Abstract

The purpose of this work was to design ophthalmic lenses that correct peripheral refractive errors of human eyes along a meridian. We designed lenses with the tangential section of one surface based on a figured spheroid but figured in the tangential section only. The curvature of the sagittal section of this surface was adjusted separately. A merit function was used to modify these surfaces until the lenses had power errors that corrected the eye. Examples are presented of lenses that correct a schematic eye. They do excellent jobs of correcting the peripheral power errors of the eye and are relatively insensitive to small changes in fitting distance. We conclude that it is theoretically feasible to design lenses to correct peripheral refractive errors.

© 2002 Optical Society of America

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References

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  1. D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth-Heinemann, Oxford, UK, 2000), 147–149.
  2. C. E. Ferree, G. Rand, C. Hardy, “Refraction for the peripheral field of vision,” Arch. Ophthalmol. 9, 925–938 (1931).
    [CrossRef]
  3. T. C. A. Jenkins, “Aberrations of the eye and their effects on vision: part 2,” Br. J. Physiol. Opt. 20, 161–201 (1963).
    [PubMed]
  4. F. Rempt, J. Hoogerheide, W. P. H. Hoogenbloom, “Peripheral retinoscopy and the skiagram,” Ophthalmologica 162, 1–10 (1971).
    [CrossRef] [PubMed]
  5. G. Smith, M. Millodot, N. McBrien, “The effect of accommodation on oblique astigmatism and field curvature of the human eye,” Clin. Exp. Optom. 71, 119–125 (1988).
    [CrossRef]
  6. D. G. Green, “Regional variations in the visual acuity for interference fringes at the retina,” J. Physiol. (London) 207, 351–356 (1970).
  7. M. Millodot, C. A. Johnson, A. Lamont, H. W. Leibowitz, “Effect of dioptrics on peripheral visual acuity,” Vision Res. 15, 1357–1362 (1975).
    [CrossRef] [PubMed]
  8. L. Frisen, A. Glansholm, “Optical and neural resolution in peripheral vision,” Invest. Ophthalmol. 14, 528–536 (1975).
    [PubMed]
  9. F. Rempt, J. Hoogerheide, W. P. H. Hoogenbloom, “Influence of correction of peripheral refractive errors on peripheral static vision,” Ophthalmologica 173, 128–135 (1976).
    [CrossRef] [PubMed]
  10. C. A. Johnson, H. W. Leibowitz, M. Millodot, A. Lamont, “Peripheral visual acuity and refractive error: evidence for ‘two visual systems’?” Percept. Psychophys. 20, 460–462 (1976).
    [CrossRef]
  11. L. N. Thibos, “Acuity perimetry and the sampling theory of visual resolution,” Optom. Vision Sci. 75, 399–406 (1998).
    [CrossRef]
  12. H. W. Leibowitz, C. A. Johnson, E. Isabelle, “Peripheral motion detection and refractive error,” Science 177, 1207–1208 (1972).
    [CrossRef] [PubMed]
  13. Y-Z. Wang, L. N. Thibos, A. Bradley, “Effects of refractive error on detection acuity and resolution acuity in peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, 2134–2143 (1997).
  14. D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
    [CrossRef] [PubMed]
  15. D. A. Atchison, “Effect of defocus on visual field measurement,” Ophthalmic Physiol. Opt. 7, 259–265 (1987).
    [CrossRef] [PubMed]
  16. F. Fankhauser, J. M. Enoch, “The effects of blur upon perimetric thresholds,” Arch. Ophthalmol. 68, 240–251 (1962).
    [CrossRef] [PubMed]
  17. S. M. Drance, C. Wheeler, M. Pattullo, “The use of static perimetry in the early detection of glaucoma,” Can. J. Ophthalmol. 2, 249–258 (1967).
    [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  23. L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Report from the VSIA taskforce on standards for reporting optical aberrations of the eye,” J. Refract. Surg. 16, S654–S655 (2000).
    [PubMed]
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    [CrossRef]
  25. R. Navarro, E. Moreno, C. Dorronsoro, “Monochromatic aberrations and point-spread functions of the human eye across the visual field,” J. Opt. Soc. Am. A 15, 2522–2529 (1998).
    [CrossRef]

2000

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Report from the VSIA taskforce on standards for reporting optical aberrations of the eye,” J. Refract. Surg. 16, S654–S655 (2000).
[PubMed]

1999

1998

1997

Y-Z. Wang, L. N. Thibos, A. Bradley, “Effects of refractive error on detection acuity and resolution acuity in peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, 2134–2143 (1997).

