Abstract

There is a need for a schematic eye that models vision accurately under various conditions such as refractive surgical procedures, contact lens and spectacle wear, and near vision. Here we propose a new model eye close to anatomical, biometric, and optical realities. This is a finite model with four aspheric refracting surfaces and a gradient-index lens. It has an equivalent power of 60.35 D and an axial length of 23.95 mm. The new model eye provides spherical aberration values within the limits of empirical results and predicts chromatic aberration for wavelengths between 380 and 750 nm. It provides a model for calculating optical transfer functions and predicting optical performance of the eye.

© 1997 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  8. A. Bradley, School of Optometry, Indiana University, Bloomington, Ind. 47405-3201 (personal communication, 1995): corrections to the Ye et al. abstract (Ref. 5): The refracting surface defined as Y=0.0899X2+0.0006X4 should be Y=0.0899X2+0.0005X4 instead.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  70. J. A. Parker, “Aspheric optics of the human lens,” Can. J. Ophthalmol. 7, 168–175 (1972).
    [PubMed]

1996

H. L. Liou, N. A. Brennan, “The prediction of spherical aberration with schematic eyes,” Ophthalmic. Physiol. Opt. 16, 348–354 (1996).
[CrossRef] [PubMed]

1995

1994

C. Roberts, “The accuracy of ‘power’ maps to display curvature data in corneal topography systems,” Invest. Ophthalmol. Visual Sci. 35, 3525–3532 (1994).

1993

S. Patel, J. Marshall, F. W. Fitzke, “Shape and radius of posterior corneal surface,” Refract. Corneal Surg. 9, 173–181 (1993).
[PubMed]

R. A. Applegate, V. Lakshminarayanan, “Parametric representation of Stiles–Crawford functions: normal variation of peak location and directionality,” J. Opt. Soc. Am. A 10, 1611–1623 (1993).
[CrossRef] [PubMed]

P. Artal, M. Ferro, I. Miranda, R. Navarro, “Effects of aging in retinal image quality,” J. Opt. Soc. Am. A 10, 1656–1662 (1993).
[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]

M. Ye, X. X. Zhang, L. N. Thibos, A. Bradley, “A new single-surface model eye that accurately predicts chromatic and spherical aberrations of the human eye,” Invest. Ophthalmol. Visual Sci. (Suppl.) 34, 777 (1993).

L. N. Thibos, M. Ye, X. X. Zhang, A. Bradley, “A new optical model of the human eye,” Opt. Photon. News 4, 12 (1993).
[CrossRef]

1992

L. N. Thibos, M. Ye, X. 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]

M. C. M. Dunne, J. M. Royston, D. A. Barnes, “Normal variations of the posterior corneal surface,” Acta Ophthalmol. 70, 255–261 (1992).
[CrossRef]

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

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

A. G. Rivett, A. Ho, “The posterior corneal topography,” Invest. Ophthalmol. Visual Sci. (Suppl.) 32, 1001–1001 (1991).

G. Smith, B. K. Pierscionek, D. A. Atchison, “The optical modelling of the human lens,” Ophthalmic. Physiol. Opt. 11, 359–369 (1991).
[CrossRef] [PubMed]

1990

J. M. Royston, M. C. M. Dunne, D. A. Barnes, “Measurement of the posterior corneal radius using slit lamp and Purkinje image techniques,” Ophthalmic. Physiol. Opt. 10, 385–388 (1990).
[CrossRef] [PubMed]

1989

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

B. K. Pierscionek, D. Y. C. Chan, “Refractive index gradient of human lenses,” Optom. Vis. Sci. 66, 822–829 (1989).
[CrossRef] [PubMed]

1988

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

G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
[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]

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]

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

1985

1984

M. C. W. Campbell, “Measurement of refractive index in an intact crystalline lens,” Vision Res. 24, 409–415 (1984).
[CrossRef] [PubMed]

1983

1982

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

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

1981

1980

J. W. Blaker, “Toward an adaptive model of the human eye,” J. Opt. Soc. Am. 70, 220–223 (1980).
[CrossRef] [PubMed]

S. T. Fontana, R. F. Brubaker, “Volume and depth of the anterior chamber in the normal aging human eye,” Arch. Ophthalmol. 98, 1803–1808 (1980).
[CrossRef] [PubMed]

1979

C. S. Yu, D. Kao, C. T. Chang, “Measurement of the length of the visual axis by ultrasonography in 1789 eyes,” Chin. J. Ophthalmol. 15, 45–47 (1979).

P. S. Soni, I. M. Borish, “A report on central and peripheral corneal thickness,” Int. Contact Lens Clin. 6, 66–70 (1979).

