Abstract

Photorefractive keratectomy is an evolving refractive procedure for correcting myopia, hyperopia, and astigmatism. Earlier descriptions of the patterns required for this surgery are based on paraxial optics. In this investigation the required pattern is generalized to account for spherical refractive error (defocus), axial astigmatism of arbitrary orientation, and fourth-order aberrations of the eye. The patterns described in this study can be used to customize photorefractive keratectomy and to provide corrections that account for aberration content as well as paraxial values. Furthermore, a description of the pattern along the boundary of the optical zone is given, which may prove useful in designing blending zones. An example of the use of these techniques is given for a schematic eye model.

© 1998 Optical Society of America

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References

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  1. S. L. Trokel, R. Srinivasan, B. Braren, “Excimer laser surgery of the cornea,” Am. J. Ophthalmol. 96, 710–715 (1983).
    [PubMed]
  2. R. R. Krueger, S. L. Trokel, “Quantitation of corneal ablation by ultraviolet laser light,” Arch. Opththalmol. (Chicago) 103, 1741–1742 (1985).
    [CrossRef]
  3. T. Seiler, M. Kriegerowski, N. Schnoy, T. Bende, “Ablation rate of human corneal epithelium and Bowman’s layer with the excimer laser (193 nm),” Refract. Corneal Surg. 6, 99–102 (1990).
  4. O. N. Serdarevic, Refractive Surgery: Current Techniques and Management (Igaku-Shoin, New York, 1997).
  5. C. R. Munnerlyn, S. J. Koons, J. Marshall, “Photorefractive keratectomy: a technique for laser refractive surgery,” J. Cataract Refract. Surg. 14, 46–52 (1988).
    [CrossRef] [PubMed]
  6. C. E. Martinez, R. A. Applegate, H. C. Howland, S. D. Klyce, M. B. McDonald, J. P. Medina, “Changes in corneal aberration structure after photorefractive keratectomy,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 933 (1996).
  7. J. T. Schwiegerling, J. E. Greivenkamp, R. W. Snyder, M. L. Palmer, “Using videokeratoscopic height data to construct custom photorefractive keratectomy (PRK) ablation patterns,” Invest. Ophthalmol. Visual Sci. Suppl. 38, 3245 (1997).
  8. K. M. Oliver, R. P. Hemenger, M. C. Corbett, D. P. S. O’Bart, S. Verma, J. Marshall, A. Tomlinson, “Corneal optical aberrations induced by photorefractive keratectomy,” J. Refract. Surg. 13, 246–254 (1997).
    [PubMed]
  9. A. G. Bennett, R. B. Rabbetts, Clinical Visual Optics (Butterworth-Heinemann, Oxford, 1989).
  10. G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, Cambridge, UK, 1997).
  11. J. Schwiegerling, J. E. Greivenkamp, J. M. Miller, R. W. Snyder, M. L. Palmer, “Optical modeling of radial keratotomy incision patterns,” Am. J. Ophthalmol. 122, 808–817 (1996).
    [PubMed]

1997 (2)

J. T. Schwiegerling, J. E. Greivenkamp, R. W. Snyder, M. L. Palmer, “Using videokeratoscopic height data to construct custom photorefractive keratectomy (PRK) ablation patterns,” Invest. Ophthalmol. Visual Sci. Suppl. 38, 3245 (1997).

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

1996 (2)

J. Schwiegerling, J. E. Greivenkamp, J. M. Miller, R. W. Snyder, M. L. Palmer, “Optical modeling of radial keratotomy incision patterns,” Am. J. Ophthalmol. 122, 808–817 (1996).
[PubMed]

C. E. Martinez, R. A. Applegate, H. C. Howland, S. D. Klyce, M. B. McDonald, J. P. Medina, “Changes in corneal aberration structure after photorefractive keratectomy,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 933 (1996).

1990 (1)

T. Seiler, M. Kriegerowski, N. Schnoy, T. Bende, “Ablation rate of human corneal epithelium and Bowman’s layer with the excimer laser (193 nm),” Refract. Corneal Surg. 6, 99–102 (1990).

1988 (1)

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

1985 (1)

R. R. Krueger, S. L. Trokel, “Quantitation of corneal ablation by ultraviolet laser light,” Arch. Opththalmol. (Chicago) 103, 1741–1742 (1985).
[CrossRef]

1983 (1)

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

Applegate, R. A.

