Abstract

New multifocal phase designs aiming at expanding depth of focus in the presbyopic eye are presented. The designs consist of multiple radial or angular zones of different powers or of combined low- and high-order aberrations. Multifocal performance was evaluated in terms of the dioptric range for which the optical quality is above an appropriate threshold, as well as in terms of the area under the through-focus optical quality curves. For varying optical power designs optimal through-focus performance was found for a maximum of three to four zones. Furthermore adding more zones decreased the optical performance of the solution. Angular zone designs provided better multifocal performance (1.95 times on average) than radial zone designs with identical number of zones and the same power range. The optimal design (angular design with three zones) surpassed by 33% the multifocal performance of a bifocal angular zone design and by 32% a standard multifocal phase plate with induced spherical aberration only. By using combinations of low- and high-order aberrations the through-focus range can be extended further by another 0.5 D beyond that of the best design of varying optical power. These designs can be implemented in adaptive optics systems for testing their visual performance in subjects and converted into multifocal contact lenses, intraocular lenses, or presbyopic corneal laser ablation profiles.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Glasser, M. A. Croft, and P. L. Kaufman, Int. Ophthalmol. Clin. 41, 1 (2001).
    [CrossRef]
  2. A. Lichtinger and D. S. Rootman, Curr. Opin. Ophthalmol. 23, 40 (2012).
    [CrossRef]
  3. J. A. Martin and A. Roorda, Optom. Vis. Sci. 80, 812 (2003).
    [CrossRef]
  4. F. Yi, D. Robert Iskander, and M. Collins, Vis. Res. 51, 1648 (2011).
    [CrossRef]
  5. P. de Gracia, C. Dorronsoro, E. Gambra, G. Marin, M. Hernández, and S. Marcos, Vis. Res. 50, 2008 (2010).
    [CrossRef]
  6. A. Zlotnik, I. Raveh, S. Ben Yaish, O. Yehezkel, M. Belkin, and Z. Zalevsky, Proc. SPIE 7550, 75500A (2010).
    [CrossRef]
  7. D. Fernández, S. Barbero, C. Dorronsoro, and S. Marcos, “Multifocal intraocular lens providing improved,” Spanish patentP201232043 (December27, 2012).
  8. J. D. Marsack, L. N. Thibos, and R. A. Applegate, J. Vis. 4(4), 8 (2004).
    [CrossRef]
  9. S. Manzanera, P. M. Prieto, D. B. Ayala, J. M. Lindacher, and P. Artal, Opt. Express 15, 16177 (2007).
    [CrossRef]
  10. D. R. Iskander, Optom. Vis. Sci. 83, 57 (2006).
    [CrossRef]
  11. X. Cheng, A. Bradley, and L. N. Thibos, J. Vis. 4(4), 310 (2004).
  12. B. F. M. W. Angerlo and B. J. W. Arnhem, “Ophthalmic lens with optical sectors,” U.S. patent application20120029631 A1 (May9, 2012).
  13. Y. Benard, N. Lopez-Gil, and R. Legras, Vis. Res. 51, 2471 (2011).
    [CrossRef]
  14. W. Fiala and M. Gerlach, “Multifocal lens,” U.S. patent application20130050640 (October28, 2012).
  15. D. Gatinel, C. Pagnoulle, Y. Houbrechts, and L. Gobin, J. Cataract. Refract. Surg. 37, 2060 (2011).
    [CrossRef]
  16. W. M. Lee, X. C. Yuan, and W. C. Cheong, Opt. Lett. 29, 1796 (2004).
    [CrossRef]
  17. P. de Gracia, C. Dorronsoro, G. Marin, M. Hernández, and S. Marcos, J. Vis. 11(2), 5 (2011).
    [CrossRef]
  18. L. Sawides, P. de Gracia, C. Dorronsoro, M. A. Webster, and S. Marcos, PLoS ONE 6, e27031 (2011).
    [CrossRef]
  19. S. Klein, J. Opt. Soc. Am. A 15, 2580 (1998).
    [CrossRef]
  20. S. A. Klein and B. A. Barsky, Optom. Vis. Sci. 72, 816 (1995).
    [CrossRef]
  21. C. Dorronsoro, D. Cano, J. Merayo, and S. Marcos, Opt. Express 14, 6142 (2006).
    [CrossRef]
  22. C. Dorronsoro, S. Barbero, L. Llorente, and S. Marcos, Optom. Vis. Sci. 80, 115 (2003).
    [CrossRef]
  23. M. Bass, ed., Handbook of Optics, 3rd ed. (Optical Society of America, 1995), Vol. 3, Chap. 21.