M. Millodot, J. Sivak, “Contribution of the cornea and lens to the spherical aberration of the eye,” Vision Res. 19, 685–687 (1979).
[CrossRef] [PubMed]

1978

N. K. Hirji, J. R. Larke, “Thickness of human cornea measured by topographic tachometry,” Am. J. Optom. Arch. Am. Acad. Optom. 55, 97–100 (1978).

1977

M. J. Howcroft, J. A. Parker, “Aspheric curvatures for the human lens,” Vision Res. 17, 1217–1223 (1977).
[CrossRef] [PubMed]

1976

V. Clemmensen, M. H. Luntz, “Lens thickness and angle-closure glaucoma,” Acta Ophthalmol. 54, 193–197 (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]

N. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
[CrossRef] [PubMed]

1973

R. F. Lowe, B. A. J. Clark, “Radius of curvature of the anterior lens surface,” Br. J. Ophthalmol. 57, 471–474 (1973).
[CrossRef] [PubMed]

S. G. El Hage, F. Berny, “Contribution of the crystalline lens to the spherical aberration of the eye,” J. Opt. Soc. Am. 63, 205–211 (1973).
[CrossRef] [PubMed]

B. A. J. Clark, “Variations in corneal topography,” Aust. J. Optom. 56, 399–413 (1973).

R. F. Lowe, B. A. Clark, “Posterior corneal curvature,” Br. J. Ophthalmol. 57, 464–470 (1973).
[CrossRef] [PubMed]

1972

A. Tomlinson, “A clinical study of the central and peripheral thickness and curvature of the human cornea,” Acta Ophthalmol. 50, 73–82 (1972).
[CrossRef]

D. A. Leighton, A. Tomlinson, “Changes in axial length and other dimensions of the eyeball with increasing age,” Acta Ophthalmol. 50, 815–826 (1972).
[CrossRef]

J. A. Parker, “Aspheric optics of the human lens,” Can. J. Ophthalmol. 7, 168–175 (1972).
[PubMed]

R. F. Lowe, “Anterior lens curvature,” Br. J. Ophthalmol. 56, 409–413 (1972).
[CrossRef] [PubMed]

1971

W. Lotmar, “Theoretical eye model with aspherics,” J. Opt. Soc. Am. 61, 1522–1529 (1971).
[CrossRef]

J. Larsen, “The sagittal growth of the eye,” Acta Ophthalmol. 49, 239–262 (1971).
[CrossRef]

F. K. Hansen, “A clinical study of the normal human central corneal thickness,” Acta Ophthalmol. 49, 82–89 (1971).

R. B. Mandell, R. St. Helen, “Mathematical model for the corneal contour,” Br. J. Physiol. Opt. 26, 183–197 (1971).

1970

M. Townsley, “New knowledge of the corneal contour,” Contacto 14, 38–43 (1970).

G. Westheimer, “Image quality in the human eye,” Opt. Acta 17, 641–658 (1970).
[CrossRef]

1969

S. Nakao, T. Ono, R. Nagata, K. Iwata, “The distribution of refractive index in the human crystalline lens,” Jpn. J. Clin. Ophthalmol. 23, 903–906 (1969).

R. F. Lowe, “Central corneal thickness,” Br. J. Ophthalmol. 53, 824–826 (1969).
[CrossRef] [PubMed]

1968

E. L. Martola, J. L. Baum, “Central and peripheral corneal thickness,” Arch. Opththalmol. 79, 28–30 (1968).
[CrossRef]

1963

F. Jansson, “Measurements of intraocular distances by ultrasound,” Acta Ophthalmol. Suppl. 74, 1–49 (1963).
[PubMed]

T. C. A. Jenkins, “Aberrations of the eye and their effects on vision: part 1,” Br. J. Physiol. Opt. 20, 59–91 (1963).

1961

R. Weekers, J. Grieten, “Mesure de la profondeur de la chambre antérieure en clinique,” Soc. Belg. Ophthalmol. 129, 361–381 (1961).

1960

A. Sorsby, M. Sheridan, A. G. Leary, B. Benjamin, “Vision, visual acuity and ocular refraction in young men,” Brit. Med. J. 1, 1394–1398 (1960).

1957

1951

D. M. Maurice, A. A. Giardini, “A simple optical apparatus for measuring the corneal thickness and the average thickness of the human cornea,” Br. J. Ophthalmol. 35, 169–177 (1951).
[CrossRef] [PubMed]

1948

S. Stenström, “Investigation of the variation and the correlation of the optical elements of human eyes,” Am. J. Optom. 25, 340–350 (1948).

1947

Applegate, R. A.

Artal, P.

Atchison, D. A.

G. Smith, B. K. Pierscionek, D. A. Atchison, “The optical modelling of the human lens,” Ophthalmic. Physiol. Opt. 11, 359–369 (1991).
[CrossRef] [PubMed]

Barnes, D. A.

