Abstract

We present a corneal profile in which the eccentricity, e(Q=e2), has a nonlinear continuous variation from the center outwards. This nonlinear variation is intended to fit and reproduce our current experimental data in which the anterior corneal surface of the human eye exhibits different values of e at different diameters. According to our clinical data, the variation is similar to an exponential decay. We propose a linear combination of two exponential functions to describe the variation of e. We then calculate the corneal sagittal height by substituting e in the first-order aspherical surface equation to obtain the corneal profile. This corneal profile will be used as a reference to analyze the resultant profiles of the customized corneal ablation in refractive surgery.

© 2009 Optical Society of America

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2009 (1)

A. Sinue Cruz Félix, E. López Olazagasti, M. A. Rosales, J. Ibarra, and E. Tepichín Rodríguez, “PSF and MTF comparison of two different surface ablation techniques for laser visual correction,” Proc. SPIE 7443, 7443E1 (2009).

2008 (2)

M. Mrochen and M. Büeler, “Asphärische Optiken: Physikalische Grundlagen,” Ophthalmologe 105, 224-233 (2008).
[CrossRef] [PubMed]

X. Wei and L. Thibos, “Modeling the eye's optical system by ocular wavefront tomography,” Opt. Express 16, 20490-20502 (2008).
[CrossRef] [PubMed]

2007 (4)

2006 (3)

R. Navarro, L. González, 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]

H. T. Kasprzak and D. R. Iskander, “Approximating ocular surfaces by generalised conic curves,” Ophthal. Physiol. Opt. 26, 602-609 (2006).
[CrossRef]

G. Dai, “Optical surface optimization for the correction of presbyopia,” Appl. Opt. 45, 4184-4195 (2006).
[CrossRef] [PubMed]

2005 (3)

R. G. Anera, C. Villa, J. R. Jiménez, R. Gutiérrez, and L. Jiménez del Barco, “Differences between real and predicted corneal shapes after aspherical corneal ablation,” Appl. Opt. 44, 4528-4532 (2005).
[CrossRef] [PubMed]

E. Tepichín, R. Cantú, M. A. Rosales, S. Chavez-Cerda, D. Sánchez de la Llave, A. Curioca, V. Montes, and J. Bonilla, “PSF and MTF analysis of the visual performance in undilated Mexican normal virgin whole eyes (UCVA≥20/20, 20/30 and 20/40),” Proc. SPIE 5688, 9-18 (2005).
[CrossRef]

E. Tepichín-Rodriguez, R. Cantú, M. A. Rosales, D. Sánchez de la Llave, J. Ibarra-Galitzia, G. Ramírez-Zavaleta, A. Curioca, V. Montes, and J. Bonilla, “Average PSF and MTF analysis of undilated normal virgin whole eyes,” Proc. SPIE 5959, 57-64 (2005).

2004 (6)

D. Gatinel, J. Malet, T. Hoang-Xuan, and D. T. Azar, “Corneal asphericity change after excimer laser hyperopic surgery: theoretical effects on corneal profiles and corresponding zernike expansions,” Invest. Ophthalmol. Vis. Sci. 45, 1349-1359 (2004).
[CrossRef] [PubMed]

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Whole eye wavefront aberrations in Mexican male subjects,” J. Refract. Surg. 20, S685-S688 (2004).
[PubMed]

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Advanced surface ablation for presbyopia using the Nidek EC-500 Laser,” J. Refract. Surg. 20, S711-S713(2004).
[PubMed]

J. Turuwhenua and J. Henderson, “A novel low-order method for recovery of the corneal shape,” Optom. Vis. Sci. 81, 863-871 (2004).
[CrossRef] [PubMed]

S. Somani, K. A. Tuan, and D. Chernyyak, “Corneal ashpericity and retinal image quality: a case study and simulations,” J. Refract. Surg. 20, S581-S585 (2004).
[PubMed]

V. A. D. P. Sicam, J. Coppens, T. J. T. P. van den Berg, and R. G. L. van der Heijde, “Corneal surface reconstruction algorithm that uses Zernike polynomial representation,” J. Opt. Soc. Am. A 21, 1300-1306 (2004).
[CrossRef]

2003 (2)

P. R. Preussner, J. Wahl, and C. Kramann, “Cornea model,” J. Cataract Refract. Surg. 29, 471-477 (2003).
[CrossRef] [PubMed]

J. R. Jiménez, R. G. Anera, and L. Jiménez del Barco, “Equation for corneal asphericity after corneal refractive surgery,” J. Refract. Surg. 19, 65-69 (2003).
[PubMed]

2002 (1)

D. Gatinel, J. Malet, T. Hoang-Xuan, and D. T. Azar, “Analysis of customized corneal ablations: theoretical limitations of increasing negative asphericity,” Invest. Ophthalmol. Vis. Sci. 43, 941-948 (2002).
[PubMed]

2001 (2)

