Abstract

From both a fundamental and a clinical point of view, it is necessary to know the distribution of the eye’s aberrations in the normal population and to be able to describe them as efficiently as possible. We used a modified Hartmann–Shack wave-front sensor to measure the monochromatic wave aberration of both eyes for 109 normal human subjects across a 5.7-mm pupil. We analyzed the distribution of the eye’s aberrations in the population and found that most Zernike modes are relatively uncorrelated with each other across the population. A principal components analysis was applied to our wave-aberration measurements with the resulting principal components providing only a slightly more compact description of the population data than Zernike modes. This indicates that Zernike modes are efficient basis functions for describing the eye’s wave aberration. Even though there appears to be a random variation in the eye’s aberrations from subject to subject, many aberrations in the left eye were found to be significantly correlated with their counterparts in the right eye.

© 2001 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  3. D. T. Miller, “Retinal imaging and vision at the frontiers of adaptive optics,” Phys. Today 53, 31–36 (2000).
    [CrossRef]
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    [CrossRef]
  10. J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave front of the eye by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2001

2000

D. T. Miller, “Retinal imaging and vision at the frontiers of adaptive optics,” Phys. Today 53, 31–36 (2000).
[CrossRef]

1999

A. Guirao, C. Gonzalez, M. Redondo, E. Geraghty, S. Norrby, P. Artal, “Average optical performance of the human eye as a function of age in a normal population,” Invest. Ophthalmol. Visual Sci. 40, 203–213 (1999).

1998

1997

1996

C. T. Naugler, M. D. Ludman, “A case-control study of fluctuating dermatoglyphic asymmetry as a risk marker for developmental delay,” Am. J. Med. Genet. 26, 11–14 (1996).
[CrossRef]

1995

1994

1985

1984

1983

R. D. Sperduto, D. Seigel, J. Roberts, M. Rowland, “Prevalence of myopia in the United States,” Arch. Ophthalmol. (Chicago) 101, 405–407 (1983).
[CrossRef]

1982

J. P. Carroll, “Component and correlation ametropia,” Am. J. Optom. Physiol. Opt. 59, 28–33 (1982).
[CrossRef] [PubMed]

1980

1977

1976

1973

1962

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biophys. J. 7, 766–795 (1962).

Applegate, R. A.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35of OSA Trends in Optics and Photonics Series(Optical Society of America, Washington, D.C., 2000), pp. 232–244.

Aragon, J. L.

Artal, P.

H. Hofer, P. Artal, B. Singer, J. L. Aragon, D. R. Williams, “Dynamics of the eye’s wave aberration,” J. Opt. Soc. Am. A 18, 497–506 (2001).
[CrossRef]

A. Guirao, C. Gonzalez, M. Redondo, E. Geraghty, S. Norrby, P. Artal, “Average optical performance of the human eye as a function of age in a normal population,” Invest. Ophthalmol. Visual Sci. 40, 203–213 (1999).

I. Iglesias, E. Berrio, P. Artal, “Estimates of the ocular wave aberration from pairs of double-pass retinal images,” J. Opt. Soc. Am. A 15, 2466–2476 (1998).
[CrossRef]

Berny, F.

Berrio, E.

Bescós, J.

Bille, J. F.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1985).

Burns, S. A.

Carroll, J. P.

J. P. Carroll, “Component and correlation ametropia,” Am. J. Optom. Physiol. Opt. 59, 28–33 (1982).
[CrossRef] [PubMed]

Charman, W. N.

Chisholm, W.

Creath, K.

J. C. Wyant, K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, 1992), Vol. XI, pp. 1–53.

Cummins, H.

H. Cummins, C. Midlo, Finger Prints, Palms and Soles: An Introduction to Dermatoglyphics (Blakiston, Philadelphia, 1943).

El Hage, S. G.

Geraghty, E.

A. Guirao, C. Gonzalez, M. Redondo, E. Geraghty, S. Norrby, P. Artal, “Average optical performance of the human eye as a function of age in a normal population,” Invest. Ophthalmol. Visual Sci. 40, 203–213 (1999).

Goelz, S.

Gonzalez, C.

A. Guirao, C. Gonzalez, M. Redondo, E. Geraghty, S. Norrby, P. Artal, “Average optical performance of the human eye as a function of age in a normal population,” Invest. Ophthalmol. Visual Sci. 40, 203–213 (1999).

Greivenkamp, J. E.