2012 (1)

A. Lichtinger and D. S. Rootman, Curr. Opin. Ophthalmol. 23, 40 (2012).
[CrossRef]

2011 (5)

F. Yi, D. Robert Iskander, and M. Collins, Vis. Res. 51, 1648 (2011).
[CrossRef]

Y. Benard, N. Lopez-Gil, and R. Legras, Vis. Res. 51, 2471 (2011).
[CrossRef]

D. Gatinel, C. Pagnoulle, Y. Houbrechts, and L. Gobin, J. Cataract. Refract. Surg. 37, 2060 (2011).
[CrossRef]

P. de Gracia, C. Dorronsoro, G. Marin, M. Hernández, and S. Marcos, J. Vis. 11(2), 5 (2011).
[CrossRef]

L. Sawides, P. de Gracia, C. Dorronsoro, M. A. Webster, and S. Marcos, PLoS ONE 6, e27031 (2011).
[CrossRef]

2010 (2)

P. de Gracia, C. Dorronsoro, E. Gambra, G. Marin, M. Hernández, and S. Marcos, Vis. Res. 50, 2008 (2010).
[CrossRef]

A. Zlotnik, I. Raveh, S. Ben Yaish, O. Yehezkel, M. Belkin, and Z. Zalevsky, Proc. SPIE 7550, 75500A (2010).
[CrossRef]

2007 (1)

2006 (2)

2004 (3)

X. Cheng, A. Bradley, and L. N. Thibos, J. Vis. 4(4), 310 (2004).

J. D. Marsack, L. N. Thibos, and R. A. Applegate, J. Vis. 4(4), 8 (2004).
[CrossRef]

W. M. Lee, X. C. Yuan, and W. C. Cheong, Opt. Lett. 29, 1796 (2004).
[CrossRef]

2003 (2)

C. Dorronsoro, S. Barbero, L. Llorente, and S. Marcos, Optom. Vis. Sci. 80, 115 (2003).
[CrossRef]

J. A. Martin and A. Roorda, Optom. Vis. Sci. 80, 812 (2003).
[CrossRef]

2001 (1)

A. Glasser, M. A. Croft, and P. L. Kaufman, Int. Ophthalmol. Clin. 41, 1 (2001).
[CrossRef]

1998 (1)

1995 (1)

S. A. Klein and B. A. Barsky, Optom. Vis. Sci. 72, 816 (1995).
[CrossRef]

Angerlo, B. F. M. W.

B. F. M. W. Angerlo and B. J. W. Arnhem, “Ophthalmic lens with optical sectors,” U.S. patent application20120029631 A1 (May9, 2012).

Applegate, R. A.

J. D. Marsack, L. N. Thibos, and R. A. Applegate, J. Vis. 4(4), 8 (2004).
[CrossRef]

Arnhem, B. J. W.

B. F. M. W. Angerlo and B. J. W. Arnhem, “Ophthalmic lens with optical sectors,” U.S. patent application20120029631 A1 (May9, 2012).

Artal, P.

Ayala, D. B.

Barbero, S.

C. Dorronsoro, S. Barbero, L. Llorente, and S. Marcos, Optom. Vis. Sci. 80, 115 (2003).
[CrossRef]

D. Fernández, S. Barbero, C. Dorronsoro, and S. Marcos, “Multifocal intraocular lens providing improved,” Spanish patentP201232043 (December27, 2012).

