Abstract

We studied the mechanism of compensation of aberrations within the young human eye by using experimental data and advanced ray-tracing modeling. Corneal and ocular aberrations along with the alignment properties (angle kappa, lens tilt, and decentration) were measured in eyes with different refractive errors. Predictions from individualized ray-tracing optical models were compared with the actual measurements. Ocular spherical aberration was, in general, smaller than corneal spherical aberration without relation to refractive error. However, horizontal coma compensation was found to be significantly larger for hyperopic eyes where angle kappa tended to also be larger. We propose a simple analytical model of the relationship between the corneal coma compensation effect with the field angle and corneal and crystalline shape factors. The actual shape factors corresponded approximately to the optimum shapes that automatically provide this coma compensation. We showed that the eye behaves as an aplanatic optical system, an optimized design solution rendering stable retinal image quality for different ocular geometries.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
  2. P. Artal and A. Guirao, "Contribution of cornea and lens to the aberrations of the human eye," Opt. Lett. 23, 1713-1715 (1998).
    [CrossRef]
  3. P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by the internal optics in the human eye," J. Vision 1, 1-8 (2001).
    [CrossRef]
  4. P. Artal, E. Berrio, A. Guirao, and P. Piers, "Contribution of the cornea and internal surfaces to the change of ocular aberrations with age," J. Opt. Soc. Am. 19, 137-143 (2002).
    [CrossRef]
  5. A. Glasser and M. C. W. Campbell, "Presbyopia and the optical changes in the human crystalline lens with age," Vision Res. 38, 209-229 (1998).
    [CrossRef] [PubMed]
  6. A. Guirao, M. Redondo, and P. Artal, "Optical aberrations of the human cornea as a function of age," J. Opt. Soc. Am. A 7, 1697-1702 (2000).
    [CrossRef]
  7. A. Guirao, M. Redondo, E. Geraghty, P. Piers, S. Norrby, and P. Artal, "Corneal optical aberrations and retinal image quality in patients in whom monofocal intraocular lenses were implanted," Arch. Ophthalmol. (Chicago) 120, 1143-1151 (2002).
  8. J. T. Holladay, P. A. Piers, G. Koranyi, M. van der Mooren, and N. E. Norrby, "A new intraocular lens design to reduce spherical aberration of pseudophakic eyes," J. Refract. Surg. 18, 683-691 (2002).
    [PubMed]
  9. U. Mester, P. Dillinger, and N. Anterist, "Impact of a modified optic design on visual function: clinical comparative study," J. Cataract Refractive Surg. 29, 652-660 (2003).
    [CrossRef]
  10. R. Bellucci, A. Scialdone, L. Buratto, S. Morselli, C. Chierego, A. Criscouli, G. Moretti, and P. Piers, "Visual acuity and contrast sensitivity comparison between Tecnis and AcrySof SA60AT intraocular lenses: A multicenter randomized study," J. Cataract Refractive Surg. 31, 712-717 (2005).
    [CrossRef]
  11. J. E. Kelly, T. Mihashi, and H. C. Howland, "Compensation of corneal horizontal/vertical astigmatism, lateral coma, and spherical aberration by internal optics of the eye," J. Vision 4, 262-271 (2004).
    [CrossRef]
  12. P. Artal, A. Benito, and J. Tabernero, "The human eye is an example of robust optical design," J. Vision 6, 1-7 (2006).
    [CrossRef]
  13. Y. Le Grand and S. G. El Hage, Physiological Optics (Springer Series in Optical Sciences, 1980).
  14. The same angle formed by the line of sight and the pupillary axis is referred to in the literature with two different names: for instance, kappa in and lambda in and others. The reason for this notation discrepancy can be found in the historical references and the intrinsic confusion with ocular angle definitions. In the clinical literature only kappa is commonly used, while lambda is still used by some basic researchers. According to Emsley , the first definition of angle kappa was given by Landolt as "the angle between the visual axis and the so-called central pupillary line (the pupillary axis)." This definition involved the visual axis, as the line connecting the fixation point with the object nodal point of the eye. This is not the same as the line of sight, connecting the center of the entrance pupil and the fixation point. Therefore this definition is not what was used by Le Grand and adopted here. Angle lambda was defined by Lancaster (cited in ) as the line connecting the pupillary axis and the line of sight. However, Le Grand and El Hage redefined angle kappa exactly as the angle lambda defined by Lancaster. The reason to do this is that they understand the term "visual axis" in Landolt's original definition of kappa as the line of sight, since the nodal point in the eye is a purely paraxial theoretical concept that cannot be measured. Quoting Le Grand's book, p. 73: "It is not very logical to confuse geometric and fictitious ideas (optical and visual axis) and experimental ideas (pupillary axis and the principal line of sight)." Therefore, Le Grand maintained the old name of kappa but with the modern definition of lambda by Lancaster. Moreover, in practical terms, the two angles are nearly identical as stated by Le Grand : "It seems unnecessary to distinguish this (angle lambda) from kappa which is practically equal to it when the point of fixation is not very close to the eye." We used in the manuscript this meaning for angle kappa, but the reader should be aware of the other accepted name (lambda) for the same angle to avoid confusion. A standard definition of ocular angles is required to unify terms in both basic and clinical literature. In the case of this angle, keeping only the name kappa would be, in our opinion, the most adequate.
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    [CrossRef]
  18. D. L. Guyton, H. Uozato, and H. J. Wisnicki, "Rapid determination of intraocular lens tilt and decentration through the undilated pupil," Ophthalmologica 97, 1259-1264 (1990).
  19. J. C. Barry, M. C. M. Dunne, and T. Kirschkamp, "Phakometric measurement of ocular surface radius of curvature and alignment: evaluation of method with physical model eyes," Ophthalmic Physiol. Opt. 21, 450-460 (2001).
    [CrossRef]
  20. P. Rosales and S. Marcos, "Phokometry and lens tilt and decentration using a custom-developed Purkinje imaging apparatus: validation and measurements," J. Opt. Soc. Am. A 23, 509-520 (2006).
    [CrossRef]
  21. J. Tabernero, A. Benito, V. Nourrit, and P. Artal, "Instrument for measuring the misalignments of ocular surfaces," Opt. Express 14, 10945-10956 (2006).
    [CrossRef]
  22. H. Howland, A. Glasser, and R. Applegate, "Polynomial approximations of corneal surfaces and corneal curvature topography," Tech. Dig. Ser. Opt. Soc. Am. 3, 34-37 (1992).
  23. A. Guirao and P. Artal, "Corneal wave aberration from videokeratography: accuracy and limitations of the procedure," J. Opt. Soc. Am. A 17, 955-965 (2000).
    [CrossRef]
  24. J. C. Liang, B. Grimm, S. Goelz, and J. F. Bille, "Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor," J. Opt. Soc. Am. A 11, 1949-1957 (1994).
    [CrossRef]
  25. P. M. Prieto, F. Vargas-Martín, S. Goelz, and P. Artal, "Analysis of the performance of the Hartmann-Shack sensor in the human eye," J. Opt. Soc. Am. A 17, 1388-1398 (2000).
    [CrossRef]
  26. J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, "Predicting the optical performance of eyes implanted with IOLs correcting spherical aberration," Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
    [CrossRef]
  27. H. L. Liou and N. A. Brennan, "Anatomically accurate, finite model eye for optical modelling," J. Opt. Soc. Am. A 14, 1684-1695 (1997).
    [CrossRef]
  28. V. N. Mahajan, Aberration Theory Made Simple (SPIE ,1991).
  29. L. N. Hazra and C. A. Delisle, "Primary aberrations of a thin lens with different object and image space media," J. Opt. Soc. Am. A 15, 945-953 (1998).
    [CrossRef]
  30. V. N. Mahajan, Optical Imaging and Aberrations. Part I. Ray Geometrical Optics (SPIE ,1998).
  31. D. A. Atchison, C. E. Jones, K. L. Schmid, N. Prichard, J. M. Pope, W. E. Strugnell, and R. A. Riley, "Eye shape in emmetropia and myopia," Invest. Ophthalmol. Visual Sci. 45, 3380-3386 (2004).
    [CrossRef]

