Abstract

A conventional Shack–Hartmann wavefront sensor works with an array of lenslets which produces an array of focal spots in the back focal plane of the lenses. The displacements of the focal spots from a reference position give a measure of the mean local wavefront slopes. To determine the positions of the focal spots, centroiding algorithms have to be used. In this work, the use of superresolution pupil filters to reduce the size of the focal spots is analyzed, as well as its effect on the variance of the centroid estimate, seeking for an enhancing of the sensor accuracy.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Porter, H. Queener, J. Lin, K. Thorn, and A. Awwal, eds., Adaptive Optics for Vision Science (Wiley-Interscience, 2006).
    [Crossref]
  2. R. Noll, “Zernike Polynomials and Atmospheric Turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [Crossref]
  3. G. Yoon, S. Pantanelli, and L. J. Nagy, “Large-dynamic-range Shack-Hartmann wavefront sensor for highly aberrated eyes,” J. Biomed. Opt. 11, 030,502.1–030,502.3 (2006).
    [Crossref]
  4. J. Rha, D. G. Voelz, and M. K. Giles, “Reconfigurable Shack-Hartmann wavefront sensor,” Opt. Eng. 43, 251–256 (2004).
    [Crossref]
  5. H. J. Tiziani, T. Haist, J. Liesener, M. Reicherter, and L. Seifert, “Application of SLMs for optical metrology,” Proc. SPIE 4457, 72–81 (2001).
    [Crossref]
  6. J. Lee, R. Shack, and M. Descour, “Sorting method to extend the dynamic range of the Shack-Hartmann wavefront sensor,” Appl. Opt. 44, 4838–4845 (2005).
    [Crossref] [PubMed]
  7. S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Monthly Notices of the Royal Astronomical Society 371, 323–336 (2006).
    [Crossref]
  8. G. Cao and X. Yu, “Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object,” Opt. Eng. 33, 2331–2335 (1994).
    [Crossref]
  9. J. Ares and J. Arines, “Influence of Thresholding on Centroid Statistics: Full Analytical Description,” Appl. Opt. 43, 5796–5805 (2004).
    [Crossref] [PubMed]
  10. J. Ares and J. Arines, “Effective noise in thresholded intensity distribution: influence on centroid statistics,” Opt. Lett. 26, 1831–1833 (2001).
    [Crossref]
  11. Z. Jiang, S. Gong, and Y. Dai, “Numerical study of centroid detection accuracy for Shack-Hartmann wavefront sensor,” Opt. Laser Technol. 38, 614–619 (2006).
    [Crossref]
  12. R. Irwan and R. G. Lane, “Analysis of optimal centroid estimation applied to Shack-Hartmann sensing,” Appl. Opt. 38, 6737–6743 (1999).
    [Crossref]
  13. J. Arines and J. Ares, “Minimum variance centroid thresholding,” Opt. Lett. 27, 497–499 (2002).
    [Crossref]
  14. V. F. Canales, J. E. Oti, P. J. Valle, M. P. Cagigal, and N. Devaney, “Reduction of the diffraction pattern in segmented apertures,” Opt. Eng. 45, 098,001.1–098,001.6 (2006).
    [Crossref]
  15. V. F. Canales, D. M. de Juana, and M. P. Cagigal, “Superresolution in compensated telescopes,” Opt. Lett. 29, 935–937 (2004).
    [Crossref] [PubMed]
  16. I. J. Cox, “Increasing the bit packing densities of optical disk systems,” Appl. Opt. 23, 3260–3261 (1984).
    [Crossref] [PubMed]
  17. P. Crabtree, C. L. Woods, J. Khoury, and M. Goda, “Binary phase-only filtering for turbulence compensation in fiber-coupled free-space laser communication systems,” Appl. Opt. 46, 8335–8345 (2007).
