Abstract

Presbyopia, the gradual loss of accommodation that accompanies aging, can be corrected by creating asphericity in the optical path of the eye. Bifocal and aspheric contact lenses, intraocular lenses, spectacle lenses, and laser refractive surgery are all widely used to alleviate the symptoms of presbyopia. These types of corrective surfaces try to concentrate vision in limited peaks over the full range of vergences. The methodology described in this paper is designed to correct presbyopia by optimizing vision over the entire target range of near to distant. A corrective surface was created by employing an iterative function minimization algorithm to optimize an optical metric. In most cases, it is possible to obtain an optical surface that will optically compensate for presbyopia.

© 2006 Optical Society of America

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2005

O. Stachs, H. Schneider, J. Stave, and R. Guthoff, "Potentially accommodating intraocular lenses--an in vitro and in vivo study using three-dimensional high-frequency ultrasound," J. Refract. Surg. 21, 37-45 (2005).
[PubMed]

J. A. Guggenheim and C. H. To, "Monovision slows myopia progression," Br. J. Ophthalmol. 89, 1076-1077 (2005).
[CrossRef] [PubMed]

2004

M. Küchle, B. Sitz, A. Langenbucher, G. C. Gusek-Schneider, P. Martus, and N. X. Nguyen, "Comparison of 6-month results of implantation of the 1CU accommodative intraocular lens with conventional intraocular lenses," Ophthalmology 111, 318-324 (2004).
[CrossRef] [PubMed]

L. A. Ostrin, S. Kasthurirangan, and A. Glasser, "Evaluation of a satisfied bilateral scleral expansion band patient," J. Cataract Refractive Surg. 30, 1445-1453 (2004).
[CrossRef]

S. A. Koopmans, T. Terwee, H. J. Haitjema, H. Deuring, S. van Aarle, and A. C. Kooijman, "Relation between injected volume and optical parameters in refilled isolated porcine lenses," Ophthalmic. Physiol. Opt. 24, 572-579 (2004).
[CrossRef] [PubMed]

A. Telandro, "Pseudo-accommodative cornea: a new concept for correction of presbyopia," J. Refract. Surg. 20, S714-S717 (2004).
[PubMed]

M. B. McDonald, D. Durrie, P. Asbell, R. Maloney, and L. Nichamin, "Treatment of presbyopia with conductive keratoplasty: six-month results of the 1-Year United States FDA clinical trial," Cornea 23, 661-668 (2004).
[CrossRef] [PubMed]

X. Cheng and A. Bradley, "Predicting subjective judgment of best focus with objective image quality metrics," J. Vision 4, 310-321 (2004).
[CrossRef]

J. D. Marsack, L. N. Thibos, and R. A. Applegate, "Metrics of optical quality derived from wave aberrations predict visual performance," J. Vision 4, 322-328 (2004).
[CrossRef]

G.-m. Dai, "Using wavefront measurements to predict visual acuity," in Ophthalmic Technologies XIV, F. Manns, P. G. Söderberg, and A. Ho, eds., Proc. SPIE 5314, 220-228 (2004).
[CrossRef]

2003

A. Guirao and D. R. Williams, "A method to predict refractive errors from wave aberration data," Optom. Vision Sci. 80, 36-42 (2003).
[CrossRef]

R. A. Applegate, C. Ballentine, H. Gross, E. J. Sarver, and C. A. Sarver, "Visual acuity as a function of Zernike mode and level of root mean square error," Optom. Vision Sci. 80, 97-105 (2003).
[CrossRef]

Y. K. Han, J. W. Kwon, J. S. Kim, C.-S. Cho, W. R. Wee, and J. H. Lee, "In vitro and in vivo study of lens refilling with poloxamer hydrogel," Br. J. Ophthalmol. 87, 1399-1402 (2003).
[CrossRef] [PubMed]

A. Langenbucher, S. Huber, N. X. Nguyen, B. Seitz, G. C. Gusek-Schneider, and M. Küchle, "Measurement of accommodation after implantation of an accommodating posterior chamber intraocular lens," J. Cataract Refractive Surg. 29, 677-685 (2003).
[CrossRef]

J. Pujol, J. Gispets, and M. Arjona, "Optical performance in eyes wearing two multifocal contact lens designs," Ophthalmic Physiol. Opt. 23, 347-360 (2003).
[CrossRef] [PubMed]

2002

S. Pieh, P. Marvan, B. Lackner, G. Hanselmayer, G. Schmidinger, R. Leitgeb, M. Sticker, C. K. Hitzenberger, A. F. Fercher, and C. Skorpik, "Quantitative performance of bifocal and multifocal intraocular lenses in a model eye: point spread function in multifocal intraocular lenses," Arch. Ophthalmol. 120, 23-28 (2002).
[PubMed]

D. R. Hamilton, J. M. Davidorf, and R. K. Maloney, "Anterior ciliary sclerotomy for treatment of presbyopia: a prospective controlled study," Ophthalmology 109, 1970-1977 (2002).
[CrossRef] [PubMed]

2001

H. Fukasaku and J. A. Marron, "Anterior ciliary sclerectomy with silicone expansion plug implantation: effect on presbyopia and intraocular pressure," Int. Ophthalmol. Clin. 41, 133-141 (2001).
[CrossRef] [PubMed]

J. S. Cumming, S. G. Slade, and A. Chayet, "Clinical evaluation of the Model AT-45 silicone accommodating intraocular lens," Ophthalmology 108, 2005-2010 (2001).
[CrossRef] [PubMed]

J. F. Malecaze, C. S. Gazagne, M. C. Tarroux, and J. M. Gorrand, "Scleral expansion bands for presbyopia," Ophthalmology 108, 2165-2171 (2001).
[CrossRef] [PubMed]

S. Jain, R. Ou, and D. T. Azar, "Monovision outcomes in presbyopic individuals after refractive surgery," Ophthalmology 108, 1430-1433 (2001).
[CrossRef] [PubMed]

K. C. Sippel, S. Jain, and D. T. Azar, "Monovision achieved with excimer laser refractive surgery," Int. Ophthalmol. Clin. 41, 91-101 (2001).
[CrossRef] [PubMed]

P. A. Asbell, R. K. Maloney, J. Davidorf, P. Hersh, M. McDonald, and E. Manche, "Conductive keratoplasty study group. Conductive keratoplasty for the correction of hyperopia," Trans. Am. Ophthalmol. Soc. 99, 79-84 (2001).