2007 (1)

2006 (4)

P. Rosales and S. Marcos, "Phokometry and lens tilt and decentration using a custom-developed Purkinje imaging apparatus: validation and measurements," J. Opt. Soc. Am. A 23, 509-520 (2006).
[CrossRef]

J. Tabernero, A. Benito, V. Nourrit, and P. Artal, "Instrument for measuring the misalignments of ocular surfaces," Opt. Express 14, 10945-10956 (2006).
[CrossRef]

P. Artal, A. Benito, and J. Tabernero, "The human eye is an example of robust optical design," J. Vision 6, 1-7 (2006).
[CrossRef]

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, "Predicting the optical performance of eyes implanted with IOLs correcting spherical aberration," Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
[CrossRef]

2005 (1)

R. Bellucci, A. Scialdone, L. Buratto, S. Morselli, C. Chierego, A. Criscouli, G. Moretti, and P. Piers, "Visual acuity and contrast sensitivity comparison between Tecnis and AcrySof SA60AT intraocular lenses: A multicenter randomized study," J. Cataract Refractive Surg. 31, 712-717 (2005).
[CrossRef]

2004 (2)

J. E. Kelly, T. Mihashi, and H. C. Howland, "Compensation of corneal horizontal/vertical astigmatism, lateral coma, and spherical aberration by internal optics of the eye," J. Vision 4, 262-271 (2004).
[CrossRef]

D. A. Atchison, C. E. Jones, K. L. Schmid, N. Prichard, J. M. Pope, W. E. Strugnell, and R. A. Riley, "Eye shape in emmetropia and myopia," Invest. Ophthalmol. Visual Sci. 45, 3380-3386 (2004).
[CrossRef]

2003 (1)

U. Mester, P. Dillinger, and N. Anterist, "Impact of a modified optic design on visual function: clinical comparative study," J. Cataract Refractive Surg. 29, 652-660 (2003).
[CrossRef]

2002 (3)

P. Artal, E. Berrio, A. Guirao, and P. Piers, "Contribution of the cornea and internal surfaces to the change of ocular aberrations with age," J. Opt. Soc. Am. 19, 137-143 (2002).
[CrossRef]

A. Guirao, M. Redondo, E. Geraghty, P. Piers, S. Norrby, and P. Artal, "Corneal optical aberrations and retinal image quality in patients in whom monofocal intraocular lenses were implanted," Arch. Ophthalmol. (Chicago) 120, 1143-1151 (2002).