    [Crossref] [PubMed]
  18. L. Qiu, W. Zhao, Z. Feng, and X. Ding, “A lateral super-resolution differential confocal technology with phase-only pupil filter,” Optik - International Journal for Light and Electron Optics 118, 67–73(2007).
    [Crossref]
  19. M. Martínez-Corral, P. Andrés, J. Ojeda-Castañeda, and G. Saavedra, “Tunable axial superresolution by annular binary filters. Application to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
    [Crossref]
  20. T. R. M. Sales, “Smallest Focal Spot,” Phys. Rev. Lett. 81, 3844–3847 (1998).
    [Crossref]
  21. T. R.M. Sales and G. M. Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 22, 582–584 (1997).
    [Crossref] [PubMed]
  22. H. Wang and F. Gan, “High Focal Depth with a Pure-Phase Apodizer,” Appl. Opt. 40, 5658–5662 (2001).
    [Crossref]
  23. D.M. de Juana, V. F. Canales, P. J. Valle, and M. P. Cagigal, “Focusing properties of annular binary phase filters,” Opt. Commun. 229, 71–77 (2004).
    [Crossref]
  24. 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]
  25. H. Luo and C. Zhou, “Comparison of Superresolution Effects with Annular Phase and Amplitude Filters,” Appl. Opt. 43, 6242–6247 (2004).
    [Crossref] [PubMed]
  26. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).
  27. C. J. R. Sheppard and Z. S. Hegedus, “Axial behavior of pupil-plane filters,” J. Opt. Soc. Am. A 5, 643–647 (1988).
    [Crossref]
  28. M. M. Matalgah, J. Knopp, and L. Eifler, “Geometric Approach for Designing Optical Binary Amplitude and Binary Phase-Only Filters,” Appl. Opt. 37, 8233–8246 (1998).
    [Crossref]
  29. C. J. R. Sheppard, G. Calvert, and M. Wheatland, “Focal distribution for superresolving toraldo filters,” J. Opt. Soc. Am. A 15, 849–856 (1998).
    [Crossref]
  30. V. F. Canales, P. J. Valle, J. E. Oti, and M. P. Cagigal, “Variable resolution with pupil masks,” Opt. Commun. 257, 247–254 (2006).
    [Crossref]
  31. H. Liu, Y. Yan, D. Yi, and G. Jin, “Design of Three-Dimensional Superresolution Filters and Limits of Axial Optical Superresolution,” Appl. Opt. 42, 1463–1476 (2003).
    [Crossref] [PubMed]
  32. Y. Xu, J. Singh, C. J. R. Sheppard, and N. Chen, “Ultra long high resolution beam by multi-zone rotationally symmetrical complex pupil filter,” Opt. Express 15, 6409–6413 (2007).
    [Crossref] [PubMed]
  33. J. Wei and M. Xiao, “Laser tunable Toraldo superresolution with a uniform nonlinear pupil filter,” Appl. Opt. 47, 3689–3693 (2008).
    [Crossref] [PubMed]
  34. 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]
  35. H. F. A. Tschunko, “Imaging Performance of Annular Apertures,” Appl. Opt. 13, 1820–1823 (1974).
    [Crossref] [PubMed]
  36. 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]
  37. A. Tokovinin, “From Differential Image Motion to Seeing,” Publ. Astron. Soc. Pac. 114, 1156–1166 (2002).
    [Crossref]
  38. Hamamatsu Photonics, “IEEE1394-based Digital Camera Orca-285 data sheet,” http://sales.hamamatsu.com/assets/pdf/hpspdf/C4742-95-12G04.pdf.
  39. W. Zhao, L. Qiu, and Z. Feng, “Effect of fabrication errors on superresolution property of a pupil filter,” Opt. Express 14, 7024–7036 (2006).
    [Crossref] [PubMed]