2000

K. Fisher, E. Bauman, and J. Schwallie, "Evaluation of two new soft contact lenses for correction of presbyopia. The Focus Progressives multifocal and the Acuvue bifocal," Int. Contact Lens Clin. 26, 92-103 (2000).
[CrossRef] [PubMed]

K. W. Brydon, A. C. Tokarewicz, and B. D. Nichols, "AMO array multifocal lens versus monofocal correction in cataract surgery," J. Cataract Refractive Surg. 26, 96-100 (2000).
[CrossRef]

1999

S. Mathews, "Scleral expansion surgery does not restore accommodation in human presbyopia," Ophthalmology 106, 873-877 (1999).
[CrossRef] [PubMed]

1998

O. Nishi and K. Nishi, "Accommodation amplitude after lens refilling with injectable silicone by sealing the capsule with a plug in primates," Arch. Ophthalmol. 116, 1358-1361 (1998).
[PubMed]

P. Vinciguerra, G. M. Nizzola, G. Bailo, F. Niezzola, A. Ascari, and D. Epstein, "Excimer laser photorefractive keratectomy for presbyopia: 24-month follow-up in three eyes," J. Refract. Surg. 14, 31-37 (1998).
[PubMed]

1997

D. A. Atchison, W. N. Charman, and R. L. Woods, "Subjective depth-of-focus of the eye," Optom. Vision Sci. 74, 511-520 (1997).
[CrossRef]

N. Chateau and D. Baude, "Simulated in situ optical performance of bifocal contact lenses," Optom. Vision Sci. 74, 532-539 (1997).
[CrossRef]

1996

S. Jain, I. Arora, and D. T. Azar, "Success of monovision in presbyopes: review of the literature and potential applications to refractive surgery," Surv. Ophthalmol. 40, 491-499 (1996).
[CrossRef] [PubMed]

R. A. Schachar, C. Tello, D. P. Cudmore, J. M. Liebmann, T. D. Black, and R. Ritch, "In vivo increase of the human lens equatorial diameter during accommodation," Am. J. Physiol. 271, 670-676 (1996).

1993

J. S. Cumming, "Postoperative complications and uncorrected acuities after implantation of plate haptic silicone and three-piece silicone intraocular lenses," J. Cataract Refractive Surg. 19, 263-274 (1993).

R. A. Schachar, T. Huang, and X. Huang, "Mathematic proof of Schachar's hypothesis of accommodation," Ann. Ophthalmol. 25, 5-9 (1993).
[PubMed]

S. P. B. Percival and S. S. Setty, "Prospectively randomized trial comparing the pseudoaccommodation of the AMO ARRAY multifocal lens and a monofocal lens," J. Cataract Refractive Surg. 19, 26-31 (1993).

R. A. Applegate and V. Lakshminarayanan, "Parametric representation of Stiles-Crawford functions: normal variation of peak location and directionality," J. Opt. Soc. Am. A 10, 1611-1623 (1993).
[CrossRef] [PubMed]

1992

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, "The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans," Appl. Opt. 31, 3594-3600 (1992).
[CrossRef] [PubMed]

H. Moreira, J. J. Garhus, A. Fasano, M. Lee, T. N. Clapham, and P. J. McDonell, "Multifocal corneal topographic changes with excimer laser photorefractive keratectomy," Arch. Ophthalmol. 110, 994-999 (1992).
[CrossRef] [PubMed]

R. A. Schachar, "Cause and treatment of presbyopia with a method for increasing the amplitude of accommodation," Ann. Ophthalmol. 24, 445-452 (1992).
[PubMed]

1990

J. T. Holladay, H. V. van Dijk, A. Lang, V. Protney, T. R. Willis, R. Sun, and H. C. Oksman, "Optical performance of multifocal intraocular lenses," J. Cataract Refractive Surg. 16, 413-422 (1990).

1987

1983

1982

1976

1965

F. W. Campbell and D. G. Green, "Optical and retinal factors affecting visual resolution," J. Physiol. 181, 576-593 (1965).
[PubMed]

J. A. Nelder and R. Mead, "A simplex method for function minimization," Comput. J. 7, 308-313 (1965).

1964

J. Kessler, "Experiments in refilling the lens," Arch. Ophthalmol. 71, 412-416 (1964).
[CrossRef] [PubMed]

1958

M. J. Turner, "Observations on the normal subjective amplitude of accommodation," Br. J. Physiol. Opt. 15, 70-100 (1958).
[PubMed]

1956

D. Hamasaki, J. Ong, and E. Marg, "The amplitude of accommodation in presbyopia," Am. J. Optom. Arch. Am. Acad. Optom. 33, 3-14 (1956).
[PubMed]

1922

A. Duane, "Studies in monocular and binocular accommodation with their clinical applications," Am. J. Ophthalmol. 5, 865-877 (1922).

1912

A. Duane, "Normal values of the accommodation at all ages," J. Am. Med. Assoc. 59, 1010-1013 (1912).
[CrossRef]

Agarwal, A.

