Abstract

We deduce a mathematical equation for corneal asphericity after refractive surgery when the Munnerlyn formula is used. For this, an analytical least-squares procedure is used. The equation explains the discrepancies found by different authors when the Munnerlyn formula or its paraxial approximation is used. Equations for corneal asphericity deduced here may be of clinical relevance, for example, in studying quantitatively the role of different factors (decentration, type of laser, optical role of the flap, wound healing, biomechanical effects, technical procedures) during corneal ablation.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. T. Holladay, D. R. Dudeja, J. Chang, “Functional vision and corneal changes after laser in situ keratomileusis determined by contrast sensitivity, glare testing, and corneal topography,” J. Cataract Refract. Surg. 25, 663–669 (1999).
    [CrossRef] [PubMed]
  2. J. T. Holladay, J. A. Janes, “Topographic changes in corneal asphericity and effective optical zone after laser in situ keratomileusis,” J. Cataract Refract. Surg. 28, 942–947 (2002).
    [CrossRef] [PubMed]
  3. E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).
  4. R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, J. Bermúdez, E. Hita, “Changes in corneal asphericity after laser in situ keratomileusis,” J. Cataract Refract. Surg. 29, 762–768 (2003).
    [CrossRef] [PubMed]
  5. C. C. Chen, A. Izadshenas, A. A. Rana, D. T. Azar, “Corneal asphericity after hyperopic laser in situ keratomileusis,” J. Cataract Refract. Surg. 28, 1539–1545 (2002).
    [CrossRef] [PubMed]
  6. J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, “Equation for corneal asphericity after corneal refractive surgery,” J. Refract. Surg. 19, 65–69 (2003).
    [PubMed]
  7. J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, “Effect on laser-ablation algorithms of reflection losses and nonnormal incidence on the anterior cornea,” Appl. Phys. Lett. 81, 1521–1523 (2002).
    [CrossRef]
  8. J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, “Predicting changes in corneal asphericity after hyperopic laser in situ keratomileusis,” J. Cataract Refract. Surg. 29, 1468 (2003).
    [CrossRef]
  9. D. Gatinel, T. Hoang-Xuan, D. T. Azar, “Determination of corneal asphericity after myopia surgery with the excimer laser: a mathematical model,” Invest. Ophthalmol. Visual Sci. 42, 1736–1742 (2001).
  10. C. R. Munnerlyn, S. J. Koons, J. Marshall, “Photorefractive keratotomy: a technique for laser refractive surgery,” J. Cataract Refract. Surg. 14, 46–52 (1988).
    [CrossRef] [PubMed]
  11. J. T. Lin, “Critical review on refractive surgical lasers,” Opt. Eng. 34, 668–675 (1995).
    [CrossRef]
  12. J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, “Effect on visual function of approximations of the corneal-ablation profile during refractive surgery,” Appl. Opt. 40, 2200–2205 (2001).
    [CrossRef]
  13. D. Gatinel, J. Malet, T. Hoang-Xuan, D. T. Azar, “Analysis of customized corneal ablation: theoretical limitations of increasing negative asphericity,” Invest. Ophthalmol. Visual Sci. 43, 941–948 (2002).
  14. D. Huang, M. Tang, R. Shekhar, “Mathematical model of corneal surface smoothing after laser refractive surgery,” Am. J. Ophthalmol. 135, 267–278 (2003).
    [CrossRef] [PubMed]
  15. M. Mrochen, M. Kaemmerer, P. Mierdel, T. Seiler, “Increased higher-order optical aberrations after laser refractive surgery,” J. Cataract Refract. Surg. 27, 362–369 (2001).
    [CrossRef] [PubMed]
  16. A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29, 1204–1210 (2003).
    [CrossRef] [PubMed]
  17. C. Roberts, W. Dupps, “Corneal biomechanics and their role in corneal ablative procedures,” in Customized Corneal Ablation: the Quest for Supervision, S. M. MacRae, R. R. Krueger, R. A. Applegate, eds. (SLACK Inc., Thorofare, N.J., 2001), pp. 109–132.
  18. R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, E. Hita, “Changes in corneal asphericity after laser refractive surgery, including reflection losses and nonnormal incidence upon the anterior cornea,” Opt. Lett. 28, 417–419 (2003).
    [CrossRef] [PubMed]
  19. R. A. Applegate, G. Hilmantel, H. C. Howland, E. Y. Tu, T. Starck, E. J. Zayac, “Corneal first surface optical aberrations and visual performance,” J. Refract. Surg. 16, 507–514 (2000).
    [PubMed]
  20. T. Seiler, U. Genth, A. Holschbach, M. Derse, “Aspheric photorefractive keratectomy with excimer laser,” Refract. Corneal Surg. 9, 166–172 (1993).
    [PubMed]
  21. J. Schwiegerling, R. W. Snyder, “Corneal ablation atterns to correct for spherical aberration in photorefractive keratectomy,” J. Cataract Refract. Surg. 26, 214–221 (2000).
    [CrossRef] [PubMed]
  22. S. MacRae, J. Schwiegerling, R. W. Snyder, “Customized and low spherical aberration corneal ablation design,” J. Refract. Surg. (Suppl.) 15, S246–S248 (1999).
  23. F. Manns, A. Ho, J. M. Parel, W. Culbertson, “Ablation profiles for wavefront-guided correction of myopia and primary spheical aberration,” J. Cataract Refract. Surg. 28, 766–774 (2002).
    [CrossRef] [PubMed]
  24. J. A. Dı́az, R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, “Optimum corneal asphericity of myopic eyes for refractive surgery,” J. Mod. Opt. 50, 1903–1915 (2003).
    [CrossRef]