Barsky, B. A.

S. A. Klein and B. A. Barsky, Optom. Vis. Sci. 72, 816 (1995).
[CrossRef]

Belkin, M.

A. Zlotnik, I. Raveh, S. Ben Yaish, O. Yehezkel, M. Belkin, and Z. Zalevsky, Proc. SPIE 7550, 75500A (2010).
[CrossRef]

Ben Yaish, S.

A. Zlotnik, I. Raveh, S. Ben Yaish, O. Yehezkel, M. Belkin, and Z. Zalevsky, Proc. SPIE 7550, 75500A (2010).
[CrossRef]

Benard, Y.

Y. Benard, N. Lopez-Gil, and R. Legras, Vis. Res. 51, 2471 (2011).
[CrossRef]

Bradley, A.

X. Cheng, A. Bradley, and L. N. Thibos, J. Vis. 4(4), 310 (2004).

Cano, D.

Cheng, X.

X. Cheng, A. Bradley, and L. N. Thibos, J. Vis. 4(4), 310 (2004).

Cheong, W. C.

Collins, M.

F. Yi, D. Robert Iskander, and M. Collins, Vis. Res. 51, 1648 (2011).
[CrossRef]

Croft, M. A.

A. Glasser, M. A. Croft, and P. L. Kaufman, Int. Ophthalmol. Clin. 41, 1 (2001).
[CrossRef]

de Gracia, P.

P. de Gracia, C. Dorronsoro, G. Marin, M. Hernández, and S. Marcos, J. Vis. 11(2), 5 (2011).
[CrossRef]

L. Sawides, P. de Gracia, C. Dorronsoro, M. A. Webster, and S. Marcos, PLoS ONE 6, e27031 (2011).
[CrossRef]

P. de Gracia, C. Dorronsoro, E. Gambra, G. Marin, M. Hernández, and S. Marcos, Vis. Res. 50, 2008 (2010).
[CrossRef]

Dorronsoro, C.

L. Sawides, P. de Gracia, C. Dorronsoro, M. A. Webster, and S. Marcos, PLoS ONE 6, e27031 (2011).
[CrossRef]

P. de Gracia, C. Dorronsoro, G. Marin, M. Hernández, and S. Marcos, J. Vis. 11(2), 5 (2011).
[CrossRef]

P. de Gracia, C. Dorronsoro, E. Gambra, G. Marin, M. Hernández, and S. Marcos, Vis. Res. 50, 2008 (2010).
[CrossRef]

C. Dorronsoro, D. Cano, J. Merayo, and S. Marcos, Opt. Express 14, 6142 (2006).
[CrossRef]

C. Dorronsoro, S. Barbero, L. Llorente, and S. Marcos, Optom. Vis. Sci. 80, 115 (2003).
[CrossRef]

D. Fernández, S. Barbero, C. Dorronsoro, and S. Marcos, “Multifocal intraocular lens providing improved,” Spanish patentP201232043 (December27, 2012).

Fernández, D.

D. Fernández, S. Barbero, C. Dorronsoro, and S. Marcos, “Multifocal intraocular lens providing improved,” Spanish patentP201232043 (December27, 2012).

Fiala, W.

W. Fiala and M. Gerlach, “Multifocal lens,” U.S. patent application20130050640 (October28, 2012).

Gambra, E.

P. de Gracia, C. Dorronsoro, E. Gambra, G. Marin, M. Hernández, and S. Marcos, Vis. Res. 50, 2008 (2010).
[CrossRef]

Gatinel, D.

D. Gatinel, C. Pagnoulle, Y. Houbrechts, and L. Gobin, J. Cataract. Refract. Surg. 37, 2060 (2011).
[CrossRef]

Gerlach, M.

W. Fiala and M. Gerlach, “Multifocal lens,” U.S. patent application20130050640 (October28, 2012).

Glasser, A.

