Abstract

A general method to analyze the loss of ablation efficiency at non-normal incidence in a geometrical way is provided. The model is comprehensive and directly considers curvature, system geometry, applied correction, and astigmatism as model parameters, and indirectly laser beam characteristics and ablative spot properties. The model replaces the direct dependency on the fluence by a direct dependence on the nominal spot volume and on considerations about the area illuminated by the beam, reducing the analysis to pure geometry of impact. Compensation of the loss of ablation efficiency at non-normal incidence can be made at relatively low cost and would directly improve the quality of results.

© 2008 Optical Society of America

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  1. I. G. Pallikaris and D. S. Siganos, "Excimer laser in situ keratomileusis and photorefractive keratectomy for correction of high myopia," J. Refract. Corneal. Surg. 10, 498-510 (1994).
    [PubMed]
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    [PubMed]
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    [PubMed]
  4. E. Moreno-Barriuso, J. Merayo-Lloves, and S. Marcos, "Ocular Aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with LASER ray tracing," Invest. Ophthalmol. Vis. Sci. 42, 1396-1403 (2001).
    [PubMed]
  5. C. Dorronsoro, D. Cano, J. Merayo-Lloves, and S. Marcos, "Experiments on PMMA models to predict the impact of corneal refractive surgery on corneal shape," Opt. Express,  146142-6156 (2006).
    [CrossRef] [PubMed]
  6. A. S. Chayet, M. Montes, L. Gomez, X. Rodriguez, N. Robledo, and S. MacRae, "Bitoric laser in situ keratomileusis for the correction of simple myopic and mixed astigmatism," Ophthalmology 108, 303-308 (2001).
    [CrossRef] [PubMed]
  7. G. Geerling and W. Sekundo, "Phototherapeutic keratectomy. Undesirable effects, complications, and preventive strategies," Ophthalmologe 103, 576-82 (2006).
    [CrossRef] [PubMed]
  8. H. S. Ginis, V. J. Katsanevaki, and I. G. Pallikaris, "Influence of ablation parameters on refractive changes after phototherapeutic keratectomy," J. Refract. Surg. 19, 443-448 (2003).
    [PubMed]
  9. M. Mrochen and T. Seiler, "Influence of Corneal Curvature on Calculation of Ablation Patterns used in photorefractive Laser Surgery," J. Refract. Surg. 17, 584-587 (2001).
  10. J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, and 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]
  11. J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, and F. Pérez-Ocón, "Correlation factor for ablation agorithms used in corneal refractive surgery with gaussian-profile beams," Opt. Express 13, 336-343 (2005).
    [CrossRef] [PubMed]
  12. J. R. Jiménez, F. Rodríguez-Marín, R. G. Anera, and L. Jiménez del Barco, "Deviations of Lambert-Beer’s law affect corneal refractive parameters after refractive surgery," Opt. Express 14, 5411-5417 (2006).
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    [CrossRef]
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    [PubMed]
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    [PubMed]
  21. M. Mrochen, M. Kaemmerer, and T. Seiler, "Clinical results of wavefront-guided laser in situ keratomileusis 3 months after surgery," J. Cataract Refract. Surg 27, 201-7 (2001).
    [CrossRef] [PubMed]
  22. M. Mrochen, C. Donetzky, C. Wüllner, and J. Löffler, "Wavefront-optimized ablation profiles: Theoretical background," J. Cataract Refract. Surg. 30, 775-785 (2004).
    [CrossRef] [PubMed]
  23. T. Koller, H. P. Iseli, F. Hafezi, M. Mrochen, and T. Seiler, "Q-factor customized ablation profile for the correction of myopic astigmatism," J. Cataract Refract. Surg. 32, 584-589 (2006).
    [CrossRef] [PubMed]
  24. 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]

2006 (4)

G. Geerling and W. Sekundo, "Phototherapeutic keratectomy. Undesirable effects, complications, and preventive strategies," Ophthalmologe 103, 576-82 (2006).
[CrossRef] [PubMed]

T. Koller, H. P. Iseli, F. Hafezi, M. Mrochen, and T. Seiler, "Q-factor customized ablation profile for the correction of myopic astigmatism," J. Cataract Refract. Surg. 32, 584-589 (2006).
[CrossRef] [PubMed]

J. R. Jiménez, F. Rodríguez-Marín, R. G. Anera, and L. Jiménez del Barco, "Deviations of Lambert-Beer’s law affect corneal refractive parameters after refractive surgery," Opt. Express 14, 5411-5417 (2006).
[CrossRef] [PubMed]