D. Gatinel, T. Hoang-Xuan, and D. T. Azar, “Determination of corneal asphericity after myopia surgery with the excimer laser: a mathematical model,” Invest. Ophthalmol. Vis. Sci. 42, 1736-1742 (2001).
[PubMed]

J. R. Jiménez, R. González Anera, and L. Jiménez del Barco, “Effects on visual function of approximations of the corneal-ablation profile during refractive surgery,” Appl. Opt. 40, 2200-2205 (2001).
[CrossRef]

1997 (3)

H. L. Liou and N. A. Brennan, “Anatomically accurate, finite model eye for optical modeling,” J. Opt. Soc. Am. A 14, 1684-1695 (1997).
[CrossRef]

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vis. Sci. 74, 548-565 (1997).
[CrossRef] [PubMed]

J. Enderlein and R. Erdmann, “Fast fitting of multi-exponential decay curves,” Opt. Commun. 134, 371-378 (1997).
[CrossRef]

1995 (1)

T. O. Salmon and D. G. Horner, “Comparison of elevation, curvature, and power descriptors for corneal topographic mapping,” Optom. Vis. Sci. 72, 800-808 (1995).
[CrossRef] [PubMed]

1993 (1)

H. Burek and W. A. Douthwaite, “Mathematical models of the general corneal surface,” Ophthalmic Physiol. Opt. 13, 68-72 (1993).
[CrossRef] [PubMed]

1985 (1)

1983 (1)

1982 (1)

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

1972 (1)

1971 (1)

Anera, R. G.

R. G. Anera, C. Villa, J. R. Jiménez, R. Gutiérrez, and L. Jiménez del Barco, “Differences between real and predicted corneal shapes after aspherical corneal ablation,” Appl. Opt. 44, 4528-4532 (2005).
[CrossRef] [PubMed]

J. R. Jiménez, R. G. Anera, and L. Jiménez del Barco, “Equation for corneal asphericity after corneal refractive surgery,” J. Refract. Surg. 19, 65-69 (2003).
[PubMed]

Anera, R. González

Atchison, D.

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

Azar, D. T.

D. Gatinel, J. Malet, T. Hoang-Xuan, and D. T. Azar, “Corneal asphericity change after excimer laser hyperopic surgery: theoretical effects on corneal profiles and corresponding zernike expansions,” Invest. Ophthalmol. Vis. Sci. 45, 1349-1359 (2004).
[CrossRef] [PubMed]

D. Gatinel, J. Malet, T. Hoang-Xuan, and D. T. Azar, “Analysis of customized corneal ablations: theoretical limitations of increasing negative asphericity,” Invest. Ophthalmol. Vis. Sci. 43, 941-948 (2002).
[PubMed]

D. Gatinel, T. Hoang-Xuan, and D. T. Azar, “Determination of corneal asphericity after myopia surgery with the excimer laser: a mathematical model,” Invest. Ophthalmol. Vis. Sci. 42, 1736-1742 (2001).
[PubMed]

Bennett, A. G.

A. G. Bennett and R. B. Rabbetts, Clinical Visual Optics (Butterworths-Heinemann, 1989).

Bescós, J.

Bonilla, J.

E. Tepichín, R. Cantú, M. A. Rosales, S. Chavez-Cerda, D. Sánchez de la Llave, A. Curioca, V. Montes, and J. Bonilla, “PSF and MTF analysis of the visual performance in undilated Mexican normal virgin whole eyes (UCVA≥20/20, 20/30 and 20/40),” Proc. SPIE 5688, 9-18 (2005).
[CrossRef]

E. Tepichín-Rodriguez, R. Cantú, M. A. Rosales, D. Sánchez de la Llave, J. Ibarra-Galitzia, G. Ramírez-Zavaleta, A. Curioca, V. Montes, and J. Bonilla, “Average PSF and MTF analysis of undilated normal virgin whole eyes,” Proc. SPIE 5959, 57-64 (2005).

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Advanced surface ablation for presbyopia using the Nidek EC-500 Laser,” J. Refract. Surg. 20, S711-S713(2004).
[PubMed]

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Whole eye wavefront aberrations in Mexican male subjects,” J. Refract. Surg. 20, S685-S688 (2004).
[PubMed]

Bradley, A.

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vis. Sci. 74, 548-565 (1997).
[CrossRef] [PubMed]

L. N. Thibos and A. Bradley, “Modeling the refractive and neuro-sensor systems of the eye,” in Visual Instrumentation: Optical Design and Engineering Principles, P. Mouroulis, ed. (McGraw-Hill, 1999), pp. 101-159.

Brennan, N. A.

Büeler, M.

M. Mrochen and M. Büeler, “Asphärische Optiken: Physikalische Grundlagen,” Ophthalmologe 105, 224-233 (2008).
[CrossRef] [PubMed]

Burek, H.

H. Burek and W. A. Douthwaite, “Mathematical models of the general corneal surface,” Ophthalmic Physiol. Opt. 13, 68-72 (1993).
[CrossRef] [PubMed]

Campbell, C.

