Abstract

Of the commonly used chromatic dispersion equations, only the Sellmeier and the Cauchy equations seem to be theoretically based. Cauchy’s equation is derived from the Sellmeier equation, is simpler to implement, and was found to give an excellent fit to published refractive-index data of the human eye. We used Cauchy’s equation to model the chromatic difference in refraction of the Gullstrand number 1 schematic eye with a gradient-index lens. To estimate the dispersion at different refractive-index levels within the lens, a single dispersion equation at one nominal refractive index was linearly scaled. This scaling was justified after exploring the effect of mean refractive index on dispersion by using Sellmeier’s equation and finding that a dispersion equation for one wavelength is just a linearly scaled version of the dispersion equation at any other wavlength. Because Cauchy’s equation is theoretically based and gives excellent fit to data in the visible spectrum, it can be used to extrapolate results into the near infrared with confidence.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. R. Krueger, R. A. Applegate, S. M. MacRae, Wavefront Customized Visual Correction: The Quest for Super Vision II (Slack, Thorofare, N.J., 2004).
  2. 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]
  3. R. E. Bedford, G. Wyszecki, “Axial chromatic aberration of the human eye,” J. Opt. Soc. Am. 37, 564–565 (1947).
  4. L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992).
    [CrossRef] [PubMed]
  5. D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth-Heinnemann, Oxford, UK, 2000).
  6. N. López-Gil, P. Artal, “Comparison of double-pass estimates of the retinal-image quality obtained with green and near infra-red light,” J. Opt. Soc. Am. A 14, 961–971 (1997).
    [CrossRef]
  7. L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26–35 (2003).
    [CrossRef]
  8. E. J. Fernández, A. Unterhuber, P. M. Prieto, B. Hermann, W. Drexler, P. Artal, “Near infrared ocular wavefront sensing with a femtosecond laser,” ARVO abstract2836 (2004).
  9. L. Wang, D. D. Koch, “Ocular higher-order aberrations in individuals screened for refractive surgery,” J. Cataract Refractive Surg. 29, 1896–1903 (2003).
    [CrossRef]
  10. P. M. Kiely, G. Smith, L. G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
    [CrossRef]
  11. M. Guillon, D. P. M. Lydon, C. Wilson, “Corneal topography: a clinical model,” Ophthalmic Physiol. Opt. 6, 47–56 (1986).
    [CrossRef] [PubMed]
  12. D. A. Atchison, G. Smith, M. D. Waterworth, “Theoretical effect of refractive error and accommodation on longitudinal chromatic aberration of the human eye,” Optom. Vision Sci. 70, 716–722 (1993).
    [CrossRef]
  13. A. Sorsby, B. Benjamin, J. B. Davey, M. Sheridan, J. M. Tanner, “Emmetropia and its aberrations,” (Her Majesty’s Stationery Office, London, 1957).
  14. Y. Le Grand, Form and Space Vision, rev. ed., translated by M. Millodot, G. Heath (Indiana University Press, Bloomington, Ind., 1967).
  15. 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]
  16. H.-L. Liou, N. A. Brennan, “Anatomically accurate, finite model eye for optical modeling,” J. Opt. Soc. Am. A 14, 1684–1695 (1997).
    [CrossRef]
  17. J. G. Sivak, T. Mandelman, “Chromatic dispersion of the ocular media,” Vision Res. 22, 997–1003 (1982).
    [CrossRef] [PubMed]
  18. A. Polack, “Le chromatisme de l’oeil,” Bull. Soc. Ophthalmol. France 9 bis (1923) (cited by Le Grand14).
  19. A. L. Cauchy, “Mémoire sur la dispersion de la lumière,” Nouveaux Exercices de Mathématiques, in Oeuvres Complètes d’Augustin Cauchy, 2nd Series, Vol. 10 (Gauthier-Villars et Fils, Paris, 1895) (cited by Longhurst,20 Smith,21 and Born and Wolf24 below).
  20. R. S. Longhurst, Geometrical and Physical Optics, 3rd ed. (Longman, London, 1973), p. 500.
  21. W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, New York, 1990), p. 164.
  22. M. Herzberger, “Colour correction in optical systems and a new dispersion formula,” Opt. Acta 6, 197–215 (1959).
    [CrossRef]
  23. A. E. Conrady, Applied Optics and Optical Design Part 2, R. Kingslake, ed. (Dover, New York, 1960), p. 659.
  24. M. Born, E. Wolf, Principles of Optics, 6th (corrected) ed. (Pergamon, Oxford, UK, 1989), p. 97.
  25. W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1986).
  26. A. G. Bennett, J. Tucker, “Correspondence: chromatic aberration of the eye between 200 and 2000 nm,” Br. J. Physiol. Opt. 30, 132–135 (1975).
  27. R. A. Houstoun, A Treatise on Light (Longmans, London, 1943), p. 464.
  28. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-HillKogaskusha, Tokyo, 1957).
  29. J. Tucker, “The chromatic aberration of the eye between wavelengths 200 nm and 2000 nm: some theoretical considerations,” Br. J. Physiol. Opt. 29, 118–125 (1974).
    [PubMed]
  30. D. A. Atchison, G. Smith, “Possible errors in determining axial length changes during accommodation with the IOLMaster,” Optom. Vision Sci. 81, 252–255 (2004).
    [CrossRef]
  31. A. Gullstrand, Appendix II in Helmholtz’sHandbuch der Physiologischen Optik, Vol. 1, 3rd ed. 1909. English translation edited by J. P. Southall (Optical Society of America, Washington, D.C., 1924), pp. 351–352.
  32. J. W. Blaker, “Toward an adaptive model of the human eye,” J. Opt. Soc. Am. 70, 220–223 (1980).
    [CrossRef] [PubMed]
  33. A. K. Sharma, D. V. Kumar, A. K. Ghatak, “Tracing rays through graded-index media,” Appl. Opt. 21, 984–987 (1982).
    [CrossRef] [PubMed]
  34. D. Van Norren, L. F. Tiemeijer, “Spectral reflectance of the human eye,” Vision Res. 26, 313–320 (1986).
    [CrossRef] [PubMed]
  35. F. C. Delori, K. P. Pflibsen, “Spectral reflectance of the human ocular fundus,” Appl. Opt. 28, 1061–1077 (1989).
    [CrossRef] [PubMed]
  36. A. E. Elsner, S. A. Burns, J. J. Weiter, F. C. Delori, “Infrared imaging of sub-retinal structures in the human ocular fundus,” Vision Res. 36, 191–205 (1996).
    [CrossRef] [PubMed]

