales, D.M. de Juana and M.P. Cagigal, "Superresolution in compensated telescopes," Opt. Lett. 29 (2004) 935-937
    [CrossRef] [PubMed]
  8. M.P. Cagigal, V.F. Canales and J.E. Oti, "Design of continuous superresolving masks for ground-based telescopes", Publ. Astron. Soc. Pac. 116, 965-970 (2004).
    [CrossRef]
  9. J. Jia, C, Zhou and L. Liu, "Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system," Opt.Commun. 228, 271-278 (2003).
    [CrossRef]
  10. G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo CimentoSuppl. 9426-435 (1952).
    [CrossRef]
  11. C.J.R. Sheppard and Z.S. Hegedus, "Axial behavior of pupil-plane filters," J. Opt. Soc. Am A 5, 643-647 (1988).
    [CrossRef]
  12. D.M. de Juana, J.E. Oti, V.F. Canales and M.P. Cagigal, "Design of superresolving continuous phase filters," Opt. Lett. 28, 607-609 (2003).
    [CrossRef] [PubMed]
  13. M. Yun, L. Liu, J. Sun and D. Liu, "Three-dimensional superresolution by three-zone complex pupil filters," J. Opt. Soc. Am A 22 (2005) 272-277.
    [CrossRef]
  14. X. Zhao, C. Li and H. Ruan, "Improvement of three-dimensional resolution in optical data storage by combination of two annular binary phase filters," Chin. Phys. Lett. 21, 1515-1517 (2004).
    [CrossRef]
  15. 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]
  16. S. Zhou and C. Zhou, "Discrete continuous-phase superresolving filters," Opt. Lett. 23, 2746-2748 (2004).
    [CrossRef]
  17. H. Ding, Q. Li and W. Zou, "Design and comparison of amplitude-type and phase-only transverse super-resolving pupil filters," Opt. Commun. 229, 117-122 (2004).
    [CrossRef]
  18. S. Ledesma, J.C. Escalera, J. Campos and M.J. Yzuel, "Evolution of the transverse response of an optical system with complex filtres," Opt. Commun. 249, 183-192 (2005).
    [CrossRef]
  19. H. Luo and C. Zhou, "Comparison of superresolution effects with annular phase and amplitude filters," Appl. Opt. 43, 6242-6247 (2004).
    [CrossRef] [PubMed]
  20. P. Narayan, E. Hack and P. Rastogi, "High efficient superesolution combination filter with twin LCD spatial light modulators," Opt. Express 13, 2835-2842 (2005).
    [CrossRef]
  21. J. Jia, C. Zhou, X. Sun and L. Liu, "Superresolution laser beam shaping," Appl. Opt. 43, 2112-2117 (2004).
    [CrossRef] [PubMed]
  22. T.R.M. Sales and G.M. Morris, "Axial superresolution with phase-only pùpil filters," Opt.Commun. 156, 227-230 (1998).
    [CrossRef]
  23. M. Martínez-Corral, P. Andrés, J. Ojeda-Castañeda and G. Saavedra, "Aunable axial superresolution by annular binary filtres. Application to confocal microscopy," Opt.Commun. 119, 491-498 (1995).
    [CrossRef]
  24. V.F. Canales, J.E. Oti and M.P. Cagigal, "Three-dimensional control of the focal light intensity distribution by analytically-designed phase masks" Opt. Commun. 247, 11-18 (2005).
    [CrossRef]
  25. H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl.Opt. 41, 5263-5266 (2002).
    [CrossRef] [PubMed]
  26. V.F. Canales, J.E. Oti, P.J. Valle and M.P. Cagigal, "Reduction of the diffraction pattern in segmented apertures", Opt. Eng. (to be published).
  27. M.P. Cagigal, J.E. Oti, V.F. Canales and P.J. Valle, "Analytical design of superresolving phase filters," Opt. Commun. 241, 249-253 (2004).
    [CrossRef]
  28. C.J.R. Sheppard and A. Choudhury, "Image formation in the scanning microscope," Optica Acta 24, 1051-1073 (1977).
    [CrossRef]

