Abstract

The relative importance of the various optical elements of the human eye are analyzed to determine which contribute most to the chromatic variance in total refractive power of the eye. The concept of differential dispersion, defined as the change in the difference in index of refraction across a refractive surface with change in wavelength, is used to provide a theoretical tool for this analysis. The theoretical treatment shows that almost all the chromatic effect will be caused by the air–tear interface. Calculations of model eyes are made that support this view. Four model eyes are examined, an emmetropic eye, a hyperopic eye, a myopic eye, and an emmetropic eye accommodating 2.5D.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. A. Atchison and G. Smith, “Chromatic dispersions of the ocular media of human eyes,” J. Opt. Soc. Am. A 22, 29-37 (2005).
    [CrossRef]
  2. F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1981), pp. 479-484.
  3. M. Dubbleman, G. L. Van der Heijde, H. A. Weeber, and G. F. J. M. Vrensen, “Changes in the internal structure of the human crystalline lens with age and accommodation,” Vision Res. 43, 2363-2375 (2003).
    [CrossRef]
  4. C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, “Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI),” Vision Res. 45, 2352-2366 (2005).
    [CrossRef] [PubMed]
  5. H.-L. Liou and N. A. Brennan, “Anatomically accurate, finite model of the human eye for optical modeling,” J. Opt. Soc. Am. A 14, 1684-1695 (1997).
    [CrossRef]
  6. W. N. Charman, “Optics of the eye,” in Handbook of Optics, Vol. 1, M.Bass, ed. (McGraw-Hill, 1995), p. 24.18.

2005 (2)

C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, “Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI),” Vision Res. 45, 2352-2366 (2005).
[CrossRef] [PubMed]

D. A. Atchison and G. Smith, “Chromatic dispersions of the ocular media of human eyes,” J. Opt. Soc. Am. A 22, 29-37 (2005).
[CrossRef]

2003 (1)

M. Dubbleman, G. L. Van der Heijde, H. A. Weeber, and G. F. J. M. Vrensen, “Changes in the internal structure of the human crystalline lens with age and accommodation,” Vision Res. 43, 2363-2375 (2003).
[CrossRef]

1997 (1)

Atchison, D. A.

C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, “Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI),” Vision Res. 45, 2352-2366 (2005).
[CrossRef] [PubMed]

D. A. Atchison and G. Smith, “Chromatic dispersions of the ocular media of human eyes,” J. Opt. Soc. Am. A 22, 29-37 (2005).
[CrossRef]

Brennan, N. A.

Charman, W. N.

W. N. Charman, “Optics of the eye,” in Handbook of Optics, Vol. 1, M.Bass, ed. (McGraw-Hill, 1995), p. 24.18.

Dubbleman, M.

M. Dubbleman, G. L. Van der Heijde, H. A. Weeber, and G. F. J. M. Vrensen, “Changes in the internal structure of the human crystalline lens with age and accommodation,” Vision Res. 43, 2363-2375 (2003).
[CrossRef]

Jenkins, F. A.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1981), pp. 479-484.

Jones, C. E.

C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, “Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI),” Vision Res. 45, 2352-2366 (2005).
[CrossRef] [PubMed]

Liou, H.-L.

Meder, R.

C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, “Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI),” Vision Res. 45, 2352-2366 (2005).
[CrossRef] [PubMed]

Pope, J. M.

C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, “Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI),” Vision Res. 45, 2352-2366 (2005).
[CrossRef] [PubMed]

Smith, G.

Van der Heijde, G. L.

M. Dubbleman, G. L. Van der Heijde, H. A. Weeber, and G. F. J. M. Vrensen, “Changes in the internal structure of the human crystalline lens with age and accommodation,” Vision Res. 43, 2363-2375 (2003).
[CrossRef]

Vrensen, G. F. J. M.

M. Dubbleman, G. L. Van der Heijde, H. A. Weeber, and G. F. J. M. Vrensen, “Changes in the internal structure of the human crystalline lens with age and accommodation,” Vision Res. 43, 2363-2375 (2003).
[CrossRef]

Weeber, H. A.

M. Dubbleman, G. L. Van der Heijde, H. A. Weeber, and G. F. J. M. Vrensen, “Changes in the internal structure of the human crystalline lens with age and accommodation,” Vision Res. 43, 2363-2375 (2003).
[CrossRef]

White, H. E.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1981), pp. 479-484.