Cantú, R.

E. Tepichín-Rodriguez, R. Cantú, M. A. Rosales, D. Sánchez de la Llave, J. Ibarra-Galitzia, G. Ramírez-Zavaleta, A. Curioca, V. Montes, and J. Bonilla, “Average PSF and MTF analysis of undilated normal virgin whole eyes,” Proc. SPIE 5959, 57-64 (2005).

E. Tepichín, R. Cantú, M. A. Rosales, S. Chavez-Cerda, D. Sánchez de la Llave, A. Curioca, V. Montes, and J. Bonilla, “PSF and MTF analysis of the visual performance in undilated Mexican normal virgin whole eyes (UCVA≥20/20, 20/30 and 20/40),” Proc. SPIE 5688, 9-18 (2005).
[CrossRef]

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Whole eye wavefront aberrations in Mexican male subjects,” J. Refract. Surg. 20, S685-S688 (2004).
[PubMed]

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Advanced surface ablation for presbyopia using the Nidek EC-500 Laser,” J. Refract. Surg. 20, S711-S713(2004).
[PubMed]

E. Tepichín, Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro # 1, Puebla, 72840, México, E. López-Olazagasti, M. A. Rosales, and R. Cantú are preparing a manuscript to be called “Frequency and aberration analysis of the presbyopia and residual ametropia correction after pseudophakia with monofocal IOL using a pseudo-accommodative corneal surface ablation profile.”

Carney, L. G.

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

Chavez-Cerda, S.

E. Tepichín, R. Cantú, M. A. Rosales, S. Chavez-Cerda, D. Sánchez de la Llave, A. Curioca, V. Montes, and J. Bonilla, “PSF and MTF analysis of the visual performance in undilated Mexican normal virgin whole eyes (UCVA≥20/20, 20/30 and 20/40),” Proc. SPIE 5688, 9-18 (2005).
[CrossRef]

Chernyyak, D.

S. Somani, K. A. Tuan, and D. Chernyyak, “Corneal ashpericity and retinal image quality: a case study and simulations,” J. Refract. Surg. 20, S581-S585 (2004).
[PubMed]

Clark, B. A. J.

Coppens, J.

Cruz Félix, A. Sinue

A. Sinue Cruz Félix, E. López Olazagasti, M. A. Rosales, J. Ibarra, and E. Tepichín Rodríguez, “PSF and MTF comparison of two different surface ablation techniques for laser visual correction,” Proc. SPIE 7443, 7443E1 (2009).

Curioca, A.

E. Tepichín, R. Cantú, M. A. Rosales, S. Chavez-Cerda, D. Sánchez de la Llave, A. Curioca, V. Montes, and J. Bonilla, “PSF and MTF analysis of the visual performance in undilated Mexican normal virgin whole eyes (UCVA≥20/20, 20/30 and 20/40),” Proc. SPIE 5688, 9-18 (2005).
[CrossRef]

E. Tepichín-Rodriguez, R. Cantú, M. A. Rosales, D. Sánchez de la Llave, J. Ibarra-Galitzia, G. Ramírez-Zavaleta, A. Curioca, V. Montes, and J. Bonilla, “Average PSF and MTF analysis of undilated normal virgin whole eyes,” Proc. SPIE 5959, 57-64 (2005).

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Advanced surface ablation for presbyopia using the Nidek EC-500 Laser,” J. Refract. Surg. 20, S711-S713(2004).
[PubMed]

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Whole eye wavefront aberrations in Mexican male subjects,” J. Refract. Surg. 20, S685-S688 (2004).
[PubMed]

Dai, G.

Dai, G. M.

G. M. Dai, Wavefront Optics for Vision Correction (SPIE, 2008).
[CrossRef]

G. M. Dai, Wavefront Optics for Vision Correction (SPIE, 2008).
[CrossRef]

Dainty, C.

de la Llave, D. Sánchez

E. Tepichín-Rodriguez, R. Cantú, M. A. Rosales, D. Sánchez de la Llave, J. Ibarra-Galitzia, G. Ramírez-Zavaleta, A. Curioca, V. Montes, and J. Bonilla, “Average PSF and MTF analysis of undilated normal virgin whole eyes,” Proc. SPIE 5959, 57-64 (2005).

E. Tepichín, R. Cantú, M. A. Rosales, S. Chavez-Cerda, D. Sánchez de la Llave, A. Curioca, V. Montes, and J. Bonilla, “PSF and MTF analysis of the visual performance in undilated Mexican normal virgin whole eyes (UCVA≥20/20, 20/30 and 20/40),” Proc. SPIE 5688, 9-18 (2005).
[CrossRef]

del Barco, L. Jiménez

Douthwaite, W. A.

H. Burek and W. A. Douthwaite, “Mathematical models of the general corneal surface,” Ophthalmic Physiol. Opt. 13, 68-72 (1993).
[CrossRef] [PubMed]

El Hague, S. G.

