Abstract

Analysis of induced wavefront aberration after refractive surgery is important in the design of vision correction and the development of visual correction technology. Based on a mathematical model of the anterior corneal surface, the influence of treatment decentration on induced wavefront aberrations was studied by considering oblique incidence. The results revealed that significant coma was induced from the treatment translation, and it was nearly proportional to the translation or corrected refraction of vision correction. The induced aberrations from the lateral translation correlated with the angle formed by the position vector and the astigmatism axis of myopia astigmatism correction. The induced spherical aberration did not relate to a lateral translation of the center of the pupil, but was determined only by the corrected refraction. Additionally, no significant higher-order aberrations were induced from eye cyclotorsion for pure myopia or myopia astigmatism correction. Oblique incidence played an important role in the impact of treatment decentration on the induced aberrations in refractive surgery. The induced coma without considering the oblique incidence was obviously larger than that with it. In order to achieve the best postoperative visual performance, the effect of oblique incidence in refractive surgery should be taken into account, and treatment decentration should be minimized by all means, particularly for high myopia.

© 2010 OSA

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    [CrossRef]
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  37. G. Yoon, S. Macrae, D. R. Williams, and I. G. Cox, “Causes of spherical aberration induced by laser refractive surgery,” J. Cataract Refract. Surg. 31(1), 127–135 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2009 (2)

P. Padmanabhan, M. Mrochen, D. Viswanathan, and S. Basuthkar, “Wavefront aberrations in eyes with decentered ablations,” J. Cataract Refract. Surg. 35(4), 695–702 (2009).
[CrossRef] [PubMed]

L. Wu, X. Zhou, R. Chu, and Q. Wang, “Photoablation centration on the corneal optical center in myopic LASIK using AOV excimer laser,” Eur. J. Ophthalmol. 19(6), 923–929 (2009).
[PubMed]

2008 (3)

H. Zhao and B. Xu, “Position tolerance analysis for wavefront aberrations correction of human eyes,” Acta Opt. Sin. 28(5), 949–954 (2008).
[CrossRef]

L. Wang and D. D. Koch, “Residual higher-order aberrations caused by clinically measured cyclotorsional misalignment or decentration during wavefront-guided excimer laser corneal ablation,” J. Cataract Refract. Surg. 34(12), 2057–2062 (2008).
[CrossRef] [PubMed]

H. Kim and C. K. Joo, “Ocular cyclotorsion according to body position and flap creation before laser in situ keratomileusis,” J. Cataract Refract. Surg. 34(4), 557–561 (2008).
[CrossRef] [PubMed]

2007 (5)

T. Hiraoka, C. Okamoto, Y. Ishii, T. Kakita, and T. Oshika, “Contrast sensitivity function and ocular higher-order aberrations following overnight orthokeratology,” Invest. Ophthalmol. Vis. Sci. 48(2), 550–556 (2007).
[CrossRef] [PubMed]

J. Bühren, G. Yoon, S. Kenner, S. MacRae, and K. Huxlin, “The effect of optical zone decentration on lower- and higher-order aberrations after photorefractive keratectomy in a cat model,” Invest. Ophthalmol. Vis. Sci. 48(12), 5806–5814 (2007).
[CrossRef] [PubMed]

Y. Wang, K. X. Zhao, J. C. He, Y. Jin, and T. Zuo, “Ocular higher-order aberrations features analysis after corneal refractive surgery,” Chin. Med. J. (Engl.) 120(4), 269–273 (2007).

T. Oshika, G. Sugita, K. Miyata, T. Tokunaga, T. Samejima, C. Okamoto, and Y. Ishii, “Influence of tilt and decentration of scleral-sutured intraocular lens on ocular higher-order wavefront aberration,” Br. J. Ophthalmol. 91(2), 185–188 (2007).
[CrossRef]

N. Sakata, T. Tokunaga, K. Miyata, and T. Oshika, “Changes in contrast sensitivity function and ocular higher order aberration by conventional myopic photorefractive keratectomy,” Jpn. J. Ophthalmol. 51(5), 347–352 (2007).
[CrossRef] [PubMed]

2006 (3)

L.-H. Fang, Z.-Q. Wang, W. Wang, and M. Liu, “The influence of wavefront aberration of single Zernike modes on optical quality of human eyes,” Acta Opt. Sin. 26, 1721–1726 (2006).

J. Shen, Y. Zhang, and W. Liao, “Mathematical model based corneal toric surface for excimer laser refractive surgery,” J. Southeast Univ. 36, 531–536 (2006) (Natural Science Edition).

G. M. Dai, E. Gross, and J. Liang, “System performance evaluation of refractive surgical lasers: a mathematical approach,” Appl. Opt. 45(9), 2124–2134 (2006).
[CrossRef] [PubMed]

2005 (5)

L. Chen, B. Singer, A. Guirao, J. Porter, and D. R. Williams, “Image metrics for predicting subjective image quality,” Optom. Vis. Sci. 82(5), 358–369 (2005).
[CrossRef] [PubMed]

J. Porter, G. Yoon, S. MacRae, G. Pan, T. Twietmeyer, I. G. Cox, and D. R. Williams, “Surgeon offsets and dynamic eye movements in laser refractive surgery,” J. Cataract Refract. Surg. 31(11), 2058–2066 (2005).
[CrossRef]

N. Asano-Kato, I. Toda, C. Sakai, Y. Hori-Komai, Y. Takano, M. Dogru, and K. Tsubota, “Pupil decentration and iris tilting detected by Orbscan: anatomic variations among healthy subjects and influence on outcomes of laser refractive surgeries,” J. Cataract Refract. Surg. 31(10), 1938–1942 (2005).
[CrossRef] [PubMed]

G. Yoon, S. Macrae, D. R. Williams, and I. G. Cox, “Causes of spherical aberration induced by laser refractive surgery,” J. Cataract Refract. Surg. 31(1), 127–135 (2005).
[CrossRef] [PubMed]

K. Pesudovs, “Wavefront aberration outcomes of LASIK for high myopia and high hyperopia,” J. Refract. Surg. 21(5), S508–S512 (2005).
[PubMed]

2004 (4)

X. Cheng, A. Bradley, and L. N. Thibos, “Predicting subjective judgment of best focus with objective image quality metrics,” J. Vis. 4(4), 310–321 (2004).
[CrossRef] [PubMed]

