Abstract

The characteristics of annular amplitude and phase filters are compared. The behavior of two-zone phase and amplitude filters as the inner zone is increased is studied in detail. Numerical simulations show that a phase filter can achieve a superresolution effect, a circular Dammann effect, and flat-topped intensity for different applications, whereas a two-zone amplitude filter can generate only a superresolution effect. The experimental results show that both amplitude and phase filters can achieve superresolution. Generally, a phase superresolution filter is recommended for its higher efficiency and its special diffraction patterns that are impossible to achieve with an amplitude filter.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
    [CrossRef]
  2. D. M. de Juana, V. F. Canales, P. J. Valle, M. P. Cagigal, “Focusing properties of annular binary phase filters,” Opt. Commun. 229, 71–77 (2004).
    [CrossRef]
  3. D. M. de Juana, J. E. Oti, V. F. Canales, M. P. Cagigal, “Design of superresolving continuous phase filters,” Opt. Lett. 28, 607–609 (2003).
    [CrossRef] [PubMed]
  4. W. D. Furlan, G. Saavedra, J. A. Monsoriu, J. D. Patrignani, “Axial behaviour of Cantor ring diffractals,” J. Opt. A 5, S361–S364 (2003).
    [CrossRef]
  5. D. M. de Juana, J. E. Oti, V. F. Canales, 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]
  6. Z. S. Hegedus, V. Sarafis, “Superresolving filters in confocally scanned imaging systems,” J. Opt. Soc. Am. A 3, 1892–1896 (1986).
    [CrossRef]
  7. R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field. I,” Opt. Acta 27, 587–610 (1980).
    [CrossRef]
  8. R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field. II,” Opt. Acta 27, 1641–1670 (1980).
    [CrossRef]
  9. M. Martínez-Corral, P. Andrés, C. J. Zapata-Rodríguez, M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
    [CrossRef]
  10. T. R. M. Sales, G. M. Morris, “Diffractive superresolution elements,” J. Opt. Soc. Am. A 14, 1637–1646 (1997).
    [CrossRef]
  11. J. Jia, C. Zhou, 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]
  12. C. Zhou, J. Jia, L. Liu, “Circular Dammann grating,” Opt. Lett. 28, 2174–2176 (2003).
    [CrossRef] [PubMed]
  13. J. Jia, C. Zhou, X. Sun, L. Liu, “Superresolution laser beam shaping,” Appl. Opt. 43, 2112–2117 (2004).
    [CrossRef] [PubMed]
  14. R. Dorn, S. Quabis, G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  15. B. Sick, B. Hecht, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485 (2000).
    [CrossRef] [PubMed]
  16. K. Bahlmann, S. W. Hell, “Electric field depolarization in high aperture focusing with emphasis on annular apertures,” J. Microsc. 200, 59–67 (2000).
    [CrossRef] [PubMed]
  17. Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express12, 3377–3382 (2004), http://www.opticsexpress.org .
    [CrossRef]

2004 (2)

D. M. de Juana, V. F. Canales, P. J. Valle, M. P. Cagigal, “Focusing properties of annular binary phase filters,” Opt. Commun. 229, 71–77 (2004).
[CrossRef]

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

2003 (6)

D. M. de Juana, J. E. Oti, V. F. Canales, 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, 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]

C. Zhou, J. Jia, L. Liu, “Circular Dammann grating,” Opt. Lett. 28, 2174–2176 (2003).
[CrossRef] [PubMed]

W. D. Furlan, G. Saavedra, J. A. Monsoriu, J. D. Patrignani, “Axial behaviour of Cantor ring diffractals,” J. Opt. A 5, S361–S364 (2003).
[CrossRef]

J. Jia, C. Zhou, 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]

R. Dorn, S. Quabis, G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

2000 (2)

B. Sick, B. Hecht, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485 (2000).
[CrossRef] [PubMed]

K. Bahlmann, S. W. Hell, “Electric field depolarization in high aperture focusing with emphasis on annular apertures,” J. Microsc. 200, 59–67 (2000).
[CrossRef] [PubMed]

1999 (1)

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

1997 (1)

1986 (1)

1980 (2)

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field. I,” Opt. Acta 27, 587–610 (1980).
[CrossRef]

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field. II,” Opt. Acta 27, 1641–1670 (1980).
[CrossRef]

1952 (1)

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

Andrés, P.