2003 (7)

R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, J. Bermúdez, E. Hita, “Changes in corneal asphericity after laser in situ keratomileusis,” J. Cataract Refract. Surg. 29, 762–768 (2003).
[CrossRef] [PubMed]

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

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, “Predicting changes in corneal asphericity after hyperopic laser in situ keratomileusis,” J. Cataract Refract. Surg. 29, 1468 (2003).
[CrossRef]

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29, 1204–1210 (2003).
[CrossRef] [PubMed]

R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, E. Hita, “Changes in corneal asphericity after laser refractive surgery, including reflection losses and nonnormal incidence upon the anterior cornea,” Opt. Lett. 28, 417–419 (2003).
[CrossRef] [PubMed]

D. Huang, M. Tang, R. Shekhar, “Mathematical model of corneal surface smoothing after laser refractive surgery,” Am. J. Ophthalmol. 135, 267–278 (2003).
[CrossRef] [PubMed]

J. A. Dı́az, R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, “Optimum corneal asphericity of myopic eyes for refractive surgery,” J. Mod. Opt. 50, 1903–1915 (2003).
[CrossRef]

2002 (5)

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

D. Gatinel, J. Malet, T. Hoang-Xuan, D. T. Azar, “Analysis of customized corneal ablation: theoretical limitations of increasing negative asphericity,” Invest. Ophthalmol. Visual Sci. 43, 941–948 (2002).

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, “Effect on laser-ablation algorithms of reflection losses and nonnormal incidence on the anterior cornea,” Appl. Phys. Lett. 81, 1521–1523 (2002).
[CrossRef]

C. C. Chen, A. Izadshenas, A. A. Rana, D. T. Azar, “Corneal asphericity after hyperopic laser in situ keratomileusis,” J. Cataract Refract. Surg. 28, 1539–1545 (2002).
[CrossRef] [PubMed]

J. T. Holladay, J. A. Janes, “Topographic changes in corneal asphericity and effective optical zone after laser in situ keratomileusis,” J. Cataract Refract. Surg. 28, 942–947 (2002).
[CrossRef] [PubMed]

2001 (4)

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

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

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

M. Mrochen, M. Kaemmerer, P. Mierdel, T. Seiler, “Increased higher-order optical aberrations after laser refractive surgery,” J. Cataract Refract. Surg. 27, 362–369 (2001).
[CrossRef] [PubMed]

2000 (2)

J. Schwiegerling, R. W. Snyder, “Corneal ablation atterns to correct for spherical aberration in photorefractive keratectomy,” J. Cataract Refract. Surg. 26, 214–221 (2000).
[CrossRef] [PubMed]

