Abstract

The optical surfaces of the eye are often described in terms of their radius and asphericity. The variations caused by experimental noise in repeated measurements of radius and asphericity of the same surface are strongly correlated. We show this correlation in experimental corneal elevation data from videokeratoscopy and Scheimpflug topography, in non-contact profilometry data of artificial lenses, and in simulations. The effect is a characteristic of the fits to conic curves, and not restricted to any experimental device or fitting procedure. A separate analysis of radius and asphericity may estimate incorrectly the statistical significance of the changes in the ocular surfaces. We propose a MANOVA-based statistical analysis that increases sensitivity by a factor of 4.

© 2010 Optical Society of America

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References

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  1. P. Kiely, G. Smith, and L. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1042 (1982).
    [CrossRef]
  2. 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]
  3. W. Lotmar, “Theoretical eye model with aspheric surfaces,” J. Opt. Soc. Am. A 61, 1522–1529 (1971).
    [CrossRef]
  4. R. Mandell and R. St Helen, “Mathematical model of the corneal contour,” Br. J. Physiol. Opt. 26, 183–197 (1971).
  5. L. Llorente, S. Barbero, D. Cano, C. Dorronsoro, and S. Marcos, “Myopic versus hyperopic eyes: axial length, corneal shape and optical aberrations,” J. Vision 4, 288–298 (2004).
    [CrossRef]
  6. P. M. Kiely, L. G. Carney, and G. Smith, “Diurnal-variations of corneal topography and thickness,” Am. J. Optom. Physiol. Opt. 59, 976–982 (1982).
    [PubMed]
  7. V. Sicam, M. Dubbelman, and R. G. L. van der Heijde, “Spherical aberration of the anterior and posterior surface of the human cornea,” J. Opt. Soc. Am. A 23, 544–549 (2006).
    [CrossRef]
  8. S. Marcos, D. Cano, and S. Barbero, “Increase of corneal asphericity after standard myopic LASIK surgery is not inherent to the Munnerlyn algorithm,” J. Refract. Surg. 19, 592–596 (2003).
  9. A. Perez-Escudero, C. Dorronsoro, L. Sawides, L. Remon, J. Merayo-Lloves, and S. Marcos, “Minor influence of myopic maser in situ keratomileusis on the posterior corneal surface,” Invest. Ophthalmol. Vis. Sci. 50, 4146–4154 (2009).
    [CrossRef] [PubMed]
  10. F. Manns, A. Ho, J. M. Parel, and W. Culbertson, “Ablation profiles for wavefront-guided correction of myopia and primary spherical aberration,” J. Cataract Refractive Surg. 28, 766–774 (2002).
    [CrossRef]
  11. F. Manns, V. Fernandez, S. Zipper, S. Sandadi, M. Hamaoui, A. Ho, and J. M. Parel, “Radius of curvature and asphericity of the anterior and posterior surface of human cadaver crystalline lenses,” Exp. Eye Res. 78, 39–51 (2004).
    [CrossRef]
  12. C. E. Jones, D. A. Atchison, and J. M. Pope, “Changes in lens dimensions and refractive index with age and accommodation,” Optom. Vision Sci. 84, 990–995 (2007).
    [CrossRef]
  13. M. Dubbelman, G. L. Van der Heijde, and H. A. Weeber, “Change in shape of the aging human crystalline lens with accommodation,” Vision Res. 45, 117–132 (2005).
    [CrossRef]
  14. M. Dubbelman and V. Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41, 1867–1877 (2001).
    [CrossRef] [PubMed]
  15. H. H. Dietze and M. J. Cox, “Correcting ocular spherical aberration with soft contact lenses,” J. Opt. Soc. Am. A 21, 473–485 (2004).
    [CrossRef]
  16. C. Dorronsoro, M. J. González, L. Llorente, and S. Marcos, “Optical and Visual quality with multifocal contact lenses,” Invest. Ophthalmol. Vis. Sci. 48, E-Abstract 5376 (2007).
  17. J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLs to correct spherical aberration,” Invest. Ophthalmol. Vis. Sci. 47, 4651–4658 (2006).
    [CrossRef] [PubMed]
  18. S. Marcos, S. Barbero, and I. Jiménez-Alfaro, “Optical quality and depth-of-field of eyes implanted with spherical and aspheric intraocular lenses,” J. Refract. Surg. 21, 223–235 (2005).
    [PubMed]
  19. J. Schwiegerling, J. Greivenkamp, and J. Miller, “Representation of videokeratoscopic height data with Zernike polynomials,” J. Opt. Soc. Am. A 12, 2105–2113 (1995).
    [CrossRef]
  20. M. Dubbelman, H. Weeber, R. Van Der Heijde, and H. Volker-Dieben, “Radius and asphericity of the posterior corneal surface determined by corrected Scheimpflug photography,” Acta Ophthalmol. Scand. 80, 379–383 (2002).
    [CrossRef] [PubMed]
  21. S. Radhakrishnan, A. Rollins, J. Roth, S. Yazdanfar, V. Westphal, D. Bardenstein, and J. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. (Chicago) 119, 1179–1185 (2001).
  22. B. J. Kaluzy, J. J. Kaluzny, A. Szkulmowska, I. Gorczynska, M. Szkulmowski, T. Bajraszewski, M. Wojtkowski, and P. Targowski, “Spectral optical coherence tomography—A novel technique for cornea imaging,” Cornea 25, 960–965 (2006).
    [CrossRef] [PubMed]
  23. A. M. Rosen, D. B. Denharn, V. Fernandez, D. Boria, A. Ho, F. Matins, J. M. Parel, and R. C. Augusteyn, “In vitro dimensions and curvatures of human lenses,” Vision Res. 46, 1002–1009 (2006).
    [CrossRef]
  24. C. Dorronsoro, L. Remon, J. Merayo-Lloves, and S. Marcos, “Experimental evaluation of optimized ablation patterns for laser refractive surgery,” Opt. Express 17, 15292–15307 (2009).
    [CrossRef] [PubMed]
  25. C. Dorronsoro, D. Cano, J. Merayo, and S. Marcos, “Experiments on PMMA models to predict the impact of corneal refractive surgery on corneal shape,” Opt. Express 14, 6142–6156 (2006).
    [CrossRef] [PubMed]
  26. K. Kanatani, “Statistical bias of conic fitting and renormalization,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 320–326 (1994).
    [CrossRef]
  27. Y. Nakagawa and A. Rosenfeld, “A note on polygonal and elliptical approximation of mechanical parts,” Pattern Recogn. 11, 133–142 (1979).
    [CrossRef]
  28. A. W. Fitzgibbon and R. B. Fischer, “A buyer’s guide to conic fitting,” in Proceedings of the British Machine Vision Conference (1995), pp. 265–271.
  29. R. Artigas, F. Laguarta, and C. Cadevall, “Dual-technology optical sensor head for 3D surface shape measurements on the micro- and nanoscales,” Proc. SPIE 5457, 166–174 (2004).
    [CrossRef]
  30. X. Hong, J. Xie, S. J. N. Van, D. Stanley, M. Karakelle, M. J. Simpson, X. Zhang, “Ophthalmic lens as intraocular lens comprises optic having anterior surface and posterior surface, where at least one of the surfaces has an aspherical base profile such that the optic exhibits specific negative spherical aberration,” patent WO2006108005-A2, 12 October 2006.
  31. R. Navarro, L. Gonzalez, and J. L. Hernandez, “Optics of the average normal cornea from general and canonical representations of its surface topography,” J. Opt. Soc. Am. A 23, 219–232 (2006).
    [CrossRef]