Y. Le Grand and S. G. El Hague, Physiological Optics (Springer-Verlag, 1980).

Enderlein, J.

J. Enderlein and R. Erdmann, “Fast fitting of multi-exponential decay curves,” Opt. Commun. 134, 371-378 (1997).
[CrossRef]

Erdmann, R.

J. Enderlein and R. Erdmann, “Fast fitting of multi-exponential decay curves,” Opt. Commun. 134, 371-378 (1997).
[CrossRef]

Gatinel, D.

D. Gatinel, J. Malet, T. Hoang-Xuan, and D. T. Azar, “Corneal asphericity change after excimer laser hyperopic surgery: theoretical effects on corneal profiles and corresponding zernike expansions,” Invest. Ophthalmol. Vis. Sci. 45, 1349-1359 (2004).
[CrossRef] [PubMed]

D. Gatinel, J. Malet, T. Hoang-Xuan, and D. T. Azar, “Analysis of customized corneal ablations: theoretical limitations of increasing negative asphericity,” Invest. Ophthalmol. Vis. Sci. 43, 941-948 (2002).
[PubMed]

D. Gatinel, T. Hoang-Xuan, and D. T. Azar, “Determination of corneal asphericity after myopia surgery with the excimer laser: a mathematical model,” Invest. Ophthalmol. Vis. Sci. 42, 1736-1742 (2001).
[PubMed]

Gomez, A.

J. M. González-Méijome, C. Villa-Collar, R. Montés-Micó, and A. Gomez, “Asphericity of the human cornea with different corneal diameters,” J. Cataract Refract. Surg. 33, 465-473 (2007).
[CrossRef] [PubMed]

Goncharov, A. V.

González, L.

R. Navarro, L. González, 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]

González-Méijome, J. M.

J. M. González-Méijome, C. Villa-Collar, R. Montés-Micó, and A. Gomez, “Asphericity of the human cornea with different corneal diameters,” J. Cataract Refract. Surg. 33, 465-473 (2007).
[CrossRef] [PubMed]

Gullstrand, A.

A. Gullstrand, “Apendix II,” in Handbuch der Physiologischen Optik, Vol. 1, 3rd ed. (Voss, 1909), English translation edited by J. P. Southall (Optical Society of America, 1962), pp. 351-352.

Gutiérrez, R.

Henderson, J.

J. Turuwhenua and J. Henderson, “A novel low-order method for recovery of the corneal shape,” Optom. Vis. Sci. 81, 863-871 (2004).
[CrossRef] [PubMed]

Hernandez, J. L.

R. Navarro, L. González, 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]

Hoang-Xuan, T.

D. Gatinel, J. Malet, T. Hoang-Xuan, and D. T. Azar, “Corneal asphericity change after excimer laser hyperopic surgery: theoretical effects on corneal profiles and corresponding zernike expansions,” Invest. Ophthalmol. Vis. Sci. 45, 1349-1359 (2004).
[CrossRef] [PubMed]

D. Gatinel, J. Malet, T. Hoang-Xuan, and D. T. Azar, “Analysis of customized corneal ablations: theoretical limitations of increasing negative asphericity,” Invest. Ophthalmol. Vis. Sci. 43, 941-948 (2002).
[PubMed]

D. Gatinel, T. Hoang-Xuan, and D. T. Azar, “Determination of corneal asphericity after myopia surgery with the excimer laser: a mathematical model,” Invest. Ophthalmol. Vis. Sci. 42, 1736-1742 (2001).
[PubMed]

Horner, D. G.

T. O. Salmon and D. G. Horner, “Comparison of elevation, curvature, and power descriptors for corneal topographic mapping,” Optom. Vis. Sci. 72, 800-808 (1995).
[CrossRef] [PubMed]

Ibarra, J.

A. Sinue Cruz Félix, E. López Olazagasti, M. A. Rosales, J. Ibarra, and E. Tepichín Rodríguez, “PSF and MTF comparison of two different surface ablation techniques for laser visual correction,” Proc. SPIE 7443, 7443E1 (2009).

Ibarra-Galitzia, J.

E. Tepichín-Rodriguez, R. Cantú, M. A. Rosales, D. Sánchez de la Llave, J. Ibarra-Galitzia, G. Ramírez-Zavaleta, A. Curioca, V. Montes, and J. Bonilla, “Average PSF and MTF analysis of undilated normal virgin whole eyes,” Proc. SPIE 5959, 57-64 (2005).

Iskander, D. R.

H. T. Kasprzak and D. R. Iskander, “Approximating ocular surfaces by generalised conic curves,” Ophthal. Physiol. Opt. 26, 602-609 (2006).
[CrossRef]

Jiménez, J. R.

Kasprzak, H. T.

H. T. Kasprzak and D. R. Iskander, “Approximating ocular surfaces by generalised conic curves,” Ophthal. Physiol. Opt. 26, 602-609 (2006).
[CrossRef]

Kiely, P. M.

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

Kooijman, A. C.

Kramann, C.