J. T. Holladay, P. A. Piers, G. Koranyi, M. van der Mooren, and N. E. Norrby, "A new intraocular lens design to reduce spherical aberration of pseudophakic eyes," J. Refract. Surg. 18, 683-691 (2002).
[PubMed]

2001 (2)

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by the internal optics in the human eye," J. Vision 1, 1-8 (2001).
[CrossRef]

J. C. Barry, M. C. M. Dunne, and T. Kirschkamp, "Phakometric measurement of ocular surface radius of curvature and alignment: evaluation of method with physical model eyes," Ophthalmic Physiol. Opt. 21, 450-460 (2001).
[CrossRef]

2000 (3)

1998 (4)

A. Glasser and M. C. W. Campbell, "Presbyopia and the optical changes in the human crystalline lens with age," Vision Res. 38, 209-229 (1998).
[CrossRef] [PubMed]

P. Artal and A. Guirao, "Contribution of cornea and lens to the aberrations of the human eye," Opt. Lett. 23, 1713-1715 (1998).
[CrossRef]

L. N. Hazra and C. A. Delisle, "Primary aberrations of a thin lens with different object and image space media," J. Opt. Soc. Am. A 15, 945-953 (1998).
[CrossRef]

V. N. Mahajan, Optical Imaging and Aberrations. Part I. Ray Geometrical Optics (SPIE ,1998).

1997 (1)

1994 (1)

1992 (1)

H. Howland, A. Glasser, and R. Applegate, "Polynomial approximations of corneal surfaces and corneal curvature topography," Tech. Dig. Ser. Opt. Soc. Am. 3, 34-37 (1992).

1991 (1)

V. N. Mahajan, Aberration Theory Made Simple (SPIE ,1991).

1990 (1)

D. L. Guyton, H. Uozato, and H. J. Wisnicki, "Rapid determination of intraocular lens tilt and decentration through the undilated pupil," Ophthalmologica 97, 1259-1264 (1990).

1973 (1)

Anterist, N.

U. Mester, P. Dillinger, and N. Anterist, "Impact of a modified optic design on visual function: clinical comparative study," J. Cataract Refractive Surg. 29, 652-660 (2003).
[CrossRef]

Applegate, R.

H. Howland, A. Glasser, and R. Applegate, "Polynomial approximations of corneal surfaces and corneal curvature topography," Tech. Dig. Ser. Opt. Soc. Am. 3, 34-37 (1992).

Artal, P.

J. Tabernero, P. Piers, and P. Artal, "Intraocular lens to correct corneal coma," Opt. Lett. 32, 406-408 (2007).
[CrossRef]

J. Tabernero, A. Benito, V. Nourrit, and P. Artal, "Instrument for measuring the misalignments of ocular surfaces," Opt. Express 14, 10945-10956 (2006).
[CrossRef]

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, "Predicting the optical performance of eyes implanted with IOLs correcting spherical aberration," Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
[CrossRef]

P. Artal, A. Benito, and J. Tabernero, "The human eye is an example of robust optical design," J. Vision 6, 1-7 (2006).
[CrossRef]

A. Guirao, M. Redondo, E. Geraghty, P. Piers, S. Norrby, and P. Artal, "Corneal optical aberrations and retinal image quality in patients in whom monofocal intraocular lenses were implanted," Arch. Ophthalmol. (Chicago) 120, 1143-1151 (2002).

P. Artal, E. Berrio, A. Guirao, and P. Piers, "Contribution of the cornea and internal surfaces to the change of ocular aberrations with age," J. Opt. Soc. Am. 19, 137-143 (2002).
[CrossRef]

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by the internal optics in the human eye," J. Vision 1, 1-8 (2001).
[CrossRef]

A. Guirao, M. Redondo, and P. Artal, "Optical aberrations of the human cornea as a function of age," J. Opt. Soc. Am. A 7, 1697-1702 (2000).
[CrossRef]

A. Guirao and P. Artal, "Corneal wave aberration from videokeratography: accuracy and limitations of the procedure," J. Opt. Soc. Am. A 17, 955-965 (2000).
[CrossRef]

P. M. Prieto, F. Vargas-Martín, S. Goelz, and P. Artal, "Analysis of the performance of the Hartmann-Shack sensor in the human eye," J. Opt. Soc. Am. A 17, 1388-1398 (2000).
[CrossRef]

P. Artal and A. Guirao, "Contribution of cornea and lens to the aberrations of the human eye," Opt. Lett. 23, 1713-1715 (1998).
[CrossRef]

Atchison, D. A.

D. A. Atchison, C. E. Jones, K. L. Schmid, N. Prichard, J. M. Pope, W. E. Strugnell, and R. A. Riley, "Eye shape in emmetropia and myopia," Invest. Ophthalmol. Visual Sci. 45, 3380-3386 (2004).
[CrossRef]

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heineman, 2000).