2009 (2)

A. Perez-Escudero, C. Dorronsoro, L. Sawides, L. Remon, J. Merayo-Lloves, and S. Marcos, “Minor influence of myopic maser in situ keratomileusis on the posterior corneal surface,” Invest. Ophthalmol. Vis. Sci. 50, 4146–4154 (2009).
[CrossRef] [PubMed]

C. Dorronsoro, L. Remon, J. Merayo-Lloves, and S. Marcos, “Experimental evaluation of optimized ablation patterns for laser refractive surgery,” Opt. Express 17, 15292–15307 (2009).
[CrossRef] [PubMed]

2007 (2)

C. E. Jones, D. A. Atchison, and J. M. Pope, “Changes in lens dimensions and refractive index with age and accommodation,” Optom. Vision Sci. 84, 990–995 (2007).
[CrossRef]

C. Dorronsoro, M. J. González, L. Llorente, and S. Marcos, “Optical and Visual quality with multifocal contact lenses,” Invest. Ophthalmol. Vis. Sci. 48, E-Abstract 5376 (2007).

2006 (6)

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLs to correct spherical aberration,” Invest. Ophthalmol. Vis. Sci. 47, 4651–4658 (2006).
[CrossRef] [PubMed]

B. J. Kaluzy, J. J. Kaluzny, A. Szkulmowska, I. Gorczynska, M. Szkulmowski, T. Bajraszewski, M. Wojtkowski, and P. Targowski, “Spectral optical coherence tomography—A novel technique for cornea imaging,” Cornea 25, 960–965 (2006).
[CrossRef] [PubMed]

A. M. Rosen, D. B. Denharn, V. Fernandez, D. Boria, A. Ho, F. Matins, J. M. Parel, and R. C. Augusteyn, “In vitro dimensions and curvatures of human lenses,” Vision Res. 46, 1002–1009 (2006).
[CrossRef]

R. Navarro, L. Gonzalez, and J. L. Hernandez, “Optics of the average normal cornea from general and canonical representations of its surface topography,” J. Opt. Soc. Am. A 23, 219–232 (2006).
[CrossRef]

V. Sicam, M. Dubbelman, and R. G. L. van der Heijde, “Spherical aberration of the anterior and posterior surface of the human cornea,” J. Opt. Soc. Am. A 23, 544–549 (2006).
[CrossRef]

C. Dorronsoro, D. Cano, J. Merayo, and S. Marcos, “Experiments on PMMA models to predict the impact of corneal refractive surgery on corneal shape,” Opt. Express 14, 6142–6156 (2006).
[CrossRef] [PubMed]

2005 (2)

S. Marcos, S. Barbero, and I. Jiménez-Alfaro, “Optical quality and depth-of-field of eyes implanted with spherical and aspheric intraocular lenses,” J. Refract. Surg. 21, 223–235 (2005).
[PubMed]

M. Dubbelman, G. L. Van der Heijde, and H. A. Weeber, “Change in shape of the aging human crystalline lens with accommodation,” Vision Res. 45, 117–132 (2005).
[CrossRef]

2004 (4)

F. Manns, V. Fernandez, S. Zipper, S. Sandadi, M. Hamaoui, A. Ho, and J. M. Parel, “Radius of curvature and asphericity of the anterior and posterior surface of human cadaver crystalline lenses,” Exp. Eye Res. 78, 39–51 (2004).
[CrossRef]

L. Llorente, S. Barbero, D. Cano, C. Dorronsoro, and S. Marcos, “Myopic versus hyperopic eyes: axial length, corneal shape and optical aberrations,” J. Vision 4, 288–298 (2004).
[CrossRef]

R. Artigas, F. Laguarta, and C. Cadevall, “Dual-technology optical sensor head for 3D surface shape measurements on the micro- and nanoscales,” Proc. SPIE 5457, 166–174 (2004).
[CrossRef]

H. H. Dietze and M. J. Cox, “Correcting ocular spherical aberration with soft contact lenses,” J. Opt. Soc. Am. A 21, 473–485 (2004).
[CrossRef]

2003 (1)

S. Marcos, D. Cano, and S. Barbero, “Increase of corneal asphericity after standard myopic LASIK surgery is not inherent to the Munnerlyn algorithm,” J. Refract. Surg. 19, 592–596 (2003).

2002 (2)

F. Manns, A. Ho, J. M. Parel, and W. Culbertson, “Ablation profiles for wavefront-guided correction of myopia and primary spherical aberration,” J. Cataract Refractive Surg. 28, 766–774 (2002).
[CrossRef]

M. Dubbelman, H. Weeber, R. Van Der Heijde, and H. Volker-Dieben, “Radius and asphericity of the posterior corneal surface determined by corrected Scheimpflug photography,” Acta Ophthalmol. Scand. 80, 379–383 (2002).
[CrossRef] [PubMed]

2001 (2)

S. Radhakrishnan, A. Rollins, J. Roth, S. Yazdanfar, V. Westphal, D. Bardenstein, and J. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. (Chicago) 119, 1179–1185 (2001).

