Abstract

A theoretical foundation for the analysis of ocular aberration correction is developed. It enables a comparative study for two different refractive surgical approaches, namely, the conventional and the Q-preserved treatment modalities. A refractive surgical factor is identified that leads to a simple cubic function for the postoperative asphericity factor for the conventional treatment. A formulation is developed that paves the way for the calculation of the induction of spherical aberration for low-order aberration correction in refractive surgery. Opposite to the general belief, the Munnerlyn shape makes myopic LASIK more prolate, not oblate. A Monte Carlo simulation was conducted for 1000 eyes for these two refractive surgical modalities. It was found that, although the postoperative spherical aberration is similar for these surgical modalities, for the induction of spherical aberration from the ablation target shape, the conventional modality appears to be slightly more predictable.

© 2012 Optical Society of America

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  1. S. L. Trokel, R. Srinivasan, and B. Braren, “Excimer laser surgery of the cornea,” Am. J. Ophthalmol. 96, 710–715(1983).
  2. C. R. Munnerlyn, S. J. Koons, and J. Marshall, “Photorefractive keratectomy: a technique for laser refractive surgery,” J. Cataract Refract. Surg. 14, 46–52 (1988).
  3. K. M. Oliver, R. P. Hemmenger, M. C. Corbett, D. P. S. O’Brart, S. Verma, J. Marshall, and A. Tomlinson, “Corneal optical aberrations induced by photorefractive keratectomy,” J. Refract. Surg. 13, 246–254 (1997).
  4. E. Moreno-Barriuso, J. M. Lloves, S. Marcos, R. Navarro, L. Llorente, and S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Investig. Ophthalmol. Vis. Sci. 42, 1396–1403 (2001).
  5. M. Mrochen, M. Kaemmerer, P. Mierdel, and T. Seiler, “Increased higher-order optical aberrations after laser refractive surgery. A problem of subclinical decentration,” J. Cataract Refract. Surg. 27, 362–369 (2001).
    [CrossRef]
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  7. P. M. Kiely, G. Smith, and L. G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
    [CrossRef]
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    [CrossRef]
  9. F. Mann, A. Ho, J.-M. Parel, and W. Culbertson, “Ablation profiles for wavefront-guided correction of myopia and primary spherical aberration,” J. Cataract Refract. Surg. 28, 766–774 (2002).
    [CrossRef]
  10. M. Mrochen, C. Donitzky, C. Müllner, and J. Löffler, “Wavefront-optimized ablation profiles: theoretical background,” J. Cataract Refract. Surg. 30, 775–785 (2004).
    [CrossRef]
  11. 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]
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    [CrossRef]
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    [CrossRef]
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  16. G.-M. Dai, Wavefront Optics for Vision Correction (SPIE, 2008), Chap. 3.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2006 (1)

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]

2005 (1)

L. Chan, M. Tse, M. Chim, W. Wong, C. Choi, J. Yu, M. Zhang, and J. Sung, “The 100th birthday of the conic constant and Schwarzschild’s revolutionary papers in optics,” Proc. SPIE 5875, 587501 (2005).
[CrossRef]

2004 (1)

M. Mrochen, C. Donitzky, C. Müllner, and J. Löffler, “Wavefront-optimized ablation profiles: theoretical background,” J. Cataract Refract. Surg. 30, 775–785 (2004).
[CrossRef]

2003 (1)

L. Wang and D. D. Koch, “Ocular high-order aberrations in individuals screened for refractive surgery,” J. Cataract Refract. Surg. 29, 1896–1903 (2003).
[CrossRef]

2002 (1)

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

2001 (5)

G. Smith, M. J. Cox, R. Calver, and L. F. Garner, “The spherical aberration of the crystalline lens of the human eye,” Vis. Res. 41, 235–243 (2001).
[CrossRef]

J. Porter, A. Guirao, I. G. Cox, and D. R. Williams, “Monochromatic aberrations of the human eye in a large population,” J. Opt. Soc. Am. A 18, 1793–1803 (2001).
[CrossRef]

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

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

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

2000 (1)

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

1998 (1)

1997 (1)

K. M. Oliver, R. P. Hemmenger, M. C. Corbett, D. P. S. O’Brart, S. Verma, J. Marshall, and A. Tomlinson, “Corneal optical aberrations induced by photorefractive keratectomy,” J. Refract. Surg. 13, 246–254 (1997).