F. Taketani, T. Matuura, E. Yukawa, and Y. Hara, “Influence of intraocular lens tilt and decentration on wavefront aberrations,” J. Cataract Refract. Surg. 30(10), 2158–2162 (2004).
[CrossRef] [PubMed]

N. Yamane, K. Miyata, T. Samejima, T. Hiraoka, T. Kiuchi, F. Okamoto, Y. Hirohara, T. Mihashi, and T. Oshika, “Ocular higher-order aberrations and contrast sensitivity after conventional laser in situ keratomileusis,” Invest. Ophthalmol. Vis. Sci. 45(11), 3986–3990 (2004).
[CrossRef] [PubMed]

D. A. Chernyak, “Cyclotorsional eye motion occurring between wavefront measurement and refractive surgery,” J. Cataract Refract. Surg. 30(3), 633–638 (2004).
[CrossRef] [PubMed]

2003 (4)

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, and E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29(6), 1204–1210 (2003).
[CrossRef] [PubMed]

R. A. Applegate, J. D. Marsack, R. Ramos, and E. J. Sarver, “Interaction between aberrations to improve or reduce visual performance,” J. Cataract Refract. Surg. 29(8), 1487–1495 (2003).
[CrossRef] [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(4), 443–448 (2003).
[PubMed]

T. Mihashi, “Higher-order wavefront aberrations induced by small ablation area and sub-clinical decentration in simulated corneal refractive surgery using a perturbed schematic eye model,” Semin. Ophthalmol. 18(1), 41–47 (2003).
[CrossRef] [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(8), 1521–1523 (2002).
[CrossRef]

A. Guirao, J. Porter, D. R. Williams, and I. G. Cox, “Calculated impact of higher-order monochromatic aberrations on retinal image quality in a population of human eyes,” J. Opt. Soc. Am. A 19(3), 620–628 (2002).
[CrossRef]

2001 (3)

M. Mrochen and T. Seiler, “Influence of corneal curvature on calculation of ablation patterns used in photorefractive laser surgery,” J. Refract. Surg. 17(5), S584–S587 (2001).
[PubMed]

A. Guirao, D. R. Williams, and I. G. Cox, “Effect of rotation and translation on the expected benefit of an ideal method to correct the eye’s higher-order aberrations,” J. Opt. Soc. Am. A 18(5), 1003–1015 (2001).
[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(3), 362–369 (2001).
[CrossRef] [PubMed]

2000 (2)

J. Schwiegerling and R. W. Snyder, “Eye movement during laser in situ keratomileusis,” J. Cataract Refract. Surg. 26(3), 345–351 (2000).
[CrossRef] [PubMed]

S. Mutyala, M. B. McDonald, K. A. Scheinblum, M. D. Ostrick, S. F. Brint, and H. Thompson, “Contrast sensitivity evaluation after laser in situ keratomileusis,” Ophthalmology 107(10), 1864–1867 (2000).
[CrossRef] [PubMed]

1996 (1)

S. K. Webber, C. N. McGhee, and I. G. Bryce, “Decentration of photorefractive keratectomy ablation zones after excimer laser surgery for myopia,” J. Cataract Refract. Surg. 22(3), 299–303 (1996).
[PubMed]

1994 (1)

1988 (1)

C. R. Munnerlyn, S. J. Koons, and J. Marshall, “Photorefractive keratectomy: a technique for laser refractive surgery,” J. Cataract Refract. Surg. 14(1), 46–52 (1988).
[PubMed]

1987 (1)

H. Uozato and D. L. Guyton, “Centering corneal surgical procedures,” Am. J. Ophthalmol. 103(3 Pt 1), 264–275 (1987).
[PubMed]

Anera, R. G.

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(8), 1521–1523 (2002).
[CrossRef]

Applegate, R. A.

R. A. Applegate, J. D. Marsack, R. Ramos, and E. J. Sarver, “Interaction between aberrations to improve or reduce visual performance,” J. Cataract Refract. Surg. 29(8), 1487–1495 (2003).
[CrossRef] [PubMed]

Asano-Kato, N.

N. Asano-Kato, I. Toda, C. Sakai, Y. Hori-Komai, Y. Takano, M. Dogru, and K. Tsubota, “Pupil decentration and iris tilting detected by Orbscan: anatomic variations among healthy subjects and influence on outcomes of laser refractive surgeries,” J. Cataract Refract. Surg. 31(10), 1938–1942 (2005).
[CrossRef] [PubMed]

Basuthkar, S.

P. Padmanabhan, M. Mrochen, D. Viswanathan, and S. Basuthkar, “Wavefront aberrations in eyes with decentered ablations,” J. Cataract Refract. Surg. 35(4), 695–702 (2009).
[CrossRef] [PubMed]

Bille, J. F.

Bradley, A.

X. Cheng, A. Bradley, and L. N. Thibos, “Predicting subjective judgment of best focus with objective image quality metrics,” J. Vis. 4(4), 310–321 (2004).
[CrossRef] [PubMed]

Brint, S. F.

S. Mutyala, M. B. McDonald, K. A. Scheinblum, M. D. Ostrick, S. F. Brint, and H. Thompson, “Contrast sensitivity evaluation after laser in situ keratomileusis,” Ophthalmology 107(10), 1864–1867 (2000).
[CrossRef] [PubMed]

Bryce, I. G.

S. K. Webber, C. N. McGhee, and I. G. Bryce, “Decentration of photorefractive keratectomy ablation zones after excimer laser surgery for myopia,” J. Cataract Refract. Surg. 22(3), 299–303 (1996).
[PubMed]

Bühren, J.

J. Bühren, G. Yoon, S. Kenner, S. MacRae, and K. Huxlin, “The effect of optical zone decentration on lower- and higher-order aberrations after photorefractive keratectomy in a cat model,” Invest. Ophthalmol. Vis. Sci. 48(12), 5806–5814 (2007).
[CrossRef] [PubMed]

Calvano, C. J.

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, and E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29(6), 1204–1210 (2003).
[CrossRef] [PubMed]

Chang, A. W.

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, and E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29(6), 1204–1210 (2003).
[CrossRef] [PubMed]

Chen, L.