M. Dubbelman and V. Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41, 1867–1877 (2001).
[CrossRef] [PubMed]

2000 (1)

1995 (2)

J. Schwiegerling, J. Greivenkamp, and J. Miller, “Representation of videokeratoscopic height data with Zernike polynomials,” J. Opt. Soc. Am. A 12, 2105–2113 (1995).
[CrossRef]

A. W. Fitzgibbon and R. B. Fischer, “A buyer’s guide to conic fitting,” in Proceedings of the British Machine Vision Conference (1995), pp. 265–271.

1994 (1)

K. Kanatani, “Statistical bias of conic fitting and renormalization,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 320–326 (1994).
[CrossRef]

1982 (2)

P. Kiely, G. Smith, and L. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1042 (1982).
[CrossRef]

P. M. Kiely, L. G. Carney, and G. Smith, “Diurnal-variations of corneal topography and thickness,” Am. J. Optom. Physiol. Opt. 59, 976–982 (1982).
[PubMed]

1979 (1)

Y. Nakagawa and A. Rosenfeld, “A note on polygonal and elliptical approximation of mechanical parts,” Pattern Recogn. 11, 133–142 (1979).
[CrossRef]

1971 (2)

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

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

Artal, P.

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLs to correct spherical aberration,” Invest. Ophthalmol. Vis. Sci. 47, 4651–4658 (2006).
[CrossRef] [PubMed]

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]

Artigas, R.

R. Artigas, F. Laguarta, and C. Cadevall, “Dual-technology optical sensor head for 3D surface shape measurements on the micro- and nanoscales,” Proc. SPIE 5457, 166–174 (2004).
[CrossRef]

Atchison, D. A.

C. E. Jones, D. A. Atchison, and J. M. Pope, “Changes in lens dimensions and refractive index with age and accommodation,” Optom. Vision Sci. 84, 990–995 (2007).
[CrossRef]

Augusteyn, R. C.

A. M. Rosen, D. B. Denharn, V. Fernandez, D. Boria, A. Ho, F. Matins, J. M. Parel, and R. C. Augusteyn, “In vitro dimensions and curvatures of human lenses,” Vision Res. 46, 1002–1009 (2006).
[CrossRef]

Bajraszewski, T.

B. J. Kaluzy, J. J. Kaluzny, A. Szkulmowska, I. Gorczynska, M. Szkulmowski, T. Bajraszewski, M. Wojtkowski, and P. Targowski, “Spectral optical coherence tomography—A novel technique for cornea imaging,” Cornea 25, 960–965 (2006).
[CrossRef] [PubMed]

Barbero, S.

S. Marcos, S. Barbero, and I. Jiménez-Alfaro, “Optical quality and depth-of-field of eyes implanted with spherical and aspheric intraocular lenses,” J. Refract. Surg. 21, 223–235 (2005).
[PubMed]

L. Llorente, S. Barbero, D. Cano, C. Dorronsoro, and S. Marcos, “Myopic versus hyperopic eyes: axial length, corneal shape and optical aberrations,” J. Vision 4, 288–298 (2004).
[CrossRef]

S. Marcos, D. Cano, and S. Barbero, “Increase of corneal asphericity after standard myopic LASIK surgery is not inherent to the Munnerlyn algorithm,” J. Refract. Surg. 19, 592–596 (2003).

Bardenstein, D.

S. Radhakrishnan, A. Rollins, J. Roth, S. Yazdanfar, V. Westphal, D. Bardenstein, and J. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. (Chicago) 119, 1179–1185 (2001).

Benito, A.

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLs to correct spherical aberration,” Invest. Ophthalmol. Vis. Sci. 47, 4651–4658 (2006).
[CrossRef] [PubMed]

Boria, D.

A. M. Rosen, D. B. Denharn, V. Fernandez, D. Boria, A. Ho, F. Matins, J. M. Parel, and R. C. Augusteyn, “In vitro dimensions and curvatures of human lenses,” Vision Res. 46, 1002–1009 (2006).
[CrossRef]

Cadevall, C.

R. Artigas, F. Laguarta, and C. Cadevall, “Dual-technology optical sensor head for 3D surface shape measurements on the micro- and nanoscales,” Proc. SPIE 5457, 166–174 (2004).
[CrossRef]

Cano, D.

C. Dorronsoro, D. Cano, J. Merayo, and S. Marcos, “Experiments on PMMA models to predict the impact of corneal refractive surgery on corneal shape,” Opt. Express 14, 6142–6156 (2006).
[CrossRef] [PubMed]

L. Llorente, S. Barbero, D. Cano, C. Dorronsoro, and S. Marcos, “Myopic versus hyperopic eyes: axial length, corneal shape and optical aberrations,” J. Vision 4, 288–298 (2004).
[CrossRef]

S. Marcos, D. Cano, and S. Barbero, “Increase of corneal asphericity after standard myopic LASIK surgery is not inherent to the Munnerlyn algorithm,” J. Refract. Surg. 19, 592–596 (2003).

Carney, L.

P. Kiely, G. Smith, and L. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1042 (1982).
[CrossRef]

Carney, L. G.

P. M. Kiely, L. G. Carney, and G. Smith, “Diurnal-variations of corneal topography and thickness,” Am. J. Optom. Physiol. Opt. 59, 976–982 (1982).
[PubMed]

Cox, M. J.

Culbertson, W.

F. Manns, A. Ho, J. M. Parel, and W. Culbertson, “Ablation profiles for wavefront-guided correction of myopia and primary spherical aberration,” J. Cataract Refractive Surg. 28, 766–774 (2002).
[CrossRef]

Denharn, D. B.

A. M. Rosen, D. B. Denharn, V. Fernandez, D. Boria, A. Ho, F. Matins, J. M. Parel, and R. C. Augusteyn, “In vitro dimensions and curvatures of human lenses,” Vision Res. 46, 1002–1009 (2006).
[CrossRef]

Dietze, H. H.

Dorronsoro, C.

A. Perez-Escudero, C. Dorronsoro, L. Sawides, L. Remon, J. Merayo-Lloves, and S. Marcos, “Minor influence of myopic maser in situ keratomileusis on the posterior corneal surface,” Invest. Ophthalmol. Vis. Sci. 50, 4146–4154 (2009).
[CrossRef] [PubMed]

C. Dorronsoro, L. Remon, J. Merayo-Lloves, and S. Marcos, “Experimental evaluation of optimized ablation patterns for laser refractive surgery,” Opt. Express 17, 15292–15307 (2009).
[CrossRef] [PubMed]

C. Dorronsoro, M. J. González, L. Llorente, and S. Marcos, “Optical and Visual quality with multifocal contact lenses,” Invest. Ophthalmol. Vis. Sci. 48, E-Abstract 5376 (2007).

