Abstract

We provide a correction factor to be added in ablation algorithms when a Gaussian beam is used in photorefractive laser surgery. This factor, which quantifies the effect of pulse overlapping, depends on beam radius and spot size. We also deduce the expected post-surgical corneal radius and asphericity when considering this factor. Data on 141 eyes operated on LASIK (laser in situ keratomileusis) with a Gaussian profile show that the discrepancy between experimental and expected data on corneal power is significantly lower when using the correction factor. For an effective improvement of post-surgical visual quality, this factor should be applied in ablation algorithms that do not consider the effects of pulse overlapping with a Gaussian beam.

© 2005 Optical Society of America

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References

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  1. S. M.  MacRae, R. R.  Krueger, R. A.  Applegate, “What is customisation?,” in Customized corneal ablation: the quest for supervision , S. M.  McRae, R. R.  Krueger, R. A.  Applegate, eds. (SLACK Incorporated, Thorofare, NJ, 2001).
  2. J. R.  Jiménez, R. G.  Anera, J. A.  Díaz, F.  Pérez-Ocón, “Corneal asphericity after refractive surgery when the Munnerlyn formula is applied,” J. Opt. Soc. Am. A 21, 98–103 (2004).
    [CrossRef]
  3. M.  Mrochen, T.  Seiler, “Influence of corneal curvature on calculation of ablation patterns used in photorefractive laser surgery,” J. Refract. Surg. 17, S584–S587 (2001).
    [PubMed]
  4. 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]
  5. 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]
  6. J. R.  Jiménez, R. G.  Anera, L.  Jiménez del Barco, E.  Hita, “Influence of laser polarization on ocular refractive parameters after refractive surgery,” Opt. Lett. 29, 962–965 (2004).
    [CrossRef] [PubMed]
  7. D.  Huang, M.  Arif, “Spot size and quality of scanning laser correction of higher-order wavefront aberrations,” J. Cataract Refract. Surg. 28, 407–416 (2002).
    [CrossRef] [PubMed]
  8. A.  Guirao, D.  Williams, S.M.  MacRae, “Effect of beam size on the expected benefit of customized laser refractive surgery,” J. Refract. Surg. 19, 15–23 (2003).
    [PubMed]
  9. F.  Manns, J.  Shen, P.  Soderberg, T.  Matsui, J.  Parel, “Development of an algorithm for corneal reshaping with a scanning laser beam,” Appl. Opt. 21, 4600–4608 (1995).
    [CrossRef]
  10. M.  Mrochen, T.  Seiler, “The Erbium Laser,” in Photorefractive Keratectomy , R.  Steiner, H.  Wu, S.  Slade, V.  Thompson, eds.(Thiem Verlag, New York, 1988).
  11. 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]
  12. D. A.  Atchison, G.  Smith, Optics of the Human Eye (Butterworth Heinemann, Oxford, 2000), Chap. 18.
  13. H. S.  Ginis, V. J.  Kasanevaki, I. G.  Pallikaris, “Influence of ablation parameters on refractive changes after phototherapeutic keratectomy,” J. Refract. Surg. 19, 443–448 (2003).
    [PubMed]

2004 (2)

2003 (4)

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]

H. S.  Ginis, V. J.  Kasanevaki, I. G.  Pallikaris, “Influence of ablation parameters on refractive changes after phototherapeutic keratectomy,” J. Refract. Surg. 19, 443–448 (2003).
[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]

A.  Guirao, D.  Williams, S.M.  MacRae, “Effect of beam size on the expected benefit of customized laser refractive surgery,” J. Refract. Surg. 19, 15–23 (2003).
[PubMed]

2002 (2)

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]

D.  Huang, M.  Arif, “Spot size and quality of scanning laser correction of higher-order wavefront aberrations,” J. Cataract Refract. Surg. 28, 407–416 (2002).
[CrossRef] [PubMed]

2001 (1)

M.  Mrochen, T.  Seiler, “Influence of corneal curvature on calculation of ablation patterns used in photorefractive laser surgery,” J. Refract. Surg. 17, S584–S587 (2001).
[PubMed]

1995 (1)

F.  Manns, J.  Shen, P.  Soderberg, T.  Matsui, J.  Parel, “Development of an algorithm for corneal reshaping with a scanning laser beam,” Appl. Opt. 21, 4600–4608 (1995).
[CrossRef]

Anera, R. G.

Applegate, R. A.

S. M.  MacRae, R. R.  Krueger, R. A.  Applegate, “What is customisation?,” in Customized corneal ablation: the quest for supervision , S. M.  McRae, R. R.  Krueger, R. A.  Applegate, eds. (SLACK Incorporated, Thorofare, NJ, 2001).

Arif, M.