J. Schwiegerling, J. E. Greivenkamp, “Using corneal height maps and polynomial decomposition to determine corneal aberrations,” Optom. Vision Sci. 74, 906–915 (1997).
[CrossRef]

Grimm, B.

Guirao, A.

A. Guirao, C. Gonzalez, M. Redondo, E. Geraghty, S. Norrby, P. Artal, “Average optical performance of the human eye as a function of age in a normal population,” Invest. Ophthalmol. Visual Sci. 40, 203–213 (1999).

He, J. C.

Hofer, H.

Howland, B.

Howland, H. C.

Iglesias, I.

Joliffe, I. T.

I. T. Joliffe, Principal Components Analysis (Springer–Verlag, New York, 1986).

Liang, J.

Lidkea, B.

Ludman, M. D.

C. T. Naugler, M. D. Ludman, “A case-control study of fluctuating dermatoglyphic asymmetry as a risk marker for developmental delay,” Am. J. Med. Genet. 26, 11–14 (1996).
[CrossRef]

Marcos, S.

Midlo, C.

H. Cummins, C. Midlo, Finger Prints, Palms and Soles: An Introduction to Dermatoglyphics (Blakiston, Philadelphia, 1943).

Miller, D. T.

Naugler, C. T.

C. T. Naugler, M. D. Ludman, “A case-control study of fluctuating dermatoglyphic asymmetry as a risk marker for developmental delay,” Am. J. Med. Genet. 26, 11–14 (1996).
[CrossRef]

Navarro, R.

Noll, R. J.

Norrby, S.

A. Guirao, C. Gonzalez, M. Redondo, E. Geraghty, S. Norrby, P. Artal, “Average optical performance of the human eye as a function of age in a normal population,” Invest. Ophthalmol. Visual Sci. 40, 203–213 (1999).

Redondo, M.

A. Guirao, C. Gonzalez, M. Redondo, E. Geraghty, S. Norrby, P. Artal, “Average optical performance of the human eye as a function of age in a normal population,” Invest. Ophthalmol. Visual Sci. 40, 203–213 (1999).

Roberts, J.

R. D. Sperduto, D. Seigel, J. Roberts, M. Rowland, “Prevalence of myopia in the United States,” Arch. Ophthalmol. (Chicago) 101, 405–407 (1983).
[CrossRef]

Rowland, M.

R. D. Sperduto, D. Seigel, J. Roberts, M. Rowland, “Prevalence of myopia in the United States,” Arch. Ophthalmol. (Chicago) 101, 405–407 (1983).
[CrossRef]

Rynders, M.

Santamari´a, J.

Schwiegerling, J.

J. Schwiegerling, J. E. Greivenkamp, “Using corneal height maps and polynomial decomposition to determine corneal aberrations,” Optom. Vision Sci. 74, 906–915 (1997).
[CrossRef]

Schwiegerling, J. T.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35of OSA Trends in Optics and Photonics Series(Optical Society of America, Washington, D.C., 2000), pp. 232–244.

Seigel, D.

R. D. Sperduto, D. Seigel, J. Roberts, M. Rowland, “Prevalence of myopia in the United States,” Arch. Ophthalmol. (Chicago) 101, 405–407 (1983).
[CrossRef]

Singer, B.

Smirnov, M. S.

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biophys. J. 7, 766–795 (1962).

Smith, W. J.

W. J. Smith, Modern Optical Engineering: The Design of Optical Systems (McGraw-Hill, New York, 1990).

Southwell, W. H.

Sperduto, R. D.

R. D. Sperduto, D. Seigel, J. Roberts, M. Rowland, “Prevalence of myopia in the United States,” Arch. Ophthalmol. (Chicago) 101, 405–407 (1983).
[CrossRef]

Thibos, L. N.

M. Rynders, B. Lidkea, W. Chisholm, L. N. Thibos, “Statistical distribution of foveal transverse chromatic aberration, pupil centration, and angle ψ in a population of young adult eyes,” J. Opt. Soc. Am. A 12, 2348–2357 (1995).
[CrossRef]

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35of OSA Trends in Optics and Photonics Series(Optical Society of America, Washington, D.C., 2000), pp. 232–244.

Walsh, G.

Webb, R.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35of OSA Trends in Optics and Photonics Series(Optical Society of America, Washington, D.C., 2000), pp. 232–244.

Webb, R. H.

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1986).

Williams, D. R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1985).

Wyant, J. C.

J. C. Wyant, K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, 1992), Vol. XI, pp. 1–53.

Wyatt, H. J.

