Abstract

New measurements of the chromatic difference of focus of the human eye were obtained with a two-color, vernier-alignment technique. The results were used to redefine the variation of refractive index of the reduced eye over the visible spectrum. The reduced eye was further modified by changing the refracting surface to an aspherical shape to reduce the amount of spherical aberration. The resulting chromatic-eye model provides an improved account of both the longitudinal and transverse forms of ocular chromatic aberration.

© 1992 Optical Society of America

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  1. A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
    [CrossRef]
  2. A. van Meeteren, C. J. W. Dunnewold, “Image quality of the human eye for eccentric entrance pupil,” Vision Res. 23, 573–579 (1983).
    [CrossRef] [PubMed]
  3. L. N. Thibos, A. Bradley, X. Zhang, “The effect of ocular chromatic aberration on monocular visual performance,” Optom. Vis. Sci. 68, 599–607 (1991).
    [CrossRef] [PubMed]
  4. A. Bradley, X. Zhang, L. N. Thibos, “Retinal image isoluminance is compromised by lateral and longitudinal chromatic aberration,” in OSA Annual Meeting Vol. 11 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 47.
  5. X. Zhang, A. Bradley, L. N. Thibos, “Theoretical analysis of the effect of chromatic aberration on chromatic appearance of isoluminance color gratings,” Optom. Vis. Sci. 66 (Suppl.), 220 (1989).
  6. A. Bradley, X. Zhang, L. N. Thibos, “Achromatizing the human eye,” Optom. Vis. Sci. 68, 608–616 (1991).
    [CrossRef] [PubMed]
  7. A. Bradley, L. N. Thibos, D. L. Still, “Visual acuity measured with clinical Maxwellian-view systems: effects of beam entry location,” Optom. Vis. Sci. 67, 811–817 (1990).
    [CrossRef] [PubMed]
  8. P. Simonet, M. C. W. Campbell, “The optical transverse chromatic aberration on the fovea of the human eye,” Vision Res. 30, 187–206 (1990).
    [CrossRef] [PubMed]
  9. L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
    [CrossRef] [PubMed]
  10. G. Wald, D. R. Griffin, “The change in refractive power of the human eye in dim and bright light,” J. Opt. Soc. Am. 37, 321–336 (1947).
    [CrossRef] [PubMed]
  11. R. E. Bedford, G. Wyszecki, “Axial chromatic aberration of the human eye,” J. Opt. Soc. Am. 47, 564–565 (1957).
    [CrossRef] [PubMed]
  12. A. Ivanoff, Les Aberrations de l’Oeil (Editions de la Revue d’Optique Theorique et Instrumentale, Paris, 1953).
  13. H. H. Emsley, Visual Optics (Hatton, London, 1952).
  14. X. Zhang, L. N. Thibos, A. Bradley, “Relation between the chromatic difference of refraction and the chromatic difference of magnification for the reduced eye,” Optom. Vis. Sci. 68, 456–458 (1991).
    [CrossRef] [PubMed]
  15. L. N. Thibos, “Optical limitations of the Maxwellian-view interferometer,” Appl. Opt. 29, 1411–1419 (1990).
    [CrossRef] [PubMed]
  16. X. Zhang, A. Bradley, L. Thibos, “Achromatizing the human eye: the problem of chromatic parallax,” J. Opt. Soc. Am. A 8, 686–691 (1991).
    [CrossRef] [PubMed]
  17. A. Ivanoff, “Sur une methode de mesure des aberrations chromatiques et spheriques de l’oeil en lumiere dirigee,” C. R. Acad. Sci. 223, 170–172 (1946).
  18. P. Simonet, M. C. W. Campbell, “Accuracy and reliability of the chromatic parallax method for measuring the longitudinal chromatic aberration of the human eye,” Optom. Vis. Sci. 67 (Suppl.), 55 (1990).
  19. Y. Le Grand, Form and Space Vision, translated by G. G. Heath, M. Millodot (Indiana U. Press, Bloomington, Ind., 1967).
  20. M. Millodot, J. G. Sivak, “Influence of accommodation on the chromatic aberration of the eye,” Br. J. Physiol. Opt. 28, 169–174 (1973).
    [PubMed]
  21. M. Millodot, “The influence of age on the chromatic aberration of the human eye,” Graefe’s Arch. Clin. Exp. Ophthalmol. 198, 235–243 (1976).
  22. W. N. Charman, J. A. M. Jennings, “Objective measurements of the longitudinal chromatic aberration the human eye,” Vision Res. 16, 99–1005 (1976).
    [CrossRef]
  23. I. Powell, “Lenses for correcting chromatic aberration of the eye,” Appl. Opt. 20, 4152–4155 (1981).
    [CrossRef] [PubMed]
  24. A. L. Lewis, M. Katz, C. Oehrlein, “A modified achromatizing lens,” Am. J. Optom. Physiol. Opt. 59, 909–911 (1982).
    [CrossRef] [PubMed]
  25. C. Ware, “Human axial chromatic aberration found not to decline with age,” Graefe’s Arch. Clin. Exp. Ophthalmol. 218, 39–41 (1982).
  26. J. A. Mordi, W. K. Adrian, “Influence of age on the chromatic aberration of the human eye,” Am. J. Optom. Physiol. Opt. 62, 864–869 (1985).
    [CrossRef] [PubMed]
  27. P. A. Howarth, A. Bradley, “The longitudinal chromatic aberration of the human eye, and its correction,” Vision Res. 26, 361–366 (1986).
    [CrossRef] [PubMed]
  28. D. P. Cooper, P. L. Pease, “Longitudinal chromatic aberration of the human eye and wavelength in focus,” Am. J. Optom. Physiol. Opt. 65, 99–107 (1988).
    [CrossRef] [PubMed]
  29. L. N. Thibos, “Calculation of the influence of lateral chromatic aberration on image quality across the visual field,” J. Opt. Soc. Am. A 4, 1673–1680 (1987).
    [CrossRef] [PubMed]
  30. G. Walsh, “The effect of mydriasis on the pupillary centration of the human eye,” Ophthal. Physiol. Opt. 8, 178–182 (1988).
    [CrossRef]
  31. M. A. Wilson, M. C. W. Campbell, P. Simonet, “Change of pupil centration with change of illumination and pupil size,” Optom. Vis. Sci. 69, 129–136 (1992).
    [CrossRef] [PubMed]
  32. H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
    [CrossRef]
  33. G. B. Thomas, Calculus and Analytic Geometry (Addison-Wesley, Reading, Mass., 1960).