1996

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

1992

1988

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

1987

D. A. Atchison, “Effect of defocus on visual field measurement,” Ophthalmic Physiol. Opt. 7, 259–265 (1987).
[CrossRef] [PubMed]

1985

1976

R. Noll, “Zernike aberrations and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
[CrossRef]

F. Rempt, J. Hoogerheide, W. P. H. Hoogenbloom, “Influence of correction of peripheral refractive errors on peripheral static vision,” Ophthalmologica 173, 128–135 (1976).
[CrossRef] [PubMed]

C. A. Johnson, H. W. Leibowitz, M. Millodot, A. Lamont, “Peripheral visual acuity and refractive error: evidence for ‘two visual systems’?” Percept. Psychophys. 20, 460–462 (1976).
[CrossRef]

1975

M. Millodot, C. A. Johnson, A. Lamont, H. W. Leibowitz, “Effect of dioptrics on peripheral visual acuity,” Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

L. Frisen, A. Glansholm, “Optical and neural resolution in peripheral vision,” Invest. Ophthalmol. 14, 528–536 (1975).
[PubMed]

1972

H. W. Leibowitz, C. A. Johnson, E. Isabelle, “Peripheral motion detection and refractive error,” Science 177, 1207–1208 (1972).
[CrossRef] [PubMed]

1971

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

1970

D. G. Green, “Regional variations in the visual acuity for interference fringes at the retina,” J. Physiol. (London) 207, 351–356 (1970).

1967

S. M. Drance, C. Wheeler, M. Pattullo, “The use of static perimetry in the early detection of glaucoma,” Can. J. Ophthalmol. 2, 249–258 (1967).
[PubMed]

1963

T. C. A. Jenkins, “Aberrations of the eye and their effects on vision: part 2,” Br. J. Physiol. Opt. 20, 161–201 (1963).
[PubMed]

1962

F. Fankhauser, J. M. Enoch, “The effects of blur upon perimetric thresholds,” Arch. Ophthalmol. 68, 240–251 (1962).
[CrossRef] [PubMed]

1931

C. E. Ferree, G. Rand, C. Hardy, “Refraction for the peripheral field of vision,” Arch. Ophthalmol. 9, 925–938 (1931).
[CrossRef]

Applegate, R. A.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Report from the VSIA taskforce on standards for reporting optical aberrations of the eye,” J. Refract. Surg. 16, S654–S655 (2000).
[PubMed]

Artal, P.

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

Atchison, D. A.

D. A. Atchison, “Spectacle lens design: a review,” Appl. Opt. 31, 3579–3585 (1992).
[CrossRef] [PubMed]

D. A. Atchison, “Effect of defocus on visual field measurement,” Ophthalmic Physiol. Opt. 7, 259–265 (1987).
[CrossRef] [PubMed]

G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, New York, 1997), p. 118.

D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth-Heinemann, Oxford, UK, 2000), 147–149.

Bescós, J.

Bradley, A.

Y-Z. Wang, L. N. Thibos, A. Bradley, “Effects of refractive error on detection acuity and resolution acuity in peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, 2134–2143 (1997).

Brainard, D. H.

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

Dorronsoro, C.

Drance, S. M.

S. M. Drance, C. Wheeler, M. Pattullo, “The use of static perimetry in the early detection of glaucoma,” Can. J. Ophthalmol. 2, 249–258 (1967).
[PubMed]

Enoch, J. M.

F. Fankhauser, J. M. Enoch, “The effects of blur upon perimetric thresholds,” Arch. Ophthalmol. 68, 240–251 (1962).
[CrossRef] [PubMed]

Escudero-Sanz, I.