A. Agarwal, Presbyopia: A Surgical Textbook (Slack, 2002).

Applegate, R. A.

J. D. Marsack, L. N. Thibos, and R. A. Applegate, "Metrics of optical quality derived from wave aberrations predict visual performance," J. Vision 4, 322-328 (2004).
[CrossRef]

R. A. Applegate, C. Ballentine, H. Gross, E. J. Sarver, and C. A. Sarver, "Visual acuity as a function of Zernike mode and level of root mean square error," Optom. Vision Sci. 80, 97-105 (2003).
[CrossRef]

R. A. Applegate and V. Lakshminarayanan, "Parametric representation of Stiles-Crawford functions: normal variation of peak location and directionality," J. Opt. Soc. Am. A 10, 1611-1623 (1993).
[CrossRef] [PubMed]

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2000), pp. 232-244.

Arjona, M.

J. Pujol, J. Gispets, and M. Arjona, "Optical performance in eyes wearing two multifocal contact lens designs," Ophthalmic Physiol. Opt. 23, 347-360 (2003).
[CrossRef] [PubMed]

Arora, I.

S. Jain, I. Arora, and D. T. Azar, "Success of monovision in presbyopes: review of the literature and potential applications to refractive surgery," Surv. Ophthalmol. 40, 491-499 (1996).
[CrossRef] [PubMed]

Asbell, P.

M. B. McDonald, D. Durrie, P. Asbell, R. Maloney, and L. Nichamin, "Treatment of presbyopia with conductive keratoplasty: six-month results of the 1-Year United States FDA clinical trial," Cornea 23, 661-668 (2004).
[CrossRef] [PubMed]

Asbell, P. A.

P. A. Asbell, R. K. Maloney, J. Davidorf, P. Hersh, M. McDonald, and E. Manche, "Conductive keratoplasty study group. Conductive keratoplasty for the correction of hyperopia," Trans. Am. Ophthalmol. Soc. 99, 79-84 (2001).

Ascari, A.

P. Vinciguerra, G. M. Nizzola, G. Bailo, F. Niezzola, A. Ascari, and D. Epstein, "Excimer laser photorefractive keratectomy for presbyopia: 24-month follow-up in three eyes," J. Refract. Surg. 14, 31-37 (1998).
[PubMed]

Atchison, D. A.

D. A. Atchison, W. N. Charman, and R. L. Woods, "Subjective depth-of-focus of the eye," Optom. Vision Sci. 74, 511-520 (1997).
[CrossRef]

Azar, D. T.

S. Jain, R. Ou, and D. T. Azar, "Monovision outcomes in presbyopic individuals after refractive surgery," Ophthalmology 108, 1430-1433 (2001).
[CrossRef] [PubMed]

K. C. Sippel, S. Jain, and D. T. Azar, "Monovision achieved with excimer laser refractive surgery," Int. Ophthalmol. Clin. 41, 91-101 (2001).
[CrossRef] [PubMed]

S. Jain, I. Arora, and D. T. Azar, "Success of monovision in presbyopes: review of the literature and potential applications to refractive surgery," Surv. Ophthalmol. 40, 491-499 (1996).
[CrossRef] [PubMed]

Bailo, G.

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Oksman, H. C.

J. T. Holladay, H. V. van Dijk, A. Lang, V. Protney, T. R. Willis, R. Sun, and H. C. Oksman, "Optical performance of multifocal intraocular lenses," J. Cataract Refractive Surg. 16, 413-422 (1990).

Ong, J.

D. Hamasaki, J. Ong, and E. Marg, "The amplitude of accommodation in presbyopia," Am. J. Optom. Arch. Am. Acad. Optom. 33, 3-14 (1956).
[PubMed]

Ostrin, L. A.

L. A. Ostrin, S. Kasthurirangan, and A. Glasser, "Evaluation of a satisfied bilateral scleral expansion band patient," J. Cataract Refractive Surg. 30, 1445-1453 (2004).
[CrossRef]

Ou, R.

S. Jain, R. Ou, and D. T. Azar, "Monovision outcomes in presbyopic individuals after refractive surgery," Ophthalmology 108, 1430-1433 (2001).
[CrossRef] [PubMed]

Percival, S. P. B.

S. P. B. Percival and S. S. Setty, "Prospectively randomized trial comparing the pseudoaccommodation of the AMO ARRAY multifocal lens and a monofocal lens," J. Cataract Refractive Surg. 19, 26-31 (1993).

Pieh, S.

S. Pieh, P. Marvan, B. Lackner, G. Hanselmayer, G. Schmidinger, R. Leitgeb, M. Sticker, C. K. Hitzenberger, A. F. Fercher, and C. Skorpik, "Quantitative performance of bifocal and multifocal intraocular lenses in a model eye: point spread function in multifocal intraocular lenses," Arch. Ophthalmol. 120, 23-28 (2002).
[PubMed]

Pope, D. R.

D. R. Pope, "Progresive addition lenses: history, design, wearer satisfaction and trends," in Vision Science and Its Applications, V. Lakschmirarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2000), pp. 342-357.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. Vetterling, and B. P. Flannery, Numerical Recipes in C++ (Cambridge U. Press, 2002).

Protney, V.

J. T. Holladay, H. V. van Dijk, A. Lang, V. Protney, T. R. Willis, R. Sun, and H. C. Oksman, "Optical performance of multifocal intraocular lenses," J. Cataract Refractive Surg. 16, 413-422 (1990).

Pujol, J.

J. Pujol, J. Gispets, and M. Arjona, "Optical performance in eyes wearing two multifocal contact lens designs," Ophthalmic Physiol. Opt. 23, 347-360 (2003).
[CrossRef] [PubMed]

Ritch, R.