1992

M. A. Wilson, M. C. W. Campbell, P. Simonet, “Change of pupil centration with change of illumination and pupil size,” Optom. Vis. Sci. 69, 129–136 (1992).
[CrossRef] [PubMed]

1991

X. Zhang, L. N. Thibos, A. Bradley, “Relation between the chromatic difference of refraction and the chromatic difference of magnification for the reduced eye,” Optom. Vis. Sci. 68, 456–458 (1991).
[CrossRef] [PubMed]

X. Zhang, A. Bradley, L. Thibos, “Achromatizing the human eye: the problem of chromatic parallax,” J. Opt. Soc. Am. A 8, 686–691 (1991).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, X. Zhang, “The effect of ocular chromatic aberration on monocular visual performance,” Optom. Vis. Sci. 68, 599–607 (1991).
[CrossRef] [PubMed]

A. Bradley, X. Zhang, L. N. Thibos, “Achromatizing the human eye,” Optom. Vis. Sci. 68, 608–616 (1991).
[CrossRef] [PubMed]

1990

A. Bradley, L. N. Thibos, D. L. Still, “Visual acuity measured with clinical Maxwellian-view systems: effects of beam entry location,” Optom. Vis. Sci. 67, 811–817 (1990).
[CrossRef] [PubMed]

P. Simonet, M. C. W. Campbell, “The optical transverse chromatic aberration on the fovea of the human eye,” Vision Res. 30, 187–206 (1990).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

P. Simonet, M. C. W. Campbell, “Accuracy and reliability of the chromatic parallax method for measuring the longitudinal chromatic aberration of the human eye,” Optom. Vis. Sci. 67 (Suppl.), 55 (1990).

L. N. Thibos, “Optical limitations of the Maxwellian-view interferometer,” Appl. Opt. 29, 1411–1419 (1990).
[CrossRef] [PubMed]

1989

X. Zhang, A. Bradley, L. N. Thibos, “Theoretical analysis of the effect of chromatic aberration on chromatic appearance of isoluminance color gratings,” Optom. Vis. Sci. 66 (Suppl.), 220 (1989).