C. Dorronsoro, D. Cano, J. Merayo, and S. Marcos, “Experiments on PMMA models to predict the impact of corneal refractive surgery on corneal shape,” Opt. Express 14, 6142–6156 (2006).
[CrossRef] [PubMed]

L. Llorente, S. Barbero, D. Cano, C. Dorronsoro, and S. Marcos, “Myopic versus hyperopic eyes: axial length, corneal shape and optical aberrations,” J. Vision 4, 288–298 (2004).
[CrossRef]

Dubbelman, M.

V. Sicam, M. Dubbelman, and R. G. L. van der Heijde, “Spherical aberration of the anterior and posterior surface of the human cornea,” J. Opt. Soc. Am. A 23, 544–549 (2006).
[CrossRef]

M. Dubbelman, G. L. Van der Heijde, and H. A. Weeber, “Change in shape of the aging human crystalline lens with accommodation,” Vision Res. 45, 117–132 (2005).
[CrossRef]

M. Dubbelman, H. Weeber, R. Van Der Heijde, and H. Volker-Dieben, “Radius and asphericity of the posterior corneal surface determined by corrected Scheimpflug photography,” Acta Ophthalmol. Scand. 80, 379–383 (2002).
[CrossRef] [PubMed]

M. Dubbelman and V. Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41, 1867–1877 (2001).
[CrossRef] [PubMed]

Fernandez, V.

A. M. Rosen, D. B. Denharn, V. Fernandez, D. Boria, A. Ho, F. Matins, J. M. Parel, and R. C. Augusteyn, “In vitro dimensions and curvatures of human lenses,” Vision Res. 46, 1002–1009 (2006).
[CrossRef]

F. Manns, V. Fernandez, S. Zipper, S. Sandadi, M. Hamaoui, A. Ho, and J. M. Parel, “Radius of curvature and asphericity of the anterior and posterior surface of human cadaver crystalline lenses,” Exp. Eye Res. 78, 39–51 (2004).
[CrossRef]

Fischer, R. B.

A. W. Fitzgibbon and R. B. Fischer, “A buyer’s guide to conic fitting,” in Proceedings of the British Machine Vision Conference (1995), pp. 265–271.

Fitzgibbon, A. W.

A. W. Fitzgibbon and R. B. Fischer, “A buyer’s guide to conic fitting,” in Proceedings of the British Machine Vision Conference (1995), pp. 265–271.

Gonzalez, L.

González, M. J.

C. Dorronsoro, M. J. González, L. Llorente, and S. Marcos, “Optical and Visual quality with multifocal contact lenses,” Invest. Ophthalmol. Vis. Sci. 48, E-Abstract 5376 (2007).

Gorczynska, I.

B. J. Kaluzy, J. J. Kaluzny, A. Szkulmowska, I. Gorczynska, M. Szkulmowski, T. Bajraszewski, M. Wojtkowski, and P. Targowski, “Spectral optical coherence tomography—A novel technique for cornea imaging,” Cornea 25, 960–965 (2006).
[CrossRef] [PubMed]

Greivenkamp, J.

Guirao, A.

Hamaoui, M.

F. Manns, V. Fernandez, S. Zipper, S. Sandadi, M. Hamaoui, A. Ho, and J. M. Parel, “Radius of curvature and asphericity of the anterior and posterior surface of human cadaver crystalline lenses,” Exp. Eye Res. 78, 39–51 (2004).
[CrossRef]

Heijde, V.

M. Dubbelman and V. Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41, 1867–1877 (2001).
[CrossRef] [PubMed]

Hernandez, J. L.

Ho, A.

A. M. Rosen, D. B. Denharn, V. Fernandez, D. Boria, A. Ho, F. Matins, J. M. Parel, and R. C. Augusteyn, “In vitro dimensions and curvatures of human lenses,” Vision Res. 46, 1002–1009 (2006).
[CrossRef]

F. Manns, V. Fernandez, S. Zipper, S. Sandadi, M. Hamaoui, A. Ho, and J. M. Parel, “Radius of curvature and asphericity of the anterior and posterior surface of human cadaver crystalline lenses,” Exp. Eye Res. 78, 39–51 (2004).
[CrossRef]

F. Manns, A. Ho, J. M. Parel, and W. Culbertson, “Ablation profiles for wavefront-guided correction of myopia and primary spherical aberration,” J. Cataract Refractive Surg. 28, 766–774 (2002).
[CrossRef]

Hong, X.

X. Hong, J. Xie, S. J. N. Van, D. Stanley, M. Karakelle, M. J. Simpson, X. Zhang, “Ophthalmic lens as intraocular lens comprises optic having anterior surface and posterior surface, where at least one of the surfaces has an aspherical base profile such that the optic exhibits specific negative spherical aberration,” patent WO2006108005-A2, 12 October 2006.

Izatt, J.

S. Radhakrishnan, A. Rollins, J. Roth, S. Yazdanfar, V. Westphal, D. Bardenstein, and J. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. (Chicago) 119, 1179–1185 (2001).

Jiménez-Alfaro, I.

S. Marcos, S. Barbero, and I. Jiménez-Alfaro, “Optical quality and depth-of-field of eyes implanted with spherical and aspheric intraocular lenses,” J. Refract. Surg. 21, 223–235 (2005).
[PubMed]

Jones, C. E.

C. E. Jones, D. A. Atchison, and J. M. Pope, “Changes in lens dimensions and refractive index with age and accommodation,” Optom. Vision Sci. 84, 990–995 (2007).
[CrossRef]

Kaluzny, J. J.

B. J. Kaluzy, J. J. Kaluzny, A. Szkulmowska, I. Gorczynska, M. Szkulmowski, T. Bajraszewski, M. Wojtkowski, and P. Targowski, “Spectral optical coherence tomography—A novel technique for cornea imaging,” Cornea 25, 960–965 (2006).
[CrossRef] [PubMed]

Kaluzy, B. J.