1988 (1)

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

1983 (1)

S. L. Trokel, R. Srinivasan, and B. Braren, “Excimer laser surgery of the cornea,” Am. J. Ophthalmol. 96, 710–715(1983).

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]

1943 (1)

T. Y. Baker, “Ray tracing through non-spherical surfaces,” Proc. Phys. Soc. 55, 361–364 (1943).
[CrossRef]

Artal, P.

Atchison, D. A.

G. Smith and D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge University, 1997).

Azar, D. T.

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

Baker, T. Y.

T. Y. Baker, “Ray tracing through non-spherical surfaces,” Proc. Phys. Soc. 55, 361–364 (1943).
[CrossRef]

Barbero, S.

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

Braren, B.

S. L. Trokel, R. Srinivasan, and B. Braren, “Excimer laser surgery of the cornea,” Am. J. Ophthalmol. 96, 710–715(1983).

Calver, R.

G. Smith, M. J. Cox, R. Calver, and L. F. Garner, “The spherical aberration of the crystalline lens of the human eye,” Vis. Res. 41, 235–243 (2001).
[CrossRef]

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]

Chan, L.

L. Chan, M. Tse, M. Chim, W. Wong, C. Choi, J. Yu, M. Zhang, and J. Sung, “The 100th birthday of the conic constant and Schwarzschild’s revolutionary papers in optics,” Proc. SPIE 5875, 587501 (2005).
[CrossRef]

Chim, M.

L. Chan, M. Tse, M. Chim, W. Wong, C. Choi, J. Yu, M. Zhang, and J. Sung, “The 100th birthday of the conic constant and Schwarzschild’s revolutionary papers in optics,” Proc. SPIE 5875, 587501 (2005).
[CrossRef]

Choi, C.

L. Chan, M. Tse, M. Chim, W. Wong, C. Choi, J. Yu, M. Zhang, and J. Sung, “The 100th birthday of the conic constant and Schwarzschild’s revolutionary papers in optics,” Proc. SPIE 5875, 587501 (2005).
[CrossRef]

Corbett, M. C.

K. M. Oliver, R. P. Hemmenger, M. C. Corbett, D. P. S. O’Brart, S. Verma, J. Marshall, and A. Tomlinson, “Corneal optical aberrations induced by photorefractive keratectomy,” J. Refract. Surg. 13, 246–254 (1997).

Cox, I. G.

Cox, M. J.

G. Smith, M. J. Cox, R. Calver, and L. F. Garner, “The spherical aberration of the crystalline lens of the human eye,” Vis. Res. 41, 235–243 (2001).
[CrossRef]

Culbertson, W.

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

Dai, G.-M.

G.-M. Dai, Wavefront Optics for Vision Correction (SPIE, 2008), Chap. 3.

Donitzky, C.

M. Mrochen, C. Donitzky, C. Müllner, and J. Löffler, “Wavefront-optimized ablation profiles: theoretical background,” J. Cataract Refract. Surg. 30, 775–785 (2004).
[CrossRef]

Garner, L. F.

G. Smith, M. J. Cox, R. Calver, and L. F. Garner, “The spherical aberration of the crystalline lens of the human eye,” Vis. Res. 41, 235–243 (2001).
[CrossRef]

Gatinel, D.

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

Guirao, A.

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]

Hemmenger, R. P.

K. M. Oliver, R. P. Hemmenger, M. C. Corbett, D. P. S. O’Brart, S. Verma, J. Marshall, and A. Tomlinson, “Corneal optical aberrations induced by photorefractive keratectomy,” J. Refract. Surg. 13, 246–254 (1997).

Ho, A.

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

Hoang-Xuan, T.

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

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]

Kaemmerer, M.

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

Koch, D. D.

L. Wang and D. D. Koch, “Ocular high-order aberrations in individuals screened for refractive surgery,” J. Cataract Refract. Surg. 29, 1896–1903 (2003).
[CrossRef]

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]

Koons, S. J.

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

Llorente, L.

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

Lloves, J. M.

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

Löffler, J.

M. Mrochen, C. Donitzky, C. Müllner, and J. Löffler, “Wavefront-optimized ablation profiles: theoretical background,” J. Cataract Refract. Surg. 30, 775–785 (2004).
[CrossRef]

Mann, F.

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

Marcos, S.

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

Marshall, J.

K. M. Oliver, R. P. Hemmenger, M. C. Corbett, D. P. S. O’Brart, S. Verma, J. Marshall, and A. Tomlinson, “Corneal optical aberrations induced by photorefractive keratectomy,” J. Refract. Surg. 13, 246–254 (1997).

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

Mierdel, P.

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

Moreno-Barriuso, E.