2005 (5)

M.T. Caballero, P. Andrés, A. Pons, J. Lancis and M. Martínez-Corral, "Axial resolution in two-color excitation fluorescence microscopy by phase-only apodization," Opt.Commun. 246, 313-321 (2005).
[CrossRef]

M. Yun, L. Liu, J. Sun and D. Liu, "Three-dimensional superresolution by three-zone complex pupil filters," J. Opt. Soc. Am A 22 (2005) 272-277.
[CrossRef]

S. Ledesma, J.C. Escalera, J. Campos and M.J. Yzuel, "Evolution of the transverse response of an optical system with complex filtres," Opt. Commun. 249, 183-192 (2005).
[CrossRef]

P. Narayan, E. Hack and P. Rastogi, "High efficient superesolution combination filter with twin LCD spatial light modulators," Opt. Express 13, 2835-2842 (2005).
[CrossRef]

V.F. Canales, J.E. Oti and M.P. Cagigal, "Three-dimensional control of the focal light intensity distribution by analytically-designed phase masks" Opt. Commun. 247, 11-18 (2005).
[CrossRef]

2004 (10)

M.P. Cagigal, J.E. Oti, V.F. Canales and P.J. Valle, "Analytical design of superresolving phase filters," Opt. Commun. 241, 249-253 (2004).
[CrossRef]

J. Jia, C. Zhou, X. Sun and L. Liu, "Superresolution laser beam shaping," Appl. Opt. 43, 2112-2117 (2004).
[CrossRef] [PubMed]

H. Luo and C. Zhou, "Comparison of superresolution effects with annular phase and amplitude filters," Appl. Opt. 43, 6242-6247 (2004).
[CrossRef] [PubMed]

X. Zhao, C. Li and H. Ruan, "Improvement of three-dimensional resolution in optical data storage by combination of two annular binary phase filters," Chin. Phys. Lett. 21, 1515-1517 (2004).
[CrossRef]

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. 23, 2746-2748 (2004).
[CrossRef]

H. Ding, Q. Li and W. Zou, "Design and comparison of amplitude-type and phase-only transverse super-resolving pupil filters," Opt. Commun. 229, 117-122 (2004).
[CrossRef]

S. Pereira and A.S. van de Nes, "Superresolution by means of polarisation, phase and amplitude pupil masks," Opt.Commun. 234, 119-124 (2004).
[CrossRef]

V.F. Canales, D.M. de Juana and M.P. Cagigal, "Superresolution in compensated telescopes," Opt. Lett. 29 (2004) 935-937
[CrossRef] [PubMed]

M.P. Cagigal, V.F. Canales and J.E. Oti, "Design of continuous superresolving masks for ground-based telescopes", Publ. Astron. Soc. Pac. 116, 965-970 (2004).
[CrossRef]

2003 (3)

J. Jia, C, Zhou and L. Liu, "Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system," Opt.Commun. 228, 271-278 (2003).
[CrossRef]

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]

D.M. de Juana, J.E. Oti, V.F. Canales and M.P. Cagigal, "Design of superresolving continuous phase filters," Opt. Lett. 28, 607-609 (2003).
[CrossRef] [PubMed]

2002 (2)

G. Boyer, "New class of axially apodizing filters for confocal scanning microscopy," J. Opt. Soc. Am A 19584-589 (2002).
[CrossRef]

H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl.Opt. 41, 5263-5266 (2002).
[CrossRef] [PubMed]

1999 (1)

M. Martínez-Corral, P. Andrés, C.J. Zapata-Rodríguez and M. Kowalczyk, "Three-dimensional superresolution by annular binary filtres," Opt.Commun. 165, 267-278 (1999).
[CrossRef]

1998 (1)

T.R.M. Sales and G.M. Morris, "Axial superresolution with phase-only pùpil filters," Opt.Commun. 156, 227-230 (1998).
[CrossRef]

1995 (1)

M. Martínez-Corral, P. Andrés, J. Ojeda-Castañeda and G. Saavedra, "Aunable axial superresolution by annular binary filtres. Application to confocal microscopy," Opt.Commun. 119, 491-498 (1995).
[CrossRef]

1988 (1)

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

1977 (1)

C.J.R. Sheppard and A. Choudhury, "Image formation in the scanning microscope," Optica Acta 24, 1051-1073 (1977).
[CrossRef]

1952 (1)

G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo CimentoSuppl. 9426-435 (1952).
[CrossRef]

Andrés, P.