C. Dorronsoro, D. Cano, J. Merayo-Lloves, and S. Marcos, "Experiments on PMMA models to predict the impact of corneal refractive surgery on corneal shape," Opt. Express,  146142-6156 (2006).
[CrossRef] [PubMed]

2005 (2)

2004 (1)

M. Mrochen, C. Donetzky, C. Wüllner, and J. Löffler, "Wavefront-optimized ablation profiles: Theoretical background," J. Cataract Refract. Surg. 30, 775-785 (2004).
[CrossRef] [PubMed]

2003 (3)

M. Mrochen, M. Jankov, M. Bueeler, and T. Seiler, "Correlation Between Corneal and Total Wavefront Aberrations in Myopic Eyes," J. Refract. Surg. 19, 104-112 (2003).
[PubMed]

J. L. Alio, J. I. Belda, A. A. Osman, and A. M. Shalaby, "Topography-guided laser in situ keratomileusis (TOPOLINK) to correct irregular astigmatism after previous refractive surgery," J. Refract. Surg. 19, 516-27 (2003).
[PubMed]

H. S. Ginis, V. J. Katsanevaki, and I. G. Pallikaris, "Influence of ablation parameters on refractive changes after phototherapeutic keratectomy," J. Refract. Surg. 19, 443-448 (2003).
[PubMed]

2002 (2)

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, and 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]

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 (4)

M. Mrochen, M. Kaemmerer, and T. Seiler, "Clinical results of wavefront-guided laser in situ keratomileusis 3 months after surgery," J. Cataract Refract. Surg 27, 201-7 (2001).
[CrossRef] [PubMed]

M. Mrochen and T. Seiler, "Influence of Corneal Curvature on Calculation of Ablation Patterns used in photorefractive Laser Surgery," J. Refract. Surg. 17, 584-587 (2001).

E. Moreno-Barriuso, J. Merayo-Lloves, and S. Marcos, "Ocular Aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with LASER ray tracing," Invest. Ophthalmol. Vis. Sci. 42, 1396-1403 (2001).
[PubMed]

A. S. Chayet, M. Montes, L. Gomez, X. Rodriguez, N. Robledo, and S. MacRae, "Bitoric laser in situ keratomileusis for the correction of simple myopic and mixed astigmatism," Ophthalmology 108, 303-308 (2001).
[CrossRef] [PubMed]

1999 (1)

D. N. Nikogosyan and H. Goerner, "Laser-Induced Photodecomposition of Amino Acids and Peptides: Extrapolation to Corneal Collagen," IEEE J Sel. Top. Quantum Electron. 51107-1115 (1999).
[CrossRef]

1998 (1)

K. Ditzen, H. Huschka, and S. Pieger, "Laser in situ keratomileusis for hyperopia," J. Cataract Refract. Surg. 24, 42-7 (1998).
[PubMed]

1997 (1)

M. A. el Danasoury, G. O. Waring 3rd, A. el Maghraby, and K. Mehrez, "Excimer laser in situ keratomileusis to correct compound myopic astigmatism," J. Refract. Surg. 13, 511-20 (1997).
[PubMed]

1996 (1)

1994 (1)

I. G. Pallikaris and D. S. Siganos, "Excimer laser in situ keratomileusis and photorefractive keratectomy for correction of high myopia," J. Refract. Corneal. Surg. 10, 498-510 (1994).
[PubMed]

1943 (1)

T. Y. Baker, "Ray tracing through non-spherical surfaces," Proceeds Of The Royal Society 55, 361-364 (1943).
[CrossRef]

Alio, J. L.

J. L. Alio, J. I. Belda, A. A. Osman, and A. M. Shalaby, "Topography-guided laser in situ keratomileusis (TOPOLINK) to correct irregular astigmatism after previous refractive surgery," J. Refract. Surg. 19, 516-27 (2003).
[PubMed]

Anera, R. G.

Azar, D. T.

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]

Baker, T. Y.

T. Y. Baker, "Ray tracing through non-spherical surfaces," Proceeds Of The Royal Society 55, 361-364 (1943).
[CrossRef]

Belda, J. I.

J. L. Alio, J. I. Belda, A. A. Osman, and A. M. Shalaby, "Topography-guided laser in situ keratomileusis (TOPOLINK) to correct irregular astigmatism after previous refractive surgery," J. Refract. Surg. 19, 516-27 (2003).
[PubMed]

Bueeler, M.

M. Mrochen, M. Jankov, M. Bueeler, and T. Seiler, "Correlation Between Corneal and Total Wavefront Aberrations in Myopic Eyes," J. Refract. Surg. 19, 104-112 (2003).
[PubMed]

Cano, D.

Chayet, A. S.

