Abstract

The positioning tolerances for phase plates used to compensate human eye aberrations are analyzed. Lateral displacements, in-plane rotations, and axial translations are considered, describing analytic and numerical procedures to compute the maximum degree of compensation achievable in each case. The compensation loss is found to be dependent both on the kind and the amount of misalignment and on the particular composition of the aberration pattern of each subject in terms of Zernike polynomials. We applied these procedures to a set of human eye aberrations measured with the laser ray-tracing method. The general trend of results suggests that lateral positioning, followed by angular positioning, are the key factors affecting compensation performance in practical setups, whereas axial positioning has far less stringent requirements.

© 2000 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  19. S. Marcos, S. A. Burns, E. Moreno-Barriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
    [CrossRef]

2000

R. Navarro, E. Moreno-Barriuso, S. Bará, T. Mancebo, “Phase plates for wave aberration compensation in the human eye,” Opt. Lett. 25, 236–238 (2000).
[CrossRef]

J. C. He, S. A. Burns, S. Marcos, “Monochromatic aberrations in the accommodated human eye,” Vision Res. 40, 41–48 (2000).
[CrossRef] [PubMed]

1999

S. Marcos, S. A. Burns, E. Moreno-Barriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

L. Zhu, P.-C. Sun, D.-U. Bartsch, W. R. Freeman, Y. Fainmann, “Adaptive control of a membrane deformable mirror for aberration compensation,” Appl. Opt. 38, 168–176 (1999).
[CrossRef]

1998

1997

1980

1976

Applegate, R.

Artal, P.

Bará, S.

R. Navarro, E. Moreno-Barriuso, S. Bará, T. Mancebo, “Phase plates for wave aberration compensation in the human eye,” Opt. Lett. 25, 236–238 (2000).
[CrossRef]

T. Mancebo, S. Bará, E. Moreno, R. Navarro, “Single-mask photosculpted phase plates for the compensation of optical aberrations,” in Proceedings of Seventh International Microoptics Conference (MOC’99) (Japan Society of Applied Physics, Tokyo, Japan, 1999), pp. 224–227.

Bartsch, D.-U.

Baude, D.

Blanchard, A.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), Chap. 9, pp. 464–466.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), Chap. 8, pp. 382–383.

Burns, S. A.

J. C. He, S. A. Burns, S. Marcos, “Monochromatic aberrations in the accommodated human eye,” Vision Res. 40, 41–48 (2000).
[CrossRef] [PubMed]

S. Marcos, S. A. Burns, E. Moreno-Barriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

Charman, N.

Chateau, N.

DeVore, S. L.

D. Malacara, S. L. DeVore, “Interferogram evaluation and wavefront fitting,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 13, pp. 455–499.

Dorronsoro, C.

Fainmann, Y.

Freeman, W. R.

He, J. C.

J. C. He, S. A. Burns, S. Marcos, “Monochromatic aberrations in the accommodated human eye,” Vision Res. 40, 41–48 (2000).
[CrossRef] [PubMed]

Howland, B.

Howland, H. C.

Liang, J.

Liebelt, P. B.

P. B. Liebelt, An Introduction to Optimal Estimation (Addison-Wesley, Reading, Mass., 1967), Chap. 5, pp. 135–159.

López-Gil, N.

Losada, M. A.

R. Navarro, M. A. Losada, “Aberrations and relative efficiency of light pencils in the living human eye,” Optom. Vis. Sci. 74, 540–547 (1997).
[CrossRef] [PubMed]

Love, G. D.

Malacara, D.

D. Malacara, S. L. DeVore, “Interferogram evaluation and wavefront fitting,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 13, pp. 455–499.

Mancebo, T.

R. Navarro, E. Moreno-Barriuso, S. Bará, T. Mancebo, “Phase plates for wave aberration compensation in the human eye,” Opt. Lett. 25, 236–238 (2000).
[CrossRef]

T. Mancebo, S. Bará, E. Moreno, R. Navarro, “Single-mask photosculpted phase plates for the compensation of optical aberrations,” in Proceedings of Seventh International Microoptics Conference (MOC’99) (Japan Society of Applied Physics, Tokyo, Japan, 1999), pp. 224–227.

Marcos, S.

J. C. He, S. A. Burns, S. Marcos, “Monochromatic aberrations in the accommodated human eye,” Vision Res. 40, 41–48 (2000).
[CrossRef] [PubMed]

S. Marcos, S. A. Burns, E. Moreno-Barriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

Miller, D. T.

Moreno, E.

R. Navarro, E. Moreno, C. Dorronsoro, “Monochromatic aberrations and point-spread functions of the human eye across the visual field,” J. Opt. Soc. Am. A 15, 2522–2529 (1998).
[CrossRef]

T. Mancebo, S. Bará, E. Moreno, R. Navarro, “Single-mask photosculpted phase plates for the compensation of optical aberrations,” in Proceedings of Seventh International Microoptics Conference (MOC’99) (Japan Society of Applied Physics, Tokyo, Japan, 1999), pp. 224–227.

Moreno-Barriuso, E.

R. Navarro, E. Moreno-Barriuso, S. Bará, T. Mancebo, “Phase plates for wave aberration compensation in the human eye,” Opt. Lett. 25, 236–238 (2000).
[CrossRef]

S. Marcos, S. A. Burns, E. Moreno-Barriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

Navarro, R.