R. A. Schachar, C. Tello, D. P. Cudmore, J. M. Liebmann, T. D. Black, and R. Ritch, "In vivo increase of the human lens equatorial diameter during accommodation," Am. J. Physiol. 271, 670-676 (1996).

Sarver, C. A.

R. A. Applegate, C. Ballentine, H. Gross, E. J. Sarver, and C. A. Sarver, "Visual acuity as a function of Zernike mode and level of root mean square error," Optom. Vision Sci. 80, 97-105 (2003).
[CrossRef]

Sarver, E. J.

R. A. Applegate, C. Ballentine, H. Gross, E. J. Sarver, and C. A. Sarver, "Visual acuity as a function of Zernike mode and level of root mean square error," Optom. Vision Sci. 80, 97-105 (2003).
[CrossRef]

Schachar, R. A.

R. A. Schachar, C. Tello, D. P. Cudmore, J. M. Liebmann, T. D. Black, and R. Ritch, "In vivo increase of the human lens equatorial diameter during accommodation," Am. J. Physiol. 271, 670-676 (1996).

R. A. Schachar, T. Huang, and X. Huang, "Mathematic proof of Schachar's hypothesis of accommodation," Ann. Ophthalmol. 25, 5-9 (1993).
[PubMed]

R. A. Schachar, "Cause and treatment of presbyopia with a method for increasing the amplitude of accommodation," Ann. Ophthalmol. 24, 445-452 (1992).
[PubMed]

Schmidinger, G.

S. Pieh, P. Marvan, B. Lackner, G. Hanselmayer, G. Schmidinger, R. Leitgeb, M. Sticker, C. K. Hitzenberger, A. F. Fercher, and C. Skorpik, "Quantitative performance of bifocal and multifocal intraocular lenses in a model eye: point spread function in multifocal intraocular lenses," Arch. Ophthalmol. 120, 23-28 (2002).
[PubMed]

Schneider, H.

O. Stachs, H. Schneider, J. Stave, and R. Guthoff, "Potentially accommodating intraocular lenses--an in vitro and in vivo study using three-dimensional high-frequency ultrasound," J. Refract. Surg. 21, 37-45 (2005).
[PubMed]

Schwallie, J.

K. Fisher, E. Bauman, and J. Schwallie, "Evaluation of two new soft contact lenses for correction of presbyopia. The Focus Progressives multifocal and the Acuvue bifocal," Int. Contact Lens Clin. 26, 92-103 (2000).
[CrossRef] [PubMed]

Schwiegerling, J. T.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2000), pp. 232-244.

Seitz, B.

A. Langenbucher, S. Huber, N. X. Nguyen, B. Seitz, G. C. Gusek-Schneider, and M. Küchle, "Measurement of accommodation after implantation of an accommodating posterior chamber intraocular lens," J. Cataract Refractive Surg. 29, 677-685 (2003).
[CrossRef]

Setty, S. S.

S. P. B. Percival and S. S. Setty, "Prospectively randomized trial comparing the pseudoaccommodation of the AMO ARRAY multifocal lens and a monofocal lens," J. Cataract Refractive Surg. 19, 26-31 (1993).

Sippel, K. C.

K. C. Sippel, S. Jain, and D. T. Azar, "Monovision achieved with excimer laser refractive surgery," Int. Ophthalmol. Clin. 41, 91-101 (2001).
[CrossRef] [PubMed]

Sitz, B.

M. Küchle, B. Sitz, A. Langenbucher, G. C. Gusek-Schneider, P. Martus, and N. X. Nguyen, "Comparison of 6-month results of implantation of the 1CU accommodative intraocular lens with conventional intraocular lenses," Ophthalmology 111, 318-324 (2004).
[CrossRef] [PubMed]

Skorpik, C.

S. Pieh, P. Marvan, B. Lackner, G. Hanselmayer, G. Schmidinger, R. Leitgeb, M. Sticker, C. K. Hitzenberger, A. F. Fercher, and C. Skorpik, "Quantitative performance of bifocal and multifocal intraocular lenses in a model eye: point spread function in multifocal intraocular lenses," Arch. Ophthalmol. 120, 23-28 (2002).
[PubMed]

Slade, S. G.

J. S. Cumming, S. G. Slade, and A. Chayet, "Clinical evaluation of the Model AT-45 silicone accommodating intraocular lens," Ophthalmology 108, 2005-2010 (2001).
[CrossRef] [PubMed]

Smith, W. J.

W. J. Smith, Modern Optical Engineering: The Design of Optical Systems, 2nd ed. (McGraw-Hill, 1990), pp. 125-128.

Stachs, O.

O. Stachs, H. Schneider, J. Stave, and R. Guthoff, "Potentially accommodating intraocular lenses--an in vitro and in vivo study using three-dimensional high-frequency ultrasound," J. Refract. Surg. 21, 37-45 (2005).
[PubMed]

Stave, J.

O. Stachs, H. Schneider, J. Stave, and R. Guthoff, "Potentially accommodating intraocular lenses--an in vitro and in vivo study using three-dimensional high-frequency ultrasound," J. Refract. Surg. 21, 37-45 (2005).
[PubMed]

Sticker, M.

S. Pieh, P. Marvan, B. Lackner, G. Hanselmayer, G. Schmidinger, R. Leitgeb, M. Sticker, C. K. Hitzenberger, A. F. Fercher, and C. Skorpik, "Quantitative performance of bifocal and multifocal intraocular lenses in a model eye: point spread function in multifocal intraocular lenses," Arch. Ophthalmol. 120, 23-28 (2002).
[PubMed]

Sun, R.