P. R. Preussner, J. Wahl, and C. Kramann, “Cornea model,” J. Cataract Refract. Surg. 29, 471-477 (2003).
[CrossRef] [PubMed]

Le Grand, Y.

Y. Le Grand and S. G. El Hague, Physiological Optics (Springer-Verlag, 1980).

Y. Le Grand, Optique Physiologique. La Dioptrique de L'Oeil et Su Correction (Review d'Optique, 1946).

Liou, H. L.

López-Olazagasti, E.

E. Tepichín, Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro # 1, Puebla, 72840, México, E. López-Olazagasti, M. A. Rosales, and R. Cantú are preparing a manuscript to be called “Frequency and aberration analysis of the presbyopia and residual ametropia correction after pseudophakia with monofocal IOL using a pseudo-accommodative corneal surface ablation profile.”

Lotmar, W.

Mahajan, V. N.

V. N. Mahajan, Optical Imaging and Aberrations. Part 1: Ray Geometrical Optics (SPIE, 1998), Chap. 5.

Malet, J.

D. Gatinel, J. Malet, T. Hoang-Xuan, and D. T. Azar, “Corneal asphericity change after excimer laser hyperopic surgery: theoretical effects on corneal profiles and corresponding zernike expansions,” Invest. Ophthalmol. Vis. Sci. 45, 1349-1359 (2004).
[CrossRef] [PubMed]

D. Gatinel, J. Malet, T. Hoang-Xuan, and D. T. Azar, “Analysis of customized corneal ablations: theoretical limitations of increasing negative asphericity,” Invest. Ophthalmol. Vis. Sci. 43, 941-948 (2002).
[PubMed]

Montes, V.

E. Tepichín-Rodriguez, R. Cantú, M. A. Rosales, D. Sánchez de la Llave, J. Ibarra-Galitzia, G. Ramírez-Zavaleta, A. Curioca, V. Montes, and J. Bonilla, “Average PSF and MTF analysis of undilated normal virgin whole eyes,” Proc. SPIE 5959, 57-64 (2005).

E. Tepichín, R. Cantú, M. A. Rosales, S. Chavez-Cerda, D. Sánchez de la Llave, A. Curioca, V. Montes, and J. Bonilla, “PSF and MTF analysis of the visual performance in undilated Mexican normal virgin whole eyes (UCVA≥20/20, 20/30 and 20/40),” Proc. SPIE 5688, 9-18 (2005).
[CrossRef]

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Advanced surface ablation for presbyopia using the Nidek EC-500 Laser,” J. Refract. Surg. 20, S711-S713(2004).
[PubMed]

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Whole eye wavefront aberrations in Mexican male subjects,” J. Refract. Surg. 20, S685-S688 (2004).
[PubMed]

Montés-Micó, R.

J. M. González-Méijome, C. Villa-Collar, R. Montés-Micó, and A. Gomez, “Asphericity of the human cornea with different corneal diameters,” J. Cataract Refract. Surg. 33, 465-473 (2007).
[CrossRef] [PubMed]

Mrochen, M.

M. Mrochen and M. Büeler, “Asphärische Optiken: Physikalische Grundlagen,” Ophthalmologe 105, 224-233 (2008).
[CrossRef] [PubMed]

Navarro, R.

R. Navarro, L. González, 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]

R. Navarro, J. Santamaría, and J. Bescós, “Accommodation-dependent model of the human eye with aspherics,” J. Opt. Soc. Am. A 2, 1273-1281 (1985).
[CrossRef] [PubMed]

Norrby, S.

Olazagasti, E. López

A. Sinue Cruz Félix, E. López Olazagasti, M. A. Rosales, J. Ibarra, and E. Tepichín Rodríguez, “PSF and MTF comparison of two different surface ablation techniques for laser visual correction,” Proc. SPIE 7443, 7443E1 (2009).

Piers, P.

Preussner, P. R.

P. R. Preussner, J. Wahl, and C. Kramann, “Cornea model,” J. Cataract Refract. Surg. 29, 471-477 (2003).
[CrossRef] [PubMed]

Priest, D. A.

D. A. Priest, “The development of an average, anatomically based, young adult, GRIN eye model” MSc thesis (University of Waterloo, 2004).

Rabbetts, R. B.

A. G. Bennett and R. B. Rabbetts, Clinical Visual Optics (Butterworths-Heinemann, 1989).

Ramírez-Zavaleta, G.

E. Tepichín-Rodriguez, R. Cantú, M. A. Rosales, D. Sánchez de la Llave, J. Ibarra-Galitzia, G. Ramírez-Zavaleta, A. Curioca, V. Montes, and J. Bonilla, “Average PSF and MTF analysis of undilated normal virgin whole eyes,” Proc. SPIE 5959, 57-64 (2005).

Roorda, A.

A. Roorda, “Human visual system--image formation,” in Encyclopedia of human imaging science and technology, J. P. Hornack, ed. (Wiley, 2002), pp. 539-557.

Rosales, M. A.

