Abstract

Most Shack-Hartmann based aberrometers use infrared light, for the comfort of the patients. A large amount of the light that is scattered from the retinal layers is recorded by the detector as background, from which it is not trivial to estimate the centroid of the Shack-Hartmann spot. For a centroiding algorithm, background light can lead to a systematic bias of the centroid positions towards the centre of the software window. We implement a matched filter algorithm for the estimation of the centroid positions of the Shack-Hartmann spots recorded by our aberrometer. We briefly present the performance of our algorithm, and recall the well-known robustness of the matched filter algorithm to background light. Using data collected on 5 human eyes, we parameterise a simple and fast centroiding algorithm and reduce the difference between the two algorithms down to a mean residual wavefront of 0.02 μm rms.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Bara, "Measuring eye aberrations with Hartmann-Shack wave-front sensors: Should the irradiance distribution across the eye pupil be taken into account?" J. Opt. Soc. Am. A 20,2237-2245 (2003).
    [CrossRef]
  2. L. Diaz-Santana, G. Walker, and S. Bara, "Sampling geometries for ocular aberrometry: A model for evaluation of performance," J. Opt. Soc. Am. A 13,8801-8818 (2005).
  3. S. Bara, "Characteristic functions of Hartmann-Shack wavefront sensors and laser-ray-tracing aberrometers," J. Opt. Soc. Am. A 24,3700-3707 (2007).
    [CrossRef]
  4. S. Bara, P. Prado, J. Arines, and J. Ares, "Estimation-induced correlations of the Zernike coefficients of the eye aberration," Opt. Lett. 31,2646-2648 (2006).
    [CrossRef] [PubMed]
  5. L. Llorente, S. Marcos, C. Dorronsoro, and S. Burns, "Effect of sampling on real ocular aberration measurements," J. Opt. Soc. Am. A 24,2783-2796 (2007).
    [CrossRef]
  6. R. Cannon, "Global wave-front reconstruction using Shack-Hartmann sensors," J. Opt. Soc. Am. A 12,2031-2039 (1995).
    [CrossRef]
  7. H. Barrett, C. Dainty, and D. Lara, "Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions," J. Opt. Soc. Am. A 24,391-414 (2007).
    [CrossRef]
  8. H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley-Interscience, 2003).
  9. G. Rousset, "Wave-front sensors," in Adaptive Optics in Astronomy, F. Roddier eds. (Cambridge University Press, 1999).
    [CrossRef]
  10. J. Porter, H. Queener, J. Lin, K. Thorn and A. Awwal, eds., Adaptive Optics for Vision Science: Principles, Practices, Design and Applications (Wiley, 2006).
    [CrossRef]
  11. L. Diaz-Santana Haro, Wavefront Sensing in the Human Eye with a Shack-Hartmann Sensor (PhD thesis, 2000).
  12. P. Prieto, F. Vargas-Martn, S. Goelz, and P. Artal, "Analysis of the performance of the Hartmann-Shack sensor in the human eye," J. Opt. Soc. Am. A 17,1388-1398 (2000).
    [CrossRef]
  13. T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, "Optimisation of Shack-Hartmann based wavefront sensor for XAO system," in Advancements in Adaptive Optics, Proc. SPIE 5490,1155-1166 (2004).
    [CrossRef]
