Abstract

We have tested whether a recent model [Appl. Phys. Lett. 95, 174105 (2009)] that considers the angular dependence of laser-ablation rates, including reflection losses and geometrical dependence of incident fluence, and the effect of plume absorption can have significant effects for refractive surgery patients. We have developed a mathematical procedure and deduced equations that show that this model can significantly influence postsurgical corneal parameters (radius and asphericity) and, thus, should be considered in ablation algorithms in order to achieve a better emmetropization and an effective correction of eye aberrations.

© 2010 Optical Society of America

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References

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  1. C. Dorronsoro, D. Cano, J. Merayo-Lloves, and S. Marcos, Opt. Express 14, 6142 (2006).
    [CrossRef] [PubMed]
  2. J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, E. Hita, and F. Pérez-Ocón, Opt. Express 13, 336 (2005).
    [CrossRef] [PubMed]
  3. M. Mrochen and T. Seiler, J. Refract. Surg. 17, S584 (2001).
    [PubMed]
  4. C. Dorronsoro, L. Remon, J. Merayo-Lloves, and S. Marcos, Opt. Express 17, 15292 (2009).
    [CrossRef] [PubMed]
  5. B. T. Fisher and D. W. Hahn, J. Opt. Soc. Am. A 24, 265 (2007).
    [CrossRef]
  6. J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, and E. Hita, Appl. Phys. Lett. 81, 1521 (2002).
    [CrossRef]
  7. J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, and E. Hita, Opt. Lett. 29, 962 (2004).
    [CrossRef] [PubMed]
  8. J. E. A. Pedder, A. S. Holmes, and E. Dyer, Appl. Phys. Lett. 95, 174105 (2009).
    [CrossRef]
  9. L. M. Shanyfelt, P. L. Dickrell, H. F. Edelhauser, and D. W. Hahn, Lasers Surg. Med. 40, 483 (2008).
    [CrossRef] [PubMed]

2009 (2)

J. E. A. Pedder, A. S. Holmes, and E. Dyer, Appl. Phys. Lett. 95, 174105 (2009).
[CrossRef]

C. Dorronsoro, L. Remon, J. Merayo-Lloves, and S. Marcos, Opt. Express 17, 15292 (2009).
[CrossRef] [PubMed]

2008 (1)

L. M. Shanyfelt, P. L. Dickrell, H. F. Edelhauser, and D. W. Hahn, Lasers Surg. Med. 40, 483 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

2005 (1)

2004 (1)

2002 (1)

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, and E. Hita, Appl. Phys. Lett. 81, 1521 (2002).
[CrossRef]

2001 (1)

M. Mrochen and T. Seiler, J. Refract. Surg. 17, S584 (2001).
[PubMed]

Anera, R. G.

Cano, D.

Dickrell, P. L.

L. M. Shanyfelt, P. L. Dickrell, H. F. Edelhauser, and D. W. Hahn, Lasers Surg. Med. 40, 483 (2008).
[CrossRef] [PubMed]

Dorronsoro, C.

Dyer, E.

J. E. A. Pedder, A. S. Holmes, and E. Dyer, Appl. Phys. Lett. 95, 174105 (2009).
[CrossRef]

Edelhauser, H. F.

L. M. Shanyfelt, P. L. Dickrell, H. F. Edelhauser, and D. W. Hahn, Lasers Surg. Med. 40, 483 (2008).
[CrossRef] [PubMed]

Fisher, B. T.

Hahn, D. W.

L. M. Shanyfelt, P. L. Dickrell, H. F. Edelhauser, and D. W. Hahn, Lasers Surg. Med. 40, 483 (2008).
[CrossRef] [PubMed]

B. T. Fisher and D. W. Hahn, J. Opt. Soc. Am. A 24, 265 (2007).
[CrossRef]

Hita, E.

Holmes, A. S.

J. E. A. Pedder, A. S. Holmes, and E. Dyer, Appl. Phys. Lett. 95, 174105 (2009).
[CrossRef]

Jiménez, J. R.

Jiménez del Barco, L.

Marcos, S.

Merayo-Lloves, J.

Mrochen, M.

M. Mrochen and T. Seiler, J. Refract. Surg. 17, S584 (2001).
[PubMed]

Pedder, J. E. A.

J. E. A. Pedder, A. S. Holmes, and E. Dyer, Appl. Phys. Lett. 95, 174105 (2009).
[CrossRef]

Pérez-Ocón, F.