M.T. Caballero, P. Andrés, A. Pons, J. Lancis and M. Martínez-Corral, "Axial resolution in two-color excitation fluorescence microscopy by phase-only apodization," Opt.Commun. 246, 313-321 (2005).
[CrossRef]

M. Martínez-Corral, P. Andrés, C.J. Zapata-Rodríguez and M. Kowalczyk, "Three-dimensional superresolution by annular binary filtres," Opt.Commun. 165, 267-278 (1999).
[CrossRef]

M. Martínez-Corral, P. Andrés, J. Ojeda-Castañeda and G. Saavedra, "Aunable axial superresolution by annular binary filtres. Application to confocal microscopy," Opt.Commun. 119, 491-498 (1995).
[CrossRef]

Boyer, G.

G. Boyer, "New class of axially apodizing filters for confocal scanning microscopy," J. Opt. Soc. Am A 19584-589 (2002).
[CrossRef]

Caballero, M.T.

M.T. Caballero, P. Andrés, A. Pons, J. Lancis and M. Martínez-Corral, "Axial resolution in two-color excitation fluorescence microscopy by phase-only apodization," Opt.Commun. 246, 313-321 (2005).
[CrossRef]

Cagigal, M.P.

V.F. Canales, J.E. Oti and M.P. Cagigal, "Three-dimensional control of the focal light intensity distribution by analytically-designed phase masks" Opt. Commun. 247, 11-18 (2005).
[CrossRef]

V.F. Canales, D.M. de Juana and M.P. Cagigal, "Superresolution in compensated telescopes," Opt. Lett. 29 (2004) 935-937
[CrossRef] [PubMed]

M.P. Cagigal, V.F. Canales and J.E. Oti, "Design of continuous superresolving masks for ground-based telescopes", Publ. Astron. Soc. Pac. 116, 965-970 (2004).
[CrossRef]

M.P. Cagigal, J.E. Oti, V.F. Canales and P.J. Valle, "Analytical design of superresolving phase filters," Opt. Commun. 241, 249-253 (2004).
[CrossRef]

D.M. de Juana, J.E. Oti, V.F. Canales and M.P. Cagigal, "Design of superresolving continuous phase filters," Opt. Lett. 28, 607-609 (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]

V.F. Canales, J.E. Oti, P.J. Valle and M.P. Cagigal, "Reduction of the diffraction pattern in segmented apertures", Opt. Eng. (to be published).

Campos, J.

S. Ledesma, J.C. Escalera, J. Campos and M.J. Yzuel, "Evolution of the transverse response of an optical system with complex filtres," Opt. Commun. 249, 183-192 (2005).
[CrossRef]

Canales, V.F.

V.F. Canales, J.E. Oti and M.P. Cagigal, "Three-dimensional control of the focal light intensity distribution by analytically-designed phase masks" Opt. Commun. 247, 11-18 (2005).
[CrossRef]

V.F. Canales, D.M. de Juana and M.P. Cagigal, "Superresolution in compensated telescopes," Opt. Lett. 29 (2004) 935-937
[CrossRef] [PubMed]

M.P. Cagigal, V.F. Canales and J.E. Oti, "Design of continuous superresolving masks for ground-based telescopes", Publ. Astron. Soc. Pac. 116, 965-970 (2004).
[CrossRef]

M.P. Cagigal, J.E. Oti, V.F. Canales and P.J. Valle, "Analytical design of superresolving phase filters," Opt. Commun. 241, 249-253 (2004).
[CrossRef]

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]

D.M. de Juana, J.E. Oti, V.F. Canales and M.P. Cagigal, "Design of superresolving continuous phase filters," Opt. Lett. 28, 607-609 (2003).
[CrossRef] [PubMed]

V.F. Canales, J.E. Oti, P.J. Valle and M.P. Cagigal, "Reduction of the diffraction pattern in segmented apertures", Opt. Eng. (to be published).