  14. M. Nicolle, T. Fusco, G. Rousset, and V. Michau, "Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics," Opt. Lett. 29,2743-2745 (2004).
    [CrossRef] [PubMed]
  15. K. Baker and M. Moallem, "Iteratively weighted centroiding for Shack-Hartmann wave-front sensors," Opt. Express 15,5147-5159 (2007).
    [CrossRef] [PubMed]
  16. J. Ares and J. Arines, "Effective noise in thresholded intensity distribution: influence on centroid statistics," Opt. Lett. 26,1831-1833 (2001).
    [CrossRef]
  17. J. Arines and J. Ares, "Minimum variance centroid thresholding," Opt. Lett. 27,497-499 (2002).
    [CrossRef]
  18. J. Ares and J. Arines, "Influence of thresholding on centroid statistics: full analytical description," Appl. Opt. 43,5796-5805 (2004).
    [CrossRef] [PubMed]
  19. B. Welsh, B. Ellerbroek, M. Roggemann, and T. Pennington, "Fundamental performance comparison of a Hartmann and a shearing interferometer wave-front sensor," Appl. Opt. 34,4186-4195 (1995).
    [CrossRef] [PubMed]
  20. R. Irwan and R. Lane, "Analysis of optimal centroid estimation applied to Shack-Hartmann sensing," Appl. Opt. 38,6737-6743 (1999).
    [CrossRef]
  21. M. van Dam and R. Lane, "Wave-front slope estimation," J. Opt. Soc. Am. A 17,1319-1324 (2000).
    [CrossRef]
  22. J. Arines and J. Ares, "Significance of thresholding processing in centroid based gradient wavefront sensors: effective modulation of the wavefront derivative," Opt. Commun. 237,257-266 (2004).
    [CrossRef]
  23. S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau and G. Rousset, "Comparison of centroid computation algorithms in a Shack-Hartmann sensor," Mon. Not. R. Astron. Soc. 371,323-336 (2006).
    [CrossRef]
  24. T.R. Rimmele and R.R. Radick, "Solar Adaptive Optics at the National Solar Observatory," Proc. SPIE 3353,72-81 (1998).
    [CrossRef]
  25. J. Ruggiu, C. Solomon, and G. Loos, "Gram-Charlier matched filter for Shack-Hartmann sensing at low light levels," Opt. Lett. 23,235-237 (1998).
    [CrossRef]
  26. L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, and S. Marcos, "Aberrations of the human eye in visible and near infrared illumination," Optom. Vis. Sci. 80,26-35 (2003).
    [CrossRef] [PubMed]
  27. L. Poyneer, "Scene-based Shack-Hartmann Wave-front sensing: analysis and simulation," Appl. Opt. 42,5807-5815 (2003).
    [CrossRef] [PubMed]
  28. H. Hofer, P. Artal, B. Singer, J. Aragn, and D. Williams, "Dynamics of the eye’s wave aberration," J. Opt. Soc. Am. A 18,497-506 (2001).
    [CrossRef]
  29. P. Knutsson, M. Owner-Petersen, and C. Dainty, "Extended object wavefront sensing based on the correlation spectrum phase," Opt. Express 13,9527-9536 (2005).
    [CrossRef] [PubMed]
  30. J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005).
  31. K. Winick, "Cramér-Rao lower bounds on the performance of charge-coupled-device optical position estimators," J. Opt. Soc. Am. A 3,1809-1815 (1986).
    [CrossRef]
  32. B. Saleh, "Estimation of the location of an optical object with photodetectors limited by quantum noise," Appl. Opt. 13,1824-1827 (1974).
    [CrossRef] [PubMed]