R. A. Applegate, G. Hilmantel, H. C. Howland, E. Y. Tu, T. Starck, E. J. Zayac, “Corneal first surface optical aberrations and visual performance,” J. Refract. Surg. 16, 507–514 (2000).
[PubMed]

1999 (2)

J. T. Holladay, D. R. Dudeja, J. Chang, “Functional vision and corneal changes after laser in situ keratomileusis determined by contrast sensitivity, glare testing, and corneal topography,” J. Cataract Refract. Surg. 25, 663–669 (1999).
[CrossRef] [PubMed]

S. MacRae, J. Schwiegerling, R. W. Snyder, “Customized and low spherical aberration corneal ablation design,” J. Refract. Surg. (Suppl.) 15, S246–S248 (1999).

1995 (1)

J. T. Lin, “Critical review on refractive surgical lasers,” Opt. Eng. 34, 668–675 (1995).
[CrossRef]

1993 (1)

T. Seiler, U. Genth, A. Holschbach, M. Derse, “Aspheric photorefractive keratectomy with excimer laser,” Refract. Corneal Surg. 9, 166–172 (1993).
[PubMed]

1988 (1)

C. R. Munnerlyn, S. J. Koons, J. Marshall, “Photorefractive keratotomy: a technique for laser refractive surgery,” J. Cataract Refract. Surg. 14, 46–52 (1988).
[CrossRef] [PubMed]

Anera, R. G.

R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, J. Bermúdez, E. Hita, “Changes in corneal asphericity after laser in situ keratomileusis,” J. Cataract Refract. Surg. 29, 762–768 (2003).
[CrossRef] [PubMed]

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

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, “Predicting changes in corneal asphericity after hyperopic laser in situ keratomileusis,” J. Cataract Refract. Surg. 29, 1468 (2003).
[CrossRef]

J. A. Dı́az, R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, “Optimum corneal asphericity of myopic eyes for refractive surgery,” J. Mod. Opt. 50, 1903–1915 (2003).
[CrossRef]

R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, E. Hita, “Changes in corneal asphericity after laser refractive surgery, including reflection losses and nonnormal incidence upon the anterior cornea,” Opt. Lett. 28, 417–419 (2003).
[CrossRef] [PubMed]

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, “Effect on laser-ablation algorithms of reflection losses and nonnormal incidence on the anterior cornea,” Appl. Phys. Lett. 81, 1521–1523 (2002).
[CrossRef]

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

Applegate, R. A.

R. A. Applegate, G. Hilmantel, H. C. Howland, E. Y. Tu, T. Starck, E. J. Zayac, “Corneal first surface optical aberrations and visual performance,” J. Refract. Surg. 16, 507–514 (2000).
[PubMed]

Azar, D. T.

D. Gatinel, J. Malet, T. Hoang-Xuan, D. T. Azar, “Analysis of customized corneal ablation: theoretical limitations of increasing negative asphericity,” Invest. Ophthalmol. Visual Sci. 43, 941–948 (2002).

C. C. Chen, A. Izadshenas, A. A. Rana, D. T. Azar, “Corneal asphericity after hyperopic laser in situ keratomileusis,” J. Cataract Refract. Surg. 28, 1539–1545 (2002).
[CrossRef] [PubMed]

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

Barbero, S.

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

Bermúdez, J.

R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, J. Bermúdez, E. Hita, “Changes in corneal asphericity after laser in situ keratomileusis,” J. Cataract Refract. Surg. 29, 762–768 (2003).
[CrossRef] [PubMed]

Calvano, C. J.

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29, 1204–1210 (2003).
[CrossRef] [PubMed]

Chang, A. W.

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29, 1204–1210 (2003).
[CrossRef] [PubMed]

Chang, J.

J. T. Holladay, D. R. Dudeja, J. Chang, “Functional vision and corneal changes after laser in situ keratomileusis determined by contrast sensitivity, glare testing, and corneal topography,” J. Cataract Refract. Surg. 25, 663–669 (1999).
[CrossRef] [PubMed]

Chen, C. C.