H. J. Wyatt, “The form of the human pupil,” Vision Res. 35, 2021–2036 (1995).
[CrossRef] [PubMed]

Am. J. Med. Genet.

C. T. Naugler, M. D. Ludman, “A case-control study of fluctuating dermatoglyphic asymmetry as a risk marker for developmental delay,” Am. J. Med. Genet. 26, 11–14 (1996).
[CrossRef]

Am. J. Optom. Physiol. Opt.

J. P. Carroll, “Component and correlation ametropia,” Am. J. Optom. Physiol. Opt. 59, 28–33 (1982).
[CrossRef] [PubMed]

Arch. Ophthalmol. (Chicago)

R. D. Sperduto, D. Seigel, J. Roberts, M. Rowland, “Prevalence of myopia in the United States,” Arch. Ophthalmol. (Chicago) 101, 405–407 (1983).
[CrossRef]

Biophys. J.

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biophys. J. 7, 766–795 (1962).

Invest. Ophthalmol. Visual Sci.

A. Guirao, C. Gonzalez, M. Redondo, E. Geraghty, S. Norrby, P. Artal, “Average optical performance of the human eye as a function of age in a normal population,” Invest. Ophthalmol. Visual Sci. 40, 203–213 (1999).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

M. Rynders, B. Lidkea, W. Chisholm, L. N. Thibos, “Statistical distribution of foveal transverse chromatic aberration, pupil centration, and angle ψ in a population of young adult eyes,” J. Opt. Soc. Am. A 12, 2348–2357 (1995).
[CrossRef]

R. Navarro, J. Santamarı́a, J. Bescós, “Accommodation-dependent model of the human eye with aspherics,” J. Opt. Soc. Am. A 2, 1273–1281 (1985).
[CrossRef] [PubMed]

J. Liang, B. Grimm, S. Goelz, J. F. Bille, “Objective measurement of the 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]

J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave front of the eye by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998).
[CrossRef]

I. Iglesias, E. Berrio, P. Artal, “Estimates of the ocular wave aberration from pairs of double-pass retinal images,” J. Opt. Soc. Am. A 15, 2466–2476 (1998).
[CrossRef]

J. Liang, D. R. Williams, “Aberrations and retinal image quality of the normal human eye,” J. Opt. Soc. Am. A 14, 2873–2883 (1997).
[CrossRef]

J. Liang, D. R. Williams, D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
[CrossRef]

G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberrations of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
[CrossRef] [PubMed]

H. Hofer, P. Artal, B. Singer, J. L. Aragon, D. R. Williams, “Dynamics of the eye’s wave aberration,” J. Opt. Soc. Am. A 18, 497–506 (2001).
[CrossRef]

Optom. Vision Sci.

J. Schwiegerling, J. E. Greivenkamp, “Using corneal height maps and polynomial decomposition to determine corneal aberrations,” Optom. Vision Sci. 74, 906–915 (1997).
[CrossRef]

Phys. Today

D. T. Miller, “Retinal imaging and vision at the frontiers of adaptive optics,” Phys. Today 53, 31–36 (2000).
[CrossRef]

Vision Res.

H. J. Wyatt, “The form of the human pupil,” Vision Res. 35, 2021–2036 (1995).
[CrossRef] [PubMed]

Other

H. Cummins, C. Midlo, Finger Prints, Palms and Soles: An Introduction to Dermatoglyphics (Blakiston, Philadelphia, 1943).

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1986).

W. J. Smith, Modern Optical Engineering: The Design of Optical Systems (McGraw-Hill, New York, 1990).

J. C. Wyant, K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, 1992), Vol. XI, pp. 1–53.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1985).

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35of OSA Trends in Optics and Photonics Series(Optical Society of America, Washington, D.C., 2000), pp. 232–244.

I. T. Joliffe, Principal Components Analysis (Springer–Verlag, New York, 1986).

(Laser Institute of America, Orlando, Fla., 1993).

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Figures (9)

Fig. 1
Fig. 1

Hartmann–Shack wave-front sensors used to measure the eye’s aberrations at (a) the University of Rochester and (b) Bausch & Lomb. The light from the SLD serves as a beacon, forming a point source on the retina. Light reflected from the retina emerges through the eye’s pupil as an aberrated wavefront and is propagated through the system to the lenslet array, placed conjugate with the eye’s pupil. Each lenslet forms a focused spot on the CCD, yielding an array of spots that finely samples the pupil. The wave aberration is determined from the Hartmann–Shack image.

