Abstract

The monochromatic aberrations of the human eye along the temporal meridian are studied by a novel laser ray-tracing method. It consists of delivering a narrow laser pencil into the eye through a given point on the pupil and recording the aerial image of the retinal spot with a CCD camera. The relative displacement of this image is proportional to the geometrical aberration of the ray (laser pencil) at the retina. We scanned the pupils of four observers in steps of 1 mm (effective diameter, 6.7 mm) and for five field angles (0°, 5°, 10°, 20°, and 40°). In addition, the aerial image for each chief ray is a low-pass-filtered version of the retinal point-spread function corresponding to a fully dilated pupil. The resulting spot diagrams, displaying the distribution of ray aberrations, are highly correlated with these point-spread functions. We have estimated the wave-front error by fitting Zernike polynomials (up to the fifth order). Despite the large variation found among observers, the overall rms wave-front error is relatively homogeneous. At the fovea, the average rms value was 1.49 µm when the second-order terms (defocus and astigmatism) were considered; this was reduced to 0.45 µm when the second-order terms were ignored. The rms values increase slowly, in a roughly linear fashion with eccentricity, such that at 40° they are approximately double. These results are consistent with previous findings on the off-axis optical quality of the eye.

© 1998 Optical Society of America

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References

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  1. M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1962) [Biophysics (USSR) 6, 766–795 (1962)].
  2. G. Van den Brink, “Measurements of the geometrical aberrations of the eye,” Vision Res. 2, 233–244 (1962).
    [Crossref]
  3. M. C. W. Campbell, E. H. Harrison, P. Simonet, “Psychophysical measurements of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
    [Crossref]
  4. R. H. Webb, C. M. Penney, K. P. Thompson, “Measurement of ocular local wavefront distortion with a spatially resolved refractometer,” Appl. Opt. 31, 3678–3686 (1992).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  8. J. Liang, B. Grimm, S. Goelz, 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]
  9. 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]
  10. R. Navarro, M. A. Losada, “Aberrations and relative efficiency of ray pencils in the living human eye,” Optom. Vision Sci. 74, 540–547 (1997).
    [Crossref]
  11. C. E. Ferree, G. Rand, C. Hardy, “Refraction for the peripheral field of vision,” Arch. Opththalmol. 5, 717–731 (1931).
    [Crossref]
  12. F. Rempt, J. Hoogerheide, W. P. H. Hoogenboom, “Peripheral retinoscopy and the skiagram,” Ophthalmologica 162, 1–10 (1971).
    [Crossref] [PubMed]
  13. M. Millodot, A. Lamont, “Refraction of the periphery of the eye,” J. Opt. Soc. Am. 64, 110–111 (1974).
    [Crossref] [PubMed]
  14. G. Smith, M. Millodot, N. McBrien, “The effect of accommodation on oblique astigmatism and field curvature of the human eye,” Clin. Exp. Optom. 71, 119–125 (1988).
    [Crossref]
  15. J. A. M. Jennings, W. N. Charman, “Off-axis image quality in the human eye,” Vision Res. 21, 445–455 (1981).
    [Crossref] [PubMed]
  16. R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
    [Crossref] [PubMed]
  17. D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
    [Crossref] [PubMed]
  18. S. Fisher, “Contour plots and the limit of ‘clear and comfortable vision’ in the near zone of progressive addition lenses,” in Vision Science and Its Applications, Vol. 1 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 2–5.
  19. D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources, 1st ed. (Plenum, New York, 1980).
  20. R. A. Moses, ed., Adler’s Physiology of the Eye: Clinical Application (Mosby, St. Louis, Mo., 1981), p. 747.
  21. D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).
  22. M. C. Rynders, R. Navarro, M. A. Losada, “Objective measurement of the off-axis longitudinal chromatic aberration in the human eye,” Vision Res. 37, 513–521 (1997).
  23. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975).
  24. R. Navarro, M. A. Losada, “Phase transfer and point-spread function of the human eye determined by a new asymmetric double-pass method,” J. Opt. Soc. Am. A 12, 2385–2392 (1995).
    [Crossref]
  25. R. Navarro, M. A. Losada, “Shape of stars and optical quality of the human eye,” J. Opt. Soc. Am. A 14, 353–359 (1997).
    [Crossref]
  26. 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]

1997 (5)

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]

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

M. C. Rynders, R. Navarro, M. A. Losada, “Objective measurement of the off-axis longitudinal chromatic aberration in the human eye,” Vision Res. 37, 513–521 (1997).