C. C. Chen, A. Izadshenas, A. A. Rana, D. T. Azar, “Corneal asphericity after hyperopic laser in situ keratomileusis,” J. Cataract Refract. Surg. 28, 1539–1545 (2002).
[CrossRef] [PubMed]

Contreras, J. E.

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29, 1204–1210 (2003).
[CrossRef] [PubMed]

Crnic-Rein, T. C.

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29, 1204–1210 (2003).
[CrossRef] [PubMed]

Culbertson, W.

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

Derse, M.

T. Seiler, U. Genth, A. Holschbach, M. Derse, “Aspheric photorefractive keratectomy with excimer laser,” Refract. Corneal Surg. 9, 166–172 (1993).
[PubMed]

Di´az, J. A.

J. A. Dı́az, R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, “Optimum corneal asphericity of myopic eyes for refractive surgery,” J. Mod. Opt. 50, 1903–1915 (2003).
[CrossRef]

Dudeja, D. R.

J. T. Holladay, D. R. Dudeja, J. Chang, “Functional vision and corneal changes after laser in situ keratomileusis determined by contrast sensitivity, glare testing, and corneal topography,” J. Cataract Refract. Surg. 25, 663–669 (1999).
[CrossRef] [PubMed]

Dupps, W.

C. Roberts, W. Dupps, “Corneal biomechanics and their role in corneal ablative procedures,” in Customized Corneal Ablation: the Quest for Supervision, S. M. MacRae, R. R. Krueger, R. A. Applegate, eds. (SLACK Inc., Thorofare, N.J., 2001), pp. 109–132.

Gatinel, D.

D. Gatinel, J. Malet, T. Hoang-Xuan, D. T. Azar, “Analysis of customized corneal ablation: theoretical limitations of increasing negative asphericity,” Invest. Ophthalmol. Visual Sci. 43, 941–948 (2002).

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

Genth, U.

T. Seiler, U. Genth, A. Holschbach, M. Derse, “Aspheric photorefractive keratectomy with excimer laser,” Refract. Corneal Surg. 9, 166–172 (1993).
[PubMed]

Hilmantel, G.

R. A. Applegate, G. Hilmantel, H. C. Howland, E. Y. Tu, T. Starck, E. J. Zayac, “Corneal first surface optical aberrations and visual performance,” J. Refract. Surg. 16, 507–514 (2000).
[PubMed]

Hita, E.

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, “Predicting changes in corneal asphericity after hyperopic laser in situ keratomileusis,” J. Cataract Refract. Surg. 29, 1468 (2003).
[CrossRef]

R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, J. Bermúdez, E. Hita, “Changes in corneal asphericity after laser in situ keratomileusis,” J. Cataract Refract. Surg. 29, 762–768 (2003).
[CrossRef] [PubMed]

R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, E. Hita, “Changes in corneal asphericity after laser refractive surgery, including reflection losses and nonnormal incidence upon the anterior cornea,” Opt. Lett. 28, 417–419 (2003).
[CrossRef] [PubMed]

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, “Effect on laser-ablation algorithms of reflection losses and nonnormal incidence on the anterior cornea,” Appl. Phys. Lett. 81, 1521–1523 (2002).
[CrossRef]

Ho, A.

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

Hoang-Xuan, T.

D. Gatinel, J. Malet, T. Hoang-Xuan, D. T. Azar, “Analysis of customized corneal ablation: theoretical limitations of increasing negative asphericity,” Invest. Ophthalmol. Visual Sci. 43, 941–948 (2002).

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

Holladay, J. T.

J. T. Holladay, J. A. Janes, “Topographic changes in corneal asphericity and effective optical zone after laser in situ keratomileusis,” J. Cataract Refract. Surg. 28, 942–947 (2002).
[CrossRef] [PubMed]

J. T. Holladay, D. R. Dudeja, J. Chang, “Functional vision and corneal changes after laser in situ keratomileusis determined by contrast sensitivity, glare testing, and corneal topography,” J. Cataract Refract. Surg. 25, 663–669 (1999).
[CrossRef] [PubMed]

Holschbach, A.

T. Seiler, U. Genth, A. Holschbach, M. Derse, “Aspheric photorefractive keratectomy with excimer laser,” Refract. Corneal Surg. 9, 166–172 (1993).
[PubMed]

Howland, H. C.