Choudhury, A.

C.J.R. Sheppard and A. Choudhury, "Image formation in the scanning microscope," Optica Acta 24, 1051-1073 (1977).
[CrossRef]

de Juana, D.M.

Ding, H.

H. Ding, Q. Li and W. Zou, "Design and comparison of amplitude-type and phase-only transverse super-resolving pupil filters," Opt. Commun. 229, 117-122 (2004).
[CrossRef]

Escalera, J.C.

S. Ledesma, J.C. Escalera, J. Campos and M.J. Yzuel, "Evolution of the transverse response of an optical system with complex filtres," Opt. Commun. 249, 183-192 (2005).
[CrossRef]

Gan, F.

H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl.Opt. 41, 5263-5266 (2002).
[CrossRef] [PubMed]

Hack, E.

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]

Jia, J.

J. Jia, C. Zhou, X. Sun and L. Liu, "Superresolution laser beam shaping," Appl. Opt. 43, 2112-2117 (2004).
[CrossRef] [PubMed]

J. Jia, C, Zhou and L. Liu, "Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system," Opt.Commun. 228, 271-278 (2003).
[CrossRef]

Kowalczyk, M.

M. Martínez-Corral, P. Andrés, C.J. Zapata-Rodríguez and M. Kowalczyk, "Three-dimensional superresolution by annular binary filtres," Opt.Commun. 165, 267-278 (1999).
[CrossRef]

Lancis, J.

M.T. Caballero, P. Andrés, A. Pons, J. Lancis and M. Martínez-Corral, "Axial resolution in two-color excitation fluorescence microscopy by phase-only apodization," Opt.Commun. 246, 313-321 (2005).
[CrossRef]

Ledesma, S.

S. Ledesma, J.C. Escalera, J. Campos and M.J. Yzuel, "Evolution of the transverse response of an optical system with complex filtres," Opt. Commun. 249, 183-192 (2005).
[CrossRef]

Li, C.

X. Zhao, C. Li and H. Ruan, "Improvement of three-dimensional resolution in optical data storage by combination of two annular binary phase filters," Chin. Phys. Lett. 21, 1515-1517 (2004).
[CrossRef]

Li, Q.

H. Ding, Q. Li and W. Zou, "Design and comparison of amplitude-type and phase-only transverse super-resolving pupil filters," Opt. Commun. 229, 117-122 (2004).
[CrossRef]

Liu, D.

M. Yun, L. Liu, J. Sun and D. Liu, "Three-dimensional superresolution by three-zone complex pupil filters," J. Opt. Soc. Am A 22 (2005) 272-277.
[CrossRef]

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]

Liu, L.

M. Yun, L. Liu, J. Sun and D. Liu, "Three-dimensional superresolution by three-zone complex pupil filters," J. Opt. Soc. Am A 22 (2005) 272-277.
[CrossRef]

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]

J. Jia, C. Zhou, X. Sun and L. Liu, "Superresolution laser beam shaping," Appl. Opt. 43, 2112-2117 (2004).
[CrossRef] [PubMed]

Luo, H.

Martínez-Corral, M.

M.T. Caballero, P. Andrés, A. Pons, J. Lancis and M. Martínez-Corral, "Axial resolution in two-color excitation fluorescence microscopy by phase-only apodization," Opt.Commun. 246, 313-321 (2005).
[CrossRef]

M. Martínez-Corral, P. Andrés, C.J. Zapata-Rodríguez and M. Kowalczyk, "Three-dimensional superresolution by annular binary filtres," Opt.Commun. 165, 267-278 (1999).
[CrossRef]

M. Martínez-Corral, P. Andrés, J. Ojeda-Castañeda and G. Saavedra, "Aunable axial superresolution by annular binary filtres. Application to confocal microscopy," Opt.Commun. 119, 491-498 (1995).
[CrossRef]

Morris, G.M.