2004 (2)

E. J. Fernández, A. Unterhuber, P. M. Prieto, B. Hermann, W. Drexler, P. Artal, “Near infrared ocular wavefront sensing with a femtosecond laser,” ARVO abstract2836 (2004).

D. A. Atchison, G. Smith, “Possible errors in determining axial length changes during accommodation with the IOLMaster,” Optom. Vision Sci. 81, 252–255 (2004).
[CrossRef]

2003 (2)

L. Wang, D. D. Koch, “Ocular higher-order aberrations in individuals screened for refractive surgery,” J. Cataract Refractive Surg. 29, 1896–1903 (2003).
[CrossRef]

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26–35 (2003).
[CrossRef]

1997 (2)

1996 (1)

A. E. Elsner, S. A. Burns, J. J. Weiter, F. C. Delori, “Infrared imaging of sub-retinal structures in the human ocular fundus,” Vision Res. 36, 191–205 (1996).
[CrossRef] [PubMed]

1993 (1)

D. A. Atchison, G. Smith, M. D. Waterworth, “Theoretical effect of refractive error and accommodation on longitudinal chromatic aberration of the human eye,” Optom. Vision Sci. 70, 716–722 (1993).
[CrossRef]

1992 (1)

1989 (1)

1986 (2)

D. Van Norren, L. F. Tiemeijer, “Spectral reflectance of the human eye,” Vision Res. 26, 313–320 (1986).
[CrossRef] [PubMed]

M. Guillon, D. P. M. Lydon, C. Wilson, “Corneal topography: a clinical model,” Ophthalmic Physiol. Opt. 6, 47–56 (1986).
[CrossRef] [PubMed]

1985 (1)

1982 (3)

J. G. Sivak, T. Mandelman, “Chromatic dispersion of the ocular media,” Vision Res. 22, 997–1003 (1982).
[CrossRef] [PubMed]

P. M. Kiely, G. Smith, L. G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
[CrossRef]

A. K. Sharma, D. V. Kumar, A. K. Ghatak, “Tracing rays through graded-index media,” Appl. Opt. 21, 984–987 (1982).
[CrossRef] [PubMed]

1980 (1)

1975 (1)

A. G. Bennett, J. Tucker, “Correspondence: chromatic aberration of the eye between 200 and 2000 nm,” Br. J. Physiol. Opt. 30, 132–135 (1975).