2008 (1)

2007 (3)

2006 (6)

Z. Jiang, S. Gong, and Y. Dai, “Numerical study of centroid detection accuracy for Shack-Hartmann wavefront sensor,” Opt. Laser Technol. 38, 614–619 (2006).
[Crossref]

V. F. Canales, J. E. Oti, P. J. Valle, M. P. Cagigal, and N. Devaney, “Reduction of the diffraction pattern in segmented apertures,” Opt. Eng. 45, 098,001.1–098,001.6 (2006).
[Crossref]

G. Yoon, S. Pantanelli, and L. J. Nagy, “Large-dynamic-range Shack-Hartmann wavefront sensor for highly aberrated eyes,” J. Biomed. Opt. 11, 030,502.1–030,502.3 (2006).
[Crossref]

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Monthly Notices of the Royal Astronomical Society 371, 323–336 (2006).
[Crossref]

V. F. Canales, P. J. Valle, J. E. Oti, and M. P. Cagigal, “Variable resolution with pupil masks,” Opt. Commun. 257, 247–254 (2006).
[Crossref]

W. Zhao, L. Qiu, and Z. Feng, “Effect of fabrication errors on superresolution property of a pupil filter,” Opt. Express 14, 7024–7036 (2006).
[Crossref] [PubMed]

2005 (1)

2004 (7)

V. F. Canales, D. M. de Juana, and M. P. Cagigal, “Superresolution in compensated telescopes,” Opt. Lett. 29, 935–937 (2004).
[Crossref] [PubMed]

J. Ares and J. Arines, “Influence of Thresholding on Centroid Statistics: Full Analytical Description,” Appl. Opt. 43, 5796–5805 (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]

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]

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

J. Rha, D. G. Voelz, and M. K. Giles, “Reconfigurable Shack-Hartmann wavefront sensor,” Opt. Eng. 43, 251–256 (2004).
[Crossref]

2003 (2)

2002 (2)

J. Arines and J. Ares, “Minimum variance centroid thresholding,” Opt. Lett. 27, 497–499 (2002).
[Crossref]

A. Tokovinin, “From Differential Image Motion to Seeing,” Publ. Astron. Soc. Pac. 114, 1156–1166 (2002).
[Crossref]

2001 (3)

1999 (1)

1998 (3)

1997 (1)

1995 (1)

M. Martínez-Corral, P. Andrés, J. Ojeda-Castañeda, and G. Saavedra, “Tunable axial superresolution by annular binary filters. Application to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[Crossref]

1994 (1)

G. Cao and X. Yu, “Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object,” Opt. Eng. 33, 2331–2335 (1994).
[Crossref]

1988 (1)

1984 (1)

1976 (1)

1974 (1)

Andrés, P.

M. Martínez-Corral, P. Andrés, J. Ojeda-Castañeda, and G. Saavedra, “Tunable axial superresolution by annular binary filters. Application to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[Crossref]

Ares, J.

Arines, J.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

Cagigal, M. P.

V. F. Canales, P. J. Valle, J. E. Oti, and M. P. Cagigal, “Variable resolution with pupil masks,” Opt. Commun. 257, 247–254 (2006).
[Crossref]

V. F. Canales, J. E. Oti, P. J. Valle, M. P. Cagigal, and N. Devaney, “Reduction of the diffraction pattern in segmented apertures,” Opt. Eng. 45, 098,001.1–098,001.6 (2006).
[Crossref]

V. F. Canales, D. M. de Juana, and M. P. Cagigal, “Superresolution in compensated telescopes,” Opt. Lett. 29, 935–937 (2004).
[Crossref] [PubMed]

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

Calvert, G.

Canales, V. F.

V. F. Canales, P. J. Valle, J. E. Oti, and M. P. Cagigal, “Variable resolution with pupil masks,” Opt. Commun. 257, 247–254 (2006).
[Crossref]

V. F. Canales, J. E. Oti, P. J. Valle, M. P. Cagigal, and N. Devaney, “Reduction of the diffraction pattern in segmented apertures,” Opt. Eng. 45, 098,001.1–098,001.6 (2006).
[Crossref]

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

V. F. Canales, D. M. de Juana, and M. P. Cagigal, “Superresolution in compensated telescopes,” Opt. Lett. 29, 935–937 (2004).
[Crossref] [PubMed]

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]

Cao, G.

G. Cao and X. Yu, “Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object,” Opt. Eng. 33, 2331–2335 (1994).
[Crossref]

Chen, N.