T.R.M. Sales and G.M. Morris, "Axial superresolution with phase-only pùpil filters," Opt.Commun. 156, 227-230 (1998).
[CrossRef]

Narayan, P.

Ojeda-Castañeda, J.

M. Martínez-Corral, P. Andrés, J. Ojeda-Castañeda and G. Saavedra, "Aunable axial superresolution by annular binary filtres. Application to confocal microscopy," Opt.Commun. 119, 491-498 (1995).
[CrossRef]

Oti, J.E.

V.F. Canales, J.E. Oti and M.P. Cagigal, "Three-dimensional control of the focal light intensity distribution by analytically-designed phase masks" Opt. Commun. 247, 11-18 (2005).
[CrossRef]

M.P. Cagigal, V.F. Canales and J.E. Oti, "Design of continuous superresolving masks for ground-based telescopes", Publ. Astron. Soc. Pac. 116, 965-970 (2004).
[CrossRef]

M.P. Cagigal, J.E. Oti, V.F. Canales and P.J. Valle, "Analytical design of superresolving phase filters," Opt. Commun. 241, 249-253 (2004).
[CrossRef]

D.M. de Juana, J.E. Oti, V.F. Canales and M.P. Cagigal, "Design of superresolving continuous phase filters," Opt. Lett. 28, 607-609 (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]

V.F. Canales, J.E. Oti, P.J. Valle and M.P. Cagigal, "Reduction of the diffraction pattern in segmented apertures", Opt. Eng. (to be published).

Pereira, S.

S. Pereira and A.S. van de Nes, "Superresolution by means of polarisation, phase and amplitude pupil masks," Opt.Commun. 234, 119-124 (2004).
[CrossRef]

Pons, A.

M.T. Caballero, P. Andrés, A. Pons, J. Lancis and M. Martínez-Corral, "Axial resolution in two-color excitation fluorescence microscopy by phase-only apodization," Opt.Commun. 246, 313-321 (2005).
[CrossRef]

Rastogi, P.

Ruan, H.

X. Zhao, C. Li and H. Ruan, "Improvement of three-dimensional resolution in optical data storage by combination of two annular binary phase filters," Chin. Phys. Lett. 21, 1515-1517 (2004).
[CrossRef]

Saavedra, G.

M. Martínez-Corral, P. Andrés, J. Ojeda-Castañeda and G. Saavedra, "Aunable axial superresolution by annular binary filtres. Application to confocal microscopy," Opt.Commun. 119, 491-498 (1995).
[CrossRef]

Sales, T.R.M.

T.R.M. Sales and G.M. Morris, "Axial superresolution with phase-only pùpil filters," Opt.Commun. 156, 227-230 (1998).
[CrossRef]

Sheppard, C.J.R.

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

C.J.R. Sheppard and A. Choudhury, "Image formation in the scanning microscope," Optica Acta 24, 1051-1073 (1977).
[CrossRef]

Sun, J.

M. Yun, L. Liu, J. Sun and D. Liu, "Three-dimensional superresolution by three-zone complex pupil filters," J. Opt. Soc. Am A 22 (2005) 272-277.
[CrossRef]

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]

Sun, X.

Toraldo di Francia, G.

G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo CimentoSuppl. 9426-435 (1952).
[CrossRef]

Valle, P.J.

M.P. Cagigal, J.E. Oti, V.F. Canales and P.J. Valle, "Analytical design of superresolving phase filters," Opt. Commun. 241, 249-253 (2004).
[CrossRef]

V.F. Canales, J.E. Oti, P.J. Valle and M.P. Cagigal, "Reduction of the diffraction pattern in segmented apertures", Opt. Eng. (to be published).

van de Nes, A.S.

S. Pereira and A.S. van de Nes, "Superresolution by means of polarisation, phase and amplitude pupil masks," Opt.Commun. 234, 119-124 (2004).
[CrossRef]

Wang, H.

H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl.Opt. 41, 5263-5266 (2002).
[CrossRef] [PubMed]

Yun, M.