B. J. Kaluzy, J. J. Kaluzny, A. Szkulmowska, I. Gorczynska, M. Szkulmowski, T. Bajraszewski, M. Wojtkowski, and P. Targowski, “Spectral optical coherence tomography—A novel technique for cornea imaging,” Cornea 25, 960–965 (2006).
[CrossRef] [PubMed]

Kanatani, K.

K. Kanatani, “Statistical bias of conic fitting and renormalization,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 320–326 (1994).
[CrossRef]

Karakelle, M.

X. Hong, J. Xie, S. J. N. Van, D. Stanley, M. Karakelle, M. J. Simpson, X. Zhang, “Ophthalmic lens as intraocular lens comprises optic having anterior surface and posterior surface, where at least one of the surfaces has an aspherical base profile such that the optic exhibits specific negative spherical aberration,” patent WO2006108005-A2, 12 October 2006.

Kiely, P.

P. Kiely, G. Smith, and L. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1042 (1982).
[CrossRef]

Kiely, P. M.

P. M. Kiely, L. G. Carney, and G. Smith, “Diurnal-variations of corneal topography and thickness,” Am. J. Optom. Physiol. Opt. 59, 976–982 (1982).
[PubMed]

Laguarta, F.

R. Artigas, F. Laguarta, and C. Cadevall, “Dual-technology optical sensor head for 3D surface shape measurements on the micro- and nanoscales,” Proc. SPIE 5457, 166–174 (2004).
[CrossRef]

Llorente, L.

C. Dorronsoro, M. J. González, L. Llorente, and S. Marcos, “Optical and Visual quality with multifocal contact lenses,” Invest. Ophthalmol. Vis. Sci. 48, E-Abstract 5376 (2007).

L. Llorente, S. Barbero, D. Cano, C. Dorronsoro, and S. Marcos, “Myopic versus hyperopic eyes: axial length, corneal shape and optical aberrations,” J. Vision 4, 288–298 (2004).
[CrossRef]

Lotmar, W.

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

Mandell, R.

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

Manns, F.

F. Manns, V. Fernandez, S. Zipper, S. Sandadi, M. Hamaoui, A. Ho, and J. M. Parel, “Radius of curvature and asphericity of the anterior and posterior surface of human cadaver crystalline lenses,” Exp. Eye Res. 78, 39–51 (2004).
[CrossRef]

F. Manns, A. Ho, J. M. Parel, and W. Culbertson, “Ablation profiles for wavefront-guided correction of myopia and primary spherical aberration,” J. Cataract Refractive Surg. 28, 766–774 (2002).
[CrossRef]

Marcos, S.

C. Dorronsoro, L. Remon, J. Merayo-Lloves, and S. Marcos, “Experimental evaluation of optimized ablation patterns for laser refractive surgery,” Opt. Express 17, 15292–15307 (2009).
[CrossRef] [PubMed]

A. Perez-Escudero, C. Dorronsoro, L. Sawides, L. Remon, J. Merayo-Lloves, and S. Marcos, “Minor influence of myopic maser in situ keratomileusis on the posterior corneal surface,” Invest. Ophthalmol. Vis. Sci. 50, 4146–4154 (2009).
[CrossRef] [PubMed]

C. Dorronsoro, M. J. González, L. Llorente, and S. Marcos, “Optical and Visual quality with multifocal contact lenses,” Invest. Ophthalmol. Vis. Sci. 48, E-Abstract 5376 (2007).

C. Dorronsoro, D. Cano, J. Merayo, and S. Marcos, “Experiments on PMMA models to predict the impact of corneal refractive surgery on corneal shape,” Opt. Express 14, 6142–6156 (2006).
[CrossRef] [PubMed]

S. Marcos, S. Barbero, and I. Jiménez-Alfaro, “Optical quality and depth-of-field of eyes implanted with spherical and aspheric intraocular lenses,” J. Refract. Surg. 21, 223–235 (2005).
[PubMed]

L. Llorente, S. Barbero, D. Cano, C. Dorronsoro, and S. Marcos, “Myopic versus hyperopic eyes: axial length, corneal shape and optical aberrations,” J. Vision 4, 288–298 (2004).
[CrossRef]

S. Marcos, D. Cano, and S. Barbero, “Increase of corneal asphericity after standard myopic LASIK surgery is not inherent to the Munnerlyn algorithm,” J. Refract. Surg. 19, 592–596 (2003).

Matins, F.

A. M. Rosen, D. B. Denharn, V. Fernandez, D. Boria, A. Ho, F. Matins, J. M. Parel, and R. C. Augusteyn, “In vitro dimensions and curvatures of human lenses,” Vision Res. 46, 1002–1009 (2006).
[CrossRef]

Merayo, J.

Merayo-Lloves, J.

C. Dorronsoro, L. Remon, J. Merayo-Lloves, and S. Marcos, “Experimental evaluation of optimized ablation patterns for laser refractive surgery,” Opt. Express 17, 15292–15307 (2009).
[CrossRef] [PubMed]

A. Perez-Escudero, C. Dorronsoro, L. Sawides, L. Remon, J. Merayo-Lloves, and S. Marcos, “Minor influence of myopic maser in situ keratomileusis on the posterior corneal surface,” Invest. Ophthalmol. Vis. Sci. 50, 4146–4154 (2009).
[CrossRef] [PubMed]

Miller, J.

Nakagawa, Y.

Y. Nakagawa and A. Rosenfeld, “A note on polygonal and elliptical approximation of mechanical parts,” Pattern Recogn. 11, 133–142 (1979).
[CrossRef]

Navarro, R.

Parel, J. M.

A. M. Rosen, D. B. Denharn, V. Fernandez, D. Boria, A. Ho, F. Matins, J. M. Parel, and R. C. Augusteyn, “In vitro dimensions and curvatures of human lenses,” Vision Res. 46, 1002–1009 (2006).
[CrossRef]

F. Manns, V. Fernandez, S. Zipper, S. Sandadi, M. Hamaoui, A. Ho, and J. M. Parel, “Radius of curvature and asphericity of the anterior and posterior surface of human cadaver crystalline lenses,” Exp. Eye Res. 78, 39–51 (2004).
[CrossRef]

F. Manns, A. Ho, J. M. Parel, and W. Culbertson, “Ablation profiles for wavefront-guided correction of myopia and primary spherical aberration,” J. Cataract Refractive Surg. 28, 766–774 (2002).
[CrossRef]

Perez-Escudero, A.