Cox, I. J.

Crabtree, P.

Dai, Y.

Z. Jiang, S. Gong, and Y. Dai, “Numerical study of centroid detection accuracy for Shack-Hartmann wavefront sensor,” Opt. Laser Technol. 38, 614–619 (2006).
[Crossref]

de Juana, D. M.

de Juana, D.M.

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

Descour, M.

Devaney, N.

V. F. Canales, J. E. Oti, P. J. Valle, M. P. Cagigal, and N. Devaney, “Reduction of the diffraction pattern in segmented apertures,” Opt. Eng. 45, 098,001.1–098,001.6 (2006).
[Crossref]

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]

Ding, X.

L. Qiu, W. Zhao, Z. Feng, and X. Ding, “A lateral super-resolution differential confocal technology with phase-only pupil filter,” Optik - International Journal for Light and Electron Optics 118, 67–73(2007).
[Crossref]

Eifler, L.

Feng, Z.

L. Qiu, W. Zhao, Z. Feng, and X. Ding, “A lateral super-resolution differential confocal technology with phase-only pupil filter,” Optik - International Journal for Light and Electron Optics 118, 67–73(2007).
[Crossref]

W. Zhao, L. Qiu, and Z. Feng, “Effect of fabrication errors on superresolution property of a pupil filter,” Opt. Express 14, 7024–7036 (2006).
[Crossref] [PubMed]

Fusco, T.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Monthly Notices of the Royal Astronomical Society 371, 323–336 (2006).
[Crossref]

Gan, F.

Giles, M. K.

J. Rha, D. G. Voelz, and M. K. Giles, “Reconfigurable Shack-Hartmann wavefront sensor,” Opt. Eng. 43, 251–256 (2004).
[Crossref]

Goda, M.

Gong, S.

Z. Jiang, S. Gong, and Y. Dai, “Numerical study of centroid detection accuracy for Shack-Hartmann wavefront sensor,” Opt. Laser Technol. 38, 614–619 (2006).
[Crossref]

Haist, T.

H. J. Tiziani, T. Haist, J. Liesener, M. Reicherter, and L. Seifert, “Application of SLMs for optical metrology,” Proc. SPIE 4457, 72–81 (2001).
[Crossref]

Hegedus, Z. S.

Irwan, R.

Jiang, Z.

Z. Jiang, S. Gong, and Y. Dai, “Numerical study of centroid detection accuracy for Shack-Hartmann wavefront sensor,” Opt. Laser Technol. 38, 614–619 (2006).
[Crossref]

Jin, G.

Khoury, J.

Knopp, J.

Lane, R. G.

Lee, J.

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]

Liesener, J.

H. J. Tiziani, T. Haist, J. Liesener, M. Reicherter, and L. Seifert, “Application of SLMs for optical metrology,” Proc. SPIE 4457, 72–81 (2001).
[Crossref]

Liu, H.

Luo, H.

Martínez-Corral, M.

M. Martínez-Corral, P. Andrés, J. Ojeda-Castañeda, and G. Saavedra, “Tunable axial superresolution by annular binary filters. Application to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[Crossref]

Matalgah, M. M.

Michau, V.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Monthly Notices of the Royal Astronomical Society 371, 323–336 (2006).
[Crossref]

Morris, G. M.

Nagy, L. J.

G. Yoon, S. Pantanelli, and L. J. Nagy, “Large-dynamic-range Shack-Hartmann wavefront sensor for highly aberrated eyes,” J. Biomed. Opt. 11, 030,502.1–030,502.3 (2006).
[Crossref]

Nicolle, M.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Monthly Notices of the Royal Astronomical Society 371, 323–336 (2006).
[Crossref]

Noll, R.

Ojeda-Castañeda, J.

M. Martínez-Corral, P. Andrés, J. Ojeda-Castañeda, and G. Saavedra, “Tunable axial superresolution by annular binary filters. Application to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[Crossref]

Oti, J. E.