R. Navarro, M. A. Losada, “Shape of stars and optical quality of the human eye,” J. Opt. Soc. Am. A 14, 353–359 (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]

1996 (1)

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[Crossref] [PubMed]

1995 (1)

1994 (1)

1993 (1)

1992 (1)

1990 (1)

M. C. W. Campbell, E. H. Harrison, P. Simonet, “Psychophysical measurements of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[Crossref]

1988 (1)

G. Smith, M. Millodot, N. McBrien, “The effect of accommodation on oblique astigmatism and field curvature of the human eye,” Clin. Exp. Optom. 71, 119–125 (1988).
[Crossref]

1984 (1)

1981 (1)

J. A. M. Jennings, W. N. Charman, “Off-axis image quality in the human eye,” Vision Res. 21, 445–455 (1981).
[Crossref] [PubMed]

1977 (1)

1974 (1)

1971 (1)

F. Rempt, J. Hoogerheide, W. P. H. Hoogenboom, “Peripheral retinoscopy and the skiagram,” Ophthalmologica 162, 1–10 (1971).
[Crossref] [PubMed]

1969 (1)

F. Berny, “Etude de la formation des images retiniennes et determination de l’aberration de sphericite de l’oeil humain,” Vision Res. 9, 977–990 (1969).
[Crossref] [PubMed]

1962 (2)

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1962) [Biophysics (USSR) 6, 766–795 (1962)].

G. Van den Brink, “Measurements of the geometrical aberrations of the eye,” Vision Res. 2, 233–244 (1962).
[Crossref]

1931 (1)

C. E. Ferree, G. Rand, C. Hardy, “Refraction for the peripheral field of vision,” Arch. Opththalmol. 5, 717–731 (1931).
[Crossref]

Artal, P.

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[Crossref] [PubMed]

R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
[Crossref] [PubMed]

Berny, F.

F. Berny, “Etude de la formation des images retiniennes et determination de l’aberration de sphericite de l’oeil humain,” Vision Res. 9, 977–990 (1969).
[Crossref] [PubMed]

Bille, J. F.

Born, M.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975).

Brainard, D. H.

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[Crossref] [PubMed]

Campbell, M. C. W.

M. C. W. Campbell, E. H. Harrison, P. Simonet, “Psychophysical measurements of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[Crossref]

Charman, W. N.

Ferree, C. E.

C. E. Ferree, G. Rand, C. Hardy, “Refraction for the peripheral field of vision,” Arch. Opththalmol. 5, 717–731 (1931).
[Crossref]

Fisher, S.

S. Fisher, “Contour plots and the limit of ‘clear and comfortable vision’ in the near zone of progressive addition lenses,” in Vision Science and Its Applications, Vol. 1 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 2–5.

Goelz, S.

Grimm, B.

Hardy, C.

C. E. Ferree, G. Rand, C. Hardy, “Refraction for the peripheral field of vision,” Arch. Opththalmol. 5, 717–731 (1931).
[Crossref]

Harrison, E. H.

M. C. W. Campbell, E. H. Harrison, P. Simonet, “Psychophysical measurements of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[Crossref]

Hoogenboom, W. P. H.

F. Rempt, J. Hoogerheide, W. P. H. Hoogenboom, “Peripheral retinoscopy and the skiagram,” Ophthalmologica 162, 1–10 (1971).
[Crossref] [PubMed]

Hoogerheide, J.

F. Rempt, J. Hoogerheide, W. P. H. Hoogenboom, “Peripheral retinoscopy and the skiagram,” Ophthalmologica 162, 1–10 (1971).
[Crossref] [PubMed]

Howland, B.

Howland, H. C.

Jennings, J. A. M.