2007 (4)

2006 (2)

S. Bara, P. Prado, J. Arines, and J. Ares, "Estimation-induced correlations of the Zernike coefficients of the eye aberration," Opt. Lett. 31,2646-2648 (2006).
[CrossRef] [PubMed]

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau and G. Rousset, "Comparison of centroid computation algorithms in a Shack-Hartmann sensor," Mon. Not. R. Astron. Soc. 371,323-336 (2006).
[CrossRef]

2005 (2)

L. Diaz-Santana, G. Walker, and S. Bara, "Sampling geometries for ocular aberrometry: A model for evaluation of performance," J. Opt. Soc. Am. A 13,8801-8818 (2005).

P. Knutsson, M. Owner-Petersen, and C. Dainty, "Extended object wavefront sensing based on the correlation spectrum phase," Opt. Express 13,9527-9536 (2005).
[CrossRef] [PubMed]

2004 (4)

J. Ares and J. Arines, "Influence of thresholding on centroid statistics: full analytical description," Appl. Opt. 43,5796-5805 (2004).
[CrossRef] [PubMed]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, "Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics," Opt. Lett. 29,2743-2745 (2004).
[CrossRef] [PubMed]

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, "Optimisation of Shack-Hartmann based wavefront sensor for XAO system," in Advancements in Adaptive Optics, Proc. SPIE 5490,1155-1166 (2004).
[CrossRef]

J. Arines and J. Ares, "Significance of thresholding processing in centroid based gradient wavefront sensors: effective modulation of the wavefront derivative," Opt. Commun. 237,257-266 (2004).
[CrossRef]

2003 (3)

2002 (1)

2001 (2)

2000 (2)

1999 (1)

1998 (2)

J. Ruggiu, C. Solomon, and G. Loos, "Gram-Charlier matched filter for Shack-Hartmann sensing at low light levels," Opt. Lett. 23,235-237 (1998).
[CrossRef]

T.R. Rimmele and R.R. Radick, "Solar Adaptive Optics at the National Solar Observatory," Proc. SPIE 3353,72-81 (1998).
[CrossRef]

1995 (2)

1986 (1)

1974 (1)

Aragn, J.

Ares, J.

Arines, J.

Artal, P.

Baker, K.

Bara, S.

Barrett, H.

Beuzit, J.-L.

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, "Optimisation of Shack-Hartmann based wavefront sensor for XAO system," in Advancements in Adaptive Optics, Proc. SPIE 5490,1155-1166 (2004).
[CrossRef]

Burns, S.

Cannon, R.

Dainty, C.

Diaz-Santana, L.

L. Diaz-Santana, G. Walker, and S. Bara, "Sampling geometries for ocular aberrometry: A model for evaluation of performance," J. Opt. Soc. Am. A 13,8801-8818 (2005).

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, and S. Marcos, "Aberrations of the human eye in visible and near infrared illumination," Optom. Vis. Sci. 80,26-35 (2003).
[CrossRef] [PubMed]

Dorronsoro, C.

Ellerbroek, B.

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," Mon. Not. R. Astron. Soc. 371,323-336 (2006).
[CrossRef]

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, "Optimisation of Shack-Hartmann based wavefront sensor for XAO system," in Advancements in Adaptive Optics, Proc. SPIE 5490,1155-1166 (2004).
[CrossRef]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, "Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics," Opt. Lett. 29,2743-2745 (2004).
[CrossRef] [PubMed]

Goelz, S.

Hofer, H.

Irwan, R.

Knutsson, P.

Lane, R.

Lara, D.

Lara-Saucedo, D.

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, and S. Marcos, "Aberrations of the human eye in visible and near infrared illumination," Optom. Vis. Sci. 80,26-35 (2003).
[CrossRef] [PubMed]

Llorente, L.

L. Llorente, S. Marcos, C. Dorronsoro, and S. Burns, "Effect of sampling on real ocular aberration measurements," J. Opt. Soc. Am. A 24,2783-2796 (2007).
[CrossRef]

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, and S. Marcos, "Aberrations of the human eye in visible and near infrared illumination," Optom. Vis. Sci. 80,26-35 (2003).
[CrossRef] [PubMed]

Loos, G.

Marcos, S.

L. Llorente, S. Marcos, C. Dorronsoro, and S. Burns, "Effect of sampling on real ocular aberration measurements," J. Opt. Soc. Am. A 24,2783-2796 (2007).
[CrossRef]

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, and S. Marcos, "Aberrations of the human eye in visible and near infrared illumination," Optom. Vis. Sci. 80,26-35 (2003).
[CrossRef] [PubMed]

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," Mon. Not. R. Astron. Soc. 371,323-336 (2006).
[CrossRef]

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, "Optimisation of Shack-Hartmann based wavefront sensor for XAO system," in Advancements in Adaptive Optics, Proc. SPIE 5490,1155-1166 (2004).
[CrossRef]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, "Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics," Opt. Lett. 29,2743-2745 (2004).
[CrossRef] [PubMed]

Moallem, M.