M. C. M. Dunne, J. M. Royston, D. A. Barnes, “Normal variations of the posterior corneal surface,” Acta Ophthalmol. 70, 255–261 (1992).
[CrossRef]

J. M. Royston, M. C. M. Dunne, D. A. Barnes, “Measurement of the posterior corneal radius using slit lamp and Purkinje image techniques,” Ophthalmic. Physiol. Opt. 10, 385–388 (1990).
[CrossRef] [PubMed]

Baum, J. L.

E. L. Martola, J. L. Baum, “Central and peripheral corneal thickness,” Arch. Opththalmol. 79, 28–30 (1968).
[CrossRef]

Bedford, R. E.

Benjamin, B.

A. Sorsby, M. Sheridan, A. G. Leary, B. Benjamin, “Vision, visual acuity and ocular refraction in young men,” Brit. Med. J. 1, 1394–1398 (1960).

A. Sorsby, B. Benjamin, J. B. Davey, M. Sheridan, J. M. Tanner, Emmetropia and Its Aberrations. A Study in the Correlation of the Optical Components of the Eye.  (Her Majesty’s Stationary Office, London, 1957).

Bennett, A. G.

A. G. Bennett, R. B. Rabbetts, Clinical Visual Optics, 2nd ed. (Butterworth-Heinemann, Oxford, 1989), pp. 17–18.

Berny, F.

Bescós, J.

Blaker, J. W.

Borish, I. M.

P. S. Soni, I. M. Borish, “A report on central and peripheral corneal thickness,” Int. Contact Lens Clin. 6, 66–70 (1979).

Bradley, A.

M. Ye, X. X. Zhang, L. N. Thibos, A. Bradley, “A new single-surface model eye that accurately predicts chromatic and spherical aberrations of the human eye,” Invest. Ophthalmol. Visual Sci. (Suppl.) 34, 777 (1993).

L. N. Thibos, M. Ye, X. X. Zhang, A. Bradley, “A new optical model of the human eye,” Opt. Photon. News 4, 12 (1993).
[CrossRef]

L. N. Thibos, M. Ye, X. 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]

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

A. Bradley, School of Optometry, Indiana University, Bloomington, Ind. 47405-3201 (personal communication, 1995): corrections to the Ye et al. abstract (Ref. 5): The refracting surface defined as Y=0.0899X2+0.0006X4 should be Y=0.0899X2+0.0005X4 instead.

Brennan, N. A.

H. L. Liou, N. A. Brennan, “The prediction of spherical aberration with schematic eyes,” Ophthalmic. Physiol. Opt. 16, 348–354 (1996).
[CrossRef] [PubMed]

Brown, N.

N. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
[CrossRef] [PubMed]

Brubaker, R. F.

S. T. Fontana, R. F. Brubaker, “Volume and depth of the anterior chamber in the normal aging human eye,” Arch. Ophthalmol. 98, 1803–1808 (1980).
[CrossRef] [PubMed]

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]

M. C. W. Campbell, “Measurement of refractive index in an intact crystalline lens,” Vision Res. 24, 409–415 (1984).
[CrossRef] [PubMed]

Carney, G.

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

Chan, D. Y. C.

B. K. Pierscionek, D. Y. C. Chan, “Refractive index gradient of human lenses,” Optom. Vis. Sci. 66, 822–829 (1989).
[CrossRef] [PubMed]

Chang, C. T.

C. S. Yu, D. Kao, C. T. Chang, “Measurement of the length of the visual axis by ultrasonography in 1789 eyes,” Chin. J. Ophthalmol. 15, 45–47 (1979).

Charman, W. N.

G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
[CrossRef] [PubMed]

Chisholm, W.

Clark, B. A.

R. F. Lowe, B. A. Clark, “Posterior corneal curvature,” Br. J. Ophthalmol. 57, 464–470 (1973).
[CrossRef] [PubMed]

Clark, B. A. J.

B. A. J. Clark, “Variations in corneal topography,” Aust. J. Optom. 56, 399–413 (1973).

R. F. Lowe, B. A. J. Clark, “Radius of curvature of the anterior lens surface,” Br. J. Ophthalmol. 57, 471–474 (1973).
[CrossRef] [PubMed]

Clemmensen, V.

V. Clemmensen, M. H. Luntz, “Lens thickness and angle-closure glaucoma,” Acta Ophthalmol. 54, 193–197 (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]

Davey, J. B.

A. Sorsby, B. Benjamin, J. B. Davey, M. Sheridan, J. M. Tanner, Emmetropia and Its Aberrations. A Study in the Correlation of the Optical Components of the Eye.  (Her Majesty’s Stationary Office, London, 1957).

Dunne, M. C. M.

M. C. M. Dunne, J. M. Royston, D. A. Barnes, “Normal variations of the posterior corneal surface,” Acta Ophthalmol. 70, 255–261 (1992).
[CrossRef]

J. M. Royston, M. C. M. Dunne, D. A. Barnes, “Measurement of the posterior corneal radius using slit lamp and Purkinje image techniques,” Ophthalmic. Physiol. Opt. 10, 385–388 (1990).
[CrossRef] [PubMed]

El Hage, S. G.