R. A. Applegate, G. Hilmantel, H. C. Howland, E. Y. Tu, T. Starck, E. J. Zayac, “Corneal first surface optical aberrations and visual performance,” J. Refract. Surg. 16, 507–514 (2000).
[PubMed]

Huang, D.

D. Huang, M. Tang, R. Shekhar, “Mathematical model of corneal surface smoothing after laser refractive surgery,” Am. J. Ophthalmol. 135, 267–278 (2003).
[CrossRef] [PubMed]

Huynh, P. D.

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29, 1204–1210 (2003).
[CrossRef] [PubMed]

Izadshenas, A.

C. C. Chen, A. Izadshenas, A. A. Rana, D. T. Azar, “Corneal asphericity after hyperopic laser in situ keratomileusis,” J. Cataract Refract. Surg. 28, 1539–1545 (2002).
[CrossRef] [PubMed]

Janes, J. A.

J. T. Holladay, J. A. Janes, “Topographic changes in corneal asphericity and effective optical zone after laser in situ keratomileusis,” J. Cataract Refract. Surg. 28, 942–947 (2002).
[CrossRef] [PubMed]

Jiménez, J. R.

R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, J. Bermúdez, E. Hita, “Changes in corneal asphericity after laser in situ keratomileusis,” J. Cataract Refract. Surg. 29, 762–768 (2003).
[CrossRef] [PubMed]

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, “Predicting changes in corneal asphericity after hyperopic laser in situ keratomileusis,” J. Cataract Refract. Surg. 29, 1468 (2003).
[CrossRef]

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

J. A. Dı́az, R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, “Optimum corneal asphericity of myopic eyes for refractive surgery,” J. Mod. Opt. 50, 1903–1915 (2003).
[CrossRef]

R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, E. Hita, “Changes in corneal asphericity after laser refractive surgery, including reflection losses and nonnormal incidence upon the anterior cornea,” Opt. Lett. 28, 417–419 (2003).
[CrossRef] [PubMed]

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, “Effect on laser-ablation algorithms of reflection losses and nonnormal incidence on the anterior cornea,” Appl. Phys. Lett. 81, 1521–1523 (2002).
[CrossRef]

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

Jiménez del Barco, L.

R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, E. Hita, “Changes in corneal asphericity after laser refractive surgery, including reflection losses and nonnormal incidence upon the anterior cornea,” Opt. Lett. 28, 417–419 (2003).
[CrossRef] [PubMed]

J. A. Dı́az, R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, “Optimum corneal asphericity of myopic eyes for refractive surgery,” J. Mod. Opt. 50, 1903–1915 (2003).
[CrossRef]

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

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, “Predicting changes in corneal asphericity after hyperopic laser in situ keratomileusis,” J. Cataract Refract. Surg. 29, 1468 (2003).
[CrossRef]

R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, J. Bermúdez, E. Hita, “Changes in corneal asphericity after laser in situ keratomileusis,” J. Cataract Refract. Surg. 29, 762–768 (2003).
[CrossRef] [PubMed]

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, “Effect on laser-ablation algorithms of reflection losses and nonnormal incidence on the anterior cornea,” Appl. Phys. Lett. 81, 1521–1523 (2002).
[CrossRef]

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

Kaemmerer, M.

M. Mrochen, M. Kaemmerer, P. Mierdel, T. Seiler, “Increased higher-order optical aberrations after laser refractive surgery,” J. Cataract Refract. Surg. 27, 362–369 (2001).
[CrossRef] [PubMed]

Koons, S. J.

C. R. Munnerlyn, S. J. Koons, J. Marshall, “Photorefractive keratotomy: a technique for laser refractive surgery,” J. Cataract Refract. Surg. 14, 46–52 (1988).
[CrossRef] [PubMed]

Lin, J. T.

J. T. Lin, “Critical review on refractive surgical lasers,” Opt. Eng. 34, 668–675 (1995).
[CrossRef]

Llorente, L.

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

MacRae, S.

S. MacRae, J. Schwiegerling, R. W. Snyder, “Customized and low spherical aberration corneal ablation design,” J. Refract. Surg. (Suppl.) 15, S246–S248 (1999).