Barry, J. C.

J. C. Barry, M. C. M. Dunne, and T. Kirschkamp, "Phakometric measurement of ocular surface radius of curvature and alignment: evaluation of method with physical model eyes," Ophthalmic Physiol. Opt. 21, 450-460 (2001).
[CrossRef]

Bellucci, R.

R. Bellucci, A. Scialdone, L. Buratto, S. Morselli, C. Chierego, A. Criscouli, G. Moretti, and P. Piers, "Visual acuity and contrast sensitivity comparison between Tecnis and AcrySof SA60AT intraocular lenses: A multicenter randomized study," J. Cataract Refractive Surg. 31, 712-717 (2005).
[CrossRef]

Benito, A.

P. Artal, A. Benito, and J. Tabernero, "The human eye is an example of robust optical design," J. Vision 6, 1-7 (2006).
[CrossRef]

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, "Predicting the optical performance of eyes implanted with IOLs correcting spherical aberration," Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
[CrossRef]

J. Tabernero, A. Benito, V. Nourrit, and P. Artal, "Instrument for measuring the misalignments of ocular surfaces," Opt. Express 14, 10945-10956 (2006).
[CrossRef]

Berny, F.

Berrio, E.

P. Artal, E. Berrio, A. Guirao, and P. Piers, "Contribution of the cornea and internal surfaces to the change of ocular aberrations with age," J. Opt. Soc. Am. 19, 137-143 (2002).
[CrossRef]

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by the internal optics in the human eye," J. Vision 1, 1-8 (2001).
[CrossRef]

Bille, J. F.

Brennan, N. A.

Buratto, L.

R. Bellucci, A. Scialdone, L. Buratto, S. Morselli, C. Chierego, A. Criscouli, G. Moretti, and P. Piers, "Visual acuity and contrast sensitivity comparison between Tecnis and AcrySof SA60AT intraocular lenses: A multicenter randomized study," J. Cataract Refractive Surg. 31, 712-717 (2005).
[CrossRef]

Campbell, M. C. W.

A. Glasser and M. C. W. Campbell, "Presbyopia and the optical changes in the human crystalline lens with age," Vision Res. 38, 209-229 (1998).
[CrossRef] [PubMed]

Chierego, C.

R. Bellucci, A. Scialdone, L. Buratto, S. Morselli, C. Chierego, A. Criscouli, G. Moretti, and P. Piers, "Visual acuity and contrast sensitivity comparison between Tecnis and AcrySof SA60AT intraocular lenses: A multicenter randomized study," J. Cataract Refractive Surg. 31, 712-717 (2005).
[CrossRef]

Criscouli, A.

R. Bellucci, A. Scialdone, L. Buratto, S. Morselli, C. Chierego, A. Criscouli, G. Moretti, and P. Piers, "Visual acuity and contrast sensitivity comparison between Tecnis and AcrySof SA60AT intraocular lenses: A multicenter randomized study," J. Cataract Refractive Surg. 31, 712-717 (2005).
[CrossRef]

Delisle, C. A.

Dillinger, P.

U. Mester, P. Dillinger, and N. Anterist, "Impact of a modified optic design on visual function: clinical comparative study," J. Cataract Refractive Surg. 29, 652-660 (2003).
[CrossRef]

Dunne, M. C. M.

J. C. Barry, M. C. M. Dunne, and T. Kirschkamp, "Phakometric measurement of ocular surface radius of curvature and alignment: evaluation of method with physical model eyes," Ophthalmic Physiol. Opt. 21, 450-460 (2001).
[CrossRef]

El Hage, S. G.

Emsley, H. H.

H. H. Emsley, Visual Optics (Hatton Press, 1948).

Geraghty, E.

A. Guirao, M. Redondo, E. Geraghty, P. Piers, S. Norrby, and P. Artal, "Corneal optical aberrations and retinal image quality in patients in whom monofocal intraocular lenses were implanted," Arch. Ophthalmol. (Chicago) 120, 1143-1151 (2002).

Glasser, A.

A. Glasser and M. C. W. Campbell, "Presbyopia and the optical changes in the human crystalline lens with age," Vision Res. 38, 209-229 (1998).
[CrossRef] [PubMed]

H. Howland, A. Glasser, and R. Applegate, "Polynomial approximations of corneal surfaces and corneal curvature topography," Tech. Dig. Ser. Opt. Soc. Am. 3, 34-37 (1992).

Goelz, S.

Grimm, B.

Guirao, A.

A. Guirao, M. Redondo, E. Geraghty, P. Piers, S. Norrby, and P. Artal, "Corneal optical aberrations and retinal image quality in patients in whom monofocal intraocular lenses were implanted," Arch. Ophthalmol. (Chicago) 120, 1143-1151 (2002).