1974 (1)

J. Tucker, “The chromatic aberration of the eye between wavelengths 200 nm and 2000 nm: some theoretical considerations,” Br. J. Physiol. Opt. 29, 118–125 (1974).
[PubMed]

1959 (1)

M. Herzberger, “Colour correction in optical systems and a new dispersion formula,” Opt. Acta 6, 197–215 (1959).
[CrossRef]

1947 (2)

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]

R. E. Bedford, G. Wyszecki, “Axial chromatic aberration of the human eye,” J. Opt. Soc. Am. 37, 564–565 (1947).

1923 (1)

A. Polack, “Le chromatisme de l’oeil,” Bull. Soc. Ophthalmol. France 9 bis (1923) (cited by Le Grand14).

Applegate, R. A.

R. R. Krueger, R. A. Applegate, S. M. MacRae, Wavefront Customized Visual Correction: The Quest for Super Vision II (Slack, Thorofare, N.J., 2004).

Artal, P.

E. J. Fernández, A. Unterhuber, P. M. Prieto, B. Hermann, W. Drexler, P. Artal, “Near infrared ocular wavefront sensing with a femtosecond laser,” ARVO abstract2836 (2004).

N. López-Gil, P. Artal, “Comparison of double-pass estimates of the retinal-image quality obtained with green and near infra-red light,” J. Opt. Soc. Am. A 14, 961–971 (1997).
[CrossRef]

Atchison, D. A.

D. A. Atchison, G. Smith, “Possible errors in determining axial length changes during accommodation with the IOLMaster,” Optom. Vision Sci. 81, 252–255 (2004).
[CrossRef]

D. A. Atchison, G. Smith, M. D. Waterworth, “Theoretical effect of refractive error and accommodation on longitudinal chromatic aberration of the human eye,” Optom. Vision Sci. 70, 716–722 (1993).
[CrossRef]

D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth-Heinnemann, Oxford, UK, 2000).

Bedford, R. E.

R. E. Bedford, G. Wyszecki, “Axial chromatic aberration of the human eye,” J. Opt. Soc. Am. 37, 564–565 (1947).

Benjamin, B.

A. Sorsby, B. Benjamin, J. B. Davey, M. Sheridan, J. M. Tanner, “Emmetropia and its aberrations,” (Her Majesty’s Stationery Office, London, 1957).

Bennett, A. G.

A. G. Bennett, J. Tucker, “Correspondence: chromatic aberration of the eye between 200 and 2000 nm,” Br. J. Physiol. Opt. 30, 132–135 (1975).

Bescós, J.

Blaker, J. W.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th (corrected) ed. (Pergamon, Oxford, UK, 1989), p. 97.

Bradley, A.

Brennan, N. A.

Burns, S. A.

A. E. Elsner, S. A. Burns, J. J. Weiter, F. C. Delori, “Infrared imaging of sub-retinal structures in the human ocular fundus,” Vision Res. 36, 191–205 (1996).
[CrossRef] [PubMed]

Carney, L. G.

P. M. Kiely, G. Smith, L. G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
[CrossRef]

Cauchy, A. L.

A. L. Cauchy, “Mémoire sur la dispersion de la lumière,” Nouveaux Exercices de Mathématiques, in Oeuvres Complètes d’Augustin Cauchy, 2nd Series, Vol. 10 (Gauthier-Villars et Fils, Paris, 1895) (cited by Longhurst,20 Smith,21 and Born and Wolf24 below).

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design Part 2, R. Kingslake, ed. (Dover, New York, 1960), p. 659.

Davey, J. B.

A. Sorsby, B. Benjamin, J. B. Davey, M. Sheridan, J. M. Tanner, “Emmetropia and its aberrations,” (Her Majesty’s Stationery Office, London, 1957).

Delori, F. C.