1988

G. Walsh, “The effect of mydriasis on the pupillary centration of the human eye,” Ophthal. Physiol. Opt. 8, 178–182 (1988).
[CrossRef]

D. P. Cooper, P. L. Pease, “Longitudinal chromatic aberration of the human eye and wavelength in focus,” Am. J. Optom. Physiol. Opt. 65, 99–107 (1988).
[CrossRef] [PubMed]

1987

1986

P. A. Howarth, A. Bradley, “The longitudinal chromatic aberration of the human eye, and its correction,” Vision Res. 26, 361–366 (1986).
[CrossRef] [PubMed]

1985

J. A. Mordi, W. K. Adrian, “Influence of age on the chromatic aberration of the human eye,” Am. J. Optom. Physiol. Opt. 62, 864–869 (1985).
[CrossRef] [PubMed]

1983

A. van Meeteren, C. J. W. Dunnewold, “Image quality of the human eye for eccentric entrance pupil,” Vision Res. 23, 573–579 (1983).
[CrossRef] [PubMed]

1982

A. L. Lewis, M. Katz, C. Oehrlein, “A modified achromatizing lens,” Am. J. Optom. Physiol. Opt. 59, 909–911 (1982).
[CrossRef] [PubMed]

C. Ware, “Human axial chromatic aberration found not to decline with age,” Graefe’s Arch. Clin. Exp. Ophthalmol. 218, 39–41 (1982).

1981

1976

M. Millodot, “The influence of age on the chromatic aberration of the human eye,” Graefe’s Arch. Clin. Exp. Ophthalmol. 198, 235–243 (1976).

W. N. Charman, J. A. M. Jennings, “Objective measurements of the longitudinal chromatic aberration the human eye,” Vision Res. 16, 99–1005 (1976).
[CrossRef]

1974

A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
[CrossRef]

1973

M. Millodot, J. G. Sivak, “Influence of accommodation on the chromatic aberration of the eye,” Br. J. Physiol. Opt. 28, 169–174 (1973).
[PubMed]

1957

1955

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
[CrossRef]

1947

1946

A. Ivanoff, “Sur une methode de mesure des aberrations chromatiques et spheriques de l’oeil en lumiere dirigee,” C. R. Acad. Sci. 223, 170–172 (1946).

Adrian, W. K.

J. A. Mordi, W. K. Adrian, “Influence of age on the chromatic aberration of the human eye,” Am. J. Optom. Physiol. Opt. 62, 864–869 (1985).
[CrossRef] [PubMed]

Bedford, R. E.

Bradley, A.

X. Zhang, A. Bradley, L. Thibos, “Achromatizing the human eye: the problem of chromatic parallax,” J. Opt. Soc. Am. A 8, 686–691 (1991).
[CrossRef] [PubMed]

X. Zhang, L. N. Thibos, A. Bradley, “Relation between the chromatic difference of refraction and the chromatic difference of magnification for the reduced eye,” Optom. Vis. Sci. 68, 456–458 (1991).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, X. Zhang, “The effect of ocular chromatic aberration on monocular visual performance,” Optom. Vis. Sci. 68, 599–607 (1991).
[CrossRef] [PubMed]

A. Bradley, X. Zhang, L. N. Thibos, “Achromatizing the human eye,” Optom. Vis. Sci. 68, 608–616 (1991).
[CrossRef] [PubMed]

A. Bradley, L. N. Thibos, D. L. Still, “Visual acuity measured with clinical Maxwellian-view systems: effects of beam entry location,” Optom. Vis. Sci. 67, 811–817 (1990).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

X. Zhang, A. Bradley, L. N. Thibos, “Theoretical analysis of the effect of chromatic aberration on chromatic appearance of isoluminance color gratings,” Optom. Vis. Sci. 66 (Suppl.), 220 (1989).

P. A. Howarth, A. Bradley, “The longitudinal chromatic aberration of the human eye, and its correction,” Vision Res. 26, 361–366 (1986).
[CrossRef] [PubMed]

A. Bradley, X. Zhang, L. N. Thibos, “Retinal image isoluminance is compromised by lateral and longitudinal chromatic aberration,” in OSA Annual Meeting Vol. 11 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 47.

Campbell, M. C. W.

