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

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2008 (1)

2007 (2)

2006 (4)

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]

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]

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]

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]

2005 (1)

2004 (7)

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

J. Ares and J. Arines, "Influence of Thresholding on Centroid Statistics: Full Analytical Description," Appl. Opt. 43, 5796-5805 (2004).
[CrossRef] [PubMed]

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

H. Ding, Q. Li, and W. Zou, "Design and comparison of amplitude-type and phase-only transverse superresolving 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]

H. Luo and C. Zhou, "Comparison of Superresolution Effects with Annular Phase and Amplitude Filters," Appl. Opt. 43, 6242-6247 (2004).
[CrossRef] [PubMed]

2003 (2)

2002 (2)

A. Tokovinin, "From Differential Image Motion to Seeing," Publ. Astron. Soc. Pac. 114, 1156-1166 (2002).
[CrossRef]

J. Arines and J. Ares, "Minimum variance centroid thresholding," Opt. Lett. 27, 497-499 (2002).
[CrossRef]

2001 (3)

1999 (1)

1998 (3)

1997 (1)

1995 (1)

M. Martınez-Corral, P. Andres, J. Ojeda-Castaneda, 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)

Andres, P.

M. Martınez-Corral, P. Andres, J. Ojeda-Castaneda, 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.

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, 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]

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]

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

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, V. F. Canales, P. J. Valle, and M. P. Cagigal, "Focusing properties of annular binary phase filters," Opt. Commun. 229, 71 - 77 (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]

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]

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.

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 superresolving 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 phaseonly pupil filter," Optik - International Journal for Light and Electron Optics 118, 67 - 73 (2007).
[CrossRef]

Eifler, L.

Feng, Z.

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]

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

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 superresolving 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.

Martinez-Corral, M.

M. Martınez-Corral, P. Andres, J. Ojeda-Castaneda, 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.

Oti, J. E.

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]

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]

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.

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]

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

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]

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]

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, 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]

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.

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.

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]

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

Zhou, C.

Zou, W.

H. Ding, Q. Li, and W. Zou, "Design and comparison of amplitude-type and phase-only transverse superresolving 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]

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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

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