A. E. Elsner, S. A. Burns, J. J. Weiter, F. C. Delori, “Infrared imaging of sub-retinal structures in the human ocular fundus,” Vision Res. 36, 191–205 (1996).
[CrossRef] [PubMed]

F. C. Delori, K. P. Pflibsen, “Spectral reflectance of the human ocular fundus,” Appl. Opt. 28, 1061–1077 (1989).
[CrossRef] [PubMed]

Diaz-Santana, L.

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26–35 (2003).
[CrossRef]

Drexler, W.

E. J. Fernández, A. Unterhuber, P. M. Prieto, B. Hermann, W. Drexler, P. Artal, “Near infrared ocular wavefront sensing with a femtosecond laser,” ARVO abstract2836 (2004).

Elsner, A. E.

A. E. Elsner, S. A. Burns, J. J. Weiter, F. C. Delori, “Infrared imaging of sub-retinal structures in the human ocular fundus,” Vision Res. 36, 191–205 (1996).
[CrossRef] [PubMed]

Fernández, E. J.

E. J. Fernández, A. Unterhuber, P. M. Prieto, B. Hermann, W. Drexler, P. Artal, “Near infrared ocular wavefront sensing with a femtosecond laser,” ARVO abstract2836 (2004).

Ghatak, A. K.

Griffin, D. R.

Guillon, M.

M. Guillon, D. P. M. Lydon, C. Wilson, “Corneal topography: a clinical model,” Ophthalmic Physiol. Opt. 6, 47–56 (1986).
[CrossRef] [PubMed]

Gullstrand, A.

A. Gullstrand, Appendix II in Helmholtz’sHandbuch der Physiologischen Optik, Vol. 1, 3rd ed. 1909. English translation edited by J. P. Southall (Optical Society of America, Washington, D.C., 1924), pp. 351–352.

Helmholtz’s,

A. Gullstrand, Appendix II in Helmholtz’sHandbuch der Physiologischen Optik, Vol. 1, 3rd ed. 1909. English translation edited by J. P. Southall (Optical Society of America, Washington, D.C., 1924), pp. 351–352.

Hermann, B.

E. J. Fernández, A. Unterhuber, P. M. Prieto, B. Hermann, W. Drexler, P. Artal, “Near infrared ocular wavefront sensing with a femtosecond laser,” ARVO abstract2836 (2004).

Herzberger, M.

M. Herzberger, “Colour correction in optical systems and a new dispersion formula,” Opt. Acta 6, 197–215 (1959).
[CrossRef]

Houstoun, R. A.

R. A. Houstoun, A Treatise on Light (Longmans, London, 1943), p. 464.

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-HillKogaskusha, Tokyo, 1957).

Kiely, P. M.

P. M. Kiely, G. Smith, L. G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
[CrossRef]

Koch, D. D.

L. Wang, D. D. Koch, “Ocular higher-order aberrations in individuals screened for refractive surgery,” J. Cataract Refractive Surg. 29, 1896–1903 (2003).
[CrossRef]

Krueger, R. R.

R. R. Krueger, R. A. Applegate, S. M. MacRae, Wavefront Customized Visual Correction: The Quest for Super Vision II (Slack, Thorofare, N.J., 2004).

Kumar, D. V.

Lara-Saucedo, D.

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26–35 (2003).
[CrossRef]

Le Grand, Y.

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

Liou, H.-L.

Llorente, L.

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26–35 (2003).
[CrossRef]

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics, 3rd ed. (Longman, London, 1973), p. 500.

López-Gil, N.

Lydon, D. P. M.

M. Guillon, D. P. M. Lydon, C. Wilson, “Corneal topography: a clinical model,” Ophthalmic Physiol. Opt. 6, 47–56 (1986).
[CrossRef] [PubMed]

MacRae, S. M.

R. R. Krueger, R. A. Applegate, S. M. MacRae, Wavefront Customized Visual Correction: The Quest for Super Vision II (Slack, Thorofare, N.J., 2004).

Mandelman, T.

J. G. Sivak, T. Mandelman, “Chromatic dispersion of the ocular media,” Vision Res. 22, 997–1003 (1982).
[CrossRef] [PubMed]

Marcos, S.

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26–35 (2003).
[CrossRef]

Navarro, R.

Pflibsen, K. P.

Polack, A.

A. Polack, “Le chromatisme de l’oeil,” Bull. Soc. Ophthalmol. France 9 bis (1923) (cited by Le Grand14).

Prieto, P. M.