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

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]

M. Mrochen, C. Donitzky, C. Müllner, and J. Löffler, “Wavefront-optimized ablation profiles: theoretical background,” J. Cataract Refract. Surg. 30, 775–785 (2004).
[CrossRef]

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

Müllner, C.

M. Mrochen, C. Donitzky, C. Müllner, and J. Löffler, “Wavefront-optimized ablation profiles: theoretical background,” J. Cataract Refract. Surg. 30, 775–785 (2004).
[CrossRef]

Munnerlyn, C. R.

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

Navarro, R.

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

O’Brart, D. P. S.

K. M. Oliver, R. P. Hemmenger, M. C. Corbett, D. P. S. O’Brart, S. Verma, J. Marshall, and A. Tomlinson, “Corneal optical aberrations induced by photorefractive keratectomy,” J. Refract. Surg. 13, 246–254 (1997).

Oliver, K. M.

K. M. Oliver, R. P. Hemmenger, M. C. Corbett, D. P. S. O’Brart, S. Verma, J. Marshall, and A. Tomlinson, “Corneal optical aberrations induced by photorefractive keratectomy,” J. Refract. Surg. 13, 246–254 (1997).

Parel, J.-M.

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

Porter, J.

Schwiegerling, J.

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

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]

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

Smith, G.

G. Smith, M. J. Cox, R. Calver, and L. F. Garner, “The spherical aberration of the crystalline lens of the human eye,” Vis. Res. 41, 235–243 (2001).
[CrossRef]

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

G. Smith and D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge University, 1997).

Snyder, R. W.

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

Srinivasan, R.

S. L. Trokel, R. Srinivasan, and B. Braren, “Excimer laser surgery of the cornea,” Am. J. Ophthalmol. 96, 710–715(1983).

Sung, J.

L. Chan, M. Tse, M. Chim, W. Wong, C. Choi, J. Yu, M. Zhang, and J. Sung, “The 100th birthday of the conic constant and Schwarzschild’s revolutionary papers in optics,” Proc. SPIE 5875, 587501 (2005).
[CrossRef]

Tomlinson, A.

K. M. Oliver, R. P. Hemmenger, M. C. Corbett, D. P. S. O’Brart, S. Verma, J. Marshall, and A. Tomlinson, “Corneal optical aberrations induced by photorefractive keratectomy,” J. Refract. Surg. 13, 246–254 (1997).

Trokel, S. L.

S. L. Trokel, R. Srinivasan, and B. Braren, “Excimer laser surgery of the cornea,” Am. J. Ophthalmol. 96, 710–715(1983).

Tse, M.

L. Chan, M. Tse, M. Chim, W. Wong, C. Choi, J. Yu, M. Zhang, and J. Sung, “The 100th birthday of the conic constant and Schwarzschild’s revolutionary papers in optics,” Proc. SPIE 5875, 587501 (2005).
[CrossRef]

Verma, S.

K. M. Oliver, R. P. Hemmenger, M. C. Corbett, D. P. S. O’Brart, S. Verma, J. Marshall, and A. Tomlinson, “Corneal optical aberrations induced by photorefractive keratectomy,” J. Refract. Surg. 13, 246–254 (1997).

Wang, L.

L. Wang and D. D. Koch, “Ocular high-order aberrations in individuals screened for refractive surgery,” J. Cataract Refract. Surg. 29, 1896–1903 (2003).
[CrossRef]

Williams, D. R.

Wong, W.

L. Chan, M. Tse, M. Chim, W. Wong, C. Choi, J. Yu, M. Zhang, and J. Sung, “The 100th birthday of the conic constant and Schwarzschild’s revolutionary papers in optics,” Proc. SPIE 5875, 587501 (2005).
[CrossRef]

Yu, J.

L. Chan, M. Tse, M. Chim, W. Wong, C. Choi, J. Yu, M. Zhang, and J. Sung, “The 100th birthday of the conic constant and Schwarzschild’s revolutionary papers in optics,” Proc. SPIE 5875, 587501 (2005).
[CrossRef]

Zhang, M.