M. A. Wilson, M. C. W. Campbell, P. Simonet, “Change of pupil centration with change of illumination and pupil size,” Optom. Vis. Sci. 69, 129–136 (1992).
[CrossRef] [PubMed]

P. Simonet, M. C. W. Campbell, “The optical transverse chromatic aberration on the fovea of the human eye,” Vision Res. 30, 187–206 (1990).
[CrossRef] [PubMed]

P. Simonet, M. C. W. Campbell, “Accuracy and reliability of the chromatic parallax method for measuring the longitudinal chromatic aberration of the human eye,” Optom. Vis. Sci. 67 (Suppl.), 55 (1990).

Charman, W. N.

W. N. Charman, J. A. M. Jennings, “Objective measurements of the longitudinal chromatic aberration the human eye,” Vision Res. 16, 99–1005 (1976).
[CrossRef]

Cooper, D. P.

D. P. Cooper, P. L. Pease, “Longitudinal chromatic aberration of the human eye and wavelength in focus,” Am. J. Optom. Physiol. Opt. 65, 99–107 (1988).
[CrossRef] [PubMed]

Dunnewold, C. J. W.

A. van Meeteren, C. J. W. Dunnewold, “Image quality of the human eye for eccentric entrance pupil,” Vision Res. 23, 573–579 (1983).
[CrossRef] [PubMed]

Emsley, H. H.

H. H. Emsley, Visual Optics (Hatton, London, 1952).

Griffin, D. R.

Hopkins, H. H.

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
[CrossRef]

Howarth, P. A.

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

P. A. Howarth, A. Bradley, “The longitudinal chromatic aberration of the human eye, and its correction,” Vision Res. 26, 361–366 (1986).
[CrossRef] [PubMed]

Ivanoff, A.

A. Ivanoff, “Sur une methode de mesure des aberrations chromatiques et spheriques de l’oeil en lumiere dirigee,” C. R. Acad. Sci. 223, 170–172 (1946).

A. Ivanoff, Les Aberrations de l’Oeil (Editions de la Revue d’Optique Theorique et Instrumentale, Paris, 1953).

Jennings, J. A. M.

W. N. Charman, J. A. M. Jennings, “Objective measurements of the longitudinal chromatic aberration the human eye,” Vision Res. 16, 99–1005 (1976).
[CrossRef]

Katz, M.

A. L. Lewis, M. Katz, C. Oehrlein, “A modified achromatizing lens,” Am. J. Optom. Physiol. Opt. 59, 909–911 (1982).
[CrossRef] [PubMed]

Le Grand, Y.

Y. Le Grand, Form and Space Vision, translated by G. G. Heath, M. Millodot (Indiana U. Press, Bloomington, Ind., 1967).

Lewis, A. L.

A. L. Lewis, M. Katz, C. Oehrlein, “A modified achromatizing lens,” Am. J. Optom. Physiol. Opt. 59, 909–911 (1982).
[CrossRef] [PubMed]

Millodot, M.

M. Millodot, “The influence of age on the chromatic aberration of the human eye,” Graefe’s Arch. Clin. Exp. Ophthalmol. 198, 235–243 (1976).

M. Millodot, J. G. Sivak, “Influence of accommodation on the chromatic aberration of the eye,” Br. J. Physiol. Opt. 28, 169–174 (1973).
[PubMed]

Mordi, J. A.

J. A. Mordi, W. K. Adrian, “Influence of age on the chromatic aberration of the human eye,” Am. J. Optom. Physiol. Opt. 62, 864–869 (1985).
[CrossRef] [PubMed]

Oehrlein, C.

A. L. Lewis, M. Katz, C. Oehrlein, “A modified achromatizing lens,” Am. J. Optom. Physiol. Opt. 59, 909–911 (1982).
[CrossRef] [PubMed]

Pease, P. L.

D. P. Cooper, P. L. Pease, “Longitudinal chromatic aberration of the human eye and wavelength in focus,” Am. J. Optom. Physiol. Opt. 65, 99–107 (1988).
[CrossRef] [PubMed]

Powell, I.

Simonet, P.

M. A. Wilson, M. C. W. Campbell, P. Simonet, “Change of pupil centration with change of illumination and pupil size,” Optom. Vis. Sci. 69, 129–136 (1992).
[CrossRef] [PubMed]

P. Simonet, M. C. W. Campbell, “Accuracy and reliability of the chromatic parallax method for measuring the longitudinal chromatic aberration of the human eye,” Optom. Vis. Sci. 67 (Suppl.), 55 (1990).