Fig. 2
Fig. 2

Distribution of age for the 109 normal subjects included in our population study.

Fig. 3
Fig. 3

(a) Mean absolute rms wave-front error of all 18 Zernike modes for the 109 normal subjects across a 5.7-mm pupil. The percentages listed above the first eight modes represent the percentage of the variance of the wave aberration accounted for by each Zernike mode. The magnitudes of the higher-order aberrations may be seen in the inset figure, which shows all modes except Zernike defocus (Z20) with the ordinate expanded. (b) Mean values of all Zernike modes in the population across a 5.7-mm pupil. The error bars represent plus and minus one standard deviation from the mean value. The variability of the higher-order modes is shown in the inset of the figure, which excludes all second-order modes (Z2-2, Z20, and Z22) and again expands the ordinate.

Fig. 4
Fig. 4

Mirror symmetry in the wave aberration between left and right eyes for a 5.7-mm pupil. Defocus and astigmatism (second-order modes Z2-2, Z20, and Z22) were not included in the wave aberration. (a) Plots of the wave aberration of left and right eyes of four subjects that show a high degree of mirror symmetry between eyes. (b) Plots of the wave aberration of both eyes for subject MAK, who shows a lesser degree of symmetry across eyes. Not all subjects display the near-perfect mirror symmetry between left and right eyes as evidenced in (a). (c) An example of one of the few subjects who displays almost no mirror symmetry in the wave aberration between left and right eyes.

Fig. 5
Fig. 5

The first six principal components used to describe the wave aberration of the normal population. Adjacent to each principal component is a picture of the Zernike mode that is most highly correlated with that particular principal component. The first few principal components are very similar to lower-order Zernike modes.

Fig. 6
Fig. 6

Similarity between a principal component and Zernike representation of the wave aberration in the population for left eyes only (5.7-mm pupil). The solid curves show a principal components description of the wave aberration, and the Zernike representation is illustrated by a dashed curve. The Zernike modes were ordered from the Zernike coefficient having the highest variance to that with the lowest. (a) Percentage that each mode contributes to the cumulative variance across the population. Zernike defocus and principal component 1 account for over 90% of the cumulative variance. The inset figure shows the cumulative contribution of higher-order modes on the residual variance upon removing the contributions from the first three Zernike modes (defocus and astigmatism) and the first three principal components. The percent of the contribution has been renormalized so that modes 1–3 have no contribution to the cumulative residual variance and modes 4–18 have a contribution of 100%. (b) The mean rms wave-front error (in micrometers) of the residual wave aberration when a given number of Zernike modes or principal components are corrected in the wave aberration of our population. The dotted line shows the mean rms of the wave aberration when no modes are corrected for all normal subjects. Both descriptions yield nearly identical results.

Fig. 7
Fig. 7

Dispersion of the residual Strehl ratio for each subject (averaged from the separate analyses performed on left and right eyes) when a fixed number of (a) principal components or (b) Zernike modes are corrected in the wave aberration (5.7-mm pupil).

Fig. 8
Fig. 8

The mean residual Strehl ratio (based on Fig. 7) for all normal subjects when correcting a fixed number of principal components (solid curve) or Zernike modes (dashed curve) across a 5.7-mm pupil. Principal components are slightly more efficient and yield slightly better image quality than Zernike modes. Correcting one fewer or the same number of Zernike modes as principal components can provide the same average image quality in the eye.

Fig. 9
Fig. 9

Percentage of subjects having a residual Strehl ratio greater than 0.1, 0.3, or 0.8 when correcting a given number of principal components (solid curves) or Zernike modes (dashed curves) for a 5.7-mm pupil. (Each curve was obtained by averaging the results obtained from the separate analyses of the left and right eyes.) For all three values of the Strehl ratio, principal components provide a more efficient representation of the eye’s wave aberration in the population.

Tables (1)

Tables Icon

Table 1 Correlation Coefficients for Each Zernike Mode between the Left and Right Eyes of All 109 Subjects and the Modes That are Significantly Correlated

Equations (8)

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

WAj=i=118AijZi,
X=Z20Z22Z2-2Z5-3Subject1A1,1A2,1A3,1A18,1Subject2A1,2A2,2A3,2A18,2Subject109A1,109A2,109A3,109A18,109.
 
C=Cov(Aij).
|C-λI|=0
(C-λI)v=0,
PC=VZ.
WAj=i=118AijPCi,

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