Mouillet, D.

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, "Optimisation of Shack-Hartmann based wavefront sensor for XAO system," in Advancements in Adaptive Optics, Proc. SPIE 5490,1155-1166 (2004).
[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," Mon. Not. R. Astron. Soc. 371,323-336 (2006).
[CrossRef]

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, "Optimisation of Shack-Hartmann based wavefront sensor for XAO system," in Advancements in Adaptive Optics, Proc. SPIE 5490,1155-1166 (2004).
[CrossRef]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, "Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics," Opt. Lett. 29,2743-2745 (2004).
[CrossRef] [PubMed]

Owner-Petersen, M.

Pennington, T.

Poyneer, L.

Prado, P.

Prieto, P.

Radick, R.R.

T.R. Rimmele and R.R. Radick, "Solar Adaptive Optics at the National Solar Observatory," Proc. SPIE 3353,72-81 (1998).
[CrossRef]

Rimmele, T.R.

T.R. Rimmele and R.R. Radick, "Solar Adaptive Optics at the National Solar Observatory," Proc. SPIE 3353,72-81 (1998).
[CrossRef]

Roggemann, M.

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," Mon. Not. R. Astron. Soc. 371,323-336 (2006).
[CrossRef]

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, "Optimisation of Shack-Hartmann based wavefront sensor for XAO system," in Advancements in Adaptive Optics, Proc. SPIE 5490,1155-1166 (2004).
[CrossRef]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, "Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics," Opt. Lett. 29,2743-2745 (2004).
[CrossRef] [PubMed]

Ruggiu, J.

Saleh, B.

Singer, B.

Solomon, C.

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," Mon. Not. R. Astron. Soc. 371,323-336 (2006).
[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," Mon. Not. R. Astron. Soc. 371,323-336 (2006).
[CrossRef]

van Dam, M.

Vargas-Martn, F.

Walker, G.

L. Diaz-Santana, G. Walker, and S. Bara, "Sampling geometries for ocular aberrometry: A model for evaluation of performance," J. Opt. Soc. Am. A 13,8801-8818 (2005).

Welsh, B.

Williams, D.

Winick, K.

Appl. Opt. (5)

J. Opt. Soc. Am. A (10)

S. Bara, "Measuring eye aberrations with Hartmann-Shack wave-front sensors: Should the irradiance distribution across the eye pupil be taken into account?" J. Opt. Soc. Am. A 20,2237-2245 (2003).
[CrossRef]

R. Cannon, "Global wave-front reconstruction using Shack-Hartmann sensors," J. Opt. Soc. Am. A 12,2031-2039 (1995).
[CrossRef]

H. Barrett, C. Dainty, and D. Lara, "Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions," J. Opt. Soc. Am. A 24,391-414 (2007).
[CrossRef]

L. Llorente, S. Marcos, C. Dorronsoro, and S. Burns, "Effect of sampling on real ocular aberration measurements," J. Opt. Soc. Am. A 24,2783-2796 (2007).
[CrossRef]

S. Bara, "Characteristic functions of Hartmann-Shack wavefront sensors and laser-ray-tracing aberrometers," J. Opt. Soc. Am. A 24,3700-3707 (2007).
[CrossRef]

P. Prieto, F. Vargas-Martn, S. Goelz, and P. Artal, "Analysis of the performance of the Hartmann-Shack sensor in the human eye," J. Opt. Soc. Am. A 17,1388-1398 (2000).
[CrossRef]

H. Hofer, P. Artal, B. Singer, J. Aragn, and D. Williams, "Dynamics of the eye’s wave aberration," J. Opt. Soc. Am. A 18,497-506 (2001).
[CrossRef]

M. van Dam and R. Lane, "Wave-front slope estimation," J. Opt. Soc. Am. A 17,1319-1324 (2000).
[CrossRef]

K. Winick, "Cramér-Rao lower bounds on the performance of charge-coupled-device optical position estimators," J. Opt. Soc. Am. A 3,1809-1815 (1986).
[CrossRef]

L. Diaz-Santana, G. Walker, and S. Bara, "Sampling geometries for ocular aberrometry: A model for evaluation of performance," J. Opt. Soc. Am. A 13,8801-8818 (2005).