J. T. Holladay, H. V. van Dijk, A. Lang, V. Protney, T. R. Willis, R. Sun, and H. C. Oksman, "Optical performance of multifocal intraocular lenses," J. Cataract Refractive Surg. 16, 413-422 (1990).

Tarroux, M. C.

J. F. Malecaze, C. S. Gazagne, M. C. Tarroux, and J. M. Gorrand, "Scleral expansion bands for presbyopia," Ophthalmology 108, 2165-2171 (2001).
[CrossRef] [PubMed]

Telandro, A.

A. Telandro, "Pseudo-accommodative cornea: a new concept for correction of presbyopia," J. Refract. Surg. 20, S714-S717 (2004).
[PubMed]

Tello, C.

R. A. Schachar, C. Tello, D. P. Cudmore, J. M. Liebmann, T. D. Black, and R. Ritch, "In vivo increase of the human lens equatorial diameter during accommodation," Am. J. Physiol. 271, 670-676 (1996).

Terwee, T.

S. A. Koopmans, T. Terwee, H. J. Haitjema, H. Deuring, S. van Aarle, and A. C. Kooijman, "Relation between injected volume and optical parameters in refilled isolated porcine lenses," Ophthalmic. Physiol. Opt. 24, 572-579 (2004).
[CrossRef] [PubMed]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. Vetterling, and B. P. Flannery, Numerical Recipes in C++ (Cambridge U. Press, 2002).

Thibos, L. N.

J. D. Marsack, L. N. Thibos, and R. A. Applegate, "Metrics of optical quality derived from wave aberrations predict visual performance," J. Vision 4, 322-328 (2004).
[CrossRef]

L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, "The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans," Appl. Opt. 31, 3594-3600 (1992).
[CrossRef] [PubMed]

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2000), pp. 232-244.

Thornton, S. P.

S. P. Thornton, "Anterior ciliary sclerotomy, a procedure to reverse presbyopia," in Surgery for Hyperopia and Presbyopia, N.A.Sher, ed. (Williams & Wilkins, 1997), pp. 33-36.

To, C. H.

J. A. Guggenheim and C. H. To, "Monovision slows myopia progression," Br. J. Ophthalmol. 89, 1076-1077 (2005).
[CrossRef] [PubMed]

Tokarewicz, A. C.

K. W. Brydon, A. C. Tokarewicz, and B. D. Nichols, "AMO array multifocal lens versus monofocal correction in cataract surgery," J. Cataract Refractive Surg. 26, 96-100 (2000).
[CrossRef]

Turner, M. J.

M. J. Turner, "Observations on the normal subjective amplitude of accommodation," Br. J. Physiol. Opt. 15, 70-100 (1958).
[PubMed]

Tyson, R. K.

van Aarle, S.

S. A. Koopmans, T. Terwee, H. J. Haitjema, H. Deuring, S. van Aarle, and A. C. Kooijman, "Relation between injected volume and optical parameters in refilled isolated porcine lenses," Ophthalmic. Physiol. Opt. 24, 572-579 (2004).
[CrossRef] [PubMed]

van Dijk, H. V.

J. T. Holladay, H. V. van Dijk, A. Lang, V. Protney, T. R. Willis, R. Sun, and H. C. Oksman, "Optical performance of multifocal intraocular lenses," J. Cataract Refractive Surg. 16, 413-422 (1990).

Vetterling, W.

W. H. Press, S. A. Teukolsky, W. Vetterling, and B. P. Flannery, Numerical Recipes in C++ (Cambridge U. Press, 2002).

Vinciguerra, P.

P. Vinciguerra, G. M. Nizzola, G. Bailo, F. Niezzola, A. Ascari, and D. Epstein, "Excimer laser photorefractive keratectomy for presbyopia: 24-month follow-up in three eyes," J. Refract. Surg. 14, 31-37 (1998).
[PubMed]

von Helmholtz, H.

H. von Helmholtz, Physiological Optics, J.P. C.Southall, ed. (Dover, 1896).

Webb, R.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2000), pp. 232-244.

Wee, W. R.

Y. K. Han, J. W. Kwon, J. S. Kim, C.-S. Cho, W. R. Wee, and J. H. Lee, "In vitro and in vivo study of lens refilling with poloxamer hydrogel," Br. J. Ophthalmol. 87, 1399-1402 (2003).
[CrossRef] [PubMed]

Williams, D. R.

A. Guirao and D. R. Williams, "A method to predict refractive errors from wave aberration data," Optom. Vision Sci. 80, 36-42 (2003).
[CrossRef]

Willis, T. R.

J. T. Holladay, H. V. van Dijk, A. Lang, V. Protney, T. R. Willis, R. Sun, and H. C. Oksman, "Optical performance of multifocal intraocular lenses," J. Cataract Refractive Surg. 16, 413-422 (1990).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1965).

Woo, G. C.

Woods, R. L.

D. A. Atchison, W. N. Charman, and R. L. Woods, "Subjective depth-of-focus of the eye," Optom. Vision Sci. 74, 511-520 (1997).
[CrossRef]

Ye, M.

Zhang, X.

Am. J. Ophthalmol.

A. Duane, "Studies in monocular and binocular accommodation with their clinical applications," Am. J. Ophthalmol. 5, 865-877 (1922).

Am. J. Optom. Arch. Am. Acad. Optom.

D. Hamasaki, J. Ong, and E. Marg, "The amplitude of accommodation in presbyopia," Am. J. Optom. Arch. Am. Acad. Optom. 33, 3-14 (1956).
[PubMed]

Am. J. Physiol.

R. A. Schachar, C. Tello, D. P. Cudmore, J. M. Liebmann, T. D. Black, and R. Ritch, "In vivo increase of the human lens equatorial diameter during accommodation," Am. J. Physiol. 271, 670-676 (1996).