A. Sinue Cruz Félix, E. López Olazagasti, M. A. Rosales, J. Ibarra, and E. Tepichín Rodríguez, “PSF and MTF comparison of two different surface ablation techniques for laser visual correction,” Proc. SPIE 7443, 7443E1 (2009).

E. Tepichín-Rodriguez, R. Cantú, M. A. Rosales, D. Sánchez de la Llave, J. Ibarra-Galitzia, G. Ramírez-Zavaleta, A. Curioca, V. Montes, and J. Bonilla, “Average PSF and MTF analysis of undilated normal virgin whole eyes,” Proc. SPIE 5959, 57-64 (2005).

E. Tepichín, R. Cantú, M. A. Rosales, S. Chavez-Cerda, D. Sánchez de la Llave, A. Curioca, V. Montes, and J. Bonilla, “PSF and MTF analysis of the visual performance in undilated Mexican normal virgin whole eyes (UCVA≥20/20, 20/30 and 20/40),” Proc. SPIE 5688, 9-18 (2005).
[CrossRef]

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Whole eye wavefront aberrations in Mexican male subjects,” J. Refract. Surg. 20, S685-S688 (2004).
[PubMed]

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Advanced surface ablation for presbyopia using the Nidek EC-500 Laser,” J. Refract. Surg. 20, S711-S713(2004).
[PubMed]

E. Tepichín, Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro # 1, Puebla, 72840, México, E. López-Olazagasti, M. A. Rosales, and R. Cantú are preparing a manuscript to be called “Frequency and aberration analysis of the presbyopia and residual ametropia correction after pseudophakia with monofocal IOL using a pseudo-accommodative corneal surface ablation profile.”

Salmon, T. O.

T. O. Salmon and D. G. Horner, “Comparison of elevation, curvature, and power descriptors for corneal topographic mapping,” Optom. Vis. Sci. 72, 800-808 (1995).
[CrossRef] [PubMed]

Santamaría, J.

Schwiegerling, J.

J. Schwiegerling, Field Guide to Visual and Ophtalmic Optics (SPIE, 2004).
[CrossRef]

Sicam, V. A. D. P.

Smith, G.

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

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

Somani, S.

S. Somani, K. A. Tuan, and D. Chernyyak, “Corneal ashpericity and retinal image quality: a case study and simulations,” J. Refract. Surg. 20, S581-S585 (2004).
[PubMed]

Tepichin, E.

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Whole eye wavefront aberrations in Mexican male subjects,” J. Refract. Surg. 20, S685-S688 (2004).
[PubMed]

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Advanced surface ablation for presbyopia using the Nidek EC-500 Laser,” J. Refract. Surg. 20, S711-S713(2004).
[PubMed]

Tepichín, E.

E. Tepichín, R. Cantú, M. A. Rosales, S. Chavez-Cerda, D. Sánchez de la Llave, A. Curioca, V. Montes, and J. Bonilla, “PSF and MTF analysis of the visual performance in undilated Mexican normal virgin whole eyes (UCVA≥20/20, 20/30 and 20/40),” Proc. SPIE 5688, 9-18 (2005).
[CrossRef]

E. Tepichín, Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro # 1, Puebla, 72840, México, E. López-Olazagasti, M. A. Rosales, and R. Cantú are preparing a manuscript to be called “Frequency and aberration analysis of the presbyopia and residual ametropia correction after pseudophakia with monofocal IOL using a pseudo-accommodative corneal surface ablation profile.”

Tepichín Rodríguez, E.

A. Sinue Cruz Félix, E. López Olazagasti, M. A. Rosales, J. Ibarra, and E. Tepichín Rodríguez, “PSF and MTF comparison of two different surface ablation techniques for laser visual correction,” Proc. SPIE 7443, 7443E1 (2009).

Tepichín-Rodriguez, E.

E. Tepichín-Rodriguez, R. Cantú, M. A. Rosales, D. Sánchez de la Llave, J. Ibarra-Galitzia, G. Ramírez-Zavaleta, A. Curioca, V. Montes, and J. Bonilla, “Average PSF and MTF analysis of undilated normal virgin whole eyes,” Proc. SPIE 5959, 57-64 (2005).

Thibos, L.

Thibos, L. N.

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vis. Sci. 74, 548-565 (1997).
[CrossRef] [PubMed]

L. N. Thibos and A. Bradley, “Modeling the refractive and neuro-sensor systems of the eye,” in Visual Instrumentation: Optical Design and Engineering Principles, P. Mouroulis, ed. (McGraw-Hill, 1999), pp. 101-159.

Tuan, K. A.

S. Somani, K. A. Tuan, and D. Chernyyak, “Corneal ashpericity and retinal image quality: a case study and simulations,” J. Refract. Surg. 20, S581-S585 (2004).
[PubMed]

Turuwhenua, J.