L. Chen, B. Singer, A. Guirao, J. Porter, and D. R. Williams, “Image metrics for predicting subjective image quality,” Optom. Vis. Sci. 82(5), 358–369 (2005).
[CrossRef] [PubMed]

Cheng, X.

X. Cheng, A. Bradley, and L. N. Thibos, “Predicting subjective judgment of best focus with objective image quality metrics,” J. Vis. 4(4), 310–321 (2004).
[CrossRef] [PubMed]

Chernyak, D. A.

D. A. Chernyak, “Cyclotorsional eye motion occurring between wavefront measurement and refractive surgery,” J. Cataract Refract. Surg. 30(3), 633–638 (2004).
[CrossRef] [PubMed]

Chu, R.

L. Wu, X. Zhou, R. Chu, and Q. Wang, “Photoablation centration on the corneal optical center in myopic LASIK using AOV excimer laser,” Eur. J. Ophthalmol. 19(6), 923–929 (2009).
[PubMed]

Contreras, J. E.

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, and E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29(6), 1204–1210 (2003).
[CrossRef] [PubMed]

Cox, I. G.

J. Porter, G. Yoon, S. MacRae, G. Pan, T. Twietmeyer, I. G. Cox, and D. R. Williams, “Surgeon offsets and dynamic eye movements in laser refractive surgery,” J. Cataract Refract. Surg. 31(11), 2058–2066 (2005).
[CrossRef]

G. Yoon, S. Macrae, D. R. Williams, and I. G. Cox, “Causes of spherical aberration induced by laser refractive surgery,” J. Cataract Refract. Surg. 31(1), 127–135 (2005).
[CrossRef] [PubMed]

A. Guirao, J. Porter, D. R. Williams, and I. G. Cox, “Calculated impact of higher-order monochromatic aberrations on retinal image quality in a population of human eyes,” J. Opt. Soc. Am. A 19(3), 620–628 (2002).
[CrossRef]

A. Guirao, D. R. Williams, and I. G. Cox, “Effect of rotation and translation on the expected benefit of an ideal method to correct the eye’s higher-order aberrations,” J. Opt. Soc. Am. A 18(5), 1003–1015 (2001).
[CrossRef]

Crnic-Rein, T. C.

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, and E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29(6), 1204–1210 (2003).
[CrossRef] [PubMed]

Dai, G. M.

Dogru, M.

N. Asano-Kato, I. Toda, C. Sakai, Y. Hori-Komai, Y. Takano, M. Dogru, and K. Tsubota, “Pupil decentration and iris tilting detected by Orbscan: anatomic variations among healthy subjects and influence on outcomes of laser refractive surgeries,” J. Cataract Refract. Surg. 31(10), 1938–1942 (2005).
[CrossRef] [PubMed]

Fang, L.-H.

L.-H. Fang, Z.-Q. Wang, W. Wang, and M. Liu, “The influence of wavefront aberration of single Zernike modes on optical quality of human eyes,” Acta Opt. Sin. 26, 1721–1726 (2006).

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(4), 443–448 (2003).
[PubMed]

Goelz, S.

Grimm, B.

Gross, E.

Guirao, A.

Guyton, D. L.

H. Uozato and D. L. Guyton, “Centering corneal surgical procedures,” Am. J. Ophthalmol. 103(3 Pt 1), 264–275 (1987).
[PubMed]

Hara, Y.

F. Taketani, T. Matuura, E. Yukawa, and Y. Hara, “Influence of intraocular lens tilt and decentration on wavefront aberrations,” J. Cataract Refract. Surg. 30(10), 2158–2162 (2004).
[CrossRef] [PubMed]

He, J. C.

Y. Wang, K. X. Zhao, J. C. He, Y. Jin, and T. Zuo, “Ocular higher-order aberrations features analysis after corneal refractive surgery,” Chin. Med. J. (Engl.) 120(4), 269–273 (2007).

Hiraoka, T.

T. Hiraoka, C. Okamoto, Y. Ishii, T. Kakita, and T. Oshika, “Contrast sensitivity function and ocular higher-order aberrations following overnight orthokeratology,” Invest. Ophthalmol. Vis. Sci. 48(2), 550–556 (2007).
[CrossRef] [PubMed]

N. Yamane, K. Miyata, T. Samejima, T. Hiraoka, T. Kiuchi, F. Okamoto, Y. Hirohara, T. Mihashi, and T. Oshika, “Ocular higher-order aberrations and contrast sensitivity after conventional laser in situ keratomileusis,” Invest. Ophthalmol. Vis. Sci. 45(11), 3986–3990 (2004).
[CrossRef] [PubMed]

Hirohara, Y.

N. Yamane, K. Miyata, T. Samejima, T. Hiraoka, T. Kiuchi, F. Okamoto, Y. Hirohara, T. Mihashi, and T. Oshika, “Ocular higher-order aberrations and contrast sensitivity after conventional laser in situ keratomileusis,” Invest. Ophthalmol. Vis. Sci. 45(11), 3986–3990 (2004).
[CrossRef] [PubMed]

Hita, E.

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(8), 1521–1523 (2002).
[CrossRef]

Hori-Komai, Y.

N. Asano-Kato, I. Toda, C. Sakai, Y. Hori-Komai, Y. Takano, M. Dogru, and K. Tsubota, “Pupil decentration and iris tilting detected by Orbscan: anatomic variations among healthy subjects and influence on outcomes of laser refractive surgeries,” J. Cataract Refract. Surg. 31(10), 1938–1942 (2005).
[CrossRef] [PubMed]

Huxlin, K.

J. Bühren, G. Yoon, S. Kenner, S. MacRae, and K. Huxlin, “The effect of optical zone decentration on lower- and higher-order aberrations after photorefractive keratectomy in a cat model,” Invest. Ophthalmol. Vis. Sci. 48(12), 5806–5814 (2007).
[CrossRef] [PubMed]

Huynh, P. D.

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, and E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29(6), 1204–1210 (2003).
[CrossRef] [PubMed]

Ishii, Y.