Ferro, M.

Fitzke, F. W.

S. Patel, J. Marshall, F. W. Fitzke, “Shape and radius of posterior corneal surface,” Refract. Corneal Surg. 9, 173–181 (1993).
[PubMed]

Fontana, S. T.

S. T. Fontana, R. F. Brubaker, “Volume and depth of the anterior chamber in the normal aging human eye,” Arch. Ophthalmol. 98, 1803–1808 (1980).
[CrossRef] [PubMed]

Giardini, A. A.

D. M. Maurice, A. A. Giardini, “A simple optical apparatus for measuring the corneal thickness and the average thickness of the human cornea,” Br. J. Ophthalmol. 35, 169–177 (1951).
[CrossRef] [PubMed]

Goeckner, P. A.

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

Grieten, J.

R. Weekers, J. Grieten, “Mesure de la profondeur de la chambre antérieure en clinique,” Soc. Belg. Ophthalmol. 129, 361–381 (1961).

Griffin, D. R.

Guillon, M.

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

Gullstrand, A.

A. Gullstrand, Helmholtz’s Physiological Optics (Optical Society of America, New York, 1924), Appendix, pp. 350–358.

Hansen, F. K.

F. K. Hansen, “A clinical study of the normal human central corneal thickness,” Acta Ophthalmol. 49, 82–89 (1971).

Hartridge, H.

H. Hartridge, Recent Advances in the Physiology of Vision (Churchill, London, 1950), pp. 78–84.

Hirji, N. K.

N. K. Hirji, J. R. Larke, “Thickness of human cornea measured by topographic tachometry,” Am. J. Optom. Arch. Am. Acad. Optom. 55, 97–100 (1978).

Ho, A.

A. G. Rivett, A. Ho, “The posterior corneal topography,” Invest. Ophthalmol. Visual Sci. (Suppl.) 32, 1001–1001 (1991).

Howarth, P. A.

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

Howcroft, M. J.

M. J. Howcroft, J. A. Parker, “Aspheric curvatures for the human lens,” Vision Res. 17, 1217–1223 (1977).
[CrossRef] [PubMed]

Iwata, K.

S. Nakao, T. Ono, R. Nagata, K. Iwata, “The distribution of refractive index in the human crystalline lens,” Jpn. J. Clin. Ophthalmol. 23, 903–906 (1969).

Jansson, F.

F. Jansson, “Measurements of intraocular distances by ultrasound,” Acta Ophthalmol. Suppl. 74, 1–49 (1963).
[PubMed]

Jenkins, T. C. A.

T. C. A. Jenkins, “Aberrations of the eye and their effects on vision: part 1,” Br. J. Physiol. Opt. 20, 59–91 (1963).

Kao, D.

C. S. Yu, D. Kao, C. T. Chang, “Measurement of the length of the visual axis by ultrasonography in 1789 eyes,” Chin. J. Ophthalmol. 15, 45–47 (1979).

Kaufman, P. L.

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

Kiely, P. H.

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

Kooijman, A. C.

Koretz, J. F.

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

Lakshminarayanan, V.

Larke, J. R.

N. K. Hirji, J. R. Larke, “Thickness of human cornea measured by topographic tachometry,” Am. J. Optom. Arch. Am. Acad. Optom. 55, 97–100 (1978).

Larsen, J.

J. Larsen, “The sagittal growth of the eye,” Acta Ophthalmol. 49, 239–262 (1971).
[CrossRef]

Le Grand, Y.

Y. Le Grand, Physiological Optics (Springer-Verlag, New York, 1980), pp. 54–55.

Leary, A. G.

A. Sorsby, M. Sheridan, A. G. Leary, B. Benjamin, “Vision, visual acuity and ocular refraction in young men,” Brit. Med. J. 1, 1394–1398 (1960).

Leighton, D. A.

D. A. Leighton, A. Tomlinson, “Changes in axial length and other dimensions of the eyeball with increasing age,” Acta Ophthalmol. 50, 815–826 (1972).
[CrossRef]

Lidkea, B.

Liou, H. L.

H. L. Liou, N. A. Brennan, “The prediction of spherical aberration with schematic eyes,” Ophthalmic. Physiol. Opt. 16, 348–354 (1996).
[CrossRef] [PubMed]

Lotmar, W.

Lowe, R. F.