Fankhauser, F.

F. Fankhauser, J. M. Enoch, “The effects of blur upon perimetric thresholds,” Arch. Ophthalmol. 68, 240–251 (1962).
[CrossRef] [PubMed]

Ferree, C. E.

C. E. Ferree, G. Rand, C. Hardy, “Refraction for the peripheral field of vision,” Arch. Ophthalmol. 9, 925–938 (1931).
[CrossRef]

Frisen, L.

L. Frisen, A. Glansholm, “Optical and neural resolution in peripheral vision,” Invest. Ophthalmol. 14, 528–536 (1975).
[PubMed]

Glansholm, A.

L. Frisen, A. Glansholm, “Optical and neural resolution in peripheral vision,” Invest. Ophthalmol. 14, 528–536 (1975).
[PubMed]

Green, D. G.

D. G. Green, “Regional variations in the visual acuity for interference fringes at the retina,” J. Physiol. (London) 207, 351–356 (1970).

Hardy, C.

C. E. Ferree, G. Rand, C. Hardy, “Refraction for the peripheral field of vision,” Arch. Ophthalmol. 9, 925–938 (1931).
[CrossRef]

Hoogenbloom, W. P. H.

F. Rempt, J. Hoogerheide, W. P. H. Hoogenbloom, “Influence of correction of peripheral refractive errors on peripheral static vision,” Ophthalmologica 173, 128–135 (1976).
[CrossRef] [PubMed]

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

Hoogerheide, J.

F. Rempt, J. Hoogerheide, W. P. H. Hoogenbloom, “Influence of correction of peripheral refractive errors on peripheral static vision,” Ophthalmologica 173, 128–135 (1976).
[CrossRef] [PubMed]

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

Isabelle, E.

H. W. Leibowitz, C. A. Johnson, E. Isabelle, “Peripheral motion detection and refractive error,” Science 177, 1207–1208 (1972).
[CrossRef] [PubMed]

Jalie, M.

M. Jalie, Principles of Ophthalmic Lenses, 4th ed. (Association of Dispensing Opticians, London, 1984).

Jenkins, T. C. A.

T. C. A. Jenkins, “Aberrations of the eye and their effects on vision: part 2,” Br. J. Physiol. Opt. 20, 161–201 (1963).
[PubMed]

Johnson, C. A.

C. A. Johnson, H. W. Leibowitz, M. Millodot, A. Lamont, “Peripheral visual acuity and refractive error: evidence for ‘two visual systems’?” Percept. Psychophys. 20, 460–462 (1976).
[CrossRef]

M. Millodot, C. A. Johnson, A. Lamont, H. W. Leibowitz, “Effect of dioptrics on peripheral visual acuity,” Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

H. W. Leibowitz, C. A. Johnson, E. Isabelle, “Peripheral motion detection and refractive error,” Science 177, 1207–1208 (1972).
[CrossRef] [PubMed]

Lamont, A.

C. A. Johnson, H. W. Leibowitz, M. Millodot, A. Lamont, “Peripheral visual acuity and refractive error: evidence for ‘two visual systems’?” Percept. Psychophys. 20, 460–462 (1976).
[CrossRef]

M. Millodot, C. A. Johnson, A. Lamont, H. W. Leibowitz, “Effect of dioptrics on peripheral visual acuity,” Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

Leibowitz, H. W.

C. A. Johnson, H. W. Leibowitz, M. Millodot, A. Lamont, “Peripheral visual acuity and refractive error: evidence for ‘two visual systems’?” Percept. Psychophys. 20, 460–462 (1976).
[CrossRef]

M. Millodot, C. A. Johnson, A. Lamont, H. W. Leibowitz, “Effect of dioptrics on peripheral visual acuity,” Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

H. W. Leibowitz, C. A. Johnson, E. Isabelle, “Peripheral motion detection and refractive error,” Science 177, 1207–1208 (1972).
[CrossRef] [PubMed]

McBrien, N.

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

McMahon, M. J.

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

Millodot, M.