V. F. Canales, J. E. Oti, P. J. Valle, M. P. Cagigal, and N. Devaney, “Reduction of the diffraction pattern in segmented apertures,” Opt. Eng. 45, 098,001.1–098,001.6 (2006).
[Crossref]

V. F. Canales, P. J. Valle, J. E. Oti, and M. P. Cagigal, “Variable resolution with pupil masks,” Opt. Commun. 257, 247–254 (2006).
[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]

Pantanelli, S.

G. Yoon, S. Pantanelli, and L. J. Nagy, “Large-dynamic-range Shack-Hartmann wavefront sensor for highly aberrated eyes,” J. Biomed. Opt. 11, 030,502.1–030,502.3 (2006).
[Crossref]

Qiu, L.

L. Qiu, W. Zhao, Z. Feng, and X. Ding, “A lateral super-resolution differential confocal technology with phase-only pupil filter,” Optik - International Journal for Light and Electron Optics 118, 67–73(2007).
[Crossref]

W. Zhao, L. Qiu, and Z. Feng, “Effect of fabrication errors on superresolution property of a pupil filter,” Opt. Express 14, 7024–7036 (2006).
[Crossref] [PubMed]

Reicherter, M.

H. J. Tiziani, T. Haist, J. Liesener, M. Reicherter, and L. Seifert, “Application of SLMs for optical metrology,” Proc. SPIE 4457, 72–81 (2001).
[Crossref]

Rha, J.

J. Rha, D. G. Voelz, and M. K. Giles, “Reconfigurable Shack-Hartmann wavefront sensor,” Opt. Eng. 43, 251–256 (2004).
[Crossref]

Rousset, G.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Monthly Notices of the Royal Astronomical Society 371, 323–336 (2006).
[Crossref]

Saavedra, G.

M. Martínez-Corral, P. Andrés, J. Ojeda-Castañeda, and G. Saavedra, “Tunable axial superresolution by annular binary filters. Application to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[Crossref]

Sales, T. R. M.

T. R. M. Sales, “Smallest Focal Spot,” Phys. Rev. Lett. 81, 3844–3847 (1998).
[Crossref]

Sales, T. R.M.

Seifert, L.

H. J. Tiziani, T. Haist, J. Liesener, M. Reicherter, and L. Seifert, “Application of SLMs for optical metrology,” Proc. SPIE 4457, 72–81 (2001).
[Crossref]

Shack, R.

Sheppard, C. J. R.

Singh, J.

Thomas, S.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Monthly Notices of the Royal Astronomical Society 371, 323–336 (2006).
[Crossref]

Tiziani, H. J.

H. J. Tiziani, T. Haist, J. Liesener, M. Reicherter, and L. Seifert, “Application of SLMs for optical metrology,” Proc. SPIE 4457, 72–81 (2001).
[Crossref]

Tokovinin, A.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Monthly Notices of the Royal Astronomical Society 371, 323–336 (2006).
[Crossref]

A. Tokovinin, “From Differential Image Motion to Seeing,” Publ. Astron. Soc. Pac. 114, 1156–1166 (2002).
[Crossref]

Tschunko, H. F. A.

Valle, P. J.

V. F. Canales, P. J. Valle, J. E. Oti, and M. P. Cagigal, “Variable resolution with pupil masks,” Opt. Commun. 257, 247–254 (2006).
[Crossref]

V. F. Canales, J. E. Oti, P. J. Valle, M. P. Cagigal, and N. Devaney, “Reduction of the diffraction pattern in segmented apertures,” Opt. Eng. 45, 098,001.1–098,001.6 (2006).
[Crossref]

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

Voelz, D. G.

J. Rha, D. G. Voelz, and M. K. Giles, “Reconfigurable Shack-Hartmann wavefront sensor,” Opt. Eng. 43, 251–256 (2004).
[Crossref]

Wang, H.

Wei, J.

Wheatland, M.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

Woods, C. L.

Xiao, M.

Xu, Y.

Yan, Y.

Yi, D.

Yoon, G.