A. S. Chayet, M. Montes, L. Gomez, X. Rodriguez, N. Robledo, and S. MacRae, "Bitoric laser in situ keratomileusis for the correction of simple myopic and mixed astigmatism," Ophthalmology 108, 303-308 (2001).
[CrossRef] [PubMed]

Ditzen, K.

K. Ditzen, H. Huschka, and S. Pieger, "Laser in situ keratomileusis for hyperopia," J. Cataract Refract. Surg. 24, 42-7 (1998).
[PubMed]

Donetzky, C.

M. Mrochen, C. Donetzky, C. Wüllner, and J. Löffler, "Wavefront-optimized ablation profiles: Theoretical background," J. Cataract Refract. Surg. 30, 775-785 (2004).
[CrossRef] [PubMed]

Dorronsoro, C.

Ediger, M. N.

el Danasoury, M. A.

M. A. el Danasoury, G. O. Waring 3rd, A. el Maghraby, and K. Mehrez, "Excimer laser in situ keratomileusis to correct compound myopic astigmatism," J. Refract. Surg. 13, 511-20 (1997).
[PubMed]

el Maghraby, A.

M. A. el Danasoury, G. O. Waring 3rd, A. el Maghraby, and K. Mehrez, "Excimer laser in situ keratomileusis to correct compound myopic astigmatism," J. Refract. Surg. 13, 511-20 (1997).
[PubMed]

Funkb, D. J.

M. Hauera, D. J. Funkb, T. Lipperta, and A. Wokauna, "Time-resolved techniques as probes for the laser ablation process," Opt. Lasers Eng. 43545-556 (2005).
[CrossRef]

Gatinel, D.

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]

Geerling, G.

G. Geerling and W. Sekundo, "Phototherapeutic keratectomy. Undesirable effects, complications, and preventive strategies," Ophthalmologe 103, 576-82 (2006).
[CrossRef] [PubMed]

Ginis, H. S.

H. S. Ginis, V. J. Katsanevaki, and I. G. Pallikaris, "Influence of ablation parameters on refractive changes after phototherapeutic keratectomy," J. Refract. Surg. 19, 443-448 (2003).
[PubMed]

Goerner, H.

D. N. Nikogosyan and H. Goerner, "Laser-Induced Photodecomposition of Amino Acids and Peptides: Extrapolation to Corneal Collagen," IEEE J Sel. Top. Quantum Electron. 51107-1115 (1999).
[CrossRef]

Gomez, L.

A. S. Chayet, M. Montes, L. Gomez, X. Rodriguez, N. Robledo, and S. MacRae, "Bitoric laser in situ keratomileusis for the correction of simple myopic and mixed astigmatism," Ophthalmology 108, 303-308 (2001).
[CrossRef] [PubMed]

Hafezi, F.

T. Koller, H. P. Iseli, F. Hafezi, M. Mrochen, and T. Seiler, "Q-factor customized ablation profile for the correction of myopic astigmatism," J. Cataract Refract. Surg. 32, 584-589 (2006).
[CrossRef] [PubMed]

Hauera, M.

M. Hauera, D. J. Funkb, T. Lipperta, and A. Wokauna, "Time-resolved techniques as probes for the laser ablation process," Opt. Lasers Eng. 43545-556 (2005).
[CrossRef]

Hita, E.

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, and F. Pérez-Ocón, "Correlation factor for ablation agorithms used in corneal refractive surgery with gaussian-profile beams," Opt. Express 13, 336-343 (2005).
[CrossRef] [PubMed]

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, and 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]

Hoang-Xuan, T.

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]

Huschka, H.

K. Ditzen, H. Huschka, and S. Pieger, "Laser in situ keratomileusis for hyperopia," J. Cataract Refract. Surg. 24, 42-7 (1998).
[PubMed]

Iseli, H. P.

T. Koller, H. P. Iseli, F. Hafezi, M. Mrochen, and T. Seiler, "Q-factor customized ablation profile for the correction of myopic astigmatism," J. Cataract Refract. Surg. 32, 584-589 (2006).
[CrossRef] [PubMed]

Jankov, M.

M. Mrochen, M. Jankov, M. Bueeler, and T. Seiler, "Correlation Between Corneal and Total Wavefront Aberrations in Myopic Eyes," J. Refract. Surg. 19, 104-112 (2003).
[PubMed]

Jiménez, J. R.

Jiménez del Barco, L.

Kaemmerer, M.

M. Mrochen, M. Kaemmerer, and T. Seiler, "Clinical results of wavefront-guided laser in situ keratomileusis 3 months after surgery," J. Cataract Refract. Surg 27, 201-7 (2001).
[CrossRef] [PubMed]

Katsanevaki, V. J.