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

C. A. Johnson, H. W. Leibowitz, M. Millodot, A. Lamont, “Peripheral visual acuity and refractive error: evidence for ‘two visual systems’?” Percept. Psychophys. 20, 460–462 (1976).
[CrossRef]

M. Millodot, C. A. Johnson, A. Lamont, H. W. Leibowitz, “Effect of dioptrics on peripheral visual acuity,” Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

Moreno, E.

Navarro, R.

Noll, R.

Pattullo, M.

S. M. Drance, C. Wheeler, M. Pattullo, “The use of static perimetry in the early detection of glaucoma,” Can. J. Ophthalmol. 2, 249–258 (1967).
[PubMed]

Rand, G.

C. E. Ferree, G. Rand, C. Hardy, “Refraction for the peripheral field of vision,” Arch. Ophthalmol. 9, 925–938 (1931).
[CrossRef]

Rempt, F.

F. Rempt, J. Hoogerheide, W. P. H. Hoogenbloom, “Influence of correction of peripheral refractive errors on peripheral static vision,” Ophthalmologica 173, 128–135 (1976).
[CrossRef] [PubMed]

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

Santamari´a, J.

Schwiegerling, J. T.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Report from the VSIA taskforce on standards for reporting optical aberrations of the eye,” J. Refract. Surg. 16, S654–S655 (2000).
[PubMed]

Smith, G.

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

G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, New York, 1997), p. 118.

D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth-Heinemann, Oxford, UK, 2000), 147–149.

Thibos, L. N.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Report from the VSIA taskforce on standards for reporting optical aberrations of the eye,” J. Refract. Surg. 16, S654–S655 (2000).
[PubMed]

L. N. Thibos, “Acuity perimetry and the sampling theory of visual resolution,” Optom. Vision Sci. 75, 399–406 (1998).
[CrossRef]

Y-Z. Wang, L. N. Thibos, A. Bradley, “Effects of refractive error on detection acuity and resolution acuity in peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, 2134–2143 (1997).

Wang, Y-Z.

Y-Z. Wang, L. N. Thibos, A. Bradley, “Effects of refractive error on detection acuity and resolution acuity in peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, 2134–2143 (1997).

Webb, R.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Report from the VSIA taskforce on standards for reporting optical aberrations of the eye,” J. Refract. Surg. 16, S654–S655 (2000).
[PubMed]

Wheeler, C.

S. M. Drance, C. Wheeler, M. Pattullo, “The use of static perimetry in the early detection of glaucoma,” Can. J. Ophthalmol. 2, 249–258 (1967).
[PubMed]

Williams, D. R.

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

Appl. Opt.

Arch. Ophthalmol.

C. E. Ferree, G. Rand, C. Hardy, “Refraction for the peripheral field of vision,” Arch. Ophthalmol. 9, 925–938 (1931).
[CrossRef]

F. Fankhauser, J. M. Enoch, “The effects of blur upon perimetric thresholds,” Arch. Ophthalmol. 68, 240–251 (1962).
[CrossRef] [PubMed]

Br. J. Physiol. Opt.

T. C. A. Jenkins, “Aberrations of the eye and their effects on vision: part 2,” Br. J. Physiol. Opt. 20, 161–201 (1963).
[PubMed]

Can. J. Ophthalmol.

S. M. Drance, C. Wheeler, M. Pattullo, “The use of static perimetry in the early detection of glaucoma,” Can. J. Ophthalmol. 2, 249–258 (1967).
[PubMed]

Clin. Exp. Optom.

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

Invest. Ophthalmol.

L. Frisen, A. Glansholm, “Optical and neural resolution in peripheral vision,” Invest. Ophthalmol. 14, 528–536 (1975).
[PubMed]

Invest. Ophthalmol. Visual Sci.

Y-Z. Wang, L. N. Thibos, A. Bradley, “Effects of refractive error on detection acuity and resolution acuity in peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, 2134–2143 (1997).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Physiol. (London)

D. G. Green, “Regional variations in the visual acuity for interference fringes at the retina,” J. Physiol. (London) 207, 351–356 (1970).

J. Refract. Surg.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Report from the VSIA taskforce on standards for reporting optical aberrations of the eye,” J. Refract. Surg. 16, S654–S655 (2000).
[PubMed]

Ophthalmic Physiol. Opt.