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

Bahlmann, K.

K. Bahlmann, S. W. Hell, “Electric field depolarization in high aperture focusing with emphasis on annular apertures,” J. Microsc. 200, 59–67 (2000).
[CrossRef] [PubMed]

Boivin, A.

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field. I,” Opt. Acta 27, 587–610 (1980).
[CrossRef]

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field. II,” Opt. Acta 27, 1641–1670 (1980).
[CrossRef]

Boivin, R.

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field. II,” Opt. Acta 27, 1641–1670 (1980).
[CrossRef]

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field. I,” Opt. Acta 27, 587–610 (1980).
[CrossRef]

Cagigal, M. P.

Canales, V. F.

de Juana, D. M.

Dorn, R.

R. Dorn, S. Quabis, G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Furlan, W. D.

W. D. Furlan, G. Saavedra, J. A. Monsoriu, J. D. Patrignani, “Axial behaviour of Cantor ring diffractals,” J. Opt. A 5, S361–S364 (2003).
[CrossRef]

Hecht, B.

B. Sick, B. Hecht, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485 (2000).
[CrossRef] [PubMed]

Hegedus, Z. S.

Hell, S. W.

K. Bahlmann, S. W. Hell, “Electric field depolarization in high aperture focusing with emphasis on annular apertures,” J. Microsc. 200, 59–67 (2000).
[CrossRef] [PubMed]

Jia, J.

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

J. Jia, C. Zhou, 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]

C. Zhou, J. Jia, L. Liu, “Circular Dammann grating,” Opt. Lett. 28, 2174–2176 (2003).
[CrossRef] [PubMed]

Kowalczyk, M.

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

Leuchs, G.

R. Dorn, S. Quabis, G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Liu, L.

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

C. Zhou, J. Jia, L. Liu, “Circular Dammann grating,” Opt. Lett. 28, 2174–2176 (2003).
[CrossRef] [PubMed]

J. Jia, C. Zhou, 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]

Martínez-Corral, M.

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

Monsoriu, J. A.

W. D. Furlan, G. Saavedra, J. A. Monsoriu, J. D. Patrignani, “Axial behaviour of Cantor ring diffractals,” J. Opt. A 5, S361–S364 (2003).
[CrossRef]

Morris, G. M.

Oti, J. E.

Patrignani, J. D.

W. D. Furlan, G. Saavedra, J. A. Monsoriu, J. D. Patrignani, “Axial behaviour of Cantor ring diffractals,” J. Opt. A 5, S361–S364 (2003).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Saavedra, G.

W. D. Furlan, G. Saavedra, J. A. Monsoriu, J. D. Patrignani, “Axial behaviour of Cantor ring diffractals,” J. Opt. A 5, S361–S364 (2003).
[CrossRef]

Sales, T. R. M.

Sarafis, V.

Sick, B.

B. Sick, B. Hecht, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485 (2000).
[CrossRef] [PubMed]

Sun, X.

Toraldo di Francia, G.

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

Valle, P. J.

D. M. de Juana, V. F. Canales, P. J. Valle, M. P. Cagigal, “Focusing properties of annular binary phase filters,” Opt. Commun. 229, 71–77 (2004).
[CrossRef]

Zapata-Rodríguez, C. J.

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

Zhou, C.