J. Opt. Soc. Am. A (2)

Vision Res. (2)

M. Dubbleman, G. L. Van der Heijde, H. A. Weeber, and G. F. J. M. Vrensen, “Changes in the internal structure of the human crystalline lens with age and accommodation,” Vision Res. 43, 2363-2375 (2003).
[CrossRef]

C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, “Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI),” Vision Res. 45, 2352-2366 (2005).
[CrossRef] [PubMed]

Other (2)

W. N. Charman, “Optics of the eye,” in Handbook of Optics, Vol. 1, M.Bass, ed. (McGraw-Hill, 1995), p. 24.18.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1981), pp. 479-484.

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.


Tables (12)

Tables Icon

Table 1 Values of the Cauchy Coefficients A, B, C, and D Used to Calculate the Indices of Refraction of the Ocular Media a

Tables Icon

Table 2 Differences d B , d C , and d D in Cauchy Coefficient Values at the Refractive Surface Interfaces of the Human Eye Based on the Values of B, C, and D in Table 1 a

Tables Icon

Table 3 Values of the Central Radii of Curvature, the Distances between Refractive Surfaces, and the Rate of Change of Surface Power with Wavelength of Light Change for the Refractive Surfaces of the Emmetropic Eye a

Tables Icon

Table 4 Surface Power Values in Diopters for the Refractive Surfaces of the Emmetropic Eye Calculated for Wavelengths of 400 nm , 578 nm , and 800 nm a

Tables Icon

Table 5 Values of the Reduced Vergence as Light Progresses from the Retina to Exit from the Emmetropic Eye Are Given in Diopters for Each Refractive Surface at Wavelengths of 400 nm , 578 nm , and 800 nm a

Tables Icon

Table 6 Values of the Central Radii of Curvature of and the Distances between the Refractive Surfaces of the + 4 D Hyperopic Eye

Tables Icon

Table 7 Values of the Central Radii of Curvature of and the Distances between the Refractive Surfaces of the 4 D Myopic Eye

Tables Icon

Table 8 Values of the Reduced Vergence in Diopters as Light Progresses from the Retina to Exit from the + 4 D Hyperopic Eye Are Given for Each Refractive Surface at Wavelengths of 400 nm , 578 nm , and 800 nm a

Tables Icon

Table 9 Values of the Reduced Vergence in Diopters as Light Progresses from the Retina to Exit from the 4 D Myopic Eye Are Given for Each Refractive Surface at Wavelengths of 400 nm , 578 nm , and 800 nm a

Tables Icon

Table 10 Values of the Central Radii of Curvature of and the Distances between the Refractive Surfaces of the Emmetropic Eye Accommodating 2.5 D

Tables Icon

Table 11 Values of the Reduced Vergence in Diopters as Light Progresses from the Retina to Exit from the Emmetropic Eye Accommodating 2.5 D Are Given for Each Refractive Surface at Wavelengths of 400 nm , 578 nm , and 800 nm a

Tables Icon

Table 12 Differences in Power in Diopters of the Air–Tear Film Refractive Surface, the Calculated Total Refractive Error, and the Experimentally Measured Total Refractive Error between the Value Found at 578 nm for the Emmetropic Eye and Nine Other Wavelengths in the Visual Spectral Range a

Equations (20)

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

F i = ( n i n i 1 ) K i ,
F i λ = { ( n i n i 1 ) K i } λ = { n i λ n i 1 λ } K i + ( n i n i 1 ) K i λ = { n i d λ n i 1 λ } K i ,
n ( λ ) = A + B λ 2 + C λ 4 + D λ 6 , to use only the first four terms .
( n ( λ ) ) λ = { 2 B λ 3 + 4 C λ 5 + 6 D λ 7 } .
F i λ = 2 { ( B i λ 3 + 2 C i λ 5 + 3 D i λ 7 ) ( B i 1 λ 3 + 2 C i 1 λ 5 + 3 D i 1 λ 7 ) } K ,
F i λ = 2 ( d B λ 3 + 2 λ 5 d C + 3 λ 7 d D ) K ,
V i = F + V o .
V i = V i 1 d n i V i .
V n = i = 1 n F i + V o ,
V n λ = λ i = 1 n F i + V o λ = i = 1 n { n i d λ n i 1 λ } K i + n o λ 1 o .
n s = 1.3709 3 × 10 7 age ,
n n = 1.4204 5.1 × 10 5 age ,
x 2 = 2 R y .
R a h a = R p h p .
h a = R p t R a + R p and h p = R a t R a + R p .
V = 0 h d A ( y ) d y = 0 h π x 2 d y = 0 h π 2 R y d y = π R h 2 .
R a R a h a = h a and R p R p h p = h p ,
R p R p h p = R a h a R p .
R p = R a R a R p ( h a h p ) 2 .
h a + h p = t .

Metrics