A. Perez-Escudero, C. Dorronsoro, L. Sawides, L. Remon, J. Merayo-Lloves, and S. Marcos, “Minor influence of myopic maser in situ keratomileusis on the posterior corneal surface,” Invest. Ophthalmol. Vis. Sci. 50, 4146–4154 (2009).
[CrossRef] [PubMed]

Piers, P.

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLs to correct spherical aberration,” Invest. Ophthalmol. Vis. Sci. 47, 4651–4658 (2006).
[CrossRef] [PubMed]

Pope, J. M.

C. E. Jones, D. A. Atchison, and J. M. Pope, “Changes in lens dimensions and refractive index with age and accommodation,” Optom. Vision Sci. 84, 990–995 (2007).
[CrossRef]

Radhakrishnan, S.

S. Radhakrishnan, A. Rollins, J. Roth, S. Yazdanfar, V. Westphal, D. Bardenstein, and J. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. (Chicago) 119, 1179–1185 (2001).

Redondo, M.

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLs to correct spherical aberration,” Invest. Ophthalmol. Vis. Sci. 47, 4651–4658 (2006).
[CrossRef] [PubMed]

Remon, L.

A. Perez-Escudero, C. Dorronsoro, L. Sawides, L. Remon, J. Merayo-Lloves, and S. Marcos, “Minor influence of myopic maser in situ keratomileusis on the posterior corneal surface,” Invest. Ophthalmol. Vis. Sci. 50, 4146–4154 (2009).
[CrossRef] [PubMed]

C. Dorronsoro, L. Remon, J. Merayo-Lloves, and S. Marcos, “Experimental evaluation of optimized ablation patterns for laser refractive surgery,” Opt. Express 17, 15292–15307 (2009).
[CrossRef] [PubMed]

Rollins, A.

S. Radhakrishnan, A. Rollins, J. Roth, S. Yazdanfar, V. Westphal, D. Bardenstein, and J. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. (Chicago) 119, 1179–1185 (2001).

Rosen, A. M.

A. M. Rosen, D. B. Denharn, V. Fernandez, D. Boria, A. Ho, F. Matins, J. M. Parel, and R. C. Augusteyn, “In vitro dimensions and curvatures of human lenses,” Vision Res. 46, 1002–1009 (2006).
[CrossRef]

Rosenfeld, A.

Y. Nakagawa and A. Rosenfeld, “A note on polygonal and elliptical approximation of mechanical parts,” Pattern Recogn. 11, 133–142 (1979).
[CrossRef]

Roth, J.

S. Radhakrishnan, A. Rollins, J. Roth, S. Yazdanfar, V. Westphal, D. Bardenstein, and J. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. (Chicago) 119, 1179–1185 (2001).

Sandadi, S.

F. Manns, V. Fernandez, S. Zipper, S. Sandadi, M. Hamaoui, A. Ho, and J. M. Parel, “Radius of curvature and asphericity of the anterior and posterior surface of human cadaver crystalline lenses,” Exp. Eye Res. 78, 39–51 (2004).
[CrossRef]

Sawides, L.

A. Perez-Escudero, C. Dorronsoro, L. Sawides, L. Remon, J. Merayo-Lloves, and S. Marcos, “Minor influence of myopic maser in situ keratomileusis on the posterior corneal surface,” Invest. Ophthalmol. Vis. Sci. 50, 4146–4154 (2009).
[CrossRef] [PubMed]

Schwiegerling, J.

Sicam, V.

Simpson, M. J.

X. Hong, J. Xie, S. J. N. Van, D. Stanley, M. Karakelle, M. J. Simpson, X. Zhang, “Ophthalmic lens as intraocular lens comprises optic having anterior surface and posterior surface, where at least one of the surfaces has an aspherical base profile such that the optic exhibits specific negative spherical aberration,” patent WO2006108005-A2, 12 October 2006.

Smith, G.

P. Kiely, G. Smith, and L. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1042 (1982).
[CrossRef]

P. M. Kiely, L. G. Carney, and G. Smith, “Diurnal-variations of corneal topography and thickness,” Am. J. Optom. Physiol. Opt. 59, 976–982 (1982).
[PubMed]

St Helen, R.

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

Stanley, D.

X. Hong, J. Xie, S. J. N. Van, D. Stanley, M. Karakelle, M. J. Simpson, X. Zhang, “Ophthalmic lens as intraocular lens comprises optic having anterior surface and posterior surface, where at least one of the surfaces has an aspherical base profile such that the optic exhibits specific negative spherical aberration,” patent WO2006108005-A2, 12 October 2006.

Szkulmowska, A.

B. J. Kaluzy, J. J. Kaluzny, A. Szkulmowska, I. Gorczynska, M. Szkulmowski, T. Bajraszewski, M. Wojtkowski, and P. Targowski, “Spectral optical coherence tomography—A novel technique for cornea imaging,” Cornea 25, 960–965 (2006).
[CrossRef] [PubMed]

Szkulmowski, M.

B. J. Kaluzy, J. J. Kaluzny, A. Szkulmowska, I. Gorczynska, M. Szkulmowski, T. Bajraszewski, M. Wojtkowski, and P. Targowski, “Spectral optical coherence tomography—A novel technique for cornea imaging,” Cornea 25, 960–965 (2006).
[CrossRef] [PubMed]

Tabernero, J.

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLs to correct spherical aberration,” Invest. Ophthalmol. Vis. Sci. 47, 4651–4658 (2006).
[CrossRef] [PubMed]

Targowski, P.

B. J. Kaluzy, J. J. Kaluzny, A. Szkulmowska, I. Gorczynska, M. Szkulmowski, T. Bajraszewski, M. Wojtkowski, and P. Targowski, “Spectral optical coherence tomography—A novel technique for cornea imaging,” Cornea 25, 960–965 (2006).
[CrossRef] [PubMed]

Van, S. J. N.

X. Hong, J. Xie, S. J. N. Van, D. Stanley, M. Karakelle, M. J. Simpson, X. Zhang, “Ophthalmic lens as intraocular lens comprises optic having anterior surface and posterior surface, where at least one of the surfaces has an aspherical base profile such that the optic exhibits specific negative spherical aberration,” patent WO2006108005-A2, 12 October 2006.

Van der Heijde, G. L.