D.  Huang, M.  Arif, “Spot size and quality of scanning laser correction of higher-order wavefront aberrations,” J. Cataract Refract. Surg. 28, 407–416 (2002).
[CrossRef] [PubMed]

Atchison, D. A.

D. A.  Atchison, G.  Smith, Optics of the Human Eye (Butterworth Heinemann, Oxford, 2000), Chap. 18.

Díaz, J. A.

Ginis, H. S.

H. S.  Ginis, V. J.  Kasanevaki, I. G.  Pallikaris, “Influence of ablation parameters on refractive changes after phototherapeutic keratectomy,” J. Refract. Surg. 19, 443–448 (2003).
[PubMed]

Guirao, A.

A.  Guirao, D.  Williams, S.M.  MacRae, “Effect of beam size on the expected benefit of customized laser refractive surgery,” J. Refract. Surg. 19, 15–23 (2003).
[PubMed]

Hita, E.

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]

D.  Huang, M.  Arif, “Spot size and quality of scanning laser correction of higher-order wavefront aberrations,” J. Cataract Refract. Surg. 28, 407–416 (2002).
[CrossRef] [PubMed]

Jiménez, J. R.

Jiménez del Barco, L.

Kasanevaki, V. J.

H. S.  Ginis, V. J.  Kasanevaki, I. G.  Pallikaris, “Influence of ablation parameters on refractive changes after phototherapeutic keratectomy,” J. Refract. Surg. 19, 443–448 (2003).
[PubMed]

Krueger, R. R.

S. M.  MacRae, R. R.  Krueger, R. A.  Applegate, “What is customisation?,” in Customized corneal ablation: the quest for supervision , S. M.  McRae, R. R.  Krueger, R. A.  Applegate, eds. (SLACK Incorporated, Thorofare, NJ, 2001).

MacRae, S. M.

S. M.  MacRae, R. R.  Krueger, R. A.  Applegate, “What is customisation?,” in Customized corneal ablation: the quest for supervision , S. M.  McRae, R. R.  Krueger, R. A.  Applegate, eds. (SLACK Incorporated, Thorofare, NJ, 2001).

MacRae, S.M.

A.  Guirao, D.  Williams, S.M.  MacRae, “Effect of beam size on the expected benefit of customized laser refractive surgery,” J. Refract. Surg. 19, 15–23 (2003).
[PubMed]

Manns, F.

F.  Manns, J.  Shen, P.  Soderberg, T.  Matsui, J.  Parel, “Development of an algorithm for corneal reshaping with a scanning laser beam,” Appl. Opt. 21, 4600–4608 (1995).
[CrossRef]

Matsui, T.

F.  Manns, J.  Shen, P.  Soderberg, T.  Matsui, J.  Parel, “Development of an algorithm for corneal reshaping with a scanning laser beam,” Appl. Opt. 21, 4600–4608 (1995).
[CrossRef]

Mrochen, M.

M.  Mrochen, T.  Seiler, “Influence of corneal curvature on calculation of ablation patterns used in photorefractive laser surgery,” J. Refract. Surg. 17, S584–S587 (2001).
[PubMed]

M.  Mrochen, T.  Seiler, “The Erbium Laser,” in Photorefractive Keratectomy , R.  Steiner, H.  Wu, S.  Slade, V.  Thompson, eds.(Thiem Verlag, New York, 1988).

Pallikaris, I. G.

H. S.  Ginis, V. J.  Kasanevaki, I. G.  Pallikaris, “Influence of ablation parameters on refractive changes after phototherapeutic keratectomy,” J. Refract. Surg. 19, 443–448 (2003).
[PubMed]

Parel, J.

F.  Manns, J.  Shen, P.  Soderberg, T.  Matsui, J.  Parel, “Development of an algorithm for corneal reshaping with a scanning laser beam,” Appl. Opt. 21, 4600–4608 (1995).
[CrossRef]

Pérez-Ocón, F.

Seiler, T.

M.  Mrochen, T.  Seiler, “Influence of corneal curvature on calculation of ablation patterns used in photorefractive laser surgery,” J. Refract. Surg. 17, S584–S587 (2001).
[PubMed]

M.  Mrochen, T.  Seiler, “The Erbium Laser,” in Photorefractive Keratectomy , R.  Steiner, H.  Wu, S.  Slade, V.  Thompson, eds.(Thiem Verlag, New York, 1988).

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]

Shen, J.

F.  Manns, J.  Shen, P.  Soderberg, T.  Matsui, J.  Parel, “Development of an algorithm for corneal reshaping with a scanning laser beam,” Appl. Opt. 21, 4600–4608 (1995).
[CrossRef]

Smith, G.