J. Turuwhenua, “Corneal surface reconstruction algorithm using Zernike polynomial representation: improvements,” J. Opt. Soc. Am. A 24, 1551-1561 (2007).
[CrossRef]

J. Turuwhenua and J. Henderson, “A novel low-order method for recovery of the corneal shape,” Optom. Vis. Sci. 81, 863-871 (2004).
[CrossRef] [PubMed]

van den Berg, T. J. T. P.

van der Heijde, R. G. L.

van der Mooren, M.

Villa, C.

Villa-Collar, C.

J. M. González-Méijome, C. Villa-Collar, R. Montés-Micó, and A. Gomez, “Asphericity of the human cornea with different corneal diameters,” J. Cataract Refract. Surg. 33, 465-473 (2007).
[CrossRef] [PubMed]

Wahl, J.

P. R. Preussner, J. Wahl, and C. Kramann, “Cornea model,” J. Cataract Refract. Surg. 29, 471-477 (2003).
[CrossRef] [PubMed]

Wei, X.

Weisstein, E. W.

E. W. Weisstein, “Nelder-Mead method in MathWorld,” http://mathworld.wolfram.com/Nelder-MeadMethod.html.

Ye, M.

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vis. Sci. 74, 548-565 (1997).
[CrossRef] [PubMed]

Zhang, X.

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vis. Sci. 74, 548-565 (1997).
[CrossRef] [PubMed]

Appl. Opt. (4)

Invest. Ophthalmol. Vis. Sci. (3)

D. Gatinel, J. Malet, T. Hoang-Xuan, and D. T. Azar, “Corneal asphericity change after excimer laser hyperopic surgery: theoretical effects on corneal profiles and corresponding zernike expansions,” Invest. Ophthalmol. Vis. Sci. 45, 1349-1359 (2004).
[CrossRef] [PubMed]

D. Gatinel, T. Hoang-Xuan, and D. T. Azar, “Determination of corneal asphericity after myopia surgery with the excimer laser: a mathematical model,” Invest. Ophthalmol. Vis. Sci. 42, 1736-1742 (2001).
[PubMed]

D. Gatinel, J. Malet, T. Hoang-Xuan, and D. T. Azar, “Analysis of customized corneal ablations: theoretical limitations of increasing negative asphericity,” Invest. Ophthalmol. Vis. Sci. 43, 941-948 (2002).
[PubMed]

J. Cataract Refract. Surg. (2)

P. R. Preussner, J. Wahl, and C. Kramann, “Cornea model,” J. Cataract Refract. Surg. 29, 471-477 (2003).
[CrossRef] [PubMed]

J. M. González-Méijome, C. Villa-Collar, R. Montés-Micó, and A. Gomez, “Asphericity of the human cornea with different corneal diameters,” J. Cataract Refract. Surg. 33, 465-473 (2007).
[CrossRef] [PubMed]

J. Opt. Soc. Am A (1)

R. Navarro, L. González, 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]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (5)

J. Refract. Surg. (4)

S. Somani, K. A. Tuan, and D. Chernyyak, “Corneal ashpericity and retinal image quality: a case study and simulations,” J. Refract. Surg. 20, S581-S585 (2004).
[PubMed]

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Advanced surface ablation for presbyopia using the Nidek EC-500 Laser,” J. Refract. Surg. 20, S711-S713(2004).
[PubMed]

J. R. Jiménez, R. G. Anera, and L. Jiménez del Barco, “Equation for corneal asphericity after corneal refractive surgery,” J. Refract. Surg. 19, 65-69 (2003).
[PubMed]

R. Cantú, M. A. Rosales, E. Tepichin, A. Curioca, V. Montes, and J. Bonilla, “Whole eye wavefront aberrations in Mexican male subjects,” J. Refract. Surg. 20, S685-S688 (2004).
[PubMed]

Ophthal. Physiol. Opt. (1)

H. T. Kasprzak and D. R. Iskander, “Approximating ocular surfaces by generalised conic curves,” Ophthal. Physiol. Opt. 26, 602-609 (2006).
[CrossRef]

Ophthalmic Physiol. Opt. (1)

H. Burek and W. A. Douthwaite, “Mathematical models of the general corneal surface,” Ophthalmic Physiol. Opt. 13, 68-72 (1993).
[CrossRef] [PubMed]

Ophthalmologe (1)

M. Mrochen and M. Büeler, “Asphärische Optiken: Physikalische Grundlagen,” Ophthalmologe 105, 224-233 (2008).
[CrossRef] [PubMed]

Opt. Acta (1)

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

Opt. Commun. (1)

J. Enderlein and R. Erdmann, “Fast fitting of multi-exponential decay curves,” Opt. Commun. 134, 371-378 (1997).
[CrossRef]

Opt. Express (1)

Optom. Vis. Sci. (3)

T. O. Salmon and D. G. Horner, “Comparison of elevation, curvature, and power descriptors for corneal topographic mapping,” Optom. Vis. Sci. 72, 800-808 (1995).
[CrossRef] [PubMed]