E. J. Fernández, A. Unterhuber, P. M. Prieto, B. Hermann, W. Drexler, P. Artal, “Near infrared ocular wavefront sensing with a femtosecond laser,” ARVO abstract2836 (2004).

Santamari´a, J.

Sharma, A. K.

Sheridan, M.

A. Sorsby, B. Benjamin, J. B. Davey, M. Sheridan, J. M. Tanner, “Emmetropia and its aberrations,” (Her Majesty’s Stationery Office, London, 1957).

Sivak, J. G.

J. G. Sivak, T. Mandelman, “Chromatic dispersion of the ocular media,” Vision Res. 22, 997–1003 (1982).
[CrossRef] [PubMed]

Smith, G.

D. A. Atchison, G. Smith, “Possible errors in determining axial length changes during accommodation with the IOLMaster,” Optom. Vision Sci. 81, 252–255 (2004).
[CrossRef]

D. A. Atchison, G. Smith, M. D. Waterworth, “Theoretical effect of refractive error and accommodation on longitudinal chromatic aberration of the human eye,” Optom. Vision Sci. 70, 716–722 (1993).
[CrossRef]

P. M. Kiely, G. Smith, L. G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
[CrossRef]

D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth-Heinnemann, Oxford, UK, 2000).

Smith, W. J.

W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, New York, 1990), p. 164.

Sorsby, A.

A. Sorsby, B. Benjamin, J. B. Davey, M. Sheridan, J. M. Tanner, “Emmetropia and its aberrations,” (Her Majesty’s Stationery Office, London, 1957).

Tanner, J. M.

A. Sorsby, B. Benjamin, J. B. Davey, M. Sheridan, J. M. Tanner, “Emmetropia and its aberrations,” (Her Majesty’s Stationery Office, London, 1957).

Thibos, L. N.

Tiemeijer, L. F.

D. Van Norren, L. F. Tiemeijer, “Spectral reflectance of the human eye,” Vision Res. 26, 313–320 (1986).
[CrossRef] [PubMed]

Tucker, J.

A. G. Bennett, J. Tucker, “Correspondence: chromatic aberration of the eye between 200 and 2000 nm,” Br. J. Physiol. Opt. 30, 132–135 (1975).

J. Tucker, “The chromatic aberration of the eye between wavelengths 200 nm and 2000 nm: some theoretical considerations,” Br. J. Physiol. Opt. 29, 118–125 (1974).
[PubMed]

Unterhuber, A.

E. J. Fernández, A. Unterhuber, P. M. Prieto, B. Hermann, W. Drexler, P. Artal, “Near infrared ocular wavefront sensing with a femtosecond laser,” ARVO abstract2836 (2004).

Van Norren, D.

D. Van Norren, L. F. Tiemeijer, “Spectral reflectance of the human eye,” Vision Res. 26, 313–320 (1986).
[CrossRef] [PubMed]

Wald, G.

Wang, L.

L. Wang, D. D. Koch, “Ocular higher-order aberrations in individuals screened for refractive surgery,” J. Cataract Refractive Surg. 29, 1896–1903 (2003).
[CrossRef]

Waterworth, M. D.

D. A. Atchison, G. Smith, M. D. Waterworth, “Theoretical effect of refractive error and accommodation on longitudinal chromatic aberration of the human eye,” Optom. Vision Sci. 70, 716–722 (1993).
[CrossRef]

Weiter, J. J.

A. E. Elsner, S. A. Burns, J. J. Weiter, F. C. Delori, “Infrared imaging of sub-retinal structures in the human ocular fundus,” Vision Res. 36, 191–205 (1996).
[CrossRef] [PubMed]

Welford, W. T.

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

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-HillKogaskusha, Tokyo, 1957).

Wilson, C.

M. Guillon, D. P. M. Lydon, C. Wilson, “Corneal topography: a clinical model,” Ophthalmic Physiol. Opt. 6, 47–56 (1986).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th (corrected) ed. (Pergamon, Oxford, UK, 1989), p. 97.

Wyszecki, G.

R. E. Bedford, G. Wyszecki, “Axial chromatic aberration of the human eye,” J. Opt. Soc. Am. 37, 564–565 (1947).

Ye, M.

Zhang, X.

Appl. Opt. (3)

ARVO abstract (1)

E. J. Fernández, A. Unterhuber, P. M. Prieto, B. Hermann, W. Drexler, P. Artal, “Near infrared ocular wavefront sensing with a femtosecond laser,” ARVO abstract2836 (2004).

