Abstract

We describe a new wave-front sensor based on the previously proposed pyramid sensor. This new sensor uses an extended source instead of a point-like source avoiding in this manner the oscillation of the pyramid. After an introductory background the sensor functioning is described. Among other possible optical testing uses, we apply the sensor to measure the wave-front aberration of the human eye. An experimental system built to test this specific application is described. Results obtained both in an articficial eye and in a real eye are presented. A discussion about the sensor characteristics, the experimental results and future work prospects is also included.

© 2002 Optical Society of America

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References

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  1. E.J. Fernandez, I. Iglesias, and P. Artal, “Closed-loop adaptive optics in the human eye,” Opt. Lett. 26, 746–748 (2001).
    [CrossRef]
  2. H. Hofer, L. Chen, G. Yoon, B. Singer, Y. Yamauchi, and D.R. Williams, “Improvement in retinal image quality with dynamic correction of the eye’s aberration,” Opt. Express 10, 631–643 (2001) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-11-631
    [CrossRef]
  3. J. Liang, B. Grimm, S. Goelz, and J.F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt.Soc. Am. A. 11, 1949–1957 (1994).
    [CrossRef]
  4. P.M. Prieto, P.M., F. Vargas-Martin, 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]
  5. R. Ragazzoni, “Pupil plane wavefront sensing with an oscillating prism,” J. of Mod. Opt. 43, 289–293 (1996).
    [CrossRef]
  6. W.H. Southwell. “Wavefront estimation from wavefront slope measurements,”. J. Opt. Soc. Am. A. 70, 998–1006 (1980).
    [CrossRef]
  7. R. Cubalchini, “Modal wavefront estimation from phase derivative measurements,” J. Opt. Soc. Am. A. 69, 972–977(1979).
    [CrossRef]
  8. W.H. Press, W.H., S.A. Teukolsky, Vetterling, W.T., and B.P. FlanneryNumerical recipes in C, Second Edition, Cambridge University Press (Cambridge, 1992).
  9. R.J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]

2001 (2)

H. Hofer, L. Chen, G. Yoon, B. Singer, Y. Yamauchi, and D.R. Williams, “Improvement in retinal image quality with dynamic correction of the eye’s aberration,” Opt. Express 10, 631–643 (2001) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-11-631
[CrossRef]

E.J. Fernandez, I. Iglesias, and P. Artal, “Closed-loop adaptive optics in the human eye,” Opt. Lett. 26, 746–748 (2001).
[CrossRef]

2000 (1)

P.M. Prieto, P.M., F. Vargas-Martin, 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]

1996 (1)

R. Ragazzoni, “Pupil plane wavefront sensing with an oscillating prism,” J. of Mod. Opt. 43, 289–293 (1996).
[CrossRef]

1994 (1)

J. Liang, B. Grimm, S. Goelz, and J.F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt.Soc. Am. A. 11, 1949–1957 (1994).
[CrossRef]

1980 (1)

W.H. Southwell. “Wavefront estimation from wavefront slope measurements,”. J. Opt. Soc. Am. A. 70, 998–1006 (1980).
[CrossRef]

1979 (1)

R. Cubalchini, “Modal wavefront estimation from phase derivative measurements,” J. Opt. Soc. Am. A. 69, 972–977(1979).
[CrossRef]

1976 (1)

Artal, P.

E.J. Fernandez, I. Iglesias, and P. Artal, “Closed-loop adaptive optics in the human eye,” Opt. Lett. 26, 746–748 (2001).
[CrossRef]

P.M. Prieto, P.M., F. Vargas-Martin, 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]

Bille, J.F.

J. Liang, B. Grimm, S. Goelz, and J.F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt.Soc. Am. A. 11, 1949–1957 (1994).
[CrossRef]

Chen, L.

H. Hofer, L. Chen, G. Yoon, B. Singer, Y. Yamauchi, and D.R. Williams, “Improvement in retinal image quality with dynamic correction of the eye’s aberration,” Opt. Express 10, 631–643 (2001) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-11-631
[CrossRef]

Cubalchini, R.

R. Cubalchini, “Modal wavefront estimation from phase derivative measurements,” J. Opt. Soc. Am. A. 69, 972–977(1979).
[CrossRef]

Fernandez, E.J.

Flannery, B.P.