Ann. Ophthalmol.

R. A. Schachar, "Cause and treatment of presbyopia with a method for increasing the amplitude of accommodation," Ann. Ophthalmol. 24, 445-452 (1992).
[PubMed]

R. A. Schachar, T. Huang, and X. Huang, "Mathematic proof of Schachar's hypothesis of accommodation," Ann. Ophthalmol. 25, 5-9 (1993).
[PubMed]

Appl. Opt.

Arch. Ophthalmol.

S. Pieh, P. Marvan, B. Lackner, G. Hanselmayer, G. Schmidinger, R. Leitgeb, M. Sticker, C. K. Hitzenberger, A. F. Fercher, and C. Skorpik, "Quantitative performance of bifocal and multifocal intraocular lenses in a model eye: point spread function in multifocal intraocular lenses," Arch. Ophthalmol. 120, 23-28 (2002).
[PubMed]

J. Kessler, "Experiments in refilling the lens," Arch. Ophthalmol. 71, 412-416 (1964).
[CrossRef] [PubMed]

O. Nishi and K. Nishi, "Accommodation amplitude after lens refilling with injectable silicone by sealing the capsule with a plug in primates," Arch. Ophthalmol. 116, 1358-1361 (1998).
[PubMed]

H. Moreira, J. J. Garhus, A. Fasano, M. Lee, T. N. Clapham, and P. J. McDonell, "Multifocal corneal topographic changes with excimer laser photorefractive keratectomy," Arch. Ophthalmol. 110, 994-999 (1992).
[CrossRef] [PubMed]

Br. J. Ophthalmol.

J. A. Guggenheim and C. H. To, "Monovision slows myopia progression," Br. J. Ophthalmol. 89, 1076-1077 (2005).
[CrossRef] [PubMed]

Y. K. Han, J. W. Kwon, J. S. Kim, C.-S. Cho, W. R. Wee, and J. H. Lee, "In vitro and in vivo study of lens refilling with poloxamer hydrogel," Br. J. Ophthalmol. 87, 1399-1402 (2003).
[CrossRef] [PubMed]

Br. J. Physiol. Opt.

M. J. Turner, "Observations on the normal subjective amplitude of accommodation," Br. J. Physiol. Opt. 15, 70-100 (1958).
[PubMed]

Comput. J.

J. A. Nelder and R. Mead, "A simplex method for function minimization," Comput. J. 7, 308-313 (1965).

Cornea

M. B. McDonald, D. Durrie, P. Asbell, R. Maloney, and L. Nichamin, "Treatment of presbyopia with conductive keratoplasty: six-month results of the 1-Year United States FDA clinical trial," Cornea 23, 661-668 (2004).
[CrossRef] [PubMed]

Int. Contact Lens Clin.

K. Fisher, E. Bauman, and J. Schwallie, "Evaluation of two new soft contact lenses for correction of presbyopia. The Focus Progressives multifocal and the Acuvue bifocal," Int. Contact Lens Clin. 26, 92-103 (2000).
[CrossRef] [PubMed]

Int. Ophthalmol. Clin.

H. Fukasaku and J. A. Marron, "Anterior ciliary sclerectomy with silicone expansion plug implantation: effect on presbyopia and intraocular pressure," Int. Ophthalmol. Clin. 41, 133-141 (2001).
[CrossRef] [PubMed]

K. C. Sippel, S. Jain, and D. T. Azar, "Monovision achieved with excimer laser refractive surgery," Int. Ophthalmol. Clin. 41, 91-101 (2001).
[CrossRef] [PubMed]

J. Am. Med. Assoc.

A. Duane, "Normal values of the accommodation at all ages," J. Am. Med. Assoc. 59, 1010-1013 (1912).
[CrossRef]

J. Cataract Refractive Surg.

J. S. Cumming, "Postoperative complications and uncorrected acuities after implantation of plate haptic silicone and three-piece silicone intraocular lenses," J. Cataract Refractive Surg. 19, 263-274 (1993).

A. Langenbucher, S. Huber, N. X. Nguyen, B. Seitz, G. C. Gusek-Schneider, and M. Küchle, "Measurement of accommodation after implantation of an accommodating posterior chamber intraocular lens," J. Cataract Refractive Surg. 29, 677-685 (2003).
[CrossRef]

J. T. Holladay, H. V. van Dijk, A. Lang, V. Protney, T. R. Willis, R. Sun, and H. C. Oksman, "Optical performance of multifocal intraocular lenses," J. Cataract Refractive Surg. 16, 413-422 (1990).

S. P. B. Percival and S. S. Setty, "Prospectively randomized trial comparing the pseudoaccommodation of the AMO ARRAY multifocal lens and a monofocal lens," J. Cataract Refractive Surg. 19, 26-31 (1993).

K. W. Brydon, A. C. Tokarewicz, and B. D. Nichols, "AMO array multifocal lens versus monofocal correction in cataract surgery," J. Cataract Refractive Surg. 26, 96-100 (2000).
[CrossRef]

L. A. Ostrin, S. Kasthurirangan, and A. Glasser, "Evaluation of a satisfied bilateral scleral expansion band patient," J. Cataract Refractive Surg. 30, 1445-1453 (2004).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Physiol.