T. Hiraoka, C. Okamoto, Y. Ishii, T. Kakita, and T. Oshika, “Contrast sensitivity function and ocular higher-order aberrations following overnight orthokeratology,” Invest. Ophthalmol. Vis. Sci. 48(2), 550–556 (2007).
[CrossRef] [PubMed]

T. Oshika, G. Sugita, K. Miyata, T. Tokunaga, T. Samejima, C. Okamoto, and Y. Ishii, “Influence of tilt and decentration of scleral-sutured intraocular lens on ocular higher-order wavefront aberration,” Br. J. Ophthalmol. 91(2), 185–188 (2007).
[CrossRef]

Jiménez, J. R.

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(8), 1521–1523 (2002).
[CrossRef]

Jiménez del Barco, L.

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(8), 1521–1523 (2002).
[CrossRef]

Jin, Y.

Y. Wang, K. X. Zhao, J. C. He, Y. Jin, and T. Zuo, “Ocular higher-order aberrations features analysis after corneal refractive surgery,” Chin. Med. J. (Engl.) 120(4), 269–273 (2007).

Joo, C. K.

H. Kim and C. K. Joo, “Ocular cyclotorsion according to body position and flap creation before laser in situ keratomileusis,” J. Cataract Refract. Surg. 34(4), 557–561 (2008).
[CrossRef] [PubMed]

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(3), 362–369 (2001).
[CrossRef] [PubMed]

Kakita, T.

T. Hiraoka, C. Okamoto, Y. Ishii, T. Kakita, and T. Oshika, “Contrast sensitivity function and ocular higher-order aberrations following overnight orthokeratology,” Invest. Ophthalmol. Vis. Sci. 48(2), 550–556 (2007).
[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(4), 443–448 (2003).
[PubMed]

Kenner, S.

J. Bühren, G. Yoon, S. Kenner, S. MacRae, and K. Huxlin, “The effect of optical zone decentration on lower- and higher-order aberrations after photorefractive keratectomy in a cat model,” Invest. Ophthalmol. Vis. Sci. 48(12), 5806–5814 (2007).
[CrossRef] [PubMed]

Kim, H.

H. Kim and C. K. Joo, “Ocular cyclotorsion according to body position and flap creation before laser in situ keratomileusis,” J. Cataract Refract. Surg. 34(4), 557–561 (2008).
[CrossRef] [PubMed]

Kiuchi, T.

N. Yamane, K. Miyata, T. Samejima, T. Hiraoka, T. Kiuchi, F. Okamoto, Y. Hirohara, T. Mihashi, and T. Oshika, “Ocular higher-order aberrations and contrast sensitivity after conventional laser in situ keratomileusis,” Invest. Ophthalmol. Vis. Sci. 45(11), 3986–3990 (2004).
[CrossRef] [PubMed]

Koch, D. D.

L. Wang and D. D. Koch, “Residual higher-order aberrations caused by clinically measured cyclotorsional misalignment or decentration during wavefront-guided excimer laser corneal ablation,” J. Cataract Refract. Surg. 34(12), 2057–2062 (2008).
[CrossRef] [PubMed]

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(1), 46–52 (1988).
[PubMed]

Liang, J.

Liao, W.

J. Shen, Y. Zhang, and W. Liao, “Mathematical model based corneal toric surface for excimer laser refractive surgery,” J. Southeast Univ. 36, 531–536 (2006) (Natural Science Edition).

Liu, M.

L.-H. Fang, Z.-Q. Wang, W. Wang, and M. Liu, “The influence of wavefront aberration of single Zernike modes on optical quality of human eyes,” Acta Opt. Sin. 26, 1721–1726 (2006).

MacRae, S.

J. Bühren, G. Yoon, S. Kenner, S. MacRae, and K. Huxlin, “The effect of optical zone decentration on lower- and higher-order aberrations after photorefractive keratectomy in a cat model,” Invest. Ophthalmol. Vis. Sci. 48(12), 5806–5814 (2007).
[CrossRef] [PubMed]

J. Porter, G. Yoon, S. MacRae, G. Pan, T. Twietmeyer, I. G. Cox, and D. R. Williams, “Surgeon offsets and dynamic eye movements in laser refractive surgery,” J. Cataract Refract. Surg. 31(11), 2058–2066 (2005).
[CrossRef]

G. Yoon, S. Macrae, D. R. Williams, and I. G. Cox, “Causes of spherical aberration induced by laser refractive surgery,” J. Cataract Refract. Surg. 31(1), 127–135 (2005).
[CrossRef] [PubMed]

Marsack, J. D.

R. A. Applegate, J. D. Marsack, R. Ramos, and E. J. Sarver, “Interaction between aberrations to improve or reduce visual performance,” J. Cataract Refract. Surg. 29(8), 1487–1495 (2003).
[CrossRef] [PubMed]

Marshall, J.

C. R. Munnerlyn, S. J. Koons, and J. Marshall, “Photorefractive keratectomy: a technique for laser refractive surgery,” J. Cataract Refract. Surg. 14(1), 46–52 (1988).
[PubMed]

Matuura, T.

F. Taketani, T. Matuura, E. Yukawa, and Y. Hara, “Influence of intraocular lens tilt and decentration on wavefront aberrations,” J. Cataract Refract. Surg. 30(10), 2158–2162 (2004).
[CrossRef] [PubMed]

McDonald, M. B.

S. Mutyala, M. B. McDonald, K. A. Scheinblum, M. D. Ostrick, S. F. Brint, and H. Thompson, “Contrast sensitivity evaluation after laser in situ keratomileusis,” Ophthalmology 107(10), 1864–1867 (2000).
[CrossRef] [PubMed]

McGhee, C. N.

S. K. Webber, C. N. McGhee, and I. G. Bryce, “Decentration of photorefractive keratectomy ablation zones after excimer laser surgery for myopia,” J. Cataract Refract. Surg. 22(3), 299–303 (1996).
[PubMed]

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(3), 362–369 (2001).
[CrossRef] [PubMed]

Mihashi, T.

N. Yamane, K. Miyata, T. Samejima, T. Hiraoka, T. Kiuchi, F. Okamoto, Y. Hirohara, T. Mihashi, and T. Oshika, “Ocular higher-order aberrations and contrast sensitivity after conventional laser in situ keratomileusis,” Invest. Ophthalmol. Vis. Sci. 45(11), 3986–3990 (2004).
[CrossRef] [PubMed]

T. Mihashi, “Higher-order wavefront aberrations induced by small ablation area and sub-clinical decentration in simulated corneal refractive surgery using a perturbed schematic eye model,” Semin. Ophthalmol. 18(1), 41–47 (2003).
[CrossRef] [PubMed]

Miyata, K.