Remon, L.

Seiler, T.

M. Mrochen and T. Seiler, J. Refract. Surg. 17, S584 (2001).
[PubMed]

Shanyfelt, L. M.

L. M. Shanyfelt, P. L. Dickrell, H. F. Edelhauser, and D. W. Hahn, Lasers Surg. Med. 40, 483 (2008).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

J. R. Jiménez, R. G. Anera, L. Jiménez del Barco, and E. Hita, Appl. Phys. Lett. 81, 1521 (2002).
[CrossRef]

J. E. A. Pedder, A. S. Holmes, and E. Dyer, Appl. Phys. Lett. 95, 174105 (2009).
[CrossRef]

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

J. Refract. Surg. (1)

M. Mrochen and T. Seiler, J. Refract. Surg. 17, S584 (2001).
[PubMed]

Lasers Surg. Med. (1)

L. M. Shanyfelt, P. L. Dickrell, H. F. Edelhauser, and D. W. Hahn, Lasers Surg. Med. 40, 483 (2008).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

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Figures (1)

Fig. 1
Fig. 1

Corneal-power differences (absolute number of diopters) as a function of the presurgical degree of myopia (absolute number of diopters to correct) for two μ / μ p values, μ / μ p = 1.20 and μ / μ p = 0.8 . ( R = 7.8 mm , d = 6.5 mm , F 0 = 150 mJ / cm 2 , and F th = 50 mJ / cm 2 ).

Equations (16)

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d p = m · ln ( F 0 F th ) ,
d p corr = b · m · cos θ · ln ( 1 + b ( 1 R ˜ ) F 0 1 R ˜ ( 0 ) F th b α 0 α θ cos θ ) ,
ρ = d p corr d p .
Φ ( x , y , z ) = x 2 + y 2 + p z 2 2 R z = 0 ,
cos θ = ( 1 p z / R ) ( p ( p 1 ) ( z / R ) 2 + 2 ( 1 p ) ( z / R ) + 1 ) 1 / 2 .
R ˜ = 1 / 2 ( ( 1.52 cos θ cos θ 1.52 cos θ + cos θ ) 2 + ( cos θ 1.52 cos θ cos θ + 1.52 cos θ ) 2 ) ,
z R = 1 p ( 1 p ( y / R ) 2 ) p 1 / 2 .
ρ ( a , b , y , R , p ) = b ln ( 1 + a b 1 b ) ln a + 0.5 b 1 + b + a b 2 0.5 b ln ( 1 1 b + a b ) ln a y 2 R 2 + ( 0.125 b ( 1 + a b 1 b ) 2 + 0.375 0.0175 a b 2 0.5 p ( 1 + a b 1 b ) + b ln ( 1 1 b + a b ) ( 0.375 0.5 p ) ) y 4 R 4 ,
z ( y ) = 4 D y 2 3 D d 2 3 ,
1 R Munner = 1 R + 8 D 3 p Munner = R 3 Munner R 3 p .
z ( y ) = ρ ( a , b , y , R , p ) · ( 4 D y 2 3 D d 2 3 ) .
h ( R , p ) 0 d / 2 ( D d 2 3 + R p ( R 2 p y 2 ) 1 / 2 p ' ρ ( a , y , R ) · ( 4 D y 2 3 D d 2 3 ) R p + ( R 2 p y 2 ) 1 / 2 p ) 2 d y .
/ R [ h ( R , p ) ] ( p corr , R corr ) = 0 , / p [ h ( R , p ) ] ( p corr , R corr ) = 0.
1 R corr = 1 R + 8 c 1 D 3 2 c 2 d 2 D 3 R 2 , p corr = R 3 corr R 3 p 8 c 3 D d 2 3 R + 10.667 c 2 D R ,
c 1 = b ln ( 1 + a b 1 b ) ln a , c 2 = 0.5 b 1 + b + a b 2 0.5 b ln ( 1 1 b + a b ) ln a , c 3 = ( 0.125 b ( 1 + a b 1 b ) 2 + 0.375 0.0175 a b 2 0.5 p ( 1 + a b 1 b ) + b ln ( 1 1 b + a b ) ( 0.375 0.5 p ) ) .
Δ φ = Δ n ( 1 R corr 1 R Munner ) = ( c 1 1 ) D 0.25 c 2 d 2 D R 2 , Δ p = ( p corr p Munner ) = 8 c 3 D d 2 3 R + 10.667 c 2 D R .

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