M. Yun, L. Liu, J. Sun and D. Liu, "Three-dimensional superresolution by three-zone complex pupil filters," J. Opt. Soc. Am A 22 (2005) 272-277.
[CrossRef]

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]

Yzuel, M.J.

S. Ledesma, J.C. Escalera, J. Campos and M.J. Yzuel, "Evolution of the transverse response of an optical system with complex filtres," Opt. Commun. 249, 183-192 (2005).
[CrossRef]

Zapata-Rodríguez, C.J.

M. Martínez-Corral, P. Andrés, C.J. Zapata-Rodríguez and M. Kowalczyk, "Three-dimensional superresolution by annular binary filtres," Opt.Commun. 165, 267-278 (1999).
[CrossRef]

Zhao, X.

X. Zhao, C. Li and H. Ruan, "Improvement of three-dimensional resolution in optical data storage by combination of two annular binary phase filters," Chin. Phys. Lett. 21, 1515-1517 (2004).
[CrossRef]

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Zhou, S.

S. Zhou and C. Zhou, "Discrete continuous-phase superresolving filters," Opt. Lett. 23, 2746-2748 (2004).
[CrossRef]

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H. Ding, Q. Li and W. Zou, "Design and comparison of amplitude-type and phase-only transverse super-resolving pupil filters," Opt. Commun. 229, 117-122 (2004).
[CrossRef]

Appl. Opt. (2)

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Chin. Phys. Lett. (1)

X. Zhao, C. Li and H. Ruan, "Improvement of three-dimensional resolution in optical data storage by combination of two annular binary phase filters," Chin. Phys. Lett. 21, 1515-1517 (2004).
[CrossRef]

J. Opt. Soc. Am A (5)

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[CrossRef]

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H. Ding, Q. Li and W. Zou, "Design and comparison of amplitude-type and phase-only transverse super-resolving pupil filters," Opt. Commun. 229, 117-122 (2004).
[CrossRef]

S. Ledesma, J.C. Escalera, J. Campos and M.J. Yzuel, "Evolution of the transverse response of an optical system with complex filtres," Opt. Commun. 249, 183-192 (2005).
[CrossRef]

M.P. Cagigal, J.E. Oti, V.F. Canales and P.J. Valle, "Analytical design of superresolving phase filters," Opt. Commun. 241, 249-253 (2004).
[CrossRef]

V.F. Canales, J.E. Oti and M.P. Cagigal, "Three-dimensional control of the focal light intensity distribution by analytically-designed phase masks" Opt. Commun. 247, 11-18 (2005).
[CrossRef]

Opt. Eng. (1)

V.F. Canales, J.E. Oti, P.J. Valle and M.P. Cagigal, "Reduction of the diffraction pattern in segmented apertures", Opt. Eng. (to be published).

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[CrossRef]

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[CrossRef]

M.T. Caballero, P. Andrés, A. Pons, J. Lancis and M. Martínez-Corral, "Axial resolution in two-color excitation fluorescence microscopy by phase-only apodization," Opt.Commun. 246, 313-321 (2005).
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M.P. Cagigal, V.F. Canales and J.E. Oti, "Design of continuous superresolving masks for ground-based telescopes", Publ. Astron. Soc. Pac. 116, 965-970 (2004).
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Other (1)

<jrn>. X. Zhao, C. Li and H. Ruan, "A new approach for improving transverse superresolution in optical data storage," Opt. Eng. 44, 125202 1-4 (2005).</jrn>
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Transverse PSF designed with our procedure to obtain a G value of 0.64 with S = 0.14 (solid curve) in comparison with the result found by Narayan et al. (dotted curve). For comparison the PSFs for an unobstructed pupil (dashed double-dotted curve) is also shown. v is normalized, so that the first zero of the PSF for the unobstructed pupil is unity.

Fig. 2.
Fig. 2.

Axial PSFs corresponding to the filters in figure 1: filter designed with our procedure (solid curve), the one designed by Narayan et al. (dotted curve) and the unobstructed pupil (dashed double-dotted curve). u is normalized, so that the first zero of the PSF for the unobstructed pupil is unity.

Fig. 3.
Fig. 3.