P. Artal, E. Berrio, A. Guirao, and P. Piers, "Contribution of the cornea and internal surfaces to the change of ocular aberrations with age," J. Opt. Soc. Am. 19, 137-143 (2002).
[CrossRef]

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by the internal optics in the human eye," J. Vision 1, 1-8 (2001).
[CrossRef]

A. Guirao, M. Redondo, and P. Artal, "Optical aberrations of the human cornea as a function of age," J. Opt. Soc. Am. A 7, 1697-1702 (2000).
[CrossRef]

A. Guirao and P. Artal, "Corneal wave aberration from videokeratography: accuracy and limitations of the procedure," J. Opt. Soc. Am. A 17, 955-965 (2000).
[CrossRef]

P. Artal and A. Guirao, "Contribution of cornea and lens to the aberrations of the human eye," Opt. Lett. 23, 1713-1715 (1998).
[CrossRef]

Guyton, D. L.

D. L. Guyton, H. Uozato, and H. J. Wisnicki, "Rapid determination of intraocular lens tilt and decentration through the undilated pupil," Ophthalmologica 97, 1259-1264 (1990).

Hazra, L. N.

Holladay, J. T.

J. T. Holladay, P. A. Piers, G. Koranyi, M. van der Mooren, and N. E. Norrby, "A new intraocular lens design to reduce spherical aberration of pseudophakic eyes," J. Refract. Surg. 18, 683-691 (2002).
[PubMed]

Howland, H.

H. Howland, A. Glasser, and R. Applegate, "Polynomial approximations of corneal surfaces and corneal curvature topography," Tech. Dig. Ser. Opt. Soc. Am. 3, 34-37 (1992).

Howland, H. C.

J. E. Kelly, T. Mihashi, and H. C. Howland, "Compensation of corneal horizontal/vertical astigmatism, lateral coma, and spherical aberration by internal optics of the eye," J. Vision 4, 262-271 (2004).
[CrossRef]

Jones, C. E.

D. A. Atchison, C. E. Jones, K. L. Schmid, N. Prichard, J. M. Pope, W. E. Strugnell, and R. A. Riley, "Eye shape in emmetropia and myopia," Invest. Ophthalmol. Visual Sci. 45, 3380-3386 (2004).
[CrossRef]

Kelly, J. E.

J. E. Kelly, T. Mihashi, and H. C. Howland, "Compensation of corneal horizontal/vertical astigmatism, lateral coma, and spherical aberration by internal optics of the eye," J. Vision 4, 262-271 (2004).
[CrossRef]

Kirschkamp, T.

J. C. Barry, M. C. M. Dunne, and T. Kirschkamp, "Phakometric measurement of ocular surface radius of curvature and alignment: evaluation of method with physical model eyes," Ophthalmic Physiol. Opt. 21, 450-460 (2001).
[CrossRef]

Koranyi, G.

J. T. Holladay, P. A. Piers, G. Koranyi, M. van der Mooren, and N. E. Norrby, "A new intraocular lens design to reduce spherical aberration of pseudophakic eyes," J. Refract. Surg. 18, 683-691 (2002).
[PubMed]

Le Grand, Y.

Y. Le Grand and S. G. El Hage, Physiological Optics (Springer Series in Optical Sciences, 1980).

Liang, J. C.

Liou, H. L.

Mahajan, V. N.

V. N. Mahajan, Optical Imaging and Aberrations. Part I. Ray Geometrical Optics (SPIE ,1998).

V. N. Mahajan, Aberration Theory Made Simple (SPIE ,1991).

Marcos, S.

Mester, U.

U. Mester, P. Dillinger, and N. Anterist, "Impact of a modified optic design on visual function: clinical comparative study," J. Cataract Refractive Surg. 29, 652-660 (2003).
[CrossRef]

Mihashi, T.

J. E. Kelly, T. Mihashi, and H. C. Howland, "Compensation of corneal horizontal/vertical astigmatism, lateral coma, and spherical aberration by internal optics of the eye," J. Vision 4, 262-271 (2004).
[CrossRef]

Moretti, G.

R. Bellucci, A. Scialdone, L. Buratto, S. Morselli, C. Chierego, A. Criscouli, G. Moretti, and P. Piers, "Visual acuity and contrast sensitivity comparison between Tecnis and AcrySof SA60AT intraocular lenses: A multicenter randomized study," J. Cataract Refractive Surg. 31, 712-717 (2005).
[CrossRef]

Morselli, S.

R. Bellucci, A. Scialdone, L. Buratto, S. Morselli, C. Chierego, A. Criscouli, G. Moretti, and P. Piers, "Visual acuity and contrast sensitivity comparison between Tecnis and AcrySof SA60AT intraocular lenses: A multicenter randomized study," J. Cataract Refractive Surg. 31, 712-717 (2005).
[CrossRef]

Norrby, N. E.

J. T. Holladay, P. A. Piers, G. Koranyi, M. van der Mooren, and N. E. Norrby, "A new intraocular lens design to reduce spherical aberration of pseudophakic eyes," J. Refract. Surg. 18, 683-691 (2002).
[PubMed]

Norrby, S.

A. Guirao, M. Redondo, E. Geraghty, P. Piers, S. Norrby, and P. Artal, "Corneal optical aberrations and retinal image quality in patients in whom monofocal intraocular lenses were implanted," Arch. Ophthalmol. (Chicago) 120, 1143-1151 (2002).