G. Yoon, S. Pantanelli, and L. J. Nagy, “Large-dynamic-range Shack-Hartmann wavefront sensor for highly aberrated eyes,” J. Biomed. Opt. 11, 030,502.1–030,502.3 (2006).
[Crossref]

Yu, X.

G. Cao and X. Yu, “Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object,” Opt. Eng. 33, 2331–2335 (1994).
[Crossref]

Zhao, W.

L. Qiu, W. Zhao, Z. Feng, and X. Ding, “A lateral super-resolution differential confocal technology with phase-only pupil filter,” Optik - International Journal for Light and Electron Optics 118, 67–73(2007).
[Crossref]

W. Zhao, L. Qiu, and Z. Feng, “Effect of fabrication errors on superresolution property of a pupil filter,” Opt. Express 14, 7024–7036 (2006).
[Crossref] [PubMed]

Zhou, C.

Zou, W.

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. (11)

J. Lee, R. Shack, and M. Descour, “Sorting method to extend the dynamic range of the Shack-Hartmann wavefront sensor,” Appl. Opt. 44, 4838–4845 (2005).
[Crossref] [PubMed]

J. Ares and J. Arines, “Influence of Thresholding on Centroid Statistics: Full Analytical Description,” Appl. Opt. 43, 5796–5805 (2004).
[Crossref] [PubMed]

R. Irwan and R. G. Lane, “Analysis of optimal centroid estimation applied to Shack-Hartmann sensing,” Appl. Opt. 38, 6737–6743 (1999).
[Crossref]

I. J. Cox, “Increasing the bit packing densities of optical disk systems,” Appl. Opt. 23, 3260–3261 (1984).
[Crossref] [PubMed]

P. Crabtree, C. L. Woods, J. Khoury, and M. Goda, “Binary phase-only filtering for turbulence compensation in fiber-coupled free-space laser communication systems,” Appl. Opt. 46, 8335–8345 (2007).
[Crossref] [PubMed]

H. Wang and F. Gan, “High Focal Depth with a Pure-Phase Apodizer,” Appl. Opt. 40, 5658–5662 (2001).
[Crossref]

H. Luo and C. Zhou, “Comparison of Superresolution Effects with Annular Phase and Amplitude Filters,” Appl. Opt. 43, 6242–6247 (2004).
[Crossref] [PubMed]

M. M. Matalgah, J. Knopp, and L. Eifler, “Geometric Approach for Designing Optical Binary Amplitude and Binary Phase-Only Filters,” Appl. Opt. 37, 8233–8246 (1998).
[Crossref]

H. Liu, Y. Yan, D. Yi, and G. Jin, “Design of Three-Dimensional Superresolution Filters and Limits of Axial Optical Superresolution,” Appl. Opt. 42, 1463–1476 (2003).
[Crossref] [PubMed]

J. Wei and M. Xiao, “Laser tunable Toraldo superresolution with a uniform nonlinear pupil filter,” Appl. Opt. 47, 3689–3693 (2008).
[Crossref] [PubMed]

H. F. A. Tschunko, “Imaging Performance of Annular Apertures,” Appl. Opt. 13, 1820–1823 (1974).
[Crossref] [PubMed]

J. Biomed. Opt. (1)

G. Yoon, S. Pantanelli, and L. J. Nagy, “Large-dynamic-range Shack-Hartmann wavefront sensor for highly aberrated eyes,” J. Biomed. Opt. 11, 030,502.1–030,502.3 (2006).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Monthly Notices of the Royal Astronomical Society (1)

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Monthly Notices of the Royal Astronomical Society 371, 323–336 (2006).
[Crossref]

Opt. Commun. (5)

M. Martínez-Corral, P. Andrés, J. Ojeda-Castañeda, and G. Saavedra, “Tunable axial superresolution by annular binary filters. Application to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[Crossref]

V. F. Canales, P. J. Valle, J. E. Oti, and M. P. Cagigal, “Variable resolution with pupil masks,” Opt. Commun. 257, 247–254 (2006).
[Crossref]

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

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]

Opt. Eng. (3)