F. W. Campbell and D. G. Green, "Optical and retinal factors affecting visual resolution," J. Physiol. 181, 576-593 (1965).
[PubMed]

J. Refract. Surg.

O. Stachs, H. Schneider, J. Stave, and R. Guthoff, "Potentially accommodating intraocular lenses--an in vitro and in vivo study using three-dimensional high-frequency ultrasound," J. Refract. Surg. 21, 37-45 (2005).
[PubMed]

P. Vinciguerra, G. M. Nizzola, G. Bailo, F. Niezzola, A. Ascari, and D. Epstein, "Excimer laser photorefractive keratectomy for presbyopia: 24-month follow-up in three eyes," J. Refract. Surg. 14, 31-37 (1998).
[PubMed]

A. Telandro, "Pseudo-accommodative cornea: a new concept for correction of presbyopia," J. Refract. Surg. 20, S714-S717 (2004).
[PubMed]

J. Vision

X. Cheng and A. Bradley, "Predicting subjective judgment of best focus with objective image quality metrics," J. Vision 4, 310-321 (2004).
[CrossRef]

J. D. Marsack, L. N. Thibos, and R. A. Applegate, "Metrics of optical quality derived from wave aberrations predict visual performance," J. Vision 4, 322-328 (2004).
[CrossRef]

Ophthalmic Physiol. Opt.

J. Pujol, J. Gispets, and M. Arjona, "Optical performance in eyes wearing two multifocal contact lens designs," Ophthalmic Physiol. Opt. 23, 347-360 (2003).
[CrossRef] [PubMed]

Ophthalmic. Physiol. Opt.

S. A. Koopmans, T. Terwee, H. J. Haitjema, H. Deuring, S. van Aarle, and A. C. Kooijman, "Relation between injected volume and optical parameters in refilled isolated porcine lenses," Ophthalmic. Physiol. Opt. 24, 572-579 (2004).
[CrossRef] [PubMed]

Ophthalmology

M. Küchle, B. Sitz, A. Langenbucher, G. C. Gusek-Schneider, P. Martus, and N. X. Nguyen, "Comparison of 6-month results of implantation of the 1CU accommodative intraocular lens with conventional intraocular lenses," Ophthalmology 111, 318-324 (2004).
[CrossRef] [PubMed]

J. S. Cumming, S. G. Slade, and A. Chayet, "Clinical evaluation of the Model AT-45 silicone accommodating intraocular lens," Ophthalmology 108, 2005-2010 (2001).
[CrossRef] [PubMed]

D. R. Hamilton, J. M. Davidorf, and R. K. Maloney, "Anterior ciliary sclerotomy for treatment of presbyopia: a prospective controlled study," Ophthalmology 109, 1970-1977 (2002).
[CrossRef] [PubMed]

S. Jain, R. Ou, and D. T. Azar, "Monovision outcomes in presbyopic individuals after refractive surgery," Ophthalmology 108, 1430-1433 (2001).
[CrossRef] [PubMed]

S. Mathews, "Scleral expansion surgery does not restore accommodation in human presbyopia," Ophthalmology 106, 873-877 (1999).
[CrossRef] [PubMed]

J. F. Malecaze, C. S. Gazagne, M. C. Tarroux, and J. M. Gorrand, "Scleral expansion bands for presbyopia," Ophthalmology 108, 2165-2171 (2001).
[CrossRef] [PubMed]

Opt. Lett.

Optom. Vision Sci.

A. Guirao and D. R. Williams, "A method to predict refractive errors from wave aberration data," Optom. Vision Sci. 80, 36-42 (2003).
[CrossRef]

R. A. Applegate, C. Ballentine, H. Gross, E. J. Sarver, and C. A. Sarver, "Visual acuity as a function of Zernike mode and level of root mean square error," Optom. Vision Sci. 80, 97-105 (2003).
[CrossRef]

D. A. Atchison, W. N. Charman, and R. L. Woods, "Subjective depth-of-focus of the eye," Optom. Vision Sci. 74, 511-520 (1997).
[CrossRef]

N. Chateau and D. Baude, "Simulated in situ optical performance of bifocal contact lenses," Optom. Vision Sci. 74, 532-539 (1997).
[CrossRef]

Proc. SPIE

G.-m. Dai, "Using wavefront measurements to predict visual acuity," in Ophthalmic Technologies XIV, F. Manns, P. G. Söderberg, and A. Ho, eds., Proc. SPIE 5314, 220-228 (2004).
[CrossRef]

Surv. Ophthalmol.

S. Jain, I. Arora, and D. T. Azar, "Success of monovision in presbyopes: review of the literature and potential applications to refractive surgery," Surv. Ophthalmol. 40, 491-499 (1996).
[CrossRef] [PubMed]

Trans. Am. Ophthalmol. Soc.

P. A. Asbell, R. K. Maloney, J. Davidorf, P. Hersh, M. McDonald, and E. Manche, "Conductive keratoplasty study group. Conductive keratoplasty for the correction of hyperopia," Trans. Am. Ophthalmol. Soc. 99, 79-84 (2001).

Other

D. R. Pope, "Progresive addition lenses: history, design, wearer satisfaction and trends," in Vision Science and Its Applications, V. Lakschmirarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2000), pp. 342-357.

A. Agarwal, Presbyopia: A Surgical Textbook (Slack, 2002).

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2000), pp. 232-244.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1965).

I. E. Lowenfeld, The Pupil: Anatomoy, Physiology, and Clinical Applications (Butterworth-Heinemann, 1999).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

W. H. Press, S. A. Teukolsky, W. Vetterling, and B. P. Flannery, Numerical Recipes in C++ (Cambridge U. Press, 2002).

W. J. Smith, Modern Optical Engineering: The Design of Optical Systems, 2nd ed. (McGraw-Hill, 1990), pp. 125-128.

A. Mendez and N. A. Mendez, "Conductive keratoplasty for the correction of hyperopia," in Surgery for Hyperopia and Presbyopia, N.A.Sher, ed. (Williams & Wilkins, 1997), pp. 163-171.