Malet, J.

D. Gatinel, J. Malet, T. Hoang-Xuan, D. T. Azar, “Analysis of customized corneal ablation: theoretical limitations of increasing negative asphericity,” Invest. Ophthalmol. Visual Sci. 43, 941–948 (2002).

Manns, F.

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

Marcos, S.

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

Marshall, J.

C. R. Munnerlyn, S. J. Koons, J. Marshall, “Photorefractive keratotomy: a technique for laser refractive surgery,” J. Cataract Refract. Surg. 14, 46–52 (1988).
[CrossRef] [PubMed]

Merayo-Lloves, J.

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

Mierdel, P.

M. Mrochen, M. Kaemmerer, P. Mierdel, T. Seiler, “Increased higher-order optical aberrations after laser refractive surgery,” J. Cataract Refract. Surg. 27, 362–369 (2001).
[CrossRef] [PubMed]

Moreno-Barriuso, E.

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

Mrochen, M.

M. Mrochen, M. Kaemmerer, P. Mierdel, T. Seiler, “Increased higher-order optical aberrations after laser refractive surgery,” J. Cataract Refract. Surg. 27, 362–369 (2001).
[CrossRef] [PubMed]

Munnerlyn, C. R.

C. R. Munnerlyn, S. J. Koons, J. Marshall, “Photorefractive keratotomy: a technique for laser refractive surgery,” J. Cataract Refract. Surg. 14, 46–52 (1988).
[CrossRef] [PubMed]

Navarro, R.

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

Parel, J. M.

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

Rana, A. A.

C. C. Chen, A. Izadshenas, A. A. Rana, D. T. Azar, “Corneal asphericity after hyperopic laser in situ keratomileusis,” J. Cataract Refract. Surg. 28, 1539–1545 (2002).
[CrossRef] [PubMed]

Roberts, C.

C. Roberts, W. Dupps, “Corneal biomechanics and their role in corneal ablative procedures,” in Customized Corneal Ablation: the Quest for Supervision, S. M. MacRae, R. R. Krueger, R. A. Applegate, eds. (SLACK Inc., Thorofare, N.J., 2001), pp. 109–132.

Schwiegerling, J.

J. Schwiegerling, R. W. Snyder, “Corneal ablation atterns to correct for spherical aberration in photorefractive keratectomy,” J. Cataract Refract. Surg. 26, 214–221 (2000).
[CrossRef] [PubMed]

S. MacRae, J. Schwiegerling, R. W. Snyder, “Customized and low spherical aberration corneal ablation design,” J. Refract. Surg. (Suppl.) 15, S246–S248 (1999).

Seiler, T.

M. Mrochen, M. Kaemmerer, P. Mierdel, T. Seiler, “Increased higher-order optical aberrations after laser refractive surgery,” J. Cataract Refract. Surg. 27, 362–369 (2001).
[CrossRef] [PubMed]

T. Seiler, U. Genth, A. Holschbach, M. Derse, “Aspheric photorefractive keratectomy with excimer laser,” Refract. Corneal Surg. 9, 166–172 (1993).
[PubMed]

Shekhar, R.

D. Huang, M. Tang, R. Shekhar, “Mathematical model of corneal surface smoothing after laser refractive surgery,” Am. J. Ophthalmol. 135, 267–278 (2003).
[CrossRef] [PubMed]

Snyder, R. W.

J. Schwiegerling, R. W. Snyder, “Corneal ablation atterns to correct for spherical aberration in photorefractive keratectomy,” J. Cataract Refract. Surg. 26, 214–221 (2000).
[CrossRef] [PubMed]

S. MacRae, J. Schwiegerling, R. W. Snyder, “Customized and low spherical aberration corneal ablation design,” J. Refract. Surg. (Suppl.) 15, S246–S248 (1999).

Starck, T.

R. A. Applegate, G. Hilmantel, H. C. Howland, E. Y. Tu, T. Starck, E. J. Zayac, “Corneal first surface optical aberrations and visual performance,” J. Refract. Surg. 16, 507–514 (2000).
[PubMed]

Tang, M.