M. Dubbelman, G. L. Van der Heijde, and H. A. Weeber, “Change in shape of the aging human crystalline lens with accommodation,” Vision Res. 45, 117–132 (2005).
[CrossRef]

Van Der Heijde, R.

M. Dubbelman, H. Weeber, R. Van Der Heijde, and H. Volker-Dieben, “Radius and asphericity of the posterior corneal surface determined by corrected Scheimpflug photography,” Acta Ophthalmol. Scand. 80, 379–383 (2002).
[CrossRef] [PubMed]

van der Heijde, R. G. L.

Volker-Dieben, H.

M. Dubbelman, H. Weeber, R. Van Der Heijde, and H. Volker-Dieben, “Radius and asphericity of the posterior corneal surface determined by corrected Scheimpflug photography,” Acta Ophthalmol. Scand. 80, 379–383 (2002).
[CrossRef] [PubMed]

Weeber, H.

M. Dubbelman, H. Weeber, R. Van Der Heijde, and H. Volker-Dieben, “Radius and asphericity of the posterior corneal surface determined by corrected Scheimpflug photography,” Acta Ophthalmol. Scand. 80, 379–383 (2002).
[CrossRef] [PubMed]

Weeber, H. A.

M. Dubbelman, G. L. Van der Heijde, and H. A. Weeber, “Change in shape of the aging human crystalline lens with accommodation,” Vision Res. 45, 117–132 (2005).
[CrossRef]

Westphal, V.

S. Radhakrishnan, A. Rollins, J. Roth, S. Yazdanfar, V. Westphal, D. Bardenstein, and J. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. (Chicago) 119, 1179–1185 (2001).

Wojtkowski, M.

B. J. Kaluzy, J. J. Kaluzny, A. Szkulmowska, I. Gorczynska, M. Szkulmowski, T. Bajraszewski, M. Wojtkowski, and P. Targowski, “Spectral optical coherence tomography—A novel technique for cornea imaging,” Cornea 25, 960–965 (2006).
[CrossRef] [PubMed]

Xie, J.

X. Hong, J. Xie, S. J. N. Van, D. Stanley, M. Karakelle, M. J. Simpson, X. Zhang, “Ophthalmic lens as intraocular lens comprises optic having anterior surface and posterior surface, where at least one of the surfaces has an aspherical base profile such that the optic exhibits specific negative spherical aberration,” patent WO2006108005-A2, 12 October 2006.

Yazdanfar, S.

S. Radhakrishnan, A. Rollins, J. Roth, S. Yazdanfar, V. Westphal, D. Bardenstein, and J. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. (Chicago) 119, 1179–1185 (2001).

Zhang, X.

X. Hong, J. Xie, S. J. N. Van, D. Stanley, M. Karakelle, M. J. Simpson, X. Zhang, “Ophthalmic lens as intraocular lens comprises optic having anterior surface and posterior surface, where at least one of the surfaces has an aspherical base profile such that the optic exhibits specific negative spherical aberration,” patent WO2006108005-A2, 12 October 2006.

Zipper, S.

F. Manns, V. Fernandez, S. Zipper, S. Sandadi, M. Hamaoui, A. Ho, and J. M. Parel, “Radius of curvature and asphericity of the anterior and posterior surface of human cadaver crystalline lenses,” Exp. Eye Res. 78, 39–51 (2004).
[CrossRef]

Acta Ophthalmol. Scand. (1)

M. Dubbelman, H. Weeber, R. Van Der Heijde, and H. Volker-Dieben, “Radius and asphericity of the posterior corneal surface determined by corrected Scheimpflug photography,” Acta Ophthalmol. Scand. 80, 379–383 (2002).
[CrossRef] [PubMed]

Am. J. Optom. Physiol. Opt. (1)

P. M. Kiely, L. G. Carney, and G. Smith, “Diurnal-variations of corneal topography and thickness,” Am. J. Optom. Physiol. Opt. 59, 976–982 (1982).
[PubMed]

Arch. Ophthalmol. (Chicago) (1)

S. Radhakrishnan, A. Rollins, J. Roth, S. Yazdanfar, V. Westphal, D. Bardenstein, and J. Izatt, “Real-time optical coherence tomography of the anterior segment at 1310 nm,” Arch. Ophthalmol. (Chicago) 119, 1179–1185 (2001).

Br. J. Physiol. Opt. (1)

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

Cornea (1)

B. J. Kaluzy, J. J. Kaluzny, A. Szkulmowska, I. Gorczynska, M. Szkulmowski, T. Bajraszewski, M. Wojtkowski, and P. Targowski, “Spectral optical coherence tomography—A novel technique for cornea imaging,” Cornea 25, 960–965 (2006).
[CrossRef] [PubMed]

Exp. Eye Res. (1)

F. Manns, V. Fernandez, S. Zipper, S. Sandadi, M. Hamaoui, A. Ho, and J. M. Parel, “Radius of curvature and asphericity of the anterior and posterior surface of human cadaver crystalline lenses,” Exp. Eye Res. 78, 39–51 (2004).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

K. Kanatani, “Statistical bias of conic fitting and renormalization,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 320–326 (1994).
[CrossRef]

Invest. Ophthalmol. Vis. Sci. (3)

A. Perez-Escudero, C. Dorronsoro, L. Sawides, L. Remon, J. Merayo-Lloves, and S. Marcos, “Minor influence of myopic maser in situ keratomileusis on the posterior corneal surface,” Invest. Ophthalmol. Vis. Sci. 50, 4146–4154 (2009).
[CrossRef] [PubMed]

C. Dorronsoro, M. J. González, L. Llorente, and S. Marcos, “Optical and Visual quality with multifocal contact lenses,” Invest. Ophthalmol. Vis. Sci. 48, E-Abstract 5376 (2007).

J. Tabernero, P. Piers, A. Benito, M. Redondo, and P. Artal, “Predicting the optical performance of eyes implanted with IOLs to correct spherical aberration,” Invest. Ophthalmol. Vis. Sci. 47, 4651–4658 (2006).
[CrossRef] [PubMed]

J. Cataract Refractive Surg. (1)

F. Manns, A. Ho, J. M. Parel, and W. Culbertson, “Ablation profiles for wavefront-guided correction of myopia and primary spherical aberration,” J. Cataract Refractive Surg. 28, 766–774 (2002).
[CrossRef]

J. Opt. Soc. Am. A (6)

J. Refract. Surg. (2)

S. Marcos, D. Cano, and S. Barbero, “Increase of corneal asphericity after standard myopic LASIK surgery is not inherent to the Munnerlyn algorithm,” J. Refract. Surg. 19, 592–596 (2003).