W.H. Press, W.H., S.A. Teukolsky, Vetterling, W.T., and B.P. FlanneryNumerical recipes in C, Second Edition, Cambridge University Press (Cambridge, 1992).

Goelz, S.

P.M. Prieto, P.M., F. Vargas-Martin, 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]

J. Liang, B. Grimm, S. Goelz, and J.F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt.Soc. Am. A. 11, 1949–1957 (1994).
[CrossRef]

Grimm, B.

J. Liang, B. Grimm, S. Goelz, and J.F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt.Soc. Am. A. 11, 1949–1957 (1994).
[CrossRef]

Hofer, H.

H. Hofer, L. Chen, G. Yoon, B. Singer, Y. Yamauchi, and D.R. Williams, “Improvement in retinal image quality with dynamic correction of the eye’s aberration,” Opt. Express 10, 631–643 (2001) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-11-631
[CrossRef]

Iglesias, I.

Liang, J.

J. Liang, B. Grimm, S. Goelz, and J.F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt.Soc. Am. A. 11, 1949–1957 (1994).
[CrossRef]

Noll, R.J.

P.M.,

P.M. Prieto, P.M., F. Vargas-Martin, 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]

Press, W.H.

W.H. Press, W.H., S.A. Teukolsky, Vetterling, W.T., and B.P. FlanneryNumerical recipes in C, Second Edition, Cambridge University Press (Cambridge, 1992).

Prieto, P.M.

P.M. Prieto, P.M., F. Vargas-Martin, 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]

Ragazzoni, R.

R. Ragazzoni, “Pupil plane wavefront sensing with an oscillating prism,” J. of Mod. Opt. 43, 289–293 (1996).
[CrossRef]

Singer, B.

H. Hofer, L. Chen, G. Yoon, B. Singer, Y. Yamauchi, and D.R. Williams, “Improvement in retinal image quality with dynamic correction of the eye’s aberration,” Opt. Express 10, 631–643 (2001) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-11-631
[CrossRef]

Southwell, W.H.

W.H. Southwell. “Wavefront estimation from wavefront slope measurements,”. J. Opt. Soc. Am. A. 70, 998–1006 (1980).
[CrossRef]

Teukolsky, S.A.

W.H. Press, W.H., S.A. Teukolsky, Vetterling, W.T., and B.P. FlanneryNumerical recipes in C, Second Edition, Cambridge University Press (Cambridge, 1992).

Vargas-Martin, F.

P.M. Prieto, P.M., F. Vargas-Martin, 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]

Vetterling,

W.H. Press, W.H., S.A. Teukolsky, Vetterling, W.T., and B.P. FlanneryNumerical recipes in C, Second Edition, Cambridge University Press (Cambridge, 1992).

W.H.,

W.H. Press, W.H., S.A. Teukolsky, Vetterling, W.T., and B.P. FlanneryNumerical recipes in C, Second Edition, Cambridge University Press (Cambridge, 1992).

W.T.,

W.H. Press, W.H., S.A. Teukolsky, Vetterling, W.T., and B.P. FlanneryNumerical recipes in C, Second Edition, Cambridge University Press (Cambridge, 1992).

Williams, D.R.

H. Hofer, L. Chen, G. Yoon, B. Singer, Y. Yamauchi, and D.R. Williams, “Improvement in retinal image quality with dynamic correction of the eye’s aberration,” Opt. Express 10, 631–643 (2001) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-11-631
[CrossRef]

Yamauchi, Y.

H. Hofer, L. Chen, G. Yoon, B. Singer, Y. Yamauchi, and D.R. Williams, “Improvement in retinal image quality with dynamic correction of the eye’s aberration,” Opt. Express 10, 631–643 (2001) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-11-631
[CrossRef]

Yoon, G.

H. Hofer, L. Chen, G. Yoon, B. Singer, Y. Yamauchi, and D.R. Williams, “Improvement in retinal image quality with dynamic correction of the eye’s aberration,” Opt. Express 10, 631–643 (2001) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-11-631
[CrossRef]

J. of Mod. Opt. (1)

R. Ragazzoni, “Pupil plane wavefront sensing with an oscillating prism,” J. of Mod. Opt. 43, 289–293 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

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

W.H. Southwell. “Wavefront estimation from wavefront slope measurements,”. J. Opt. Soc. Am. A. 70, 998–1006 (1980).
[CrossRef]