J. Turuwhenua and J. Henderson, “A novel low-order method for recovery of the corneal shape,” Optom. Vis. Sci. 81, 863-871 (2004).
[CrossRef] [PubMed]

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vis. Sci. 74, 548-565 (1997).
[CrossRef] [PubMed]

Proc. SPIE (3)

E. Tepichín, R. Cantú, M. A. Rosales, S. Chavez-Cerda, D. Sánchez de la Llave, A. Curioca, V. Montes, and J. Bonilla, “PSF and MTF analysis of the visual performance in undilated Mexican normal virgin whole eyes (UCVA≥20/20, 20/30 and 20/40),” Proc. SPIE 5688, 9-18 (2005).
[CrossRef]

E. Tepichín-Rodriguez, R. Cantú, M. A. Rosales, D. Sánchez de la Llave, J. Ibarra-Galitzia, G. Ramírez-Zavaleta, A. Curioca, V. Montes, and J. Bonilla, “Average PSF and MTF analysis of undilated normal virgin whole eyes,” Proc. SPIE 5959, 57-64 (2005).

A. Sinue Cruz Félix, E. López Olazagasti, M. A. Rosales, J. Ibarra, and E. Tepichín Rodríguez, “PSF and MTF comparison of two different surface ablation techniques for laser visual correction,” Proc. SPIE 7443, 7443E1 (2009).

Other (14)

E. Tepichín, Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro # 1, Puebla, 72840, México, E. López-Olazagasti, M. A. Rosales, and R. Cantú are preparing a manuscript to be called “Frequency and aberration analysis of the presbyopia and residual ametropia correction after pseudophakia with monofocal IOL using a pseudo-accommodative corneal surface ablation profile.”

D. A. Priest, “The development of an average, anatomically based, young adult, GRIN eye model” MSc thesis (University of Waterloo, 2004).

L. N. Thibos and A. Bradley, “Modeling the refractive and neuro-sensor systems of the eye,” in Visual Instrumentation: Optical Design and Engineering Principles, P. Mouroulis, ed. (McGraw-Hill, 1999), pp. 101-159.

A. Gullstrand, “Apendix II,” in Handbuch der Physiologischen Optik, Vol. 1, 3rd ed. (Voss, 1909), English translation edited by J. P. Southall (Optical Society of America, 1962), pp. 351-352.

Y. Le Grand, Optique Physiologique. La Dioptrique de L'Oeil et Su Correction (Review d'Optique, 1946).

Y. Le Grand and S. G. El Hague, Physiological Optics (Springer-Verlag, 1980).

V. N. Mahajan, Optical Imaging and Aberrations. Part 1: Ray Geometrical Optics (SPIE, 1998), Chap. 5.

G. M. Dai, Wavefront Optics for Vision Correction (SPIE, 2008).
[CrossRef]

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

A. G. Bennett and R. B. Rabbetts, Clinical Visual Optics (Butterworths-Heinemann, 1989).

A. Roorda, “Human visual system--image formation,” in Encyclopedia of human imaging science and technology, J. P. Hornack, ed. (Wiley, 2002), pp. 539-557.

G. M. Dai, Wavefront Optics for Vision Correction (SPIE, 2008).
[CrossRef]

E. W. Weisstein, “Nelder-Mead method in MathWorld,” http://mathworld.wolfram.com/Nelder-MeadMethod.html.

J. Schwiegerling, Field Guide to Visual and Ophtalmic Optics (SPIE, 2004).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Sample of our clinical data showing the variation of the eccentricity as a function of the distance to the optical axis. We also show two horizontal lines with the corresponding constant eccentricity value for the average normal cornea e = 0.51 ( Q = 0.26 ), and the zero spherical aberration eccentricity value e = 0.73 ( Q = 0.528 ).

Fig. 2
Fig. 2

(a) Data set and (b) graphical fit of two different eye samples.

Fig. 3
Fig. 3

Two-decay model fit for the average cornea.

Fig. 4
Fig. 4

Coordinate systems used for image forming systems.

Fig. 5
Fig. 5

(a) Comparison of the proposed aspherical profile and the conic profiles described in the text and (b) zoom in on the region where the differences between the profiles are manifest.

Fig. 6
Fig. 6

(a) Pre-op and post-op corneal profiles with variable eccentricity and (b) zoom in on the region where the differences between the profiles are manifest.

Tables (1)

Tables Icon

Table 1 Pre and Post-op UCVA, BSCVA, and Manifest Refraction for Both Eyes of the Patient

Equations (4)

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

e ( r ) = C 1 exp ( λ 1 r ) + C 2 exp ( λ 2 r ) ,
e ( r ) = 2.746 exp ( 0.685 r ) + 0.294 exp ( 0.131 r ) .
z = r 2 R 1 + 1 ( 1 + Q ) ( r R ) 2 .
z ( r ) = r 2 R + ( R 2 ( 1 ( C 1 exp ( λ 1 r ) + C 2 exp ( λ 2 r ) ) r 2 ) ) 1 / 2 ,

Metrics