R. F. Lowe, B. A. J. Clark, “Radius of curvature of the anterior lens surface,” Br. J. Ophthalmol. 57, 471–474 (1973).
[CrossRef] [PubMed]

R. F. Lowe, B. A. Clark, “Posterior corneal curvature,” Br. J. Ophthalmol. 57, 464–470 (1973).
[CrossRef] [PubMed]

R. F. Lowe, “Anterior lens curvature,” Br. J. Ophthalmol. 56, 409–413 (1972).
[CrossRef] [PubMed]

R. F. Lowe, “Central corneal thickness,” Br. J. Ophthalmol. 53, 824–826 (1969).
[CrossRef] [PubMed]

Luntz, M. H.

V. Clemmensen, M. H. Luntz, “Lens thickness and angle-closure glaucoma,” Acta Ophthalmol. 54, 193–197 (1976).
[CrossRef]

Lydon, P. M.

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

Mandell, R. B.

R. B. Mandell, R. St. Helen, “Mathematical model for the corneal contour,” Br. J. Physiol. Opt. 26, 183–197 (1971).

Mandelman, T.

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

Marshall, J.

S. Patel, J. Marshall, F. W. Fitzke, “Shape and radius of posterior corneal surface,” Refract. Corneal Surg. 9, 173–181 (1993).
[PubMed]

Martola, E. L.

E. L. Martola, J. L. Baum, “Central and peripheral corneal thickness,” Arch. Opththalmol. 79, 28–30 (1968).
[CrossRef]

Maurice, D. M.

D. M. Maurice, A. A. Giardini, “A simple optical apparatus for measuring the corneal thickness and the average thickness of the human cornea,” Br. J. Ophthalmol. 35, 169–177 (1951).
[CrossRef] [PubMed]

Millodot, M.

M. Millodot, J. Sivak, “Contribution of the cornea and lens to the spherical aberration of the eye,” Vision Res. 19, 685–687 (1979).
[CrossRef] [PubMed]

Miranda, I.

Nagata, R.

S. Nakao, T. Ono, R. Nagata, K. Iwata, “The distribution of refractive index in the human crystalline lens,” Jpn. J. Clin. Ophthalmol. 23, 903–906 (1969).

Nakao, S.

S. Nakao, T. Ono, R. Nagata, K. Iwata, “The distribution of refractive index in the human crystalline lens,” Jpn. J. Clin. Ophthalmol. 23, 903–906 (1969).

Navarro, R.

Neider, M. W.

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

Ono, T.

S. Nakao, T. Ono, R. Nagata, K. Iwata, “The distribution of refractive index in the human crystalline lens,” Jpn. J. Clin. Ophthalmol. 23, 903–906 (1969).

Palmer, D. A.

Parker, J. A.

M. J. Howcroft, J. A. Parker, “Aspheric curvatures for the human lens,” Vision Res. 17, 1217–1223 (1977).
[CrossRef] [PubMed]

J. A. Parker, “Aspheric optics of the human lens,” Can. J. Ophthalmol. 7, 168–175 (1972).
[PubMed]

Patel, S.

S. Patel, J. Marshall, F. W. Fitzke, “Shape and radius of posterior corneal surface,” Refract. Corneal Surg. 9, 173–181 (1993).
[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]

Pierscionek, B. K.

G. Smith, B. K. Pierscionek, D. A. Atchison, “The optical modelling of the human lens,” Ophthalmic. Physiol. Opt. 11, 359–369 (1991).
[CrossRef] [PubMed]

B. K. Pierscionek, D. Y. C. Chan, “Refractive index gradient of human lenses,” Optom. Vis. Sci. 66, 822–829 (1989).
[CrossRef] [PubMed]

Rabbetts, R. B.

A. G. Bennett, R. B. Rabbetts, Clinical Visual Optics, 2nd ed. (Butterworth-Heinemann, Oxford, 1989), pp. 17–18.

Rivett, A. G.

A. G. Rivett, A. Ho, “The posterior corneal topography,” Invest. Ophthalmol. Visual Sci. (Suppl.) 32, 1001–1001 (1991).

Roberts, C.

C. Roberts, “The accuracy of ‘power’ maps to display curvature data in corneal topography systems,” Invest. Ophthalmol. Visual Sci. 35, 3525–3532 (1994).

Royston, J. M.

M. C. M. Dunne, J. M. Royston, D. A. Barnes, “Normal variations of the posterior corneal surface,” Acta Ophthalmol. 70, 255–261 (1992).
[CrossRef]

J. M. Royston, M. C. M. Dunne, D. A. Barnes, “Measurement of the posterior corneal radius using slit lamp and Purkinje image techniques,” Ophthalmic. Physiol. Opt. 10, 385–388 (1990).
[CrossRef] [PubMed]

Rynders, M.

Santamari´a, J.

Sheridan, M.

A. Sorsby, M. Sheridan, A. G. Leary, B. Benjamin, “Vision, visual acuity and ocular refraction in young men,” Brit. Med. J. 1, 1394–1398 (1960).