V. F. Canales, J. E. Oti, P. J. Valle, M. P. Cagigal, and N. Devaney, “Reduction of the diffraction pattern in segmented apertures,” Opt. Eng. 45, 098,001.1–098,001.6 (2006).
[Crossref]

G. Cao and X. Yu, “Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object,” Opt. Eng. 33, 2331–2335 (1994).
[Crossref]

J. Rha, D. G. Voelz, and M. K. Giles, “Reconfigurable Shack-Hartmann wavefront sensor,” Opt. Eng. 43, 251–256 (2004).
[Crossref]

Opt. Express (2)

Opt. Laser Technol. (1)

Z. Jiang, S. Gong, and Y. Dai, “Numerical study of centroid detection accuracy for Shack-Hartmann wavefront sensor,” Opt. Laser Technol. 38, 614–619 (2006).
[Crossref]

Opt. Lett. (5)

Optik - International Journal for Light and Electron Optics (1)

L. Qiu, W. Zhao, Z. Feng, and X. Ding, “A lateral super-resolution differential confocal technology with phase-only pupil filter,” Optik - International Journal for Light and Electron Optics 118, 67–73(2007).
[Crossref]

Phys. Rev. Lett. (1)

T. R. M. Sales, “Smallest Focal Spot,” Phys. Rev. Lett. 81, 3844–3847 (1998).
[Crossref]

Proc. SPIE (1)

H. J. Tiziani, T. Haist, J. Liesener, M. Reicherter, and L. Seifert, “Application of SLMs for optical metrology,” Proc. SPIE 4457, 72–81 (2001).
[Crossref]

Publ. Astron. Soc. Pac. (1)

A. Tokovinin, “From Differential Image Motion to Seeing,” Publ. Astron. Soc. Pac. 114, 1156–1166 (2002).
[Crossref]

Other (3)

Hamamatsu Photonics, “IEEE1394-based Digital Camera Orca-285 data sheet,” http://sales.hamamatsu.com/assets/pdf/hpspdf/C4742-95-12G04.pdf.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

J. Porter, H. Queener, J. Lin, K. Thorn, and A. Awwal, eds., Adaptive Optics for Vision Science (Wiley-Interscience, 2006).
[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 (6)

Fig. 1.
Fig. 1.

Lateral intensity profiles for different values of the obstruction ratio

Fig. 2.
Fig. 2.

Normalized lateral intensity profiles for different values of the obstruction ratio

Fig. 3.
Fig. 3.

Mask geometry

Fig. 4.
Fig. 4.

Section of the transversal intensity profile without mask (a), and with an annular mask (O=0.75) (b)

Fig. 5.
Fig. 5.

Transversal intensity distribution without mask (a), and with an annular mask (O=0.75) (b)

Fig. 6.
Fig. 6.

Top view of the lenslets focal spots without mask (a), and with an annular mask (O=0.75) (b)

Tables (3)

Tables Icon

Table 1. Filter parameters and variance gain for different obstruction ratios

Tables Icon

Table 2. Theoretical filter parameters and variance gain

Tables Icon

Table 3. Experimental values of the filter parameters and variance gain

Equations (18)

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

θmax=d2f'
θmin=Δlf'
U(ρ)=2 01t (r)exp[iϕ(r)]J0(ηr)rdr
xc=xI(x,y)dxdyI(x,y)dxdy
xc=i,jxijIiji,jIij
x̂c=i,jxij(Iij+nij)i,j(Iij+nij)
σxc2=(x̂cxc)2
σxc2=σn2IT2 [i,jxij2+xc2Ap2xci,jxij]
IT2=(i,jIij+nij)2
σxc2=σn2IT2 [i,jxij2]
σxc2=σn2IT2π4ρmin4
IT2=[i,j(Iij+nij)]2=(i,jIij)2+σn2Ap
σxc2=σn2(i,jIij)2 π4 ρmin4
F=(i,jIij)nofilter(i,jIij)filter
R=GT4F2
R=GT4S2FN2
σxc2=σn2(i,jIij)2(2xmin)412
R=163πGT4S2FN2

Metrics