H. S. Ginis, V. J. Katsanevaki, and I. G. Pallikaris, "Influence of ablation parameters on refractive changes after phototherapeutic keratectomy," J. Refract. Surg. 19, 443-448 (2003).
[PubMed]

Koller, T.

T. Koller, H. P. Iseli, F. Hafezi, M. Mrochen, and T. Seiler, "Q-factor customized ablation profile for the correction of myopic astigmatism," J. Cataract Refract. Surg. 32, 584-589 (2006).
[CrossRef] [PubMed]

Lipperta, T.

M. Hauera, D. J. Funkb, T. Lipperta, and A. Wokauna, "Time-resolved techniques as probes for the laser ablation process," Opt. Lasers Eng. 43545-556 (2005).
[CrossRef]

Löffler, J.

M. Mrochen, C. Donetzky, C. Wüllner, and J. Löffler, "Wavefront-optimized ablation profiles: Theoretical background," J. Cataract Refract. Surg. 30, 775-785 (2004).
[CrossRef] [PubMed]

MacRae, S.

A. S. Chayet, M. Montes, L. Gomez, X. Rodriguez, N. Robledo, and S. MacRae, "Bitoric laser in situ keratomileusis for the correction of simple myopic and mixed astigmatism," Ophthalmology 108, 303-308 (2001).
[CrossRef] [PubMed]

Malet, J.

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]

Marcos, S.

C. Dorronsoro, D. Cano, J. Merayo-Lloves, and S. Marcos, "Experiments on PMMA models to predict the impact of corneal refractive surgery on corneal shape," Opt. Express,  146142-6156 (2006).
[CrossRef] [PubMed]

E. Moreno-Barriuso, J. Merayo-Lloves, and S. Marcos, "Ocular Aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with LASER ray tracing," Invest. Ophthalmol. Vis. Sci. 42, 1396-1403 (2001).
[PubMed]

Mehrez, K.

M. A. el Danasoury, G. O. Waring 3rd, A. el Maghraby, and K. Mehrez, "Excimer laser in situ keratomileusis to correct compound myopic astigmatism," J. Refract. Surg. 13, 511-20 (1997).
[PubMed]

Merayo-Lloves, J.

C. Dorronsoro, D. Cano, J. Merayo-Lloves, and S. Marcos, "Experiments on PMMA models to predict the impact of corneal refractive surgery on corneal shape," Opt. Express,  146142-6156 (2006).
[CrossRef] [PubMed]

E. Moreno-Barriuso, J. Merayo-Lloves, and S. Marcos, "Ocular Aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with LASER ray tracing," Invest. Ophthalmol. Vis. Sci. 42, 1396-1403 (2001).
[PubMed]

Montes, M.

A. S. Chayet, M. Montes, L. Gomez, X. Rodriguez, N. Robledo, and S. MacRae, "Bitoric laser in situ keratomileusis for the correction of simple myopic and mixed astigmatism," Ophthalmology 108, 303-308 (2001).
[CrossRef] [PubMed]

Moreno-Barriuso, E.

E. Moreno-Barriuso, J. Merayo-Lloves, and S. Marcos, "Ocular Aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with LASER ray tracing," Invest. Ophthalmol. Vis. Sci. 42, 1396-1403 (2001).
[PubMed]

Mrochen, M.

T. Koller, H. P. Iseli, F. Hafezi, M. Mrochen, and T. Seiler, "Q-factor customized ablation profile for the correction of myopic astigmatism," J. Cataract Refract. Surg. 32, 584-589 (2006).
[CrossRef] [PubMed]

M. Mrochen, C. Donetzky, C. Wüllner, and J. Löffler, "Wavefront-optimized ablation profiles: Theoretical background," J. Cataract Refract. Surg. 30, 775-785 (2004).
[CrossRef] [PubMed]

M. Mrochen, M. Jankov, M. Bueeler, and T. Seiler, "Correlation Between Corneal and Total Wavefront Aberrations in Myopic Eyes," J. Refract. Surg. 19, 104-112 (2003).
[PubMed]

M. Mrochen and T. Seiler, "Influence of Corneal Curvature on Calculation of Ablation Patterns used in photorefractive Laser Surgery," J. Refract. Surg. 17, 584-587 (2001).

M. Mrochen, M. Kaemmerer, and T. Seiler, "Clinical results of wavefront-guided laser in situ keratomileusis 3 months after surgery," J. Cataract Refract. Surg 27, 201-7 (2001).
[CrossRef] [PubMed]

Nikogosyan, D. N.