D. A.  Atchison, G.  Smith, Optics of the Human Eye (Butterworth Heinemann, Oxford, 2000), Chap. 18.

Soderberg, P.

F.  Manns, J.  Shen, P.  Soderberg, T.  Matsui, J.  Parel, “Development of an algorithm for corneal reshaping with a scanning laser beam,” Appl. Opt. 21, 4600–4608 (1995).
[CrossRef]

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]

Williams, D.

A.  Guirao, D.  Williams, S.M.  MacRae, “Effect of beam size on the expected benefit of customized laser refractive surgery,” J. Refract. Surg. 19, 15–23 (2003).
[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)

F.  Manns, J.  Shen, P.  Soderberg, T.  Matsui, J.  Parel, “Development of an algorithm for corneal reshaping with a scanning laser beam,” Appl. Opt. 21, 4600–4608 (1995).
[CrossRef]

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]

J. Cataract Refract. Surg. (1)

D.  Huang, M.  Arif, “Spot size and quality of scanning laser correction of higher-order wavefront aberrations,” J. Cataract Refract. Surg. 28, 407–416 (2002).
[CrossRef] [PubMed]

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

J. Refract. Surg. (3)

M.  Mrochen, T.  Seiler, “Influence of corneal curvature on calculation of ablation patterns used in photorefractive laser surgery,” J. Refract. Surg. 17, S584–S587 (2001).
[PubMed]

A.  Guirao, D.  Williams, S.M.  MacRae, “Effect of beam size on the expected benefit of customized laser refractive surgery,” J. Refract. Surg. 19, 15–23 (2003).
[PubMed]

H. S.  Ginis, V. J.  Kasanevaki, I. G.  Pallikaris, “Influence of ablation parameters on refractive changes after phototherapeutic keratectomy,” J. Refract. Surg. 19, 443–448 (2003).
[PubMed]

Opt. Lett. (2)

Other (3)

S. M.  MacRae, R. R.  Krueger, R. A.  Applegate, “What is customisation?,” in Customized corneal ablation: the quest for supervision , S. M.  McRae, R. R.  Krueger, R. A.  Applegate, eds. (SLACK Incorporated, Thorofare, NJ, 2001).

D. A.  Atchison, G.  Smith, Optics of the Human Eye (Butterworth Heinemann, Oxford, 2000), Chap. 18.

M.  Mrochen, T.  Seiler, “The Erbium Laser,” in Photorefractive Keratectomy , R.  Steiner, H.  Wu, S.  Slade, V.  Thompson, eds.(Thiem Verlag, New York, 1988).

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Figures (2)

Fig. 1.
Fig. 1.

Effect of overlapping due to the finite-size of the incident beam. A point on the cornea (Z) is affected by the ablation of surrounding pulses (e.g. Ψ1 and Ψ2 in the drawing).

Fig. 2.
Fig. 2.

Average of corneal-power difference between experimental data and theoretical data for 3 values of a. For each value of a, theoretical data are computed with or without (c=1) the use of the correction factor that takes into account the effect of pulse overlapping during corneal ablation with a Gaussian beam. Data include standard errors.

Tables (1)

Tables Icon

Table 1. Average difference between experimental and theoretical data for corneal-power (Δφ) and asphericity (Δp). Theoretical data are computed with and without the use of the correction factor that takes into account the effect of pulse overlapping.

Equations (14)

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d p = m · ln ( F 0 F th ) if F 0 > F th
= 0 if F 0 F th
F ( x , y ) = F 0 exp [ 2 ( x 2 + y 2 ) w 2 ]
c = 0 r m · ln ( F 0 exp [ 2 ( x 2 + y 2 ) w 2 ] F th ) dxdy 0 r m · ln ( F 0 F th ) dxdy
( F 0 exp ( 2 r 2 w 2 ) F th ) > 1
c = m 0 r ( ln ( F 0 F th ) 2 x 2 + y 2 w 2 ) dxdy m · ln ( F 0 F th ) 0 r dxdy
c = 1 r ' 2 w 2 ( ln F 0 F th ) 1
ρ ( a , y , R , p ) ( 1 0.0435 a ) a y 2 2 R 2 + a ( 0.232 0.5 p ) y 4 R 4
c = c · [ ( 1 0.0435 a ) a y 2 2 R 2 + a ( 0.232 0.5 p ) y 4 R 4 ]
z ( y ) = 4 D y 2 3 D d 2 3
D = Δ n R Δ n R
x 2 + y 2 + p z 2 2 Rz = 0
1 R = 1 R + 8 c D 3 0.11 a c D + a c d 2 D 3 R 2
p = R 3 R 3 [ p + a c D R ( d 2 [ 0.62 + 1.33 3 p ] 1.333 R 2 ) ]

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