P. Simonet, M. C. W. Campbell, “The optical transverse chromatic aberration on the fovea of the human eye,” Vision Res. 30, 187–206 (1990).
[CrossRef] [PubMed]

Sivak, J. G.

M. Millodot, J. G. Sivak, “Influence of accommodation on the chromatic aberration of the eye,” Br. J. Physiol. Opt. 28, 169–174 (1973).
[PubMed]

Still, D. L.

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

A. Bradley, L. N. Thibos, D. L. Still, “Visual acuity measured with clinical Maxwellian-view systems: effects of beam entry location,” Optom. Vis. Sci. 67, 811–817 (1990).
[CrossRef] [PubMed]

Thibos, L.

Thibos, L. N.

A. Bradley, X. Zhang, L. N. Thibos, “Achromatizing the human eye,” Optom. Vis. Sci. 68, 608–616 (1991).
[CrossRef] [PubMed]

X. Zhang, L. N. Thibos, A. Bradley, “Relation between the chromatic difference of refraction and the chromatic difference of magnification for the reduced eye,” Optom. Vis. Sci. 68, 456–458 (1991).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, X. Zhang, “The effect of ocular chromatic aberration on monocular visual performance,” Optom. Vis. Sci. 68, 599–607 (1991).
[CrossRef] [PubMed]

A. Bradley, L. N. Thibos, D. L. Still, “Visual acuity measured with clinical Maxwellian-view systems: effects of beam entry location,” Optom. Vis. Sci. 67, 811–817 (1990).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

L. N. Thibos, “Optical limitations of the Maxwellian-view interferometer,” Appl. Opt. 29, 1411–1419 (1990).
[CrossRef] [PubMed]

X. Zhang, A. Bradley, L. N. Thibos, “Theoretical analysis of the effect of chromatic aberration on chromatic appearance of isoluminance color gratings,” Optom. Vis. Sci. 66 (Suppl.), 220 (1989).

L. N. Thibos, “Calculation of the influence of lateral chromatic aberration on image quality across the visual field,” J. Opt. Soc. Am. A 4, 1673–1680 (1987).
[CrossRef] [PubMed]

A. Bradley, X. Zhang, L. N. Thibos, “Retinal image isoluminance is compromised by lateral and longitudinal chromatic aberration,” in OSA Annual Meeting Vol. 11 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 47.

Thomas, G. B.

G. B. Thomas, Calculus and Analytic Geometry (Addison-Wesley, Reading, Mass., 1960).

van Meeteren, A.

A. van Meeteren, C. J. W. Dunnewold, “Image quality of the human eye for eccentric entrance pupil,” Vision Res. 23, 573–579 (1983).
[CrossRef] [PubMed]

A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
[CrossRef]

Wald, G.

Walsh, G.

G. Walsh, “The effect of mydriasis on the pupillary centration of the human eye,” Ophthal. Physiol. Opt. 8, 178–182 (1988).
[CrossRef]

Ware, C.

C. Ware, “Human axial chromatic aberration found not to decline with age,” Graefe’s Arch. Clin. Exp. Ophthalmol. 218, 39–41 (1982).

Wilson, M. A.

M. A. Wilson, M. C. W. Campbell, P. Simonet, “Change of pupil centration with change of illumination and pupil size,” Optom. Vis. Sci. 69, 129–136 (1992).
[CrossRef] [PubMed]

Wyszecki, G.

Zhang, X.

X. Zhang, A. Bradley, L. Thibos, “Achromatizing the human eye: the problem of chromatic parallax,” J. Opt. Soc. Am. A 8, 686–691 (1991).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, X. Zhang, “The effect of ocular chromatic aberration on monocular visual performance,” Optom. Vis. Sci. 68, 599–607 (1991).
[CrossRef] [PubMed]

A. Bradley, X. Zhang, L. N. Thibos, “Achromatizing the human eye,” Optom. Vis. Sci. 68, 608–616 (1991).
[CrossRef] [PubMed]

X. Zhang, L. N. Thibos, A. Bradley, “Relation between the chromatic difference of refraction and the chromatic difference of magnification for the reduced eye,” Optom. Vis. Sci. 68, 456–458 (1991).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

X. Zhang, A. Bradley, L. N. Thibos, “Theoretical analysis of the effect of chromatic aberration on chromatic appearance of isoluminance color gratings,” Optom. Vis. Sci. 66 (Suppl.), 220 (1989).