R. Cubalchini, “Modal wavefront estimation from phase derivative measurements,” J. Opt. Soc. Am. A. 69, 972–977(1979).
[CrossRef]

P.M. Prieto, P.M., F. Vargas-Martin, 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]

J. Opt.Soc. Am. A. (1)

J. Liang, B. Grimm, S. Goelz, and J.F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt.Soc. Am. A. 11, 1949–1957 (1994).
[CrossRef]

Opt. Express (1)

H. Hofer, L. Chen, G. Yoon, B. Singer, Y. Yamauchi, and D.R. Williams, “Improvement in retinal image quality with dynamic correction of the eye’s aberration,” Opt. Express 10, 631–643 (2001) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-11-631
[CrossRef]

Opt. Lett. (1)

Other (1)

W.H. Press, W.H., S.A. Teukolsky, Vetterling, W.T., and B.P. FlanneryNumerical recipes in C, Second Edition, Cambridge University Press (Cambridge, 1992).

Supplementary Material (2)

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» Media 2: GIF (518 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

(a) Schematics of the wave-front sensor where L1 states for the lens used to form the Fourier transform of the probed field at its focal length where the pyramid is placed. A second lens, L2, is placed behind the pyramid to focus the exit pupil of the optical system under study on an intensity detector. (b) The glass pyramid. (c) A different view of the sensor; A, B, C and D indexes the four re-imaged pupils.

Fig. 2.
Fig. 2.

(a) A simple linear oscillation path in the Fourier plane. The pyramid vertex, marked with a crosshair, follows the dotted line around the origin. In (b) it is drawn a simple extended emitter with binary intensity (white area means light, black means no light) modeled (see text) as an infinite collection of oscillation paths, as the one in Figure (a), with different amplitudes. The doted line on the graph in panel (c) represents the sensor normalized response for the path of Figure (a). The solid line on the same graph represents the response for the extended source of Figure (b).

Fig. 3.
Fig. 3.

Schematics of the wave-front measuring apparatus. S electronic shutter; SF Spatial filter; RD rotating diffusers; A1 A2, apertures; L1, L2, L3, L4, L5, L6 lenses. M1, M2, M3, M4 mirrors (M1, M2 on a translation stage). BS beam splitter. CCD charged coupled device.

Fig. 4.
Fig. 4.

(1.8 Mb) Movie of the acquired data, (a), the gradient in both orthogonal directions, (b), and the computed phase of the pupil function represented modulus 2π obtained by moving the translation stage.

Fig. 5.
Fig. 5.

Variation of the different Zernike coefficients moving the translation stage in the artificial eye experiment. One centimeter of displacement introduces 0.97 diopters of refractive defocus (0.52 μm of Z4).

Fig. 6.
Fig. 6.

(518 KB) Movie of the acquired data, (a), the gradient in both orthogonal directions, (b), and the phase of the pupil function represented modulus 2π obtained by moving the translation stage.

Fig. 7.
Fig. 7.

Variation of the different Zernike coefficients moving the translation stage in the living eye experiment.

Equations (7)

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ξ ζ = f ( w x , w y ) = f w ,
w x | i , j c i , j + d i , j ( a i , j + b i , j ) a i , j + b i , j + c i , j + d i , j , w y | i , j a i , j + c i , j ( b i , j + d i , j ) a i , j + b i , j + c i , j + d i , j
a i , j = b i , j = { 0 ξ > Δ 2 ( Δ ξ ) Δ ξ Δ 2 2 Δ ξ < Δ c i , j = d i , j = { 2 2 Δ ξ > Δ 2 ( Δ + ξ ) Δ ξ Δ 0 ξ < Δ
ξ = { 1 ξ > Δ ξ / Δ Δ ξ Δ 1 ξ < Δ
a i , j = b i , j = { 0 ξ > Δ 1 2 ( Δ ξ ) 2 Δ ξ Δ 2 Δ 2 ξ < Δ c i , j = d i , j = { 2 Δ 2 ξ > Δ 1 2 ( Δ 2 + 2 ξΔ ξ 2 ) Δ ξ Δ 0 ξ > Δ
ξ = { 1 ξ > Δ ( 2 Δ ξ ) ξ / Δ 2 Δ ξ Δ 1 ξ < Δ
ξ = { 1 ξ > Δ 2 ξ / Δ Δ ξ Δ 1 ξ < Δ ,

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