C. E. Martinez, R. A. Applegate, H. C. Howland, S. D. Klyce, M. B. McDonald, J. P. Medina, “Changes in corneal aberration structure after photorefractive keratectomy,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 933 (1996).

Atchison, D. A.

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

Bende, T.

T. Seiler, M. Kriegerowski, N. Schnoy, T. Bende, “Ablation rate of human corneal epithelium and Bowman’s layer with the excimer laser (193 nm),” Refract. Corneal Surg. 6, 99–102 (1990).

Bennett, A. G.

A. G. Bennett, R. B. Rabbetts, Clinical Visual Optics (Butterworth-Heinemann, Oxford, 1989).

Braren, B.

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

Corbett, M. C.

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

Greivenkamp, J. E.

J. T. Schwiegerling, J. E. Greivenkamp, R. W. Snyder, M. L. Palmer, “Using videokeratoscopic height data to construct custom photorefractive keratectomy (PRK) ablation patterns,” Invest. Ophthalmol. Visual Sci. Suppl. 38, 3245 (1997).

J. Schwiegerling, J. E. Greivenkamp, J. M. Miller, R. W. Snyder, M. L. Palmer, “Optical modeling of radial keratotomy incision patterns,” Am. J. Ophthalmol. 122, 808–817 (1996).
[PubMed]

Hemenger, R. P.

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

Howland, H. C.

C. E. Martinez, R. A. Applegate, H. C. Howland, S. D. Klyce, M. B. McDonald, J. P. Medina, “Changes in corneal aberration structure after photorefractive keratectomy,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 933 (1996).

Klyce, S. D.

C. E. Martinez, R. A. Applegate, H. C. Howland, S. D. Klyce, M. B. McDonald, J. P. Medina, “Changes in corneal aberration structure after photorefractive keratectomy,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 933 (1996).

Koons, S. J.

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

Kriegerowski, M.

T. Seiler, M. Kriegerowski, N. Schnoy, T. Bende, “Ablation rate of human corneal epithelium and Bowman’s layer with the excimer laser (193 nm),” Refract. Corneal Surg. 6, 99–102 (1990).

Krueger, R. R.

R. R. Krueger, S. L. Trokel, “Quantitation of corneal ablation by ultraviolet laser light,” Arch. Opththalmol. (Chicago) 103, 1741–1742 (1985).
[CrossRef]

Marshall, J.

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

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

Martinez, C. E.

C. E. Martinez, R. A. Applegate, H. C. Howland, S. D. Klyce, M. B. McDonald, J. P. Medina, “Changes in corneal aberration structure after photorefractive keratectomy,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 933 (1996).

McDonald, M. B.

C. E. Martinez, R. A. Applegate, H. C. Howland, S. D. Klyce, M. B. McDonald, J. P. Medina, “Changes in corneal aberration structure after photorefractive keratectomy,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 933 (1996).

Medina, J. P.

C. E. Martinez, R. A. Applegate, H. C. Howland, S. D. Klyce, M. B. McDonald, J. P. Medina, “Changes in corneal aberration structure after photorefractive keratectomy,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 933 (1996).

Miller, J. M.

J. Schwiegerling, J. E. Greivenkamp, J. M. Miller, R. W. Snyder, M. L. Palmer, “Optical modeling of radial keratotomy incision patterns,” Am. J. Ophthalmol. 122, 808–817 (1996).
[PubMed]

Munnerlyn, C. R.

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

O’Bart, D. P. S.

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

Oliver, K. M.

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

Palmer, M. L.

J. T. Schwiegerling, J. E. Greivenkamp, R. W. Snyder, M. L. Palmer, “Using videokeratoscopic height data to construct custom photorefractive keratectomy (PRK) ablation patterns,” Invest. Ophthalmol. Visual Sci. Suppl. 38, 3245 (1997).

J. Schwiegerling, J. E. Greivenkamp, J. M. Miller, R. W. Snyder, M. L. Palmer, “Optical modeling of radial keratotomy incision patterns,” Am. J. Ophthalmol. 122, 808–817 (1996).
[PubMed]

Rabbetts, R. B.

A. G. Bennett, R. B. Rabbetts, Clinical Visual Optics (Butterworth-Heinemann, Oxford, 1989).

Schnoy, N.