A. Sorsby, B. Benjamin, J. B. Davey, M. Sheridan, J. M. Tanner, Emmetropia and Its Aberrations. A Study in the Correlation of the Optical Components of the Eye.  (Her Majesty’s Stationary Office, London, 1957).

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]

Sivak, J.

D. A. Palmer, J. Sivak, “Crystalline lens dispersion,” J. Opt. Soc. Am. 71, 780–782 (1981).
[CrossRef] [PubMed]

M. Millodot, J. Sivak, “Contribution of the cornea and lens to the spherical aberration of the eye,” Vision Res. 19, 685–687 (1979).
[CrossRef] [PubMed]

Sivak, J. G.

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

Smith, G.

G. Smith, B. K. Pierscionek, D. A. Atchison, “The optical modelling of the human lens,” Ophthalmic. Physiol. Opt. 11, 359–369 (1991).
[CrossRef] [PubMed]

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

Soni, P. S.

P. S. Soni, I. M. Borish, “A report on central and peripheral corneal thickness,” Int. Contact Lens Clin. 6, 66–70 (1979).

Sorsby, A.

A. Sorsby, M. Sheridan, A. G. Leary, B. Benjamin, “Vision, visual acuity and ocular refraction in young men,” Brit. Med. J. 1, 1394–1398 (1960).

A. Sorsby, B. Benjamin, J. B. Davey, M. Sheridan, J. M. Tanner, Emmetropia and Its Aberrations. A Study in the Correlation of the Optical Components of the Eye.  (Her Majesty’s Stationary Office, London, 1957).

St. Helen, R.

R. B. Mandell, R. St. Helen, “Mathematical model for the corneal contour,” Br. J. Physiol. Opt. 26, 183–197 (1971).

Stenström, S.

S. Stenström, “Investigation of the variation and the correlation of the optical elements of human eyes,” Am. J. Optom. 25, 340–350 (1948).

Tanner, J. M.

A. Sorsby, B. Benjamin, J. B. Davey, M. Sheridan, J. M. Tanner, Emmetropia and Its Aberrations. A Study in the Correlation of the Optical Components of the Eye.  (Her Majesty’s Stationary Office, London, 1957).

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]

M. Ye, X. X. Zhang, L. N. Thibos, A. Bradley, “A new single-surface model eye that accurately predicts chromatic and spherical aberrations of the human eye,” Invest. Ophthalmol. Visual Sci. (Suppl.) 34, 777 (1993).

L. N. Thibos, M. Ye, X. X. Zhang, A. Bradley, “A new optical model of the human eye,” Opt. Photon. News 4, 12 (1993).
[CrossRef]

L. N. Thibos, M. Ye, X. 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]

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

Tomlinson, A.

D. A. Leighton, A. Tomlinson, “Changes in axial length and other dimensions of the eyeball with increasing age,” Acta Ophthalmol. 50, 815–826 (1972).
[CrossRef]

A. Tomlinson, “A clinical study of the central and peripheral thickness and curvature of the human cornea,” Acta Ophthalmol. 50, 73–82 (1972).
[CrossRef]

Townsley, M.

M. Townsley, “New knowledge of the corneal contour,” Contacto 14, 38–43 (1970).

van Meeteren, A.

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,” Ophthalmic. Physiol. Opt. 8, 178–182 (1988).
[CrossRef] [PubMed]

G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
[CrossRef] [PubMed]

Weekers, R.

R. Weekers, J. Grieten, “Mesure de la profondeur de la chambre antérieure en clinique,” Soc. Belg. Ophthalmol. 129, 361–381 (1961).

Westheimer, G.

G. Westheimer, “Image quality in the human eye,” Opt. Acta 17, 641–658 (1970).
[CrossRef]

Williams, D. R.

Wilson, C.

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

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.

Ye, M.

M. Ye, X. X. Zhang, L. N. Thibos, A. Bradley, “A new single-surface model eye that accurately predicts chromatic and spherical aberrations of the human eye,” Invest. Ophthalmol. Visual Sci. (Suppl.) 34, 777 (1993).

L. N. Thibos, M. Ye, X. X. Zhang, A. Bradley, “A new optical model of the human eye,” Opt. Photon. News 4, 12 (1993).
[CrossRef]

L. N. Thibos, M. Ye, X. 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]

Yu, C. S.

C. S. Yu, D. Kao, C. T. Chang, “Measurement of the length of the visual axis by ultrasonography in 1789 eyes,” Chin. J. Ophthalmol. 15, 45–47 (1979).

Zhang, X. X.

L. N. Thibos, M. Ye, X. X. Zhang, A. Bradley, “A new optical model of the human eye,” Opt. Photon. News 4, 12 (1993).
[CrossRef]

M. Ye, X. X. Zhang, L. N. Thibos, A. Bradley, “A new single-surface model eye that accurately predicts chromatic and spherical aberrations of the human eye,” Invest. Ophthalmol. Visual Sci. (Suppl.) 34, 777 (1993).