D. N. Nikogosyan and H. Goerner, "Laser-Induced Photodecomposition of Amino Acids and Peptides: Extrapolation to Corneal Collagen," IEEE J Sel. Top. Quantum Electron. 51107-1115 (1999).
[CrossRef]

Osman, A. A.

J. L. Alio, J. I. Belda, A. A. Osman, and A. M. Shalaby, "Topography-guided laser in situ keratomileusis (TOPOLINK) to correct irregular astigmatism after previous refractive surgery," J. Refract. Surg. 19, 516-27 (2003).
[PubMed]

Pallikaris, I. G.

H. S. Ginis, V. J. Katsanevaki, and I. G. Pallikaris, "Influence of ablation parameters on refractive changes after phototherapeutic keratectomy," J. Refract. Surg. 19, 443-448 (2003).
[PubMed]

I. G. Pallikaris and D. S. Siganos, "Excimer laser in situ keratomileusis and photorefractive keratectomy for correction of high myopia," J. Refract. Corneal. Surg. 10, 498-510 (1994).
[PubMed]

Pérez-Ocón, F.

Pettit, G. H.

Pieger, S.

K. Ditzen, H. Huschka, and S. Pieger, "Laser in situ keratomileusis for hyperopia," J. Cataract Refract. Surg. 24, 42-7 (1998).
[PubMed]

Robledo, N.

A. S. Chayet, M. Montes, L. Gomez, X. Rodriguez, N. Robledo, and S. MacRae, "Bitoric laser in situ keratomileusis for the correction of simple myopic and mixed astigmatism," Ophthalmology 108, 303-308 (2001).
[CrossRef] [PubMed]

Rodriguez, X.

A. S. Chayet, M. Montes, L. Gomez, X. Rodriguez, N. Robledo, and S. MacRae, "Bitoric laser in situ keratomileusis for the correction of simple myopic and mixed astigmatism," Ophthalmology 108, 303-308 (2001).
[CrossRef] [PubMed]

Rodríguez-Marín, F.

Seiler, T.

T. Koller, H. P. Iseli, F. Hafezi, M. Mrochen, and T. Seiler, "Q-factor customized ablation profile for the correction of myopic astigmatism," J. Cataract Refract. Surg. 32, 584-589 (2006).
[CrossRef] [PubMed]

M. Mrochen, M. Jankov, M. Bueeler, and T. Seiler, "Correlation Between Corneal and Total Wavefront Aberrations in Myopic Eyes," J. Refract. Surg. 19, 104-112 (2003).
[PubMed]

M. Mrochen, M. Kaemmerer, and T. Seiler, "Clinical results of wavefront-guided laser in situ keratomileusis 3 months after surgery," J. Cataract Refract. Surg 27, 201-7 (2001).
[CrossRef] [PubMed]

M. Mrochen and T. Seiler, "Influence of Corneal Curvature on Calculation of Ablation Patterns used in photorefractive Laser Surgery," J. Refract. Surg. 17, 584-587 (2001).

Sekundo, W.

G. Geerling and W. Sekundo, "Phototherapeutic keratectomy. Undesirable effects, complications, and preventive strategies," Ophthalmologe 103, 576-82 (2006).
[CrossRef] [PubMed]

Shalaby, A. M.

J. L. Alio, J. I. Belda, A. A. Osman, and A. M. Shalaby, "Topography-guided laser in situ keratomileusis (TOPOLINK) to correct irregular astigmatism after previous refractive surgery," J. Refract. Surg. 19, 516-27 (2003).
[PubMed]

Siganos, D. S.

I. G. Pallikaris and D. S. Siganos, "Excimer laser in situ keratomileusis and photorefractive keratectomy for correction of high myopia," J. Refract. Corneal. Surg. 10, 498-510 (1994).
[PubMed]

Waring, G. O.

M. A. el Danasoury, G. O. Waring 3rd, A. el Maghraby, and K. Mehrez, "Excimer laser in situ keratomileusis to correct compound myopic astigmatism," J. Refract. Surg. 13, 511-20 (1997).
[PubMed]

Wokauna, A.

M. Hauera, D. J. Funkb, T. Lipperta, and A. Wokauna, "Time-resolved techniques as probes for the laser ablation process," Opt. Lasers Eng. 43545-556 (2005).
[CrossRef]

Wüllner, C.