T. Oshika, G. Sugita, K. Miyata, T. Tokunaga, T. Samejima, C. Okamoto, and Y. Ishii, “Influence of tilt and decentration of scleral-sutured intraocular lens on ocular higher-order wavefront aberration,” Br. J. Ophthalmol. 91(2), 185–188 (2007).
[CrossRef]

N. Sakata, T. Tokunaga, K. Miyata, and T. Oshika, “Changes in contrast sensitivity function and ocular higher order aberration by conventional myopic photorefractive keratectomy,” Jpn. J. Ophthalmol. 51(5), 347–352 (2007).
[CrossRef] [PubMed]

N. Yamane, K. Miyata, T. Samejima, T. Hiraoka, T. Kiuchi, F. Okamoto, Y. Hirohara, T. Mihashi, and T. Oshika, “Ocular higher-order aberrations and contrast sensitivity after conventional laser in situ keratomileusis,” Invest. Ophthalmol. Vis. Sci. 45(11), 3986–3990 (2004).
[CrossRef] [PubMed]

Mrochen, M.

P. Padmanabhan, M. Mrochen, D. Viswanathan, and S. Basuthkar, “Wavefront aberrations in eyes with decentered ablations,” J. Cataract Refract. Surg. 35(4), 695–702 (2009).
[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(5), S584–S587 (2001).
[PubMed]

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(3), 362–369 (2001).
[CrossRef] [PubMed]

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(1), 46–52 (1988).
[PubMed]

Mutyala, S.

S. Mutyala, M. B. McDonald, K. A. Scheinblum, M. D. Ostrick, S. F. Brint, and H. Thompson, “Contrast sensitivity evaluation after laser in situ keratomileusis,” Ophthalmology 107(10), 1864–1867 (2000).
[CrossRef] [PubMed]

Okamoto, C.

T. Hiraoka, C. Okamoto, Y. Ishii, T. Kakita, and T. Oshika, “Contrast sensitivity function and ocular higher-order aberrations following overnight orthokeratology,” Invest. Ophthalmol. Vis. Sci. 48(2), 550–556 (2007).
[CrossRef] [PubMed]

T. Oshika, G. Sugita, K. Miyata, T. Tokunaga, T. Samejima, C. Okamoto, and Y. Ishii, “Influence of tilt and decentration of scleral-sutured intraocular lens on ocular higher-order wavefront aberration,” Br. J. Ophthalmol. 91(2), 185–188 (2007).
[CrossRef]

Okamoto, F.

N. Yamane, K. Miyata, T. Samejima, T. Hiraoka, T. Kiuchi, F. Okamoto, Y. Hirohara, T. Mihashi, and T. Oshika, “Ocular higher-order aberrations and contrast sensitivity after conventional laser in situ keratomileusis,” Invest. Ophthalmol. Vis. Sci. 45(11), 3986–3990 (2004).
[CrossRef] [PubMed]

Oshika, T.

N. Sakata, T. Tokunaga, K. Miyata, and T. Oshika, “Changes in contrast sensitivity function and ocular higher order aberration by conventional myopic photorefractive keratectomy,” Jpn. J. Ophthalmol. 51(5), 347–352 (2007).
[CrossRef] [PubMed]

T. Oshika, G. Sugita, K. Miyata, T. Tokunaga, T. Samejima, C. Okamoto, and Y. Ishii, “Influence of tilt and decentration of scleral-sutured intraocular lens on ocular higher-order wavefront aberration,” Br. J. Ophthalmol. 91(2), 185–188 (2007).
[CrossRef]

T. Hiraoka, C. Okamoto, Y. Ishii, T. Kakita, and T. Oshika, “Contrast sensitivity function and ocular higher-order aberrations following overnight orthokeratology,” Invest. Ophthalmol. Vis. Sci. 48(2), 550–556 (2007).
[CrossRef] [PubMed]

N. Yamane, K. Miyata, T. Samejima, T. Hiraoka, T. Kiuchi, F. Okamoto, Y. Hirohara, T. Mihashi, and T. Oshika, “Ocular higher-order aberrations and contrast sensitivity after conventional laser in situ keratomileusis,” Invest. Ophthalmol. Vis. Sci. 45(11), 3986–3990 (2004).
[CrossRef] [PubMed]

Ostrick, M. D.

S. Mutyala, M. B. McDonald, K. A. Scheinblum, M. D. Ostrick, S. F. Brint, and H. Thompson, “Contrast sensitivity evaluation after laser in situ keratomileusis,” Ophthalmology 107(10), 1864–1867 (2000).
[CrossRef] [PubMed]

Padmanabhan, P.

P. Padmanabhan, M. Mrochen, D. Viswanathan, and S. Basuthkar, “Wavefront aberrations in eyes with decentered ablations,” J. Cataract Refract. Surg. 35(4), 695–702 (2009).
[CrossRef] [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(4), 443–448 (2003).
[PubMed]

Pan, G.

J. Porter, G. Yoon, S. MacRae, G. Pan, T. Twietmeyer, I. G. Cox, and D. R. Williams, “Surgeon offsets and dynamic eye movements in laser refractive surgery,” J. Cataract Refract. Surg. 31(11), 2058–2066 (2005).
[CrossRef]

Pesudovs, K.

K. Pesudovs, “Wavefront aberration outcomes of LASIK for high myopia and high hyperopia,” J. Refract. Surg. 21(5), S508–S512 (2005).
[PubMed]

Porter, J.

L. Chen, B. Singer, A. Guirao, J. Porter, and D. R. Williams, “Image metrics for predicting subjective image quality,” Optom. Vis. Sci. 82(5), 358–369 (2005).
[CrossRef] [PubMed]

J. Porter, G. Yoon, S. MacRae, G. Pan, T. Twietmeyer, I. G. Cox, and D. R. Williams, “Surgeon offsets and dynamic eye movements in laser refractive surgery,” J. Cataract Refract. Surg. 31(11), 2058–2066 (2005).
[CrossRef]

A. Guirao, J. Porter, D. R. Williams, and I. G. Cox, “Calculated impact of higher-order monochromatic aberrations on retinal image quality in a population of human eyes,” J. Opt. Soc. Am. A 19(3), 620–628 (2002).
[CrossRef]

Ramos, R.