S. P. Thornton, "Anterior ciliary sclerotomy, a procedure to reverse presbyopia," in Surgery for Hyperopia and Presbyopia, N.A.Sher, ed. (Williams & Wilkins, 1997), pp. 33-36.

K. J. Ciuffreda, "Accommodation and its anomalies," in Vision and Visual Dysfunction, W.N.Charman, ed. (Macmillan, 1991), Vol. 1, pp. 231-279.

H. von Helmholtz, Physiological Optics, J.P. C.Southall, ed. (Dover, 1896).

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Figures (12)

Fig. 1
Fig. 1

EE curves for a diffraction-limited optical system and optical systems with 0.25 μm of defocus, spherical aberration (SA), and secondary SA, respectively. A pupil size of 6 mm is assumed for all cases.

Fig. 2
Fig. 2

Compound MTF and its components: (a) compound MTF with three components; (b) corresponding individual MTF curves at 10, 20, and 30 cpd, respectively.

Fig. 3
Fig. 3

Flow diagram of the optimization process discussed in this paper.

Fig. 4
Fig. 4

PSF profile with 0.2 D defocus error for a 6 mm pupil with a different number of wavelengths (1, 3, and 7, with no further effect seen over 7) over the visible spectrum.

Fig. 5
Fig. 5

Optimizer values for various pupil sizes with a different number of optimization terms for (a) EPTP expansion and (b) APTP expansion, using the CMTF as the optical metric. It was assumed that there was no accommodation.

Fig. 6
Fig. 6

Optimized shapes with EPTP and APTP approaches for a 5 mm pupil with no accommodation. In both cases four terms (n = 4) were used. Note that the shape made with EPTP is much smoother than the shape made with APTP. OPD, optical path difference.

Fig. 7
Fig. 7

Optimizer value obtained with various optical metrics. (a) MTF at 20 cpd; (b) SR; (c) encircled energy at 5′; (d) CMTF with spatial frequencies at 10, 20, and 30 cpd.

Fig. 8
Fig. 8

Optical shapes optimized with different optical metrics. R = 2.5 mm, δ = 30% pupil dynamics, and 1 D of residual accommodation were assumed.

Fig. 9
Fig. 9

Simulated eye chart seen at different target distances with the following conditions (R = 2.5 mm, δ = 30%, A = 1 D). The top row shows a simulated eye chart with no correction. Optical metrics used, from the second row to bottom, are MTF at 20 cpd; SR; encircled energy at 5′; and CMTF for 10, 20, and 30 cpd, respectively. From top to bottom, the acuity lines on the eye chart are 20∕100, 20∕80, 20∕60, 20∕40, and 20∕20, respectively.

Fig. 10
Fig. 10

Optimizer value as a function of spatial frequency using CMTF as the optical metric.

Fig. 11
Fig. 11

Optimizer value as a function of field of view using encircled energy as the optical metric.

Fig. 12
Fig. 12

Optimizer value as a function of residual accommodation for various pupil sizes. δ = 0 was assumed. The optimizer value of 5 is considered the threshold for obtaining a good visual result.

Tables (3)

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Table 1 Depth of Focus From the MTF Curve Estimation as Compared to Experimental Results (Ref. 62)

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Table 2 Comparison of the Smoothness of Curves of the Optimizer Values

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Table 3 Minimum Accommodation Required a to Achieve Optimal Presbyopia Correction for Various Cases of Pupil Dynamics

Equations (22)

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W ( R r , θ ) = i = 1 c i F i ( r , θ ) ,
1 π P ( r ) F i ( r , θ ) F i ( r , θ ) d 2 r = δ i i ,
W ( R r ) i = 1 n c i r i ,
W ( R r ) = i = 1 n / 2 a 2 i r 2 i .
W ( R r ) = i = 1 n / 2 b 2 i s = 0 i ( 1 ) s ( 2 i s ) ! 2 i + 1 s ! [ ( i s ) ! ] 2 r 2 ( i s ) .
{ a 2 i = j P i j b 2 j , b 2 i = j Q i j a 2 j ,
P i j = ( 1 ) i + j 2 j + 1 ( i + j ) ! ( j i ) ! ( i ! ) 2 ,
Q i j = s = 0 i ( 1 ) s 2 i + 1 ( 2 i s ) ! ( i + j s + 1 ) s ! [ ( i s ) ! ] 2 ,
ϵ = r / R .
i ( l ) = i ( l , r , θ ) ,
S ( l ) = i max ( l , r , θ ) I max ( r , θ ) ,
( l , ν , ϕ ) = | F T [ i ( l , r , θ ) ] | ,
( l , κ ) = 0 κ 0 2 π i ( l , r , θ ) d 2 r 0 0 2 π i ( l , r , θ ) d 2 r ,
C ( m ) ( l ) = 1 m i = 1 m γ i i ( l ) ,
f = O ( c 1 , c 2 , , c n , ϵ ) = ( 1 + σ ) ( 1 + β ) Q ^ ( l ) ,
i ( l ) = λ = 0 ( λ ) | FT { P s c ( r ) exp [ j Φ ( λ ) ] } | 2 ,
Φ ( λ ) = 2 π λ [ W ( R r ) + α C ( λ ) + α V ( l ) + α A ( l ) ] .
( λ ) exp [ 279 ( λ λ 0 ) 2 ] ,
P s c ( r ) = 10 ρ ( r 2 / R 2 ) ,
C ( λ ) 21.587 + 92.87 λ 134.98 λ 2 + 67.407 λ 3 .
f = ( 3 A ) [ ( 0.53 δ 2 + 1.5 ) R 0.2 R 2 3.2 δ 2 ] + 1 , ( A 3 ) ,
A min = 3 4 ( 0.53 δ 2 + 1.5 ) R 0.2 R 2 3.2 δ 2 .

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