L. Chan, M. Tse, M. Chim, W. Wong, C. Choi, J. Yu, M. Zhang, and J. Sung, “The 100th birthday of the conic constant and Schwarzschild’s revolutionary papers in optics,” Proc. SPIE 5875, 587501 (2005).
[CrossRef]

Am. J. Ophthalmol. (1)

S. L. Trokel, R. Srinivasan, and B. Braren, “Excimer laser surgery of the cornea,” Am. J. Ophthalmol. 96, 710–715(1983).

Investig. Ophthalmol. Vis. Sci. (2)

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

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

J. Cataract Refract. Surg. (7)

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

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

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

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

M. Mrochen, C. Donitzky, C. Müllner, and J. Löffler, “Wavefront-optimized ablation profiles: theoretical background,” J. Cataract Refract. Surg. 30, 775–785 (2004).
[CrossRef]

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]

L. Wang and D. D. Koch, “Ocular high-order aberrations in individuals screened for refractive surgery,” J. Cataract Refract. Surg. 29, 1896–1903 (2003).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Refract. Surg. (1)

K. M. Oliver, R. P. Hemmenger, M. C. Corbett, D. P. S. O’Brart, S. Verma, J. Marshall, and A. Tomlinson, “Corneal optical aberrations induced by photorefractive keratectomy,” J. Refract. Surg. 13, 246–254 (1997).

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. Lett. (1)

Proc. Phys. Soc. (1)

T. Y. Baker, “Ray tracing through non-spherical surfaces,” Proc. Phys. Soc. 55, 361–364 (1943).
[CrossRef]

Proc. SPIE (1)

L. Chan, M. Tse, M. Chim, W. Wong, C. Choi, J. Yu, M. Zhang, and J. Sung, “The 100th birthday of the conic constant and Schwarzschild’s revolutionary papers in optics,” Proc. SPIE 5875, 587501 (2005).
[CrossRef]

Vis. Res. (1)

G. Smith, M. J. Cox, R. Calver, and L. F. Garner, “The spherical aberration of the crystalline lens of the human eye,” Vis. Res. 41, 235–243 (2001).
[CrossRef]

Other (3)

American National Standard Institute, “Methods for reporting optical aberrations of eyes,” ANSI Z80.28–2004 (Optical Laboratories Association, 2004), Annex B, pp. 19–28.

G. Smith and D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge University, 1997).

G.-M. Dai, Wavefront Optics for Vision Correction (SPIE, 2008), Chap. 3.

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Figures (10)

Fig. 1.
Fig. 1.

Geometry for refractive surgery. A ray from an object located at point O1 with refractive index n1 passes through corneal surface at point P with refractive index n2 and hits the retina at point O2. The object distance is l1, the image distance is l2 and the apical radius of curvature of cornea is R1.

Fig. 2.
Fig. 2.

Refractive surgical factor s as a function of the refractive correction power for three different corneal curvatures: highly flat (K=39D), normal (K=43.5D), and highly curved (K=48D) corneas.

Fig. 3.
Fig. 3.

The scaling factor for the postoperative asphericity as a function of the refractive correction power for three different corneal curvatures: highly flat (K=39D), normal (K=43.5D), and highly curved (K=48D) corneas.

Fig. 4.
Fig. 4.

Target ablation shapes for the Q-preserved for a normal cornea (K=43.5D) for three asphericity factors: 0.13, 0.26, and 0.39, respectively, as compared to the Munnerlyn shape for a 4D myopic correction.

Fig. 5.
Fig. 5.

Target ablation shapes for the Q-preserved for a highly flat (K=38D, upper panel) and for a highly curved (K=48D, lower panel) for a normal asphericity factor of 0.26, as compared to the Munnerlyn shape for a 4D myopic correction.

Fig. 6.
Fig. 6.

Induced spherical aberration over a 6 mm pupil as a function of refractive correction power for conventional treatment. Various corneal asphericity and steepness are considered.

Fig. 7.
Fig. 7.

Induced spherical aberration over a 6 mm pupil as a function of refractive correction power for Q-preserved treatment. Various corneal asphericities and steepnesses are considered.

Fig. 8.
Fig. 8.

Scatter plots for spherical aberration simulated for the entire eye (upper panel), from the cornea (middle panel) and from the crystalline lens (lower panel) preoperatively. 1000 eyes were used.

Fig. 9.
Fig. 9.

Scatter plots for the induced spherical aberration in a Monte Carlo simulation with 1000 eyes using Munnerlyn shape and the Q-preserved shape.

Fig. 10.
Fig. 10.

Scatter plots for the postoperative spherical aberration in a Monte Carlo simulation with 1000 eyes using Munnerlyn shape and the Q-preserved shape.