R. A. Applegate, J. D. Marsack, R. Ramos, and E. J. Sarver, “Interaction between aberrations to improve or reduce visual performance,” J. Cataract Refract. Surg. 29(8), 1487–1495 (2003).
[CrossRef] [PubMed]

Sakai, C.

N. Asano-Kato, I. Toda, C. Sakai, Y. Hori-Komai, Y. Takano, M. Dogru, and K. Tsubota, “Pupil decentration and iris tilting detected by Orbscan: anatomic variations among healthy subjects and influence on outcomes of laser refractive surgeries,” J. Cataract Refract. Surg. 31(10), 1938–1942 (2005).
[CrossRef] [PubMed]

Sakata, N.

N. Sakata, T. Tokunaga, K. Miyata, and T. Oshika, “Changes in contrast sensitivity function and ocular higher order aberration by conventional myopic photorefractive keratectomy,” Jpn. J. Ophthalmol. 51(5), 347–352 (2007).
[CrossRef] [PubMed]

Samejima, T.

T. Oshika, G. Sugita, K. Miyata, T. Tokunaga, T. Samejima, C. Okamoto, and Y. Ishii, “Influence of tilt and decentration of scleral-sutured intraocular lens on ocular higher-order wavefront aberration,” Br. J. Ophthalmol. 91(2), 185–188 (2007).
[CrossRef]

N. Yamane, K. Miyata, T. Samejima, T. Hiraoka, T. Kiuchi, F. Okamoto, Y. Hirohara, T. Mihashi, and T. Oshika, “Ocular higher-order aberrations and contrast sensitivity after conventional laser in situ keratomileusis,” Invest. Ophthalmol. Vis. Sci. 45(11), 3986–3990 (2004).
[CrossRef] [PubMed]

Sarver, E. J.

R. A. Applegate, J. D. Marsack, R. Ramos, and E. J. Sarver, “Interaction between aberrations to improve or reduce visual performance,” J. Cataract Refract. Surg. 29(8), 1487–1495 (2003).
[CrossRef] [PubMed]

Scheinblum, K. A.

S. Mutyala, M. B. McDonald, K. A. Scheinblum, M. D. Ostrick, S. F. Brint, and H. Thompson, “Contrast sensitivity evaluation after laser in situ keratomileusis,” Ophthalmology 107(10), 1864–1867 (2000).
[CrossRef] [PubMed]

Schwiegerling, J.

J. Schwiegerling and R. W. Snyder, “Eye movement during laser in situ keratomileusis,” J. Cataract Refract. Surg. 26(3), 345–351 (2000).
[CrossRef] [PubMed]

Seiler, T.

M. Mrochen and T. Seiler, “Influence of corneal curvature on calculation of ablation patterns used in photorefractive laser surgery,” J. Refract. Surg. 17(5), S584–S587 (2001).
[PubMed]

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(3), 362–369 (2001).
[CrossRef] [PubMed]

Shen, J.

J. Shen, Y. Zhang, and W. Liao, “Mathematical model based corneal toric surface for excimer laser refractive surgery,” J. Southeast Univ. 36, 531–536 (2006) (Natural Science Edition).

Singer, B.

L. Chen, B. Singer, A. Guirao, J. Porter, and D. R. Williams, “Image metrics for predicting subjective image quality,” Optom. Vis. Sci. 82(5), 358–369 (2005).
[CrossRef] [PubMed]

Snyder, R. W.

J. Schwiegerling and R. W. Snyder, “Eye movement during laser in situ keratomileusis,” J. Cataract Refract. Surg. 26(3), 345–351 (2000).
[CrossRef] [PubMed]

Sugita, G.

T. Oshika, G. Sugita, K. Miyata, T. Tokunaga, T. Samejima, C. Okamoto, and Y. Ishii, “Influence of tilt and decentration of scleral-sutured intraocular lens on ocular higher-order wavefront aberration,” Br. J. Ophthalmol. 91(2), 185–188 (2007).
[CrossRef]

Takano, Y.

N. Asano-Kato, I. Toda, C. Sakai, Y. Hori-Komai, Y. Takano, M. Dogru, and K. Tsubota, “Pupil decentration and iris tilting detected by Orbscan: anatomic variations among healthy subjects and influence on outcomes of laser refractive surgeries,” J. Cataract Refract. Surg. 31(10), 1938–1942 (2005).
[CrossRef] [PubMed]

Taketani, F.

F. Taketani, T. Matuura, E. Yukawa, and Y. Hara, “Influence of intraocular lens tilt and decentration on wavefront aberrations,” J. Cataract Refract. Surg. 30(10), 2158–2162 (2004).
[CrossRef] [PubMed]

Thall, E. H.

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, and E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29(6), 1204–1210 (2003).
[CrossRef] [PubMed]

Thibos, L. N.

X. Cheng, A. Bradley, and L. N. Thibos, “Predicting subjective judgment of best focus with objective image quality metrics,” J. Vis. 4(4), 310–321 (2004).
[CrossRef] [PubMed]

Thompson, H.

S. Mutyala, M. B. McDonald, K. A. Scheinblum, M. D. Ostrick, S. F. Brint, and H. Thompson, “Contrast sensitivity evaluation after laser in situ keratomileusis,” Ophthalmology 107(10), 1864–1867 (2000).
[CrossRef] [PubMed]

Toda, I.

N. Asano-Kato, I. Toda, C. Sakai, Y. Hori-Komai, Y. Takano, M. Dogru, and K. Tsubota, “Pupil decentration and iris tilting detected by Orbscan: anatomic variations among healthy subjects and influence on outcomes of laser refractive surgeries,” J. Cataract Refract. Surg. 31(10), 1938–1942 (2005).
[CrossRef] [PubMed]

Tokunaga, T.