Mon. Not. R. Astron. Soc. (1)

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau and G. Rousset, "Comparison of centroid computation algorithms in a Shack-Hartmann sensor," Mon. Not. R. Astron. Soc. 371,323-336 (2006).
[CrossRef]

Opt. Commun. (1)

J. Arines and J. Ares, "Significance of thresholding processing in centroid based gradient wavefront sensors: effective modulation of the wavefront derivative," Opt. Commun. 237,257-266 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Optom. Vis. Sci. (1)

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, and S. Marcos, "Aberrations of the human eye in visible and near infrared illumination," Optom. Vis. Sci. 80,26-35 (2003).
[CrossRef] [PubMed]

Proc. SPIE (2)

T. Fusco, M. Nicolle, G. Rousset, V. Michau, J.-L. Beuzit, and D. Mouillet, "Optimisation of Shack-Hartmann based wavefront sensor for XAO system," in Advancements in Adaptive Optics, Proc. SPIE 5490,1155-1166 (2004).
[CrossRef]

T.R. Rimmele and R.R. Radick, "Solar Adaptive Optics at the National Solar Observatory," Proc. SPIE 3353,72-81 (1998).
[CrossRef]

Other (5)

H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley-Interscience, 2003).

G. Rousset, "Wave-front sensors," in Adaptive Optics in Astronomy, F. Roddier eds. (Cambridge University Press, 1999).
[CrossRef]

J. Porter, H. Queener, J. Lin, K. Thorn and A. Awwal, eds., Adaptive Optics for Vision Science: Principles, Practices, Design and Applications (Wiley, 2006).
[CrossRef]

L. Diaz-Santana Haro, Wavefront Sensing in the Human Eye with a Shack-Hartmann Sensor (PhD thesis, 2000).

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005).

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.

Optical layout of our custom-built aberrometer.

Fig. 2.
Fig. 2.

Parameterisation of a centroiding algorithm, with a normalised threshold t and a rectangular window of size R. The gray area corresponds to the data set to zero before centroiding.

Fig. 3.
Fig. 3.

Simulation of the effect of an uniform background added to the mean data for two centroiding algorithms (R = 5 and R = 15, both with t = 0) and a matched filter.

Fig. 4.
Fig. 4.

Centroid positions estimated by the matched filter ( ρ ̂ mf , “°”) and by a centroiding algorithm. ( ρ ̂ cent : “·”, for R = 9 and t = 0.) Data collected on subject 2, with one single lenslet.

Fig. 5.
Fig. 5.

Signal dependant bias of the centroiding algorithm, for three different window sizes (R = 5, R = 9, R = 15) and no threshold (t = 0). Data collected on subject 2, using the 333 lenslets of the aberrometer.

Fig. 6.
Fig. 6.

Root mean square difference between the centroiding algorithms (R = 5, R = 9, R = 15) and the matched filter algorithm, as a function of the threshold t.

Fig. 7.
Fig. 7.

Thresholded data, obtained with subject 2 for 3 values of;. For t = 0.1 (left) and t = 0.2 (middle), the partially thresholded background leads to very large values of σ.(See Fig. 6.) For t = 0.6, the threshold is close to optimal, but there is still σ ≃ 0.13 pixels residual error due to the truncation of the spot.

Fig. 8.
Fig. 8.

Mean rms error of the (tip-tilt removed) difference between the wavefronts reconstructed from a centroiding algorithm and the matched filter algorithm, for the 5 subjects.

Tables (3)

Tables Icon

Table 1. Main parameters of our custom-built aberrometer

Tables Icon

Table 2. Parameters of the numerical simulations

Tables Icon

Table 3. Estimated peak a and background b of the mean spot (in D.U.).

Metrics