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

C. Zhou, J. Jia, L. Liu, “Circular Dammann grating,” Opt. Lett. 28, 2174–2176 (2003).
[CrossRef] [PubMed]

J. Jia, C. Zhou, 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]

Appl. Opt. (1)

J. Microsc. (1)

K. Bahlmann, S. W. Hell, “Electric field depolarization in high aperture focusing with emphasis on annular apertures,” J. Microsc. 200, 59–67 (2000).
[CrossRef] [PubMed]

J. Opt. A (1)

W. D. Furlan, G. Saavedra, J. A. Monsoriu, J. D. Patrignani, “Axial behaviour of Cantor ring diffractals,” J. Opt. A 5, S361–S364 (2003).
[CrossRef]

J. Opt. Soc. Am. A (3)

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 (2)

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field. I,” Opt. Acta 27, 587–610 (1980).
[CrossRef]

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field. II,” Opt. Acta 27, 1641–1670 (1980).
[CrossRef]

Opt. Commun. (3)

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

D. M. de Juana, V. F. Canales, P. J. Valle, M. P. Cagigal, “Focusing properties of annular binary phase filters,” Opt. Commun. 229, 71–77 (2004).
[CrossRef]

J. Jia, C. Zhou, 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]

Opt. Lett. (2)

Phys. Rev. Lett. (2)

R. Dorn, S. Quabis, G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

B. Sick, B. Hecht, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485 (2000).
[CrossRef] [PubMed]

Other (1)

Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express12, 3377–3382 (2004), http://www.opticsexpress.org .
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Experimental setup for the superresolution effect in the far field.

Fig. 2
Fig. 2

Structure of a three-zone filter plate: r j is the radius of the jth zone. Shaded areas are opaque in an amplitude filter and denote phase modulation in a phase filter.

Fig. 3
Fig. 3

Transverse diffraction patterns of the two-zone amplitude filter as the inner radius increases. See text for details.

Fig. 4
Fig. 4

Transverse diffraction patterns of the two-zone phase filter as the inner radius increases. See text for details.

Fig. 5
Fig. 5

Comparison of a three-zone phase filter and an amplitude filter for achieving circular Dammann effects: (a) the three-zone circular Dammann grating with r 1 = 0.24 and r 2 = 0.66, (b) far-field diffraction of a three-zone amplitude filter with r 1 = 0.21 and r 2 = 0.7. Note that the first and the second sidelobe orders have equal intensity in (b).

Fig. 6
Fig. 6

(a) Experimental results of the Airy pattern, (b) superresolution result (G = 0.8) of a phase filter, (c) superresolution result (G = 0.9) of an amplitude filter. Note that the phase filter that yields the superresolution pattern in (b) has the same radius structure as the amplitude filter, with a diameter of 2 mm to yield that of (c). See Figs. 2 and 7 and Table 1 for more details.

Fig. 7
Fig. 7

Experimental intensity comparison of amplitude and phase filters with the same structure and diameter of 2 mm to yield the superresolution effects in Fig. 6. Solid curves, theoretical; dashed curves, experimental.

Fig. 8
Fig. 8

Comparison of experimental intensity distributions of the pure-phase and the amplitude filters with apertures of 20 mm for achieving the same normalized compression ratio G = 0.8. The structure of the phase filter has r 1 = 0.09 and r 2 = 0.36 and phase modulation 0.9π. The structure of the amplitude filter has r 1 = 0.05 and r 2 = 0.55. Solid curves, theoretical; dashed curves, experimental. See Table 1 for more details.

Tables (1)

Tables Icon

Table 1 Comparison of Theoretical and Experimental Results with Amplitude and Phase Filters

Equations (6)

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

ψz=2 01 ΨrJ0zrrdr,
Ψr=1 transparent zones,
Ψr=0 opaque zones.
ψz=2 1Nrj-1rj ΨrJ0zrrdr.
ψz=2 r11 ΨrJ0zrrdr.
ψz=2J1zz-1-expiϕ0-1N+1j=1N-1-1j×rj22J1rjzrjz,

Metrics