J. A. M. Jennings, W. N. Charman, “Off-axis image quality in the human eye,” Vision Res. 21, 445–455 (1981).
[Crossref] [PubMed]

Lamont, A.

Liang, J.

Losada, M. A.

R. Navarro, M. A. Losada, “Shape of stars and optical quality of the human eye,” J. Opt. Soc. Am. A 14, 353–359 (1997).
[Crossref]

M. C. Rynders, R. Navarro, M. A. Losada, “Objective measurement of the off-axis longitudinal chromatic aberration in the human eye,” Vision Res. 37, 513–521 (1997).

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

R. Navarro, M. A. Losada, “Phase transfer and point-spread function of the human eye determined by a new asymmetric double-pass method,” J. Opt. Soc. Am. A 12, 2385–2392 (1995).
[Crossref]

Malacara, D.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).

McBrien, N.

G. Smith, M. Millodot, N. McBrien, “The effect of accommodation on oblique astigmatism and field curvature of the human eye,” Clin. Exp. Optom. 71, 119–125 (1988).
[Crossref]

McMahon, M. J.

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[Crossref] [PubMed]

Miller, D. T.

Millodot, M.

G. Smith, M. Millodot, N. McBrien, “The effect of accommodation on oblique astigmatism and field curvature of the human eye,” Clin. Exp. Optom. 71, 119–125 (1988).
[Crossref]

M. Millodot, A. Lamont, “Refraction of the periphery of the eye,” J. Opt. Soc. Am. 64, 110–111 (1974).
[Crossref] [PubMed]

Navarro, R.

R. Navarro, M. A. Losada, “Shape of stars and optical quality of the human eye,” J. Opt. Soc. Am. A 14, 353–359 (1997).
[Crossref]

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

M. C. Rynders, R. Navarro, M. A. Losada, “Objective measurement of the off-axis longitudinal chromatic aberration in the human eye,” Vision Res. 37, 513–521 (1997).

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[Crossref] [PubMed]

R. Navarro, M. A. Losada, “Phase transfer and point-spread function of the human eye determined by a new asymmetric double-pass method,” J. Opt. Soc. Am. A 12, 2385–2392 (1995).
[Crossref]

R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
[Crossref] [PubMed]

Penney, C. M.

Rand, G.

C. E. Ferree, G. Rand, C. Hardy, “Refraction for the peripheral field of vision,” Arch. Opththalmol. 5, 717–731 (1931).
[Crossref]

Rempt, F.

F. Rempt, J. Hoogerheide, W. P. H. Hoogenboom, “Peripheral retinoscopy and the skiagram,” Ophthalmologica 162, 1–10 (1971).
[Crossref] [PubMed]

Rynders, M. C.

M. C. Rynders, R. Navarro, M. A. Losada, “Objective measurement of the off-axis longitudinal chromatic aberration in the human eye,” Vision Res. 37, 513–521 (1997).

Simonet, P.

M. C. W. Campbell, E. H. Harrison, P. Simonet, “Psychophysical measurements of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[Crossref]

Sliney, D.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources, 1st ed. (Plenum, New York, 1980).

Smirnov, M. S.

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1962) [Biophysics (USSR) 6, 766–795 (1962)].

Smith, G.

G. Smith, M. Millodot, N. McBrien, “The effect of accommodation on oblique astigmatism and field curvature of the human eye,” Clin. Exp. Optom. 71, 119–125 (1988).
[Crossref]

Thompson, K. P.

Van den Brink, G.

G. Van den Brink, “Measurements of the geometrical aberrations of the eye,” Vision Res. 2, 233–244 (1962).
[Crossref]

Walsh, G.

Webb, R. H.

Williams, D. R.

Wolbarsht, M.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources, 1st ed. (Plenum, New York, 1980).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975).

Appl. Opt. (1)

Arch. Opththalmol. (1)

C. E. Ferree, G. Rand, C. Hardy, “Refraction for the peripheral field of vision,” Arch. Opththalmol. 5, 717–731 (1931).
[Crossref]

Biofizika (1)

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1962) [Biophysics (USSR) 6, 766–795 (1962)].