M. Mrochen, C. Donetzky, C. Wüllner, and J. Löffler, "Wavefront-optimized ablation profiles: Theoretical background," J. Cataract Refract. Surg. 30, 775-785 (2004).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, and 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]

IEEE J Sel. Top. Quantum Electron. (1)

D. N. Nikogosyan and H. Goerner, "Laser-Induced Photodecomposition of Amino Acids and Peptides: Extrapolation to Corneal Collagen," IEEE J Sel. Top. Quantum Electron. 51107-1115 (1999).
[CrossRef]

Invest. Ophthalmol. Vis. Sci. (2)

E. Moreno-Barriuso, J. Merayo-Lloves, and S. Marcos, "Ocular Aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with LASER ray tracing," Invest. Ophthalmol. Vis. Sci. 42, 1396-1403 (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 (1)

M. Mrochen, M. Kaemmerer, and T. Seiler, "Clinical results of wavefront-guided laser in situ keratomileusis 3 months after surgery," J. Cataract Refract. Surg 27, 201-7 (2001).
[CrossRef] [PubMed]

J. Cataract Refract. Surg. (3)

M. Mrochen, C. Donetzky, C. Wüllner, and J. Löffler, "Wavefront-optimized ablation profiles: Theoretical background," J. Cataract Refract. Surg. 30, 775-785 (2004).
[CrossRef] [PubMed]

T. Koller, H. P. Iseli, F. Hafezi, M. Mrochen, and T. Seiler, "Q-factor customized ablation profile for the correction of myopic astigmatism," J. Cataract Refract. Surg. 32, 584-589 (2006).
[CrossRef] [PubMed]

K. Ditzen, H. Huschka, and S. Pieger, "Laser in situ keratomileusis for hyperopia," J. Cataract Refract. Surg. 24, 42-7 (1998).
[PubMed]

J. Refract. Corneal. Surg. (1)

I. G. Pallikaris and D. S. Siganos, "Excimer laser in situ keratomileusis and photorefractive keratectomy for correction of high myopia," J. Refract. Corneal. Surg. 10, 498-510 (1994).
[PubMed]

J. Refract. Surg. (5)

H. S. Ginis, V. J. Katsanevaki, and I. G. Pallikaris, "Influence of ablation parameters on refractive changes after phototherapeutic keratectomy," J. Refract. Surg. 19, 443-448 (2003).
[PubMed]

M. Mrochen and T. Seiler, "Influence of Corneal Curvature on Calculation of Ablation Patterns used in photorefractive Laser Surgery," J. Refract. Surg. 17, 584-587 (2001).

M. A. el Danasoury, G. O. Waring 3rd, A. el Maghraby, and K. Mehrez, "Excimer laser in situ keratomileusis to correct compound myopic astigmatism," J. Refract. Surg. 13, 511-20 (1997).
[PubMed]

M. Mrochen, M. Jankov, M. Bueeler, and T. Seiler, "Correlation Between Corneal and Total Wavefront Aberrations in Myopic Eyes," J. Refract. Surg. 19, 104-112 (2003).
[PubMed]

J. L. Alio, J. I. Belda, A. A. Osman, and A. M. Shalaby, "Topography-guided laser in situ keratomileusis (TOPOLINK) to correct irregular astigmatism after previous refractive surgery," J. Refract. Surg. 19, 516-27 (2003).
[PubMed]

Ophthalmologe (1)

G. Geerling and W. Sekundo, "Phototherapeutic keratectomy. Undesirable effects, complications, and preventive strategies," Ophthalmologe 103, 576-82 (2006).
[CrossRef] [PubMed]

Ophthalmology (1)

A. S. Chayet, M. Montes, L. Gomez, X. Rodriguez, N. Robledo, and S. MacRae, "Bitoric laser in situ keratomileusis for the correction of simple myopic and mixed astigmatism," Ophthalmology 108, 303-308 (2001).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lasers Eng. (1)

M. Hauera, D. J. Funkb, T. Lipperta, and A. Wokauna, "Time-resolved techniques as probes for the laser ablation process," Opt. Lasers Eng. 43545-556 (2005).
[CrossRef]

Proceeds Of The Royal Society (1)

T. Y. Baker, "Ray tracing through non-spherical surfaces," Proceeds Of The Royal Society 55, 361-364 (1943).
[CrossRef]

Other (2)

L. Thibos, A. Bradley, and R. Applegate, "Accuracy and precision of objective refraction from wavefront aberrations," ISSN 1534-7362, ARVO (2003).

T. O. Salmon, "Corneal contribution to the Wavefront aberration of the eye," PhD Dissertation, 70 (1999).

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Figures (12)

Fig. 1.
Fig. 1.

Hyperopic shift and coupling factor. Ablating a simple myopic astigmatism, the neutral axis became refractive, and the ablation depth in the periphery was smaller than in the center.

Fig. 2.
Fig. 2.

Loss on reflection (Fresnel’s equations) dependent on the angle of incidence, and losses also dependent on the geometric distortion (angle of incidence).

Fig. 3.
Fig. 3.