Br. J. Physiol. Opt. (2)

J. Tucker, “The chromatic aberration of the eye between wavelengths 200 nm and 2000 nm: some theoretical considerations,” Br. J. Physiol. Opt. 29, 118–125 (1974).
[PubMed]

A. G. Bennett, J. Tucker, “Correspondence: chromatic aberration of the eye between 200 and 2000 nm,” Br. J. Physiol. Opt. 30, 132–135 (1975).

Bull. Soc. Ophthalmol. France (1)

A. Polack, “Le chromatisme de l’oeil,” Bull. Soc. Ophthalmol. France 9 bis (1923) (cited by Le Grand14).

J. Cataract Refractive Surg. (1)

L. Wang, D. D. Koch, “Ocular higher-order aberrations in individuals screened for refractive surgery,” J. Cataract Refractive Surg. 29, 1896–1903 (2003).
[CrossRef]

J. Opt. Soc. Am. (3)

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

Ophthalmic Physiol. Opt. (1)

M. Guillon, D. P. M. Lydon, C. Wilson, “Corneal topography: a clinical model,” Ophthalmic Physiol. Opt. 6, 47–56 (1986).
[CrossRef] [PubMed]

Opt. Acta (2)

P. M. Kiely, G. Smith, L. G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
[CrossRef]

M. Herzberger, “Colour correction in optical systems and a new dispersion formula,” Opt. Acta 6, 197–215 (1959).
[CrossRef]

Optom. Vision Sci. (3)

D. A. Atchison, G. Smith, “Possible errors in determining axial length changes during accommodation with the IOLMaster,” Optom. Vision Sci. 81, 252–255 (2004).
[CrossRef]

L. Llorente, L. Diaz-Santana, D. Lara-Saucedo, S. Marcos, “Aberrations of the human eye in visible and near infrared illumination,” Optom. Vision Sci. 80, 26–35 (2003).
[CrossRef]

D. A. Atchison, G. Smith, M. D. Waterworth, “Theoretical effect of refractive error and accommodation on longitudinal chromatic aberration of the human eye,” Optom. Vision Sci. 70, 716–722 (1993).
[CrossRef]

Vision Res. (3)

A. E. Elsner, S. A. Burns, J. J. Weiter, F. C. Delori, “Infrared imaging of sub-retinal structures in the human ocular fundus,” Vision Res. 36, 191–205 (1996).
[CrossRef] [PubMed]

D. Van Norren, L. F. Tiemeijer, “Spectral reflectance of the human eye,” Vision Res. 26, 313–320 (1986).
[CrossRef] [PubMed]

J. G. Sivak, T. Mandelman, “Chromatic dispersion of the ocular media,” Vision Res. 22, 997–1003 (1982).
[CrossRef] [PubMed]

Other (13)

R. A. Houstoun, A Treatise on Light (Longmans, London, 1943), p. 464.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-HillKogaskusha, Tokyo, 1957).

A. E. Conrady, Applied Optics and Optical Design Part 2, R. Kingslake, ed. (Dover, New York, 1960), p. 659.

M. Born, E. Wolf, Principles of Optics, 6th (corrected) ed. (Pergamon, Oxford, UK, 1989), p. 97.

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

A. Gullstrand, Appendix II in Helmholtz’sHandbuch der Physiologischen Optik, Vol. 1, 3rd ed. 1909. English translation edited by J. P. Southall (Optical Society of America, Washington, D.C., 1924), pp. 351–352.

R. R. Krueger, R. A. Applegate, S. M. MacRae, Wavefront Customized Visual Correction: The Quest for Super Vision II (Slack, Thorofare, N.J., 2004).

A. Sorsby, B. Benjamin, J. B. Davey, M. Sheridan, J. M. Tanner, “Emmetropia and its aberrations,” (Her Majesty’s Stationery Office, London, 1957).

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

A. L. Cauchy, “Mémoire sur la dispersion de la lumière,” Nouveaux Exercices de Mathématiques, in Oeuvres Complètes d’Augustin Cauchy, 2nd Series, Vol. 10 (Gauthier-Villars et Fils, Paris, 1895) (cited by Longhurst,20 Smith,21 and Born and Wolf24 below).