Nourrit, V.

Piers, P.

J. Tabernero, P. Piers, and P. Artal, "Intraocular lens to correct corneal coma," Opt. Lett. 32, 406-408 (2007).
[CrossRef]

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, "Predicting the optical performance of eyes implanted with IOLs correcting spherical aberration," Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
[CrossRef]

R. Bellucci, A. Scialdone, L. Buratto, S. Morselli, C. Chierego, A. Criscouli, G. Moretti, and P. Piers, "Visual acuity and contrast sensitivity comparison between Tecnis and AcrySof SA60AT intraocular lenses: A multicenter randomized study," J. Cataract Refractive Surg. 31, 712-717 (2005).
[CrossRef]

A. Guirao, M. Redondo, E. Geraghty, P. Piers, S. Norrby, and P. Artal, "Corneal optical aberrations and retinal image quality in patients in whom monofocal intraocular lenses were implanted," Arch. Ophthalmol. (Chicago) 120, 1143-1151 (2002).

P. Artal, E. Berrio, A. Guirao, and P. Piers, "Contribution of the cornea and internal surfaces to the change of ocular aberrations with age," J. Opt. Soc. Am. 19, 137-143 (2002).
[CrossRef]

Piers, P. A.

J. T. Holladay, P. A. Piers, G. Koranyi, M. van der Mooren, and N. E. Norrby, "A new intraocular lens design to reduce spherical aberration of pseudophakic eyes," J. Refract. Surg. 18, 683-691 (2002).
[PubMed]

Pope, J. M.

D. A. Atchison, C. E. Jones, K. L. Schmid, N. Prichard, J. M. Pope, W. E. Strugnell, and R. A. Riley, "Eye shape in emmetropia and myopia," Invest. Ophthalmol. Visual Sci. 45, 3380-3386 (2004).
[CrossRef]

Prichard, N.

D. A. Atchison, C. E. Jones, K. L. Schmid, N. Prichard, J. M. Pope, W. E. Strugnell, and R. A. Riley, "Eye shape in emmetropia and myopia," Invest. Ophthalmol. Visual Sci. 45, 3380-3386 (2004).
[CrossRef]

Prieto, P. M.

Redondo, M.

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, "Predicting the optical performance of eyes implanted with IOLs correcting spherical aberration," Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
[CrossRef]

A. Guirao, M. Redondo, E. Geraghty, P. Piers, S. Norrby, and P. Artal, "Corneal optical aberrations and retinal image quality in patients in whom monofocal intraocular lenses were implanted," Arch. Ophthalmol. (Chicago) 120, 1143-1151 (2002).

A. Guirao, M. Redondo, and P. Artal, "Optical aberrations of the human cornea as a function of age," J. Opt. Soc. Am. A 7, 1697-1702 (2000).
[CrossRef]

Riley, R. A.

D. A. Atchison, C. E. Jones, K. L. Schmid, N. Prichard, J. M. Pope, W. E. Strugnell, and R. A. Riley, "Eye shape in emmetropia and myopia," Invest. Ophthalmol. Visual Sci. 45, 3380-3386 (2004).
[CrossRef]

Rosales, P.

Schmid, K. L.

D. A. Atchison, C. E. Jones, K. L. Schmid, N. Prichard, J. M. Pope, W. E. Strugnell, and R. A. Riley, "Eye shape in emmetropia and myopia," Invest. Ophthalmol. Visual Sci. 45, 3380-3386 (2004).
[CrossRef]

Scialdone, A.

R. Bellucci, A. Scialdone, L. Buratto, S. Morselli, C. Chierego, A. Criscouli, G. Moretti, and P. Piers, "Visual acuity and contrast sensitivity comparison between Tecnis and AcrySof SA60AT intraocular lenses: A multicenter randomized study," J. Cataract Refractive Surg. 31, 712-717 (2005).
[CrossRef]

Smith, G.

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heineman, 2000).

Strugnell, W. E.

D. A. Atchison, C. E. Jones, K. L. Schmid, N. Prichard, J. M. Pope, W. E. Strugnell, and R. A. Riley, "Eye shape in emmetropia and myopia," Invest. Ophthalmol. Visual Sci. 45, 3380-3386 (2004).
[CrossRef]

Tabernero, J.

J. Tabernero, P. Piers, and P. Artal, "Intraocular lens to correct corneal coma," Opt. Lett. 32, 406-408 (2007).
[CrossRef]

J. Tabernero, A. Benito, V. Nourrit, and P. Artal, "Instrument for measuring the misalignments of ocular surfaces," Opt. Express 14, 10945-10956 (2006).
[CrossRef]

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, "Predicting the optical performance of eyes implanted with IOLs correcting spherical aberration," Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
[CrossRef]

P. Artal, A. Benito, and J. Tabernero, "The human eye is an example of robust optical design," J. Vision 6, 1-7 (2006).
[CrossRef]

Uozato, H.

D. L. Guyton, H. Uozato, and H. J. Wisnicki, "Rapid determination of intraocular lens tilt and decentration through the undilated pupil," Ophthalmologica 97, 1259-1264 (1990).

van der Mooren, M.