D. A. Atchison, “Effect of defocus on visual field measurement,” Ophthalmic Physiol. Opt. 7, 259–265 (1987).
[CrossRef] [PubMed]

Ophthalmologica

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

F. Rempt, J. Hoogerheide, W. P. H. Hoogenbloom, “Influence of correction of peripheral refractive errors on peripheral static vision,” Ophthalmologica 173, 128–135 (1976).
[CrossRef] [PubMed]

Optom. Vision Sci.

L. N. Thibos, “Acuity perimetry and the sampling theory of visual resolution,” Optom. Vision Sci. 75, 399–406 (1998).
[CrossRef]

Percept. Psychophys.

C. A. Johnson, H. W. Leibowitz, M. Millodot, A. Lamont, “Peripheral visual acuity and refractive error: evidence for ‘two visual systems’?” Percept. Psychophys. 20, 460–462 (1976).
[CrossRef]

Science

H. W. Leibowitz, C. A. Johnson, E. Isabelle, “Peripheral motion detection and refractive error,” Science 177, 1207–1208 (1972).
[CrossRef] [PubMed]

Vision Res.

M. Millodot, C. A. Johnson, A. Lamont, H. W. Leibowitz, “Effect of dioptrics on peripheral visual acuity,” Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

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

Other

D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth-Heinemann, Oxford, UK, 2000), 147–149.

M. Jalie, Principles of Ophthalmic Lenses, 4th ed. (Association of Dispensing Opticians, London, 1984).

G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, New York, 1997), p. 118.

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Figures (19)

Fig. 1
Fig. 1

Mean values of sagittal and tangential power errors. Solid curves are means fitted by Atchison and Smith.1

Fig. 2
Fig. 2

(a) Sagittal and tangential errors. (b) The sagittal and tangential object positions that would place the image at the retina. The vergences corresponding to these positions are the sagittal and tangential power errors as measured in object space. Both power errors are negative in this figure.

Fig. 3
Fig. 3

Ideal tangential correction by a lens. A thin beam from infinity is refracted and imaged by the lens to the point T, which is conjugate to the retina in the tangential section.

Fig. 4
Fig. 4

Imperfect correction in the tangential section by the lens. The lens does not have the correct power at the refraction point: The point conjugate to T is T. T is at a finite distance but should be at infinity.

Fig. 5
Fig. 5

Formation of the surface in the sagittal section. A curve of radius rh is placed on the surface to provide the correct sagittal power in the lens.

Fig. 6
Fig. 6

Ray leaving the pupil from the point P(ρ cos φ, ρ sin φ).

Fig. 7
Fig. 7

Ray-trace layout used to calculate wave-front aberrations.

Fig. 8
Fig. 8

Example of the reference surface of constant phase.

Fig. 9
Fig. 9

Sagittal and tangential power errors of the zero-accommodation Navarro schematic eye in emmetropic, axial myopic, and axial hypermetropic variants. The thick curves are means fitted by Atchison and Smith1 to the experimental data shown in Fig. 1.

Fig. 10
Fig. 10

Shape of the back surface of the lens designed to correct the peripheral power errors of the Navarro emmetropic eye. Note the difference in scale of the sag compared with that for the xy coordinates.

Fig. 11
Fig. 11

Residual sagittal and tangential power errors for the lens design to correct the peripheral aberrations of the Navarro emmetropic eye, at vertex distances of 18, 20 (design distance), and 22 mm.

Fig. 12
Fig. 12

Aberration of the lens in waves to correct the emmetropic eye as a function of normalized coordinates in the entrance pupil, for (a) 25° field angle and (b) 50° field angle. Pupil size 8 mm, wavelength 633 nm. Classical (i.e., Taylor) piston and tilt have been removed. Peak-to-valley error range and root-mean-square error are given.

Fig. 13
Fig. 13

Same as Fig. 12, but for object fields 5° away from the design meridian.