R. S. Longhurst, Geometrical and Physical Optics, 3rd ed. (Longman, London, 1973), p. 500.

W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, New York, 1990), p. 164.

D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth-Heinnemann, Oxford, UK, 2000).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Chromatic difference of refraction from three experimental studies2-4 in the visible spectrum and best-fit Cauchy equation (5a), Cornu’s equation (5c), and Herzberger’s equation to the combined studies. All data were set to be zero at 590 nm. Results of three studies6-8 with measurements in the infrared are also shown; we moved the data from these studies studies to coincide with Eq. (5a) at the lower wavelength (543 nm, Refs. 6 and 7) or at the lowest wavelength (700 nm, Ref. 8). Where shown, error bars indicate standard deviations.

Fig. 2
Fig. 2

Chromatic dispersions for the cornea and aqueous from studies of Le Grand,14 Navarro et al.,15 and Liou and Brennan.16

Fig. 3
Fig. 3

Chromatic dispersions for the lens and vitreous from studies of Le Grand,14 Navarro et al.,15 and Liou and Brennan16 and for the “high” and “low” lens from Sivak and Mandelbaum.17

Fig. 4
Fig. 4

Chromatic difference-of-refraction best fit from Fig. 1 [Eq. (5a)] and simulated results using selected chromatic dispersion data for each ocular medium with the Gullstrand number 1 schematic eye containing a gradient-index lens.

Tables (5)

Tables Icon

Table 1 Le Grand’s14 Chromatic Dispersion Data That Are Substituted into Eq. (3c)

Tables Icon

Table 2 Values of n**, nF, nC and n* in Eq. (7a) for the Navarro et al 15 Eye and Their Corresponding Wavelengths

Tables Icon

Table 3 Values of A0, A1, P , and R Used in Eq. (7b) To Determine a1, a2, a3, and a4 for the Navarro et al. 15 Eye

Tables Icon

Table 4 Cauchy’s Equations Fitted to Various Sources of Chromatic Dispersion Dataa

Tables Icon

Table 5 Coefficients for the Cauchy Equation for Each Ocular Medium, Taken from the Combined Data of Le Grand14 and Navarro et al. 15 a

Equations (24)

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

F=(n-n)/r,
F(λ)=[μ(λ)-1]/r.
Rx(λ)=-[F(λ)-F(λ¯)]/μ(λ¯),
Rx(λ)=-[μ(λ)-μ(λ¯)]F(λ¯)μ(λ¯)[μ(λ¯)-1].
n(λ)=A+B/λ2+C/λ4+D/λ6+.
n(λ)=no+A/(λ-λo)1.2.
n(λ)=n+K/(λ-λo).
n(λ)=A+Bλ2+C/(λ2-λo2)+D/(λ2-λo2)2.
n(λ)=no+A/λ+B/λ3.5.
n2(λ)=1+B1λ2/(λ2-λo12)+B2λ2/(λ2-λo22)+B3λ2/(λ2-λo32)+.
n2(λ)=a0+a1λ2+a2/λ2+a3/λ4+a4/λ6+a5/λ8+.
V=(nd-1)/(nF-nC),
W value=(value at 550 nm-value at 700 nm)/(value at 400 nm-value at 550 nm),
Rx(λ)=1.60911-6.70941×10+5/λ2+5.55334×10+10/λ4-5.59998×10+15/λ6,
Rx(λ)=1.68524-633.46/((λ-214.102).
Rx(λ)=1.74638-633.27/(λ-218.358).
n2(λ)=1.7642-1.38×10-8λ2+6.12×10+3/λ2+1.41×10+8/λ4,
n(λ)=a1(λ)n**+a2(λ)nF+a3(λ)nC+a4(λ)n*,
ai(λ)=A0+A1λ2+P/(λ2-λo2)+R/(λ2-λo2)2,
n(λ)=1.320535+4.685/(λ-214.102).
n(λ)=1.32008+4.75654/(λ-218.358).
n(λ)=n(at 555 nm)+0.0512-0.1455λ+0.0961λ2,
n(λ)H=n(λ)A[n(λ¯)H/n(λ¯)A],
n(Y, Z)=1.406-0.0062685(Z-Zo)2+0.0003834(Z-Zo)3-[0.00052375+0.00005735(Z-Zo)+0.00027875(Z-Zo)2]Y2-0.000066717Y4,

Metrics