Tables (1)

Tables Icon

Table 1. Mean and Standard Deviation for c20, c40, and c60 (in Micrometers over a 6 mm Pupil) for the Induction from the Shape as well as After Surgery (Post-Op) for the 1000 Eyes in the Simulation

Equations (52)

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r2=2R1z(1+Q1)z2,
z(r;Q1)=R1R12(1+Q1)r21+Q1.
z(r;Q1)=r2R1+R12(1+Q1)r2.
z(r)=r22R1=R22R1(rR)2,
z(ρ)=R243R1Z20(ρ)+R24R1Z00(ρ),
ξ1=(R1z)2+r2=R12Q1z2.
z(r;Q1)=r22R1+(1+Q1)r48R13+(1+Q1)2r616R15.
S=(n2n1)(1R11R1),
R1=sR1,
s=n2n1n2n1+R1S
z(r;Q1)=R1R12(1+Q1)r21+Q1=sR11+Q1[11(1+Q1)(rsR1)2].
t(r;Q1,Q1)=R1R12(1+Q1)r21+Q1sR11+Q1[11(1+Q1)r2s2R12].
t(r)=R1R12r2sR1+s2R12r2.
Q1=s3Q1.
t(r;Q)=R1R12(1+Q)r21+QsR11+Q+11+Qs2R12(1+Q)r2.
l=n1r2+(zl)2+n2r2+(l2z)2.
l=n1l1+n2l2.
W(r)=ll=n1[l1r2+(zl1)2]+n2[l2r2+(l2z)2].
W(r)=βr4+γr6,
β(n;Q1;R1)=(n1)(n2Q1+1)8n2R13,
γ(n;Q1;R1)=(n1)[n2+n1+n3Q1(nQ1+n+1)]16n4R15.
W(ρ)=c20Z20(ρ)+c40Z40(ρ)+c60Z60(ρ),
c20=360(10β+9γR2)R4,
c40=560(2β+3γR2)R4,
c60=7140γR6.
W(r)=βr4+γr6,
β(n;Q1;R1)=(n1)(n2Q1+1)8n2R13,
γ(n;Q1;R1)=(n1)[n2+n1+n3Q1(nQ1+n+1)]16n4R15.
c20=360[10(ββ)+9(γγ)R2]R4,
c40=560[2(ββ)+3(γγ)R2]R4,
c60=7140(γγ)R6,
β(n;Q1;R1)=(n1)(n2s3Q1+1)8n2s3R13,
γ(n;Q1;R1)=(n1)[n2+n1+n3s3Q1(ns3Q1+n+1)]16n4s5R15.
β(n;Q1;R1)=(n1)(n2Q1+1)8n2s3R13,
γ(n;Q1;R1)=(n1)[n2+n1+n3Q1(nQ1+n+1)]16n4s5R15.
z(r;Q1)=r22R1+(1+Q1)r48R13+(1+Q1)2r616R15.
z(r;Q1)=r22R1+(1+Q1)r48R13+(1+Q1)2r616R15.
r22R1+r48R13+r616R15r22sR1r48s3R13r616s5R15=12(1R11R1)r2+18(1+Q1R131+Q1R13)r4+116[(1+Q1)2R15(1+Q1)2R15]r6.
1R11sR1=1R11R1,
1R131s3R13=1+Q1R131+Q1R13,
1R151s5R15=(1+Q1)2R15(1+Q1)2R15.
R1=sR1,
Q1=(Q1+1s3)(R1R1)31.
Q1=s3Q1.
W(r)=n1[l1r2+(zl1)2]+n2[l2r2+(l2z)2].
W(r)=n1l1[11(2zl1z2l12r2l12)]+n2l2[11(2zl2z2l22r2l22)]=n1l1[12(2zl1z2l12r2l12)+18(2zl1z2l12r2l12)2+116(2zl1z2l12r2l12)3]+n2l2[12(2zl2z2l22r2l22)+18(2zl2z2l22r2l22)2+116(2zl2z2l22r2l22)3].
W(r)=r22[n2l2n1l1(n2n1)R1]+r48[(n2l23n1l13)2R1(n2l22n1l12)+(1+Q1)(n2n1)R13]r616[(n2l25n1l15)3R1(n2l24n1l14)+2R12(n2l23n1l13)+1+Q1R13(n2l22n1l12)(n2n1)(1+Q1)2R15]=r48[n2l2(1l21R1)2n1l1(1l11R1)2+(n2n1)Q1R13]r616[(n2l25n1l15)3R1(n2l24n1l14)+2R12(n2l23n1l13)+1+Q1R13(n2l22n1l12)(n2n1)(1+Q1)2R15].
n2l2n1l1=n2n1R1.
l2=n2R1n2n1.
W(r)=βr4+γr6,
β(n;Q1;R1)=(n1)(n2Q1+1)8n2R13,
γ(n;Q1;R1)=(n1)[n2+n1+n3Q1(nQ1+n+1)]16n4R15.

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