T. Oshika, G. Sugita, K. Miyata, T. Tokunaga, T. Samejima, C. Okamoto, and Y. Ishii, “Influence of tilt and decentration of scleral-sutured intraocular lens on ocular higher-order wavefront aberration,” Br. J. Ophthalmol. 91(2), 185–188 (2007).
[CrossRef]

N. Sakata, T. Tokunaga, K. Miyata, and T. Oshika, “Changes in contrast sensitivity function and ocular higher order aberration by conventional myopic photorefractive keratectomy,” Jpn. J. Ophthalmol. 51(5), 347–352 (2007).
[CrossRef] [PubMed]

Tsang, A. C.

A. W. Chang, A. C. Tsang, J. E. Contreras, P. D. Huynh, C. J. Calvano, T. C. Crnic-Rein, and E. H. Thall, “Corneal tissue ablation depth and the Munnerlyn formula,” J. Cataract Refract. Surg. 29(6), 1204–1210 (2003).
[CrossRef] [PubMed]

Tsubota, K.

N. Asano-Kato, I. Toda, C. Sakai, Y. Hori-Komai, Y. Takano, M. Dogru, and K. Tsubota, “Pupil decentration and iris tilting detected by Orbscan: anatomic variations among healthy subjects and influence on outcomes of laser refractive surgeries,” J. Cataract Refract. Surg. 31(10), 1938–1942 (2005).
[CrossRef] [PubMed]

Twietmeyer, T.

J. Porter, G. Yoon, S. MacRae, G. Pan, T. Twietmeyer, I. G. Cox, and D. R. Williams, “Surgeon offsets and dynamic eye movements in laser refractive surgery,” J. Cataract Refract. Surg. 31(11), 2058–2066 (2005).
[CrossRef]

Uozato, H.

H. Uozato and D. L. Guyton, “Centering corneal surgical procedures,” Am. J. Ophthalmol. 103(3 Pt 1), 264–275 (1987).
[PubMed]

Viswanathan, D.

P. Padmanabhan, M. Mrochen, D. Viswanathan, and S. Basuthkar, “Wavefront aberrations in eyes with decentered ablations,” J. Cataract Refract. Surg. 35(4), 695–702 (2009).
[CrossRef] [PubMed]

Wang, L.

L. Wang and D. D. Koch, “Residual higher-order aberrations caused by clinically measured cyclotorsional misalignment or decentration during wavefront-guided excimer laser corneal ablation,” J. Cataract Refract. Surg. 34(12), 2057–2062 (2008).
[CrossRef] [PubMed]

Wang, Q.

L. Wu, X. Zhou, R. Chu, and Q. Wang, “Photoablation centration on the corneal optical center in myopic LASIK using AOV excimer laser,” Eur. J. Ophthalmol. 19(6), 923–929 (2009).
[PubMed]

Wang, W.

L.-H. Fang, Z.-Q. Wang, W. Wang, and M. Liu, “The influence of wavefront aberration of single Zernike modes on optical quality of human eyes,” Acta Opt. Sin. 26, 1721–1726 (2006).

Wang, Y.

Y. Wang, K. X. Zhao, J. C. He, Y. Jin, and T. Zuo, “Ocular higher-order aberrations features analysis after corneal refractive surgery,” Chin. Med. J. (Engl.) 120(4), 269–273 (2007).

Wang, Z.-Q.

L.-H. Fang, Z.-Q. Wang, W. Wang, and M. Liu, “The influence of wavefront aberration of single Zernike modes on optical quality of human eyes,” Acta Opt. Sin. 26, 1721–1726 (2006).

Webber, S. K.

S. K. Webber, C. N. McGhee, and I. G. Bryce, “Decentration of photorefractive keratectomy ablation zones after excimer laser surgery for myopia,” J. Cataract Refract. Surg. 22(3), 299–303 (1996).
[PubMed]

Williams, D. R.

J. Porter, G. Yoon, S. MacRae, G. Pan, T. Twietmeyer, I. G. Cox, and D. R. Williams, “Surgeon offsets and dynamic eye movements in laser refractive surgery,” J. Cataract Refract. Surg. 31(11), 2058–2066 (2005).
[CrossRef]

L. Chen, B. Singer, A. Guirao, J. Porter, and D. R. Williams, “Image metrics for predicting subjective image quality,” Optom. Vis. Sci. 82(5), 358–369 (2005).
[CrossRef] [PubMed]

G. Yoon, S. Macrae, D. R. Williams, and I. G. Cox, “Causes of spherical aberration induced by laser refractive surgery,” J. Cataract Refract. Surg. 31(1), 127–135 (2005).
[CrossRef] [PubMed]

A. Guirao, J. Porter, D. R. Williams, and I. G. Cox, “Calculated impact of higher-order monochromatic aberrations on retinal image quality in a population of human eyes,” J. Opt. Soc. Am. A 19(3), 620–628 (2002).
[CrossRef]

A. Guirao, D. R. Williams, and I. G. Cox, “Effect of rotation and translation on the expected benefit of an ideal method to correct the eye’s higher-order aberrations,” J. Opt. Soc. Am. A 18(5), 1003–1015 (2001).
[CrossRef]

Wu, L.

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F. Taketani, T. Matuura, E. Yukawa, and Y. Hara, “Influence of intraocular lens tilt and decentration on wavefront aberrations,” J. Cataract Refract. Surg. 30(10), 2158–2162 (2004).
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J. Shen, Y. Zhang, and W. Liao, “Mathematical model based corneal toric surface for excimer laser refractive surgery,” J. Southeast Univ. 36, 531–536 (2006) (Natural Science Edition).

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H. Zhao and B. Xu, “Position tolerance analysis for wavefront aberrations correction of human eyes,” Acta Opt. Sin. 28(5), 949–954 (2008).
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Y. Wang, K. X. Zhao, J. C. He, Y. Jin, and T. Zuo, “Ocular higher-order aberrations features analysis after corneal refractive surgery,” Chin. Med. J. (Engl.) 120(4), 269–273 (2007).

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L. Wu, X. Zhou, R. Chu, and Q. Wang, “Photoablation centration on the corneal optical center in myopic LASIK using AOV excimer laser,” Eur. J. Ophthalmol. 19(6), 923–929 (2009).
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Y. Wang, K. X. Zhao, J. C. He, Y. Jin, and T. Zuo, “Ocular higher-order aberrations features analysis after corneal refractive surgery,” Chin. Med. J. (Engl.) 120(4), 269–273 (2007).