A. Bradley, X. Zhang, L. N. Thibos, “Retinal image isoluminance is compromised by lateral and longitudinal chromatic aberration,” in OSA Annual Meeting Vol. 11 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 47.

Am. J. Optom. Physiol. Opt.

A. L. Lewis, M. Katz, C. Oehrlein, “A modified achromatizing lens,” Am. J. Optom. Physiol. Opt. 59, 909–911 (1982).
[CrossRef] [PubMed]

J. A. Mordi, W. K. Adrian, “Influence of age on the chromatic aberration of the human eye,” Am. J. Optom. Physiol. Opt. 62, 864–869 (1985).
[CrossRef] [PubMed]

D. P. Cooper, P. L. Pease, “Longitudinal chromatic aberration of the human eye and wavelength in focus,” Am. J. Optom. Physiol. Opt. 65, 99–107 (1988).
[CrossRef] [PubMed]

Appl. Opt.

Br. J. Physiol. Opt.

M. Millodot, J. G. Sivak, “Influence of accommodation on the chromatic aberration of the eye,” Br. J. Physiol. Opt. 28, 169–174 (1973).
[PubMed]

C. R. Acad. Sci.

A. Ivanoff, “Sur une methode de mesure des aberrations chromatiques et spheriques de l’oeil en lumiere dirigee,” C. R. Acad. Sci. 223, 170–172 (1946).

Graefe’s Arch. Clin. Exp. Ophthalmol.

M. Millodot, “The influence of age on the chromatic aberration of the human eye,” Graefe’s Arch. Clin. Exp. Ophthalmol. 198, 235–243 (1976).

C. Ware, “Human axial chromatic aberration found not to decline with age,” Graefe’s Arch. Clin. Exp. Ophthalmol. 218, 39–41 (1982).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Ophthal. Physiol. Opt.

G. Walsh, “The effect of mydriasis on the pupillary centration of the human eye,” Ophthal. Physiol. Opt. 8, 178–182 (1988).
[CrossRef]

Opt. Acta

A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
[CrossRef]

Optom. Vis. Sci.

L. N. Thibos, A. Bradley, X. Zhang, “The effect of ocular chromatic aberration on monocular visual performance,” Optom. Vis. Sci. 68, 599–607 (1991).
[CrossRef] [PubMed]

X. Zhang, A. Bradley, L. N. Thibos, “Theoretical analysis of the effect of chromatic aberration on chromatic appearance of isoluminance color gratings,” Optom. Vis. Sci. 66 (Suppl.), 220 (1989).

A. Bradley, X. Zhang, L. N. Thibos, “Achromatizing the human eye,” Optom. Vis. Sci. 68, 608–616 (1991).
[CrossRef] [PubMed]

A. Bradley, L. N. Thibos, D. L. Still, “Visual acuity measured with clinical Maxwellian-view systems: effects of beam entry location,” Optom. Vis. Sci. 67, 811–817 (1990).
[CrossRef] [PubMed]

P. Simonet, M. C. W. Campbell, “Accuracy and reliability of the chromatic parallax method for measuring the longitudinal chromatic aberration of the human eye,” Optom. Vis. Sci. 67 (Suppl.), 55 (1990).

M. A. Wilson, M. C. W. Campbell, P. Simonet, “Change of pupil centration with change of illumination and pupil size,” Optom. Vis. Sci. 69, 129–136 (1992).
[CrossRef] [PubMed]

X. Zhang, L. N. Thibos, A. Bradley, “Relation between the chromatic difference of refraction and the chromatic difference of magnification for the reduced eye,” Optom. Vis. Sci. 68, 456–458 (1991).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. A

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
[CrossRef]

Vision Res.

W. N. Charman, J. A. M. Jennings, “Objective measurements of the longitudinal chromatic aberration the human eye,” Vision Res. 16, 99–1005 (1976).
[CrossRef]

P. A. Howarth, A. Bradley, “The longitudinal chromatic aberration of the human eye, and its correction,” Vision Res. 26, 361–366 (1986).
[CrossRef] [PubMed]

P. Simonet, M. C. W. Campbell, “The optical transverse chromatic aberration on the fovea of the human eye,” Vision Res. 30, 187–206 (1990).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

A. van Meeteren, C. J. W. Dunnewold, “Image quality of the human eye for eccentric entrance pupil,” Vision Res. 23, 573–579 (1983).
[CrossRef] [PubMed]

Other

A. Bradley, X. Zhang, L. N. Thibos, “Retinal image isoluminance is compromised by lateral and longitudinal chromatic aberration,” in OSA Annual Meeting Vol. 11 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 47.