L. N. Thibos, M. Ye, X. 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]

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

Acta Ophthalmol.

D. A. Leighton, A. Tomlinson, “Changes in axial length and other dimensions of the eyeball with increasing age,” Acta Ophthalmol. 50, 815–826 (1972).
[CrossRef]

J. Larsen, “The sagittal growth of the eye,” Acta Ophthalmol. 49, 239–262 (1971).
[CrossRef]

V. Clemmensen, M. H. Luntz, “Lens thickness and angle-closure glaucoma,” Acta Ophthalmol. 54, 193–197 (1976).
[CrossRef]

A. Tomlinson, “A clinical study of the central and peripheral thickness and curvature of the human cornea,” Acta Ophthalmol. 50, 73–82 (1972).
[CrossRef]

F. K. Hansen, “A clinical study of the normal human central corneal thickness,” Acta Ophthalmol. 49, 82–89 (1971).

M. C. M. Dunne, J. M. Royston, D. A. Barnes, “Normal variations of the posterior corneal surface,” Acta Ophthalmol. 70, 255–261 (1992).
[CrossRef]

Acta Ophthalmol. Suppl.

F. Jansson, “Measurements of intraocular distances by ultrasound,” Acta Ophthalmol. Suppl. 74, 1–49 (1963).
[PubMed]

Am. J. Optom.

S. Stenström, “Investigation of the variation and the correlation of the optical elements of human eyes,” Am. J. Optom. 25, 340–350 (1948).

Am. J. Optom. Arch. Am. Acad. Optom.

N. K. Hirji, J. R. Larke, “Thickness of human cornea measured by topographic tachometry,” Am. J. Optom. Arch. Am. Acad. Optom. 55, 97–100 (1978).

Am. J. Optom. Physiol. Opt.

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.

Arch. Ophthalmol.

S. T. Fontana, R. F. Brubaker, “Volume and depth of the anterior chamber in the normal aging human eye,” Arch. Ophthalmol. 98, 1803–1808 (1980).
[CrossRef] [PubMed]

Arch. Opththalmol.

E. L. Martola, J. L. Baum, “Central and peripheral corneal thickness,” Arch. Opththalmol. 79, 28–30 (1968).
[CrossRef]

Aust. J. Optom.

B. A. J. Clark, “Variations in corneal topography,” Aust. J. Optom. 56, 399–413 (1973).

Br. J. Ophthalmol.

R. F. Lowe, B. A. Clark, “Posterior corneal curvature,” Br. J. Ophthalmol. 57, 464–470 (1973).
[CrossRef] [PubMed]

D. M. Maurice, A. A. Giardini, “A simple optical apparatus for measuring the corneal thickness and the average thickness of the human cornea,” Br. J. Ophthalmol. 35, 169–177 (1951).
[CrossRef] [PubMed]

R. F. Lowe, “Central corneal thickness,” Br. J. Ophthalmol. 53, 824–826 (1969).
[CrossRef] [PubMed]

R. F. Lowe, “Anterior lens curvature,” Br. J. Ophthalmol. 56, 409–413 (1972).
[CrossRef] [PubMed]

R. F. Lowe, B. A. J. Clark, “Radius of curvature of the anterior lens surface,” Br. J. Ophthalmol. 57, 471–474 (1973).
[CrossRef] [PubMed]

Br. J. Physiol. Opt.

T. C. A. Jenkins, “Aberrations of the eye and their effects on vision: part 1,” Br. J. Physiol. Opt. 20, 59–91 (1963).

R. B. Mandell, R. St. Helen, “Mathematical model for the corneal contour,” Br. J. Physiol. Opt. 26, 183–197 (1971).

Brit. Med. J.

A. Sorsby, M. Sheridan, A. G. Leary, B. Benjamin, “Vision, visual acuity and ocular refraction in young men,” Brit. Med. J. 1, 1394–1398 (1960).

Can. J. Ophthalmol.

J. A. Parker, “Aspheric optics of the human lens,” Can. J. Ophthalmol. 7, 168–175 (1972).
[PubMed]

Chin. J. Ophthalmol.

C. S. Yu, D. Kao, C. T. Chang, “Measurement of the length of the visual axis by ultrasonography in 1789 eyes,” Chin. J. Ophthalmol. 15, 45–47 (1979).

Contacto

M. Townsley, “New knowledge of the corneal contour,” Contacto 14, 38–43 (1970).

Exp. Eye Res.

N. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
[CrossRef] [PubMed]

Int. Contact Lens Clin.

P. S. Soni, I. M. Borish, “A report on central and peripheral corneal thickness,” Int. Contact Lens Clin. 6, 66–70 (1979).

Invest. Ophthalmol. Visual Sci.