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Y. Wang, K. X. Zhao, J. C. He, Y. Jin, and T. Zuo, “Ocular higher-order aberrations features analysis after corneal refractive surgery,” Chin. Med. J. (Engl.) 120(4), 269–273 (2007).

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L. Wu, X. Zhou, R. Chu, and Q. Wang, “Photoablation centration on the corneal optical center in myopic LASIK using AOV excimer laser,” Eur. J. Ophthalmol. 19(6), 923–929 (2009).
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N. Yamane, K. Miyata, T. Samejima, T. Hiraoka, T. Kiuchi, F. Okamoto, Y. Hirohara, T. Mihashi, and T. Oshika, “Ocular higher-order aberrations and contrast sensitivity after conventional laser in situ keratomileusis,” Invest. Ophthalmol. Vis. Sci. 45(11), 3986–3990 (2004).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

T. Hiraoka, C. Okamoto, Y. Ishii, T. Kakita, and T. Oshika, “Contrast sensitivity function and ocular higher-order aberrations following overnight orthokeratology,” Invest. Ophthalmol. Vis. Sci. 48(2), 550–556 (2007).
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F. Taketani, T. Matuura, E. Yukawa, and Y. Hara, “Influence of intraocular lens tilt and decentration on wavefront aberrations,” J. Cataract Refract. Surg. 30(10), 2158–2162 (2004).
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Figures (9)

Fig. 1
Fig. 1

Principal meridians for anterior corneal surface with the curvature radii of the steepest and flattest meridians Rix and Riy .

Fig. 2
Fig. 2

Corneal shape and tissue ablation depth after laser refractive surgery with the curvature radii of the anterior corneal surface. After refractive surgery, Rf ; before surgery, Rix and Riy ; and the diameter of the optical zone S.

Fig. 3
Fig. 3

Actual corrected wavefront aberrations (axis X’Y’) decentered with respect to the eye (axis XY). The aberrations are the rotated (angle α) version and the translated (Δx, Δy) version of the ideal corrected aberrations.

Fig. 4
Fig. 4

Contour maps of the induced coma and spherical aberration for correcting pure myopia. Panel A corresponds to the coma and panel B corresponds to the spherical aberration. The diameter of the optical zone is 6 mm.

Fig. 5
Fig. 5

Induced third- and fourth-order aberrations for correcting myopia astigmatism from treatment decentration. Panel A corresponds to the refractive errors (–5.0DS –2.0DC × 60°) and Panel B corresponds to another refractive errors (–7.5DS –1.5DC × 180°). The diameter of the optical zone is 6 mm.

Fig. 6
Fig. 6

Contour maps of the induced astigmatism for correcting myopia astigmatism from treatment decentration. Panel A corresponds to the refractive errors (–5.0DS –2.0DC × 60°) and Panel B corresponds to another refractive errors (–7.5DS –1.5DC × 180°). The diameter of the optical zone is 6 mm.

Fig. 7
Fig. 7

Induced third- and fourth-order aberrations for correcting myopia astigmatism from treatment decentration without oblique incidence. Panel A corresponds to the refractive errors (–5.0DS –2.0DC × 60°) and Panel B corresponds to another refractive errors (–7.5DS –1.5DC × 180°). The diameter of the optical zone is 6 mm.

Fig. 8
Fig. 8

Diagrammatic sketch of position vector of translation and astigmatism axis.

Fig. 9
Fig. 9

Relationship of induced third- and fourth-order aberrations for correcting myopia astigmatism versus the angle difference. Panel A corresponds to the refractive errors (–5.0DS –2.0DC × 60°) and Panel B corresponds to another refractive errors (–7.5DS –1.5DC × 180°). The diameter of the optical zone is 6 mm.

Equations (16)

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Z i ( x , y ) = ( R i x 2 x 2 + R i y R i x ) 2 y 2 .
F 0 ' = F 0 ( cos ( α ) ( 1 R ) ) .
cos ( α ) = 1 1 + ( d d x z ( x , y ) ) 2 + ( d d y z ( x , y ) ) 2 .
R = 1 2 [ ( n 2 cos α n 2 sin 2 α n 2 cos α n 2 sin 2 α ) 2 + ( cos α n 2 sin 2 α cos α + n 2 sin 2 α ) 2 ] .
d = m ln ( F 0 F t h ) .
d = m ln ( F 0 F t h ) ( 1 + c ln ( cos ( α ) ( 1 R ) ) ) .
l ( r ) = R 1 2 r 2 R f 2 r 2 + R f 2 ( S / 2 ) 2 R 1 2 ( S / 2 ) 2 .
R f = 1000 ( n 1 ) R 1 ( n 1 ) + D s p h R 1 .
l ( x , y ) = ( R i x 2 x 2 + R i y R i x ) 2 y 2 R f 2 x 2 y 2 + R f 2 ( S / 2 ) 2 + R i x R i y R i x 2 ( S / 2 ) 2 .
R i x = 1000 ( n 1 ) D k + 0.5 D c y l , R i y = 1000 ( n 1 ) D k 0.5 D c y l , R f = 1000 ( n 1 ) ( D k + 0.5 D c y l + D s p h ) .
W d = i C i Z i ( x , y ) , W i = k a k Z k ( x , y ) .
x ' = ( x Δ x ) cos α + ( y Δ y ) sin α , y ' = ( y Δ y ) cos α ( x Δ x ) sin α .
C i = j , k T i j R j k a k .
N ( x , y ) = D ( x , y ) d = D ( x , y ) m ln ( F 0 F t h ) ( 1 + c ln ( cos ( α ) ( 1 R ) ) ) .
D ' ( x , y )     = N ( x ' , y ' ) m ln ( F 0 F t h ) (1+ c ln ( cos ( α ) ( 1 R ) )           = D ( x ' , y ' ) m ln ( F 0 F t h ) (1+ c ln ( cos ( α ' ) ( 1 R ' ) ) m ln ( F 0 F t h ) (1+c ln ( cos ( α ) ( 1 R ) )           = D ( x ' , y ' ) (1+ c ln ( cos ( α ) ( 1 R ) ) (1+ c ln ( cos ( α ' ) ( 1 R ' ) ) .
W r ( x , y ) = W i ( x , y ) + W d ( x , y )           = i = 1 M C i Z i ( x , y ) i = 1 M a i Z i ( x , y ) .

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