D. Huang, M. Tang, R. Shekhar, “Mathematical model of corneal surface smoothing after laser refractive surgery,” Am. J. Ophthalmol. 135, 267–278 (2003).
[CrossRef] [PubMed]

Thall, E. H.

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29, 1204–1210 (2003).
[CrossRef] [PubMed]

Tsang, A. C.

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29, 1204–1210 (2003).
[CrossRef] [PubMed]

Tu, E. Y.

R. A. Applegate, G. Hilmantel, H. C. Howland, E. Y. Tu, T. Starck, E. J. Zayac, “Corneal first surface optical aberrations and visual performance,” J. Refract. Surg. 16, 507–514 (2000).
[PubMed]

Zayac, E. J.

R. A. Applegate, G. Hilmantel, H. C. Howland, E. Y. Tu, T. Starck, E. J. Zayac, “Corneal first surface optical aberrations and visual performance,” J. Refract. Surg. 16, 507–514 (2000).
[PubMed]

Am. J. Ophthalmol. (1)

D. Huang, M. Tang, R. Shekhar, “Mathematical model of corneal surface smoothing after laser refractive surgery,” Am. J. Ophthalmol. 135, 267–278 (2003).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, “Effect on laser-ablation algorithms of reflection losses and nonnormal incidence on the anterior cornea,” Appl. Phys. Lett. 81, 1521–1523 (2002).
[CrossRef]

Invest. Ophthalmol. Visual Sci. (3)

E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).

D. Gatinel, J. Malet, T. Hoang-Xuan, D. T. Azar, “Analysis of customized corneal ablation: theoretical limitations of increasing negative asphericity,” Invest. Ophthalmol. Visual Sci. 43, 941–948 (2002).

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

J. Cataract Refract. Surg. (10)

C. R. Munnerlyn, S. J. Koons, J. Marshall, “Photorefractive keratotomy: a technique for laser refractive surgery,” J. Cataract Refract. Surg. 14, 46–52 (1988).
[CrossRef] [PubMed]

M. Mrochen, M. Kaemmerer, P. Mierdel, T. Seiler, “Increased higher-order optical aberrations after laser refractive surgery,” J. Cataract Refract. Surg. 27, 362–369 (2001).
[CrossRef] [PubMed]

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29, 1204–1210 (2003).
[CrossRef] [PubMed]

R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, J. Bermúdez, E. Hita, “Changes in corneal asphericity after laser in situ keratomileusis,” J. Cataract Refract. Surg. 29, 762–768 (2003).
[CrossRef] [PubMed]

C. C. Chen, A. Izadshenas, A. A. Rana, D. T. Azar, “Corneal asphericity after hyperopic laser in situ keratomileusis,” J. Cataract Refract. Surg. 28, 1539–1545 (2002).
[CrossRef] [PubMed]

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, “Predicting changes in corneal asphericity after hyperopic laser in situ keratomileusis,” J. Cataract Refract. Surg. 29, 1468 (2003).
[CrossRef]

J. T. Holladay, D. R. Dudeja, J. Chang, “Functional vision and corneal changes after laser in situ keratomileusis determined by contrast sensitivity, glare testing, and corneal topography,” J. Cataract Refract. Surg. 25, 663–669 (1999).
[CrossRef] [PubMed]

J. T. Holladay, J. A. Janes, “Topographic changes in corneal asphericity and effective optical zone after laser in situ keratomileusis,” J. Cataract Refract. Surg. 28, 942–947 (2002).
[CrossRef] [PubMed]

J. Schwiegerling, R. W. Snyder, “Corneal ablation atterns to correct for spherical aberration in photorefractive keratectomy,” J. Cataract Refract. Surg. 26, 214–221 (2000).
[CrossRef] [PubMed]

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

J. Mod. Opt. (1)

J. A. Dı́az, R. G. Anera, J. R. Jiménez, L. Jiménez del Barco, “Optimum corneal asphericity of myopic eyes for refractive surgery,” J. Mod. Opt. 50, 1903–1915 (2003).
[CrossRef]

J. Refract. Surg. (2)

R. A. Applegate, G. Hilmantel, H. C. Howland, E. Y. Tu, T. Starck, E. J. Zayac, “Corneal first surface optical aberrations and visual performance,” J. Refract. Surg. 16, 507–514 (2000).
[PubMed]

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

J. Refract. Surg. (Suppl.) (1)

S. MacRae, J. Schwiegerling, R. W. Snyder, “Customized and low spherical aberration corneal ablation design,” J. Refract. Surg. (Suppl.) 15, S246–S248 (1999).