Fig. 14
Fig. 14

Residual sagittal and tangential power errors for the lens designs to correct the peripheral aberrations of the Navarro 5 D myopic and 5 D hypermetropic eyes, at the design distance of 20 mm.

Fig. 15
Fig. 15

Aberration of the lens in waves to correct the 5 D myopic eye as a function of normalized coordinates in the entrance pupil, for (a) 25° field angle and (b) 50° field angle. Pupil size 8 mm, wavelength 633 nm. Classical (i.e., Taylor) piston and tilt have been removed. Peak-to-valley error range and root-mean-square error are given.

Fig. 16
Fig. 16

Aberration of the lens in waves to correct the 5 D hypermetropic eye as a function of normalized coordinates in the entrance pupil, for (a) 25° field angle, and (b) 45° field angle. The rest as for Fig. 15.

Fig. 17
Fig. 17

Same as Fig. 15, but for object fields 5° away from the design meridian.

Fig. 18
Fig. 18

Same as Fig. 16, but for object fields 5° away from the design meridian.

Fig. 19
Fig. 19

Aberration in waves of the emmetropic Navarro model eye at 40° field angle (a) by itself, (b) with full refractive correction, and (c) with the design lens in place. Classical (i.e., Taylor) piston and tilt have been removed. Pupil size 6 mm, wavelength 633 nm.

Tables (6)

Tables Icon

Table 1 Open Ray-Tracing Data for the Tangential Rays

Tables Icon

Table 2 Open Ray-Tracing Data for the Sagittal Rays

Tables Icon

Table 3 Lens to Correct the Emmetropic Eye

Tables Icon

Table 4 Wave Aberration Coefficients (Waves at 633 nm), for an 8-mm-Diameter Pupil, of the Lenses To Correct Peripheral Refractive Errors of the Navarro Eye at Different Values of θ a

Tables Icon

Table 5 Lens to Correct 5 D Myopia

Tables Icon

Table 6 Lens to Correct 5 D Hypermetropia

Equations (29)

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F1=(Rx-F2)[1+(Rx-F2)d/μ],
C1=F1/(μ-1),C2=F2/(1-μ).
Zo(Y)=CY21+(1-C2Y2).
Zf(Y)=f1Y4+f2Y6+ .
Zt(Y)=Zo(Y)+Zf (Y).
Ct(Y)=d2Zt(Y)/dY2[1+(dZt(Y)/dY)2]3/2.
Y=Ya+mata = Yb+mbtb,
Z=Za+nata = Zb+nbtb,
meritfunction=(vergenceoffinalrays)2.
X2+[Z-Zt(Y)-rh]2=rh2.
Z2-[2(Zt(Y)+rh)]Z+[X2+Zt(Y)2+2Zt(Y)rh]=0.
ChZ2-[2(ChZt(Y)+1)]Z
+Ch[X2+Zt(Y)2]+2Zt(Y)=0.
Z(X, Y)=[ChZt(Y)+1]-[ChZt(Y)+12]-Ch{Ch[X2+Zt(Y)2]+2Zt(Y)}Ch.
Z(X, Y)=Ch[X2+Zt(Y)2]+2Zt(Y)(ChZt(Y)+1)+[ChZt(Y)+1]2-Ch{Ch[X2+Zt(Y)2]+2Zt(Y)}.
Ch(Y)=c0+c1Y2+c2Y4+ .
(-dZ/dX, -dZ/dY,+1)
l=-dZ/dX(dZ/dX)2+(dZ/dY)2+1,
m=-dZ/dY(dZ/dX)2+(dZ/dY)2+1,
n=1(dZ/dX)2+(dZ/dY)2+1.
l=ρx/(ls2+ρx2),m=lssin θy/(ls2+ρx2),
n=lscos θy/(ls2+ρx2),
θy=cos-1[cos θ/1+(ρy2/lt2)+2ρysin θ/lt].
ltilt=cos α,
mtilt=sin α sin θy,
ntilt=sin α cos θy,
α=cos-1(l)+βx.
Zf (Y)=f1(Y/Ymax)4+f2(Y/Ymax)6+
Ch(Y) =c0+c1(Y/Ymax)2+c2(Y/Ymax)4 +,

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