R. Navarro, E. Moreno-Barriuso, S. Bará, T. Mancebo, “Phase plates for wave aberration compensation in the human eye,” Opt. Lett. 25, 236–238 (2000).
[CrossRef]

S. Marcos, S. A. Burns, E. Moreno-Barriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

R. Navarro, E. Moreno, C. Dorronsoro, “Monochromatic aberrations and point-spread functions of the human eye across the visual field,” J. Opt. Soc. Am. A 15, 2522–2529 (1998).
[CrossRef]

R. Navarro, M. A. Losada, “Aberrations and relative efficiency of light pencils in the living human eye,” Optom. Vis. Sci. 74, 540–547 (1997).
[CrossRef] [PubMed]

T. Mancebo, S. Bará, E. Moreno, R. Navarro, “Single-mask photosculpted phase plates for the compensation of optical aberrations,” in Proceedings of Seventh International Microoptics Conference (MOC’99) (Japan Society of Applied Physics, Tokyo, Japan, 1999), pp. 224–227.

Noll, R. J.

Prieto, P. M.

Silva, D. E.

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, 1986), pp. 136–140.

Sun, P.-C.

Vargas-Martin, F.

Wang, J. Y.

Williams, D. R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), Chap. 8, pp. 382–383.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), Chap. 9, pp. 464–466.

Zhu, L.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Lett.

Optom. Vis. Sci.

R. Navarro, M. A. Losada, “Aberrations and relative efficiency of light pencils in the living human eye,” Optom. Vis. Sci. 74, 540–547 (1997).
[CrossRef] [PubMed]

Vision Res.

J. C. He, S. A. Burns, S. Marcos, “Monochromatic aberrations in the accommodated human eye,” Vision Res. 40, 41–48 (2000).
[CrossRef] [PubMed]

S. Marcos, S. A. Burns, E. Moreno-Barriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

Other

T. Mancebo, S. Bará, E. Moreno, R. Navarro, “Single-mask photosculpted phase plates for the compensation of optical aberrations,” in Proceedings of Seventh International Microoptics Conference (MOC’99) (Japan Society of Applied Physics, Tokyo, Japan, 1999), pp. 224–227.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), Chap. 9, pp. 464–466.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), Chap. 8, pp. 382–383.

J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, 1986), pp. 136–140.

D. Malacara, S. L. DeVore, “Interferogram evaluation and wavefront fitting,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 13, pp. 455–499.

P. B. Liebelt, An Introduction to Optimal Estimation (Addison-Wesley, Reading, Mass., 1967), Chap. 5, pp. 135–159.

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Figures (6)

Fig. 1
Fig. 1

Laterally displaced correcting phase plate. W e (r), eye aberration; W p (r), plate OPL; P 1, region of overlapping pupils; P 2, uncompensated eye pupil area.

Fig. 2
Fig. 2

In-plane rotated correcting phase plate.

Fig. 3
Fig. 3

Axially displaced correcting phase plate.

Fig. 4
Fig. 4

Degree of compensation D versus normalized lateral displacement d/R of the correcting plate. Tilt has been removed from the residual aberration. Plots for displacements along the X axis: subjects A (filled squares), B (filled circles), C (filled diamonds). Displacements along the y axis: A (open squares), B (open circles), C (open diamonds).

Fig. 5
Fig. 5

Degree of compensation D versus in-plane rotation angle ϕ (degrees) of the correcting plate for aberrations corresponding to subjects A (squares), B (circles), C (diamonds). (a) Range, 0–360 deg; (b) Range, -15–15 deg.

Fig. 6
Fig. 6

Degree of compensation D versus normalized axial displacement z/R of the correcting plate for aberrations corresponding to subjects A (squares), B (circles), C (diamonds).

Tables (1)

Tables Icon

Table 1 Zernike Aberration Coefficients of Subjects A–C for Modes i = 3–35

Equations (26)

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Wer=i=1M aiZir/R,
Wrr=Wer+Wpr.
D=1-σr/σe,
σr=1πR2  Wr2rd2r1/2
σe=1πR2  We2rd2r1/2
Zˆir/R=ciZir/R,
1πR2  Zˆir/RZˆjr/Rd2r=δij.
D=1-i=1Maˆi+aˆi2i=1M aˆi21/2=1-i=1M aˆir2i=1M aˆi21/2,
σr2=1πR2P1Wer-Wer-d2d2r+1πR2P2 We2rd2r.
σr2=N-1α=1NWerα+Wprα2,
Wrr, θ=Wer, θ-Wer, θ-ϕ
Zˆir/RZˆn,lr/R=cn,lRnlr/RAlθ,
Alθ=coslθ,  l<0=sinlθ, l>0=1,  l=0.
Wer=n=1Nml=-nn aˆn,lcn,lRnlr/RAlθ
Wer, θ=n=1Nml0n cn,lRnlr/Raˆn,-l coslθ+aˆn,l sinlθ
Wer, θ-ϕ=n=1Nml0n cn,lRnlr/Raˆn,-l coslθ+aˆn,l sinlθ,
aˆn,laˆn,-l=coslϕsinlϕ-sinlϕcoslϕaˆn,laˆn,-l.
aˆnl=Mlϕaˆnl,
aˆnlr=I-Mlϕaˆnl,
D=1-n=1Nml0n |aˆnlr|2n=1Nml0n |aˆnl|21/2,
D=1-2 n=1Nml0n1-coslϕ|aˆnl|2n=1Nml0n |aˆnl|21/2.
D=1-|ϕ|n=1Nml0n l2|aˆnl|2n=1Nml0n |aˆnl|21/2,
Wpr=Wpr+z+12z|r-r|2,
r=r+zWpr.
σr2N-1α=1NWerα+Wprα2,  σe2N-1α=1NWerα2
Wpr=i=1M aˆiZˆir/R

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