A. Glasser, M. A. Croft, and P. L. Kaufman, Int. Ophthalmol. Clin. 41, 1 (2001).
[CrossRef]

Gobin, L.

D. Gatinel, C. Pagnoulle, Y. Houbrechts, and L. Gobin, J. Cataract. Refract. Surg. 37, 2060 (2011).
[CrossRef]

Hernández, M.

P. de Gracia, C. Dorronsoro, G. Marin, M. Hernández, and S. Marcos, J. Vis. 11(2), 5 (2011).
[CrossRef]

P. de Gracia, C. Dorronsoro, E. Gambra, G. Marin, M. Hernández, and S. Marcos, Vis. Res. 50, 2008 (2010).
[CrossRef]

Houbrechts, Y.

D. Gatinel, C. Pagnoulle, Y. Houbrechts, and L. Gobin, J. Cataract. Refract. Surg. 37, 2060 (2011).
[CrossRef]

Iskander, D. R.

D. R. Iskander, Optom. Vis. Sci. 83, 57 (2006).
[CrossRef]

Kaufman, P. L.

A. Glasser, M. A. Croft, and P. L. Kaufman, Int. Ophthalmol. Clin. 41, 1 (2001).
[CrossRef]

Klein, S.

Klein, S. A.

S. A. Klein and B. A. Barsky, Optom. Vis. Sci. 72, 816 (1995).
[CrossRef]

Lee, W. M.

Legras, R.

Y. Benard, N. Lopez-Gil, and R. Legras, Vis. Res. 51, 2471 (2011).
[CrossRef]

Lichtinger, A.

A. Lichtinger and D. S. Rootman, Curr. Opin. Ophthalmol. 23, 40 (2012).
[CrossRef]

Lindacher, J. M.

Llorente, L.

C. Dorronsoro, S. Barbero, L. Llorente, and S. Marcos, Optom. Vis. Sci. 80, 115 (2003).
[CrossRef]

Lopez-Gil, N.

Y. Benard, N. Lopez-Gil, and R. Legras, Vis. Res. 51, 2471 (2011).
[CrossRef]

Manzanera, S.

Marcos, S.

L. Sawides, P. de Gracia, C. Dorronsoro, M. A. Webster, and S. Marcos, PLoS ONE 6, e27031 (2011).
[CrossRef]

P. de Gracia, C. Dorronsoro, G. Marin, M. Hernández, and S. Marcos, J. Vis. 11(2), 5 (2011).
[CrossRef]

P. de Gracia, C. Dorronsoro, E. Gambra, G. Marin, M. Hernández, and S. Marcos, Vis. Res. 50, 2008 (2010).
[CrossRef]

C. Dorronsoro, D. Cano, J. Merayo, and S. Marcos, Opt. Express 14, 6142 (2006).
[CrossRef]

C. Dorronsoro, S. Barbero, L. Llorente, and S. Marcos, Optom. Vis. Sci. 80, 115 (2003).
[CrossRef]

D. Fernández, S. Barbero, C. Dorronsoro, and S. Marcos, “Multifocal intraocular lens providing improved,” Spanish patentP201232043 (December27, 2012).

Marin, G.

P. de Gracia, C. Dorronsoro, G. Marin, M. Hernández, and S. Marcos, J. Vis. 11(2), 5 (2011).
[CrossRef]

P. de Gracia, C. Dorronsoro, E. Gambra, G. Marin, M. Hernández, and S. Marcos, Vis. Res. 50, 2008 (2010).
[CrossRef]

Marsack, J. D.

J. D. Marsack, L. N. Thibos, and R. A. Applegate, J. Vis. 4(4), 8 (2004).
[CrossRef]

Martin, J. A.

J. A. Martin and A. Roorda, Optom. Vis. Sci. 80, 812 (2003).
[CrossRef]

Merayo, J.

Pagnoulle, C.

D. Gatinel, C. Pagnoulle, Y. Houbrechts, and