T. Seiler, M. Kriegerowski, N. Schnoy, T. Bende, “Ablation rate of human corneal epithelium and Bowman’s layer with the excimer laser (193 nm),” Refract. Corneal Surg. 6, 99–102 (1990).

Schwiegerling, J.

J. Schwiegerling, J. E. Greivenkamp, J. M. Miller, R. W. Snyder, M. L. Palmer, “Optical modeling of radial keratotomy incision patterns,” Am. J. Ophthalmol. 122, 808–817 (1996).
[PubMed]

Schwiegerling, J. T.

J. T. Schwiegerling, J. E. Greivenkamp, R. W. Snyder, M. L. Palmer, “Using videokeratoscopic height data to construct custom photorefractive keratectomy (PRK) ablation patterns,” Invest. Ophthalmol. Visual Sci. Suppl. 38, 3245 (1997).

Seiler, T.

T. Seiler, M. Kriegerowski, N. Schnoy, T. Bende, “Ablation rate of human corneal epithelium and Bowman’s layer with the excimer laser (193 nm),” Refract. Corneal Surg. 6, 99–102 (1990).

Serdarevic, O. N.

O. N. Serdarevic, Refractive Surgery: Current Techniques and Management (Igaku-Shoin, New York, 1997).

Smith, G.

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

Snyder, R. W.

J. T. Schwiegerling, J. E. Greivenkamp, R. W. Snyder, M. L. Palmer, “Using videokeratoscopic height data to construct custom photorefractive keratectomy (PRK) ablation patterns,” Invest. Ophthalmol. Visual Sci. Suppl. 38, 3245 (1997).

J. Schwiegerling, J. E. Greivenkamp, J. M. Miller, R. W. Snyder, M. L. Palmer, “Optical modeling of radial keratotomy incision patterns,” Am. J. Ophthalmol. 122, 808–817 (1996).
[PubMed]

Srinivasan, R.

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

Tomlinson, A.

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

Trokel, S. L.

R. R. Krueger, S. L. Trokel, “Quantitation of corneal ablation by ultraviolet laser light,” Arch. Opththalmol. (Chicago) 103, 1741–1742 (1985).
[CrossRef]

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

Verma, S.

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

Am. J. Ophthalmol. (2)

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

J. Schwiegerling, J. E. Greivenkamp, J. M. Miller, R. W. Snyder, M. L. Palmer, “Optical modeling of radial keratotomy incision patterns,” Am. J. Ophthalmol. 122, 808–817 (1996).
[PubMed]

Arch. Opththalmol. (Chicago) (1)

R. R. Krueger, S. L. Trokel, “Quantitation of corneal ablation by ultraviolet laser light,” Arch. Opththalmol. (Chicago) 103, 1741–1742 (1985).
[CrossRef]

Invest. Ophthalmol. Visual Sci. Suppl. (2)

C. E. Martinez, R. A. Applegate, H. C. Howland, S. D. Klyce, M. B. McDonald, J. P. Medina, “Changes in corneal aberration structure after photorefractive keratectomy,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 933 (1996).

J. T. Schwiegerling, J. E. Greivenkamp, R. W. Snyder, M. L. Palmer, “Using videokeratoscopic height data to construct custom photorefractive keratectomy (PRK) ablation patterns,” Invest. Ophthalmol. Visual Sci. Suppl. 38, 3245 (1997).

J. Cataract Refract. Surg. (1)

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

J. Refract. Surg. (1)

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

Refract. Corneal Surg. (1)

T. Seiler, M. Kriegerowski, N. Schnoy, T. Bende, “Ablation rate of human corneal epithelium and Bowman’s layer with the excimer laser (193 nm),” Refract. Corneal Surg. 6, 99–102 (1990).

Other (3)

O. N. Serdarevic, Refractive Surgery: Current Techniques and Management (Igaku-Shoin, New York, 1997).

A. G. Bennett, R. B. Rabbetts, Clinical Visual Optics (Butterworth-Heinemann, Oxford, 1989).

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

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Figures (6)

Fig. 1
Fig. 1

Optics of PRK. The preoperative corneal radius of curvature Rpre must be changed to the desired postoperative radius of curvature Rpost. The optical zone diameter D determines the central ablation depth zo for a myopic ablation.