Loss on reflection (Fresnel’s equations) dependent on the angle of incidence, and losses also dependent on the geometric distortion (angle of incidence).

Fig. 4.
Fig. 4.

The radius of corneal curvature changes during treatment, efficiency also varies over treatment, the values at 50% of the treatment represent a reasonable compromise to consider both the correction applied and the preoperative curvature.

Fig. 5.
Fig. 5.

The offset of the galvoscanners from the axis of the system is considered in the calculation of the angle of incidence of the beam onto a flat surface perpendicular to the axis of the laser.

Fig. 6.
Fig. 6.

Ablation efficiency at 3 mm radial distance for a sphere with 7.97 mm radius of curvature. The ablation efficiency was simulated for an excimer laser with a peak radiant exposure of 120 mJ/cm2 and a full-width-half-maximum (FWHM) beam size of 2 mm. The radius of corneal curvature changes during treatment, accordingly also the efficiency varies over treatment. Note the improvement of ablation efficiency during myopic corrections as opposed to the increased loss of ablation efficiency during hyperopic corrections.

Fig. 7.
Fig. 7.

Contribution of the asphericity quotient to the ablation efficiency for a radius of 7.97 mm curvature. The ablation efficiency at the cornea was simulated for an excimer laser with a peak radiant exposure of 120 mJ/cm2 and a beam size of 2 mm (FWHM). Note the identical ablation efficiency close to the vertex as opposed to differences in ablation efficiency at the periphery. A parabolic surface provides higher peripheral ablation efficiency (due to prolate peripheral flattening) compared to an oblate surface (with peripheral steepening).

Fig. 8.
Fig. 8.

Contribution of the reflection and distortion losses to ablation efficiency for a sphere with 7.97 mm radius of curvature. Note that the reflection losses already exist with normal incidence and decrease very slightly towards the periphery. Although normal reflection losses approximately amount to 5%, they do not increase excessively for non-normal incidence. As our calculation defined the ablation efficiency for a general incidence as the ratio between the spot volume for general incidence and the spot volume for normal incidence, it is evident that the so-defined efficiency equals 1 for normal incidences.

Fig. 9.
Fig. 9.

Ablation efficiency at 3 mm radial distance for a sphere with 7.97 mm radius of curvature. The ablation efficiency was simulated for an excimer laser with a peak radiant exposure up to 400 mJ/cm2 and a full-width-half-maximum (FWHM) beam size of 2 mm.

Fig. 10.
Fig. 10.

Efficiency obtained with the proposed model for the conditions reported by Dorronsoro et al. Ablation efficiency for a sphere with 7.97 mm radius of curvature. The ablation efficiency was simulated for an excimer laser with a peak radiant exposure of 120 mJ/cm2 and a full-width-half-maximum (FWHM) beam size of 2 mm.

Fig. 11.
Fig. 11.

Efficiency obtained with the proposed model for the conditions reported by Dorronsoro et al. Average ablation efficiency for a sphere with 7.97 mm preoperative radius of curvature and a correction of -12 D. The ablation efficiency was simulated for an excimer laser with a peak radiant exposure of 120 mJ/cm2 and a full-width-half-maximum (FWHM) beam size of 2 mm. The radius of corneal curvature changes during treatment, consequently, also the efficiency varies over treatment. Note the improvement of ablation efficiency.

Fig. 12.
Fig. 12.

Efficiency obtained with the proposed model for the conditions reported by Dorronsoro et al. Average ablation efficiency for a sphere with 7.97 mm preoperative radius of curvature and a correction of +6 D. The ablation efficiency was simulated for an excimer laser with a peak radiant exposure of 120 mJ/cm2 and a full-width-half-maximum (FWHM) beam size of 2 mm. The radius of corneal curvature changes during treatment, consequently also the efficiency varies over treatment. Note the increased loss of ablation efficiency during hyperopic corrections.

Equations (43)