Clin. Exp. Optom. (1)

G. Smith, M. Millodot, N. McBrien, “The effect of accommodation on oblique astigmatism and field curvature of the human eye,” Clin. Exp. Optom. 71, 119–125 (1988).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (7)

Ophthalmologica (1)

F. Rempt, J. Hoogerheide, W. P. H. Hoogenboom, “Peripheral retinoscopy and the skiagram,” Ophthalmologica 162, 1–10 (1971).
[Crossref] [PubMed]

Optom. Vision Sci. (1)

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

Vision Res. (6)

F. Berny, “Etude de la formation des images retiniennes et determination de l’aberration de sphericite de l’oeil humain,” Vision Res. 9, 977–990 (1969).
[Crossref] [PubMed]

G. Van den Brink, “Measurements of the geometrical aberrations of the eye,” Vision Res. 2, 233–244 (1962).
[Crossref]

M. C. W. Campbell, E. H. Harrison, P. Simonet, “Psychophysical measurements of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[Crossref]

J. A. M. Jennings, W. N. Charman, “Off-axis image quality in the human eye,” Vision Res. 21, 445–455 (1981).
[Crossref] [PubMed]

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[Crossref] [PubMed]

M. C. Rynders, R. Navarro, M. A. Losada, “Objective measurement of the off-axis longitudinal chromatic aberration in the human eye,” Vision Res. 37, 513–521 (1997).

Other (5)

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975).

S. Fisher, “Contour plots and the limit of ‘clear and comfortable vision’ in the near zone of progressive addition lenses,” in Vision Science and Its Applications, Vol. 1 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 2–5.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources, 1st ed. (Plenum, New York, 1980).

R. A. Moses, ed., Adler’s Physiology of the Eye: Clinical Application (Mosby, St. Louis, Mo., 1981), p. 747.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup and of the operating principle of the laser ray-tracing method. A green He–Ne laser is mounted, with a shutter attached, on an XY motor-driven micropositioning stage. The unexpanded beam is attenuated by neutral-density (ND) filters and enters the eye after reflection on a pellicle beam splitter. After reflection off the retina, a photographic objective (Lens) forms an aerial image on the CCD. The fixation target is a light-emitting diode (LED). It can be viewed either through a second beam splitter for foveal measurements or directly for off-axis measurements. When the laser pencil enters through an eccentric position of the pupil, it intersects the retina at point A. The chief ray (dashed curves) passing through the center of the pupil goes to point O. The lens of the CCD camera forms the aerial images A and O of these spots.

Fig. 2
Fig. 2

Spot diagrams for our four observers at different retinal eccentricities 0°, 5°, 10°, 20°, and 40°. All the experimental data (of three or four runs, depending on the observer), represented by small dots, are included. In each diagram the open circles represent the result of Zernike polynomial fit.

Fig. 3
Fig. 3

Aerial images obtained by delivery of the laser pencil through the center of the pupil after reversal of both axes. These images are slightly blurred versions of the corresponding retinal PSF’s.

Fig. 4
Fig. 4

Root-mean-square (rms) wave-front error averaged over our four observers. Error bars represent the standard deviation among observers. The four lines, from top to bottom, represent the mean when all Zernike terms are considered (open circles), when first-order terms are not considered (diamonds), when first-order terms and defocus are not considered (squares), and when first- and second-order terms are not considered (filled circles).

Fig. 5
Fig. 5

Second-order aberrations in diopters for our four observers (defocus, field curvature, and astigmatism). The Sturm interval is represented by error bars for only one observer, for clarity.

Fig. 6
Fig. 6

Simulated spot diagrams that would be obtained after cancellation of defocus (open circles) and of both defocus and astigmatism (dots) with ideal trial lenses in two observers and three eccentricities.

Tables (1)

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Table 1 Zernike Coefficients and Their Standard Deviations (in μm), for Observer EM, for the Different Retinal Eccentricities

Equations (2)

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Δx=1RpW(ξ¯, η¯)ξ¯,Δy=1RpW(ξ¯, η¯)η¯,
W(ξ¯, η¯)=iCiZi(ξ¯, η¯),

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