Fig. 2
Fig. 2

Sphericallike aberration of a conic section. For one of the principal meridians, the rays refracted by the cornea will remain in the plane of the paper and will converge toward the region of the image point. For nonprincipal meridians, the refracted rays leave the plane of the paper, and the aberration description becomes more complex.

Fig. 3
Fig. 3

Cross sections through the principal meridia of the cornea. In general, each meridian will have its own paraxial and marginal focus and will suffer from a sphericallike aberration.

Fig. 4
Fig. 4

Horizontal and vertical profiles through the wave-front aberration function of the postoperative eye model. There is a slight amount of overcorrected defocus, with the predominant error being fourth-order aberration. The discrepancy between the two meridians is due to a small amount of residual axial astigmatism.

Fig. 5
Fig. 5

Preoperative and postoperative spherical equivalent refractive error for the eye model. The choice of fourth-order aberration level effectively translates the preoperative curve vertically to the postoperative without significant changes in the aberration structure.

Fig. 6
Fig. 6

Ablation depth at the edge of the optical zone, as a function of meridian. The minimum ablation depth occurs at the 73° meridian, while the maximum ablation depth of -12.2 µm occurs in the orthogonal meridian. Note that the sign convention denotes negative values as being a removal of tissue.

Tables (3)

Tables Icon

Table 1 Astigmatic Decompositiona

Tables Icon

Table 2 Results of Least-Squares Fit of Subject 1’s Corneal Height Data to a Biconica

Tables Icon

Table 3 Required Postoperative Corneal Shape for Astigmatic Correction and No Additional Fourth-Order Aberration

Equations (26)

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

ϕ=(n-1)1Rpost-1Rpre,
zpre(r)=Rpre-Rpre2-r2,
zpost(r)=zo+Rpost-Rpost2-r2,
zabl(r)=zpre(r)-zpost(r)=Rpre2-D241/2-(Rpre2-r2)1/2+(n-1)RpreϕRpre+n-12-r21/2-(n-1)RpreϕRpre+n-12-D241/2.
ϕ=(n-1)1Rpost-1Rpre+zon(n-1)2RpreRpost.
h(r, θ)=r2 cos2(θ-θo)/Rx+r2 sin2(θ-θo)/Ry1+[1-(Kx+1)r2 cos2(θ-θo)/Rx2-(Ky+1)r2 sin2(θ-θo)/Ry2]1/2.
h(r, θ)=r2/Reff1+[1-(Keff+1)r2/Reff2]1/2,
Reff=RxRyRx sin2(θ-θo)+Ry cos2(θ-θo),
Keff=(Kx+1)cos2(θ-θo)Rx2+(Ky+1)sin2(θ-θo)Ry2Reff2-1.
ϕxpreDS/(ϕypre-ϕxpre)DC×θopre,
SRDS/CRDC×θR,
(ϕypre-ϕxpre)cos 2θopre+CR cos 2θR=(ϕypost-ϕxpost)cos 2θopost,
(ϕypre-ϕxpre)sin 2θopre+CR sin 2θR=(ϕypost-ϕxpost)sin 2θopost,
12(ϕxpre+ϕypre)+SR+CR2=12(ϕxpost+ϕyprost).
ϕxpost=M-C/2ifCR sin 2θR+(ϕypre-ϕxpre)sin 2θopre>0M+C/2otherwise,
ϕypost=M+C/2ifCR sin 2θR+(ϕypre-ϕxpre)sin 2θopre>0M-C/2otherwise,
θopost=12tan-1CR sin 2θR+(ϕypre-ϕxpre)sin 2θopreCR cos 2θR+(ϕypre-ϕxpre)cos 2θopre,
M=SR+CR2+12(ϕxpre+ϕxpost),
C=[CR2+(ϕypre-ϕxpre)2+2CR(ϕypre-ϕxpre)×cos 2(θR-θopre)]1/2.
w4xpost=18nL1L-1Rxpost2-1L-1L+1Rxpost+Kxpostn-18Rxpost3,
w4xpost=18ϕxpost3(1+n2Kxpost)n2(n-1)2.
w4ypost=18ϕypost3(1+n2Kypost)n2(n-1)2.
zpre(r, θ)=hpre(r, θ),
zpost(r, θ)=zo+hpost(r, θ),
zabl(r, θ)=zpre(r, θ)-zpost(r, θ),
zo=max[hpre(D/2, θ)-hpost(D/2, θ)]formyopicablations0forhyperopicablations,

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