J. T. Holladay, P. A. Piers, G. Koranyi, M. van der Mooren, and N. E. Norrby, "A new intraocular lens design to reduce spherical aberration of pseudophakic eyes," J. Refract. Surg. 18, 683-691 (2002).
[PubMed]

Vargas-Martín, F.

Williams, D. R.

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by the internal optics in the human eye," J. Vision 1, 1-8 (2001).
[CrossRef]

Wisnicki, H. J.

D. L. Guyton, H. Uozato, and H. J. Wisnicki, "Rapid determination of intraocular lens tilt and decentration through the undilated pupil," Ophthalmologica 97, 1259-1264 (1990).

Arch. Ophthalmol. (Chicago) (1)

A. Guirao, M. Redondo, E. Geraghty, P. Piers, S. Norrby, and P. Artal, "Corneal optical aberrations and retinal image quality in patients in whom monofocal intraocular lenses were implanted," Arch. Ophthalmol. (Chicago) 120, 1143-1151 (2002).

Invest. Ophthalmol. Visual Sci. (2)

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, "Predicting the optical performance of eyes implanted with IOLs correcting spherical aberration," Invest. Ophthalmol. Visual Sci. 47, 4651-4658 (2006).
[CrossRef]

D. A. Atchison, C. E. Jones, K. L. Schmid, N. Prichard, J. M. Pope, W. E. Strugnell, and R. A. Riley, "Eye shape in emmetropia and myopia," Invest. Ophthalmol. Visual Sci. 45, 3380-3386 (2004).
[CrossRef]

J. Cataract Refractive Surg. (2)

U. Mester, P. Dillinger, and N. Anterist, "Impact of a modified optic design on visual function: clinical comparative study," J. Cataract Refractive Surg. 29, 652-660 (2003).
[CrossRef]

R. Bellucci, A. Scialdone, L. Buratto, S. Morselli, C. Chierego, A. Criscouli, G. Moretti, and P. Piers, "Visual acuity and contrast sensitivity comparison between Tecnis and AcrySof SA60AT intraocular lenses: A multicenter randomized study," J. Cataract Refractive Surg. 31, 712-717 (2005).
[CrossRef]

J. Opt. Soc. Am. (2)

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

P. Artal, E. Berrio, A. Guirao, and P. Piers, "Contribution of the cornea and internal surfaces to the change of ocular aberrations with age," J. Opt. Soc. Am. 19, 137-143 (2002).
[CrossRef]

J. Opt. Soc. Am. A (7)

J. Refract. Surg. (1)

J. T. Holladay, P. A. Piers, G. Koranyi, M. van der Mooren, and N. E. Norrby, "A new intraocular lens design to reduce spherical aberration of pseudophakic eyes," J. Refract. Surg. 18, 683-691 (2002).
[PubMed]

J. Vision (3)

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by the internal optics in the human eye," J. Vision 1, 1-8 (2001).
[CrossRef]

J. E. Kelly, T. Mihashi, and H. C. Howland, "Compensation of corneal horizontal/vertical astigmatism, lateral coma, and spherical aberration by internal optics of the eye," J. Vision 4, 262-271 (2004).
[CrossRef]

P. Artal, A. Benito, and J. Tabernero, "The human eye is an example of robust optical design," J. Vision 6, 1-7 (2006).
[CrossRef]

Ophthalmic Physiol. Opt. (1)

J. C. Barry, M. C. M. Dunne, and T. Kirschkamp, "Phakometric measurement of ocular surface radius of curvature and alignment: evaluation of method with physical model eyes," Ophthalmic Physiol. Opt. 21, 450-460 (2001).
[CrossRef]

Ophthalmologica (1)

D. L. Guyton, H. Uozato, and H. J. Wisnicki, "Rapid determination of intraocular lens tilt and decentration through the undilated pupil," Ophthalmologica 97, 1259-1264 (1990).

Opt. Express (1)

Opt. Lett. (2)

SPIE (2)

V. N. Mahajan, Aberration Theory Made Simple (SPIE ,1991).

V. N. Mahajan, Optical Imaging and Aberrations. Part I. Ray Geometrical Optics (SPIE ,1998).

Tech. Dig. Ser. Opt. Soc. Am. (1)

H. Howland, A. Glasser, and R. Applegate, "Polynomial approximations of corneal surfaces and corneal curvature topography," Tech. Dig. Ser. Opt. Soc. Am. 3, 34-37 (1992).