A. Ivanoff, Les Aberrations de l’Oeil (Editions de la Revue d’Optique Theorique et Instrumentale, Paris, 1953).

H. H. Emsley, Visual Optics (Hatton, London, 1952).

Y. Le Grand, Form and Space Vision, translated by G. G. Heath, M. Millodot (Indiana U. Press, Bloomington, Ind., 1967).

G. B. Thomas, Calculus and Analytic Geometry (Addison-Wesley, Reading, Mass., 1960).

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Figures (8)

Fig. 1
Fig. 1

Principle of the two-color vernier method for measuring ocular chromatic aberration. A, ocular media have greater refractive indices for short wavelengths (dashed rays) than for long (solid rays), which results in a chromatic difference of focus. B, by isolating marginal rays with a pinhole aperture, a focusing difference becomes a difference in image location that can be measured with a vernier target. The amount of vernier misalignment is proportional to displacement h of the pinhole from the visual axis and to the chromatic difference in the refractive error of the eye.

Fig. 2
Fig. 2

Typical experimental results for one of eight subjects. A, mean (n = 5) results for the two-color vernier task are shown for three of 12 wavelengths tested. Standard errors of the means are less than the symbol radius. The slope of each line is a measure of the chromatic refractive error for the given wavelength relative to 555 nm. Pinhole displacement is from the empirically determined foveal achromatic axis. B, variation of the refractive error with the wavelength. Error bars show ±2 standard errors of dioptric value estimates that are obtained by linear regression of the individual data lines in the format shown in A.

Fig. 3
Fig. 3

Ocular chromatic aberration for eight subjects. The symbols show the mean refractive errors that are relative to 555 nm. The curve is a least-squares fit of a hyperbolic curve that describes the chromatic-eye model [see Eq. (3)].

Fig. 4
Fig. 4

Comparison of mean results with two models: Emsley’s water eye (dotted curve) and the same model filled with a different refracting medium (solid curve). Symbols show the mean refractive error (●) and the calculated refractive index (■) based on the data of Fig. 3 for eight subjects. Standard errors are less than the symbol radius.

Fig. 5
Fig. 5

Induced transverse chromatic aberration at fixed wavelengths (433, 622 nm) for five subjects. Results are compared with predictions from three versions of the reduced-eye model.

Fig. 6
Fig. 6

Comparison of published measurements of ocular chromatic aberration with the traditional water-eye model and with the new chromatic-eye model. Published results were put on a common basis by translating data points vertically until the refractive error was zero at the reference wavelength (589 nm).

Fig. 7
Fig. 7

Comparison of Emsley’s reduced eye and the proposed chromatic eye. The refracting surface is a sphere for Emsley’s model and a prolate spheroid for the chromatic eye, which corresponds, respectively, to a circle and an ellipse when viewed in cross section. Given f and f′ from Gullstrand’s schematic eye, Emsley’s model is completely determined by the pair of equations shown. The surface of the new model is given by Eqs. (A2) and (A3). By using Eq. (2) for specifying the refractive index, the emmetropic wavelength is 589 nm for both models. Dashed lines indicate the continuation of the refracting surfaces. Solid circles show the nodal point, and dashed circles show the two foci of the ellipse. Both surfaces have a radius of curvature r at vertex point P. Distances shown are in millimeters.

Fig. 8
Fig. 8

Ray diagram for stigmatic imaging at F of a distant, axial point source. Q at (x, y) is an arbitrary point on the refracting surface; N is the nodal point. R is distance Q N ¯; β and γ are included angles of triangle QNF.

Equations (9)

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Δ R x = n ref - n ( λ ) r · n D ,
n ( λ ) = a + b / ( λ - c ) ,
R x = p - q / ( λ - c ) .
x + n · Q F = n · f ,
( x - a ) 2 a 2 + y 2 b 2 = 1 ,
a = n f / ( n + 1 ) , b = f [ ( n - 1 ) / ( n + 1 ) ] 1 / 2 .
x - a = a cos ( θ ) , y = b sin ( θ ) ,
ρ = ( x ˙ 2 + y ˙ 2 ) 3 / 2 x ˙ y ¨ - x ¨ y ˙ ,
ρ = f ( n - 1 ) / n .

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