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Eff ( r ) = d ( r ) d ( 0 )
I ( r ) = I 0 e 2 ( r R 0 ) 2 N
FP = 2 R 0 ( ln ( I 0 I Th ) 2 ) 1 2 N
V S = 0 2 π 0 FP 2 ln ( I 0 I Th ) 2 ( r R 0 ) 2 N α rdrd θ
V S = π α N N + 1 ln ( I 0 I Th ) N + 1 N R 0 2 2 1 N
V S = 4 α N N + 1 ln ( I 0 I Th ) N + 1 N R 0 2 2 1 N
V S = π + 4 α N N + 1 ( ln ( I 0 I Th ) 2 ) N + 1 N R 0 2
V S = π 12 × [ ( T Z 3 O Z 3 ) × Depth TZ OZ ] NumberOfShots
V S = π × O Z 2 × Depth 4 × NumberOfShots
α ( x , y ) = arctan ( ( x X G ) 2 + ( y Y G ) 2 d G )
x 2 + y 2 + z 2 ( Q HT + 1 ) 2 z R HT = 0
θ ( x , y ) = arctan ( x 2 + y 2 R HT ( Q HT + 1 ) Q HT + 1 ( Q HT + 1 ) × x 2 + y 2 R HT 2 )
β = ang ( α , θ )
I Eff ( x , y ) = I ( x , y ) ·
· cos ( β ( x , y ) ) e 2 ( ( ( x x 0 ) 2 + ( y y 0 ) 2 cos 2 ( β ( x , y ) ) R 0 2 ) N ( ( x x 0 ) 2 + ( y y 0 ) 2 R 0 2 ) N ) .
· ( 1 R ( x , y ) )
Eff ( x , y ) = m m n n d ( x , y ) m m n n d ( 0 , 0 )
Eff ( x , y ) = 1 + Δ x 0 Δ y 0 m m n n ln cos ( β ( x , y ) ) e 2 ( ( ( x x 0 , i , j ) 2 + ( y y 0 , i , j ) 2 cos 2 ( β ( x , y ) ) R 0 2 ) N ( ( x x 0 , i , j ) 2 + ( y y 0 , i , j ) 2 R 0 2 ) N ) ( 1 R ( x , y ) ) cos ( β ( 0 , 0 ) ) e 2 ( ( ( x 0 , i , j ) 2 + ( y 0 , i , j ) 2 cos 2 ( β ( 0 , 0 ) ) R 0 2 ) N ( ( x 0 , i , j ) 2 + ( y 0 , i , j ) 2 R 0 2 ) N ) ( 1 R ( 0 , 0 ) ) α V s
β ( x , y ) = α ( x , y ) + θ ( x , y )
d r
α ( x , y ) 0
β ( x , y ) θ ( x , y )
β ( 0 , 0 ) = 0
Eff ( x , y ) = 1 + A S ln ( cos ( β ( x , y ) ) ( 1 R ( x , y ) ) ( n t + 1 ) 2 4 n t ) α V S +
+ 2 Δ x 0 Δ y 0 m m n n ( ( ( x x 0 , i , j ) 2 + ( y y 0 , i , j ) 2 cos 2 ( β ( x , y ) ) R 0 2 ) N ( ( x x 0 , i , j ) 2 + ( y y 0 , i , j ) 2 R 0 2 ) N ) α V S
Eff ( x , y ) = 1 + A S ln ( cos ( β ( x , y ) ) ( 1 R ( x , y ) ) ( n t + 1 ) 2 4 n t ) α V S +
+ 2 FP 2 + FP 2 FP 2 + FP 2 ( ( ( x x 0 ) 2 + ( y y 0 ) 2 cos 2 ( β ( x , y ) ) R 0 2 ) N ( ( x x 0 ) 2 + ( y y 0 ) 2 R 0 2 ) N ) d x 0 d y 0 α V S
κ ij = 1 Eff ij
Eff = 1 A ( r R ) 2 B ( r R ) 4 + . . .
κ = 1 + C ( r R ) 2 + D ( r R ) 4 + . . .
Eff ( R i , R f , r ) = R i R f ( Eff ) dR R i R f dR
Eff ( R i , R f , r ) 1 A r 2 R i R f B r 4 3 R i 3 R f 3 ( R i 2 + R i R f + R f 2 )
κ ( R i , R f , r ) = R i R f ( κ ) d R R i R f d R
κ ( R i , R f , r ) 1 + C r 2 R i R f + D r 4 3 R i 3 R f 3 ( R i 2 + R i R f + R f 2 )
d ¯ = 0 2 π 0 FP 2 ln ( I 0 I Th ) 2 ( r R 0 ) 2 N α r d r d θ 0 2 π 0 FP 2 r d r d θ
d ¯ = 1 α N N + 1 ln ( I 0 I Th )
d ¯ = V S A S
Eff = 1 + ln ( cos β ( 1 R ) ( n t + 1 ) 2 4 n t ) α d ¯
Eff = 1 + A S ln ( cos β ( 1 R ) ( n t + 1 ) 2 4 n t ) α V S
θ = arcsin ( X 2 + Y 2 R HT )
Eff = 1 + A s ln ( cos θ ) α V s
D Eff = D φ × cos 2 ( δ φ ) + D φ + π 2 × sin 2 ( δ φ )
R Eff = R φ × R φ + π 2 R φ × sin 2 ( δ φ ) + R φ + π 2 × cos 2 ( δ φ )

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