Vision Res. (1)

A. Glasser and M. C. W. Campbell, "Presbyopia and the optical changes in the human crystalline lens with age," Vision Res. 38, 209-229 (1998).
[CrossRef] [PubMed]

Other (4)

Y. Le Grand and S. G. El Hage, Physiological Optics (Springer Series in Optical Sciences, 1980).

The same angle formed by the line of sight and the pupillary axis is referred to in the literature with two different names: for instance, kappa in and lambda in and others. The reason for this notation discrepancy can be found in the historical references and the intrinsic confusion with ocular angle definitions. In the clinical literature only kappa is commonly used, while lambda is still used by some basic researchers. According to Emsley , the first definition of angle kappa was given by Landolt as "the angle between the visual axis and the so-called central pupillary line (the pupillary axis)." This definition involved the visual axis, as the line connecting the fixation point with the object nodal point of the eye. This is not the same as the line of sight, connecting the center of the entrance pupil and the fixation point. Therefore this definition is not what was used by Le Grand and adopted here. Angle lambda was defined by Lancaster (cited in ) as the line connecting the pupillary axis and the line of sight. However, Le Grand and El Hage redefined angle kappa exactly as the angle lambda defined by Lancaster. The reason to do this is that they understand the term "visual axis" in Landolt's original definition of kappa as the line of sight, since the nodal point in the eye is a purely paraxial theoretical concept that cannot be measured. Quoting Le Grand's book, p. 73: "It is not very logical to confuse geometric and fictitious ideas (optical and visual axis) and experimental ideas (pupillary axis and the principal line of sight)." Therefore, Le Grand maintained the old name of kappa but with the modern definition of lambda by Lancaster. Moreover, in practical terms, the two angles are nearly identical as stated by Le Grand : "It seems unnecessary to distinguish this (angle lambda) from kappa which is practically equal to it when the point of fixation is not very close to the eye." We used in the manuscript this meaning for angle kappa, but the reader should be aware of the other accepted name (lambda) for the same angle to avoid confusion. A standard definition of ocular angles is required to unify terms in both basic and clinical literature. In the case of this angle, keeping only the name kappa would be, in our opinion, the most adequate.

D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heineman, 2000).

H. H. Emsley, Visual Optics (Hatton Press, 1948).

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Figures (14)

Fig. 1
Fig. 1

Definition of angle kappa, line of sight, and pupillary axis.

Fig. 2
Fig. 2

Spherical aberration, coma, and higher-order root-mean-squared wavefront error for the cornea, eye, and internal components of all the subjects included in this work, sorted by the refractive error, from the more myopic to the more hyperopic eye.

Fig. 3
Fig. 3

Average ocular rms, compensated coma, and compensated spherical aberration grouping the subjects into myopic, emmetropic, and hyperopic eyes. Error bars represent standard deviation from the average.

Fig. 4
Fig. 4

Average higher-order wavefront maps for the hyperopic and myopic group. Corneal internal and ocular aberration maps are shown in each column separately.

Fig. 5
Fig. 5

Alignment data measured for all the subjects included in this study.

Fig. 6
Fig. 6

Lens tilt with respect to the line of sight for the refractive groups in the study.

Fig. 7
Fig. 7

Relationship between angle kappa and horizontal coma for the whole eye, cornea, and internal optics.

Fig. 8
Fig. 8

Influence of the crystalline lens alignment properties in the prediction of the horizontal coma of the eye (see text for details).

Fig. 9
Fig. 9

Influence of a gradient index crystalline lens model in the prediction of the horizontal coma of the eye (see text for details).

Fig. 10
Fig. 10

Measured internal total coma, angular generated internal coma, and residual internal coma for all the subjects included in the study, sorted by refractive error from myopic to hyperopic.

Fig. 11
Fig. 11

Measured internal total trefoil, angular generated internal trefoil, and residual internal trefoil for all subjects included in the study, sorted by refractive error from myopic to hyperopic.

Fig. 12
Fig. 12

Illustrative picture of the shape factor ( X ) concept in a symmetrical index space [ X = ( R 1 + R 2 ) ( R 1 R 2 ) , R 1 and R 2 are the radii of curvature of the anterior and posterior surface of the lens].

Fig. 13
Fig. 13

Corneal coma as function of shape factor (parabolic line) and lens coma as function of shape factor (straight lines) for three different principal ray angles ( 2 ° upper, 5 ° medium, and 8 ° lower panels) in the context of the simplified angular theory described in the text. Three different lens models were used (15, 20, and 25 diopters; see text for details). Dots represent the standard shape factor for a Gullstrand cornea model (1.25) and the standard shape factor for the Gullstrand crystalline lens model ( 0.25 ) .

Fig. 14
Fig. 14

(a) Schematic geometry of the elongation model of an eye from normal to myopic refractive states. (b) Angle kappa measured as a function of the axial length (dots) and the theoretical prediction of a simple geometrical model of eye elongation (dashed line).

Equations (7)

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A c = 1 4 n 1 h 3 K 2 u ¯ [ p 1 X 2 + p 2 Y 2 + p 3 X Y + p 4 X + p 5 Y + p 6 ] ,
X = ( n L n 1 ) R 2 + ( n L n 2 ) R 1 ( n L n 1 ) R 2 ( n L n 2 ) R 1 ,
Y = n 2 u + n 1 u n 2 u n 1 u .
C o m a C = 1 4 h C 3 K C 2 u ¯ C [ p 1 C X C 2 + ( p 3 C + p 4 C ) X C + ( p 2 C + p 5 C + p 6 C ) ] .
C o m a L = 1.336 4 h L 3 K L 2 u ¯ L [ p 4 L X L + p 5 L Y L ] .
δ C o m a = 4 s a S β ,
α M = tan 1 [ ( L L + Δ ) tan ( α N ) ] .

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