Opt. Eng. (1)

J. T. Lin, “Critical review on refractive surgical lasers,” Opt. Eng. 34, 668–675 (1995).
[CrossRef]

Opt. Lett. (1)

Refract. Corneal Surg. (1)

T. Seiler, U. Genth, A. Holschbach, M. Derse, “Aspheric photorefractive keratectomy with excimer laser,” Refract. Corneal Surg. 9, 166–172 (1993).
[PubMed]

Other (1)

C. Roberts, W. Dupps, “Corneal biomechanics and their role in corneal ablative procedures,” in Customized Corneal Ablation: the Quest for Supervision, S. M. MacRae, R. R. Krueger, R. A. Applegate, eds. (SLACK Inc., Thorofare, N.J., 2001), pp. 109–132.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Postsurgical p factor for two myopia values, D=-4 and D=-8, as a function of the presurgery p factor when the Munnerlyn formula is applied. Lines show the values calculated with Eqs. (15) and (16), and single points (triangles) are deduced from data from the numerical procedure proposed by Gatinel et al.9

Fig. 2
Fig. 2

Postsurgical p factor as a function of the degree of myopia. The solid line represents the values calculated with the equation deduced for corneal asphericity when the paraxial formula of Munnerlyn is used (see text). The dashed line was drawn by use of the Munnerlyn formula with no approximation (see text). Initial values: p=0.76 and R=7.7 mm.

Equations (26)

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

p=R3R3p,
s1(y)=(R2-y2)1/2-(R2-y2)1/2+(R2-d2/4)1/2-(R2-d2/4)1/2,
s2(y)=4Dy23-Dd23,
(1+x)1/21+x/2-x2/8.
D0.375=1R-1R.
z(y)=Rp-(R2-py2)1/2p,
z(y)=y2/2R,
z(y)=s1(y)+z(y)=(R2-y2)1/2-(R2-y2)1/2+(R2-d2/4)1/2-(R2-d2/4)1/2+Rp-(R2-py2)1/2p.
z(y)=z0+Rp-(R2-py2)1/2p,
g(z0, R, p)=0d/2[z(y)-z(y)]2dy.
/z0[g(z0, R, p)](zmin, Rmin, pmin)=0,
/R[g(z0, R, p)](zmin, Rmin, pmin)=0,
/p[g(z0, R, p)](zmin, Rmin, pmin)=0.
g(z0, R, p)=0d/2z0+Rp-(R2-py2)1/2p-[(R2-y2)1/2-(R2-y2)1/2+(R2-d2/4)1/2-(R2-d2/4)1/2]-Rp+(R2-py2)1/2p2dy.
(1+x)1/21+x/2-x2/8.
(R2-py2)1/2pRp-y22R-py48R3.
zmin=R-R+(R2-d2/4)1/2-(R2-d2/4)1/2,
Rmin=R,
pmin-1=R3R3(p-1).
Qmin=R3R3Q.
init.prolate0<p<1,Q<0R3R3Q<QQ<Q<0increaseprolateness,
init.oblatep>1,Q>0R3R3Q>QQ>Q>0increaseoblateness.
init.prolate0<p<1,Q<0R3R3p>pformediumhighmyopiap>1oblateness,
init.oblatep>1,Q>0R3R3p>pp>pincreaseoblateness.
init.prolate0<p<1,Q<0R3R3Q>QQ>Qdecreaseprolateness(asphericitymorepositive), init.oblatep>1,Q>0 Q>R3R3Q0<Q<Qdecreaseoblateness.
init.prolate0<p<1  R3R3p<pp<p<1increaseprolateness(asphericitymorenegative), init.oblatep>1  R3R3p<p  p<pdecreaseoblateness.

Metrics