S. Marcos, S. Barbero, and I. Jiménez-Alfaro, “Optical quality and depth-of-field of eyes implanted with spherical and aspheric intraocular lenses,” J. Refract. Surg. 21, 223–235 (2005).
[PubMed]

J. Vision (1)

L. Llorente, S. Barbero, D. Cano, C. Dorronsoro, and S. Marcos, “Myopic versus hyperopic eyes: axial length, corneal shape and optical aberrations,” J. Vision 4, 288–298 (2004).
[CrossRef]

Opt. Acta (1)

P. Kiely, G. Smith, and L. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1042 (1982).
[CrossRef]

Opt. Express (2)

Optom. Vision Sci. (1)

C. E. Jones, D. A. Atchison, and J. M. Pope, “Changes in lens dimensions and refractive index with age and accommodation,” Optom. Vision Sci. 84, 990–995 (2007).
[CrossRef]

Pattern Recogn. (1)

Y. Nakagawa and A. Rosenfeld, “A note on polygonal and elliptical approximation of mechanical parts,” Pattern Recogn. 11, 133–142 (1979).
[CrossRef]

Proc. SPIE (1)

R. Artigas, F. Laguarta, and C. Cadevall, “Dual-technology optical sensor head for 3D surface shape measurements on the micro- and nanoscales,” Proc. SPIE 5457, 166–174 (2004).
[CrossRef]

Vision Res. (3)

M. Dubbelman, G. L. Van der Heijde, and H. A. Weeber, “Change in shape of the aging human crystalline lens with accommodation,” Vision Res. 45, 117–132 (2005).
[CrossRef]

M. Dubbelman and V. Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41, 1867–1877 (2001).
[CrossRef] [PubMed]

A. M. Rosen, D. B. Denharn, V. Fernandez, D. Boria, A. Ho, F. Matins, J. M. Parel, and R. C. Augusteyn, “In vitro dimensions and curvatures of human lenses,” Vision Res. 46, 1002–1009 (2006).
[CrossRef]

Other (2)

X. Hong, J. Xie, S. J. N. Van, D. Stanley, M. Karakelle, M. J. Simpson, X. Zhang, “Ophthalmic lens as intraocular lens comprises optic having anterior surface and posterior surface, where at least one of the surfaces has an aspherical base profile such that the optic exhibits specific negative spherical aberration,” patent WO2006108005-A2, 12 October 2006.

A. W. Fitzgibbon and R. B. Fischer, “A buyer’s guide to conic fitting,” in Proceedings of the British Machine Vision Conference (1995), pp. 265–271.

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the experimental methodology. Experimental data are obtained from real eyes with a Scheimpflug imaging topographer (left) and a Placido disk topographer (center), and from an intraocular lens with an optical profilometer (right). The data are exported to a computer, and fitted by ellipsoids or ellipses, described by given radius and asphericity.

Fig. 2
Fig. 2

Correlation between radius and asphericity when Pentacam data from repeated measurements are fitted to ellipsoids. (a) Data of anterior corneal surface. (b) Data of posterior corneal surface. Diamonds: Subject 1. Circles: Subject 2. Triangles: Subject 3.

Fig. 3
Fig. 3

Dispersion in fitted radius and asphericity from measurements obtained with Pentacam on different subjects (pre- and post-LASIK patients and controls) on different days (within 1 month, three to six consecutive measurements per session). (a) Anterior surface of the cornea. (b) Posterior surface of the cornea.

Fig. 4
Fig. 4

Correlation between fitted radius and asphericity, for repeated measurements of the anterior corneal surface performed by Placido disk videokeratoscopy. (a) Subject 1. (b) Subject 2. Data are fitted to non-rotationally symmetric ellipsoids. The plotted data are for the horizontal meridian.

Fig. 5
Fig. 5

Correlation between fitted radii and asphericities for repeated measurements on an aspheric intraocular lens, performed with a non-contact profilometer. Data are fitted by conics. This example corresponds to aspherical intraocular lens with a very high asphericity and very different geometry from that of normal eyes, and therefore the graph has been plotted with a different aspect ratio than Figs. 2, 3, 4.

Fig. 6
Fig. 6

Results of the simulations for an ideal rotationally symmetric ellipsoid with R = 8   mm and Q = 0.3 , and added Gaussian noise of 10 μ m standard deviation. The central box shows the fitted parameters of 1000 fits, and the histograms show the dispersion in radius (top) and asphericity (right). The dashed lines indicate the nominal values. The elliptical contour limits the region where the mean squared error with respect to the nominal ellipsoid is lower than 0.5 μ m (see Fig. 7). The rectangular contour limits the region of 95% confidence intervals in R and Q.

Fig. 7
Fig. 7

Mean squared error between an ellipsoid with R = 8   mm and Q = 0.3 and ellipsoids with the radii and asphericities specified in the axes. Contours have been plotted for mean squared errors at 0.2 μ m steps between 0.1 and 0.7 μ m and at 1 μ m steps between 1 and 8 μ m .

Fig. 8
Fig. 8

Proportion of simulated experiments where a significant difference was detected between a reference ellipsoid with R = 8   mm and Q = 0.3 and a test ellipsoid with (a) R = 8 + Δ R   mm and Q = 0.3 or (b) R = 8   mm and Q = 0.3 + Δ Q . Each experiment compares five fits to the reference ellipsoid and five fits to the test one, simulating two sets of five repeated noisy measurements ( 10 μ m standard deviation at each point of the ellipsoid). For each amount of change of R or Q, we simulated 1000 experiments, and the proportion of detected significant differences is plotted. Circles: Proportion of trials where MANOVA identified a significant change. Squares: Proportion of trials where the Student’s t-test identified a significant change, either in radius or in asphericity. Triangles: Same as squares but applying the Bonferroni correction. Insets show a detail of the region near zero.

Tables (1)

Tables Icon

Table 1 Correlations between Fitted Radii and Asphericities in the Experimental Data

Equations (2)

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

x 2 = 2 R y ( 1 + Q ) y 2 ,
x 2 α + y 2 β + z 2 γ = 1.

Metrics