C. Roberts, “The accuracy of ‘power’ maps to display curvature data in corneal topography systems,” Invest. Ophthalmol. Visual Sci. 35, 3525–3532 (1994).

Invest. Ophthalmol. Visual Sci. (Suppl.)

A. G. Rivett, A. Ho, “The posterior corneal topography,” Invest. Ophthalmol. Visual Sci. (Suppl.) 32, 1001–1001 (1991).

M. Ye, X. X. Zhang, L. N. Thibos, A. Bradley, “A new single-surface model eye that accurately predicts chromatic and spherical aberrations of the human eye,” Invest. Ophthalmol. Visual Sci. (Suppl.) 34, 777 (1993).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Jpn. J. Clin. Ophthalmol.

S. Nakao, T. Ono, R. Nagata, K. Iwata, “The distribution of refractive index in the human crystalline lens,” Jpn. J. Clin. Ophthalmol. 23, 903–906 (1969).

Ophthalmic. Physiol. Opt.

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

G. Smith, B. K. Pierscionek, D. A. Atchison, “The optical modelling of the human lens,” Ophthalmic. Physiol. Opt. 11, 359–369 (1991).
[CrossRef] [PubMed]

H. L. Liou, N. A. Brennan, “The prediction of spherical aberration with schematic eyes,” Ophthalmic. Physiol. Opt. 16, 348–354 (1996).
[CrossRef] [PubMed]

J. M. Royston, M. C. M. Dunne, D. A. Barnes, “Measurement of the posterior corneal radius using slit lamp and Purkinje image techniques,” Ophthalmic. Physiol. Opt. 10, 385–388 (1990).
[CrossRef] [PubMed]

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

Opt. Acta

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

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

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[CrossRef]

Opt. Photon. News

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[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

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[CrossRef] [PubMed]

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A. Bradley, School of Optometry, Indiana University, Bloomington, Ind. 47405-3201 (personal communication, 1995): corrections to the Ye et al. abstract (Ref. 5): The refracting surface defined as Y=0.0899X2+0.0006X4 should be Y=0.0899X2+0.0005X4 instead.

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Figures (8)

Fig. 1
Fig. 1

Refractive-index distribution data of Pierscionek and Chan44 (circles). The four parabolic curves represent the various smoothed-lens refractive-index distributions with different weightings given to the experimental data points. A, weight=1-r; B, weight=1-r; C, weight=1-r4; D, no weighting (i.e., weighting=1 for all data points), where r is the normalized distance from the lens center.

Fig. 2
Fig. 2

Spherical-aberration values predicted by the new schematic eye, with various asphericity values Q for the posterior corneal surface (dashed curves) compared with the line of best linear fit (solid line) and range (shaded region) of empirical results.

Fig. 3
Fig. 3

Diagram showing the variation of corneal thickness given aspheric front and back surfaces.

Fig. 4
Fig. 4

Schematic drawing of the new schematic eye (see Table 6 for parameter values).

Fig. 5
Fig. 5

Comparison of the spherical aberration predicted by the new schematic eye with spherical aberrations estimated by various paraxial and finite model eyes and the mean experimental results.

Fig. 6
Fig. 6

Contribution of the gradient-index lens (GRIN) to the spherical aberration of the eye. Here +ve SA and -ve SA mean positive and negative spherical aberration, respectively.

Fig. 7
Fig. 7

Comparison of the chromatic aberration predicted by the new schematic eye with various experimental results.

Fig. 8
Fig. 8

Sine-wave polychromatic MTF for a 4-mm pupil calculated with horizontal gratings, compared with the most recent experimental data of Navarro et al.63 and Artal et al.62

Tables (6)

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Table 1 Axial Length Measurements Reported by Various Investigators

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Table 2 Summary of Experimental Results on Anterior Corneal Radius and Asphericity

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Table 3 Summary and Comparison of Results on Anterior and Posterior Corneal Radii of the Same Eyes

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Table 4 Summary of Experimental Results on Anterior and Posterior Lens Radius and Asphericity

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Table 5 Equivalent Powerand Axial Length of the New Schematic Eye When Different Weightings of Data Points Are Used in Curve Fitting the Gradient-Index Distribution of the Lens

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Table 6 Structural Parameters of the New Schematic Eye

Equations (10)

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x2+y2+(1+Q)z2-2zR=0,
y2+(1+Q)z2-2zR=0.
ρ=[1+(y)2]3/2y.
ρ=(R2-Qy2)3/2R2
Q=R2-(ρR2)2/3y2.
n(w, z)=n00+n01z+n02z2+n10w2,
n(water)=1.3847-0.1455λ+0.0961λ2,
n(wateratλμm)=n(waterat0.555μm)+0.0512-0.1455λ+0.0961λ2.
n(mediaaatλμm)=n(mediaat0.555μm)+0.0512-0.1455λ+0.0961λ2.
ϕ=hΔRx,

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