Transverse PSF designed with our procedure to obtain a G value of 0.7 (dotted-dashed curve). The result for a two-zones phase-only filter (dashed curve) is very similar. For comparison the PSFs for an unobstructed pupil (dashed double-dotted curve) and for the filters in figure 1, the filter designed with our procedure for G=0.64 (solid curve) and the one designed by Narayan et al. (dotted curve), are also shown. v is normalized, so that the first zero of the PSF for the unobstructed pupil is unity.

Fig. 4.
Fig. 4.

Axial PSFs corresponding to the filters in figure 3: filter designed with our procedure to obtain a G value of 0.7 (dotted-dashed curve), the two-zones phase-only filter (dashed curve), an unobstructed pupil (dashed double-dotted curve), filter designed with our procedure for G=0.64 (solid curve) and the one designed by Narayan et al. (dotted curve). u is normalized, so that the first zero of the PSF for the unobstructed pupil is unity.

Equations (15)

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U ( v , u ) = 2 0 1 P ( ρ ) J 0 ( ) exp ( ju ρ 2 / 2 ) ρ d ρ
P ( ρ ) = { t 1 e j π if ρ 0 ρ < ρ 1 t 2 e j 0 if ρ 1 ρ < ρ 2 t i ( e j π ) i if ρ i 1 ρ < ρ i t N ( e j π ) N if ρ N 1 ρ ρ N 0 if ρ > 1
U ( v , u = 0 ) = i = 1 N 2 t i ( 1 ) i ( ρ i J 1 ( ρ i v ) v ρ i 1 J 1 ( ρ i 1 v ) v ) =
= 2 t N ( 1 ) N ρ N J 1 ( ρ N v ) v + i = 1 N 1 2 ( t i + 1 + t i ) ( 1 ) i ρ i J 1 ( ρ i v ) v
J 0 ( ρ n + ρ m 1 v ) = lim ρ n ρ m 0 ( 2 ρ n J 1 ( ρ n v ) v 2 ρ m J 1 ( ρ m v ) v ) 1 ρ n 2 ρ m 2
S = PSE ( 0,0 ) PSF clear pupil ( 0,0 )
Γ = PSE ( 0,0 ) PSF ( v 1 st sidelobe , 0 )
d U d v ( v = v 1 st sidelobe , u = 0 ) = 2 t N ( 1 ) N ρ N 2 J 2 ( ρ N v ) v + i = 1 N 1 2 ( t i + 1 + t i ) ( 1 ) i ρ i 2 J 2 ( ρ i v ) v = 0
Resolution condition : PSF ( v 1 zA , 0 ) < ε Energy loss : S = PSF ( 0,0 ) > S 0 Side lobe height : Γ = PSF ( 0,0 ) PSF ( v 1 s , 0 ) > Γ 0
U ( v = 0 , u ) = i = 1 N t i ( 1 ) N i sin [ πu ( ρ i 2 ρ i 1 2 ) ] πu exp [ πju ( ρ i 2 + ρ i 1 2 ) ]
d d u PSF ( v = 0 , u ) u = 0 = 0
d d u PSF ( v = 0 , u ) = [ 0 1 2 ρP ( ρ ) d ρ exp ( juρ 2 2 ) ( 2 2 ) ] [ 0 1 2 ρP ( ρ ) d ρ exp ( juρ 2 2 ) ] * +
[ 0 1 2 ρP ( ρ ) d ρ exp ( juρ 2 2 ) ( 2 2 ) ] * [ 0 1 2 ρP ( ρ ) d ρ exp ( juρ 2 2 ) ]
d d u PSF ( v = 0 , u ) u = 0 = ( i = 1 N t i 4 j exp ( j ϕ i ) ( ρ i 4 ρ i 1 4 ) ) ( i = 1 N exp ( j ϕ i ) ( ρ i 2 ρ i 1 2 ) ) +
( i = 1 N t i 4 ( j ) exp ( j ϕ i ) ( ρ i 4 ρ i 1 4 ) ) ( i = 1 N t i exp ( j ϕ i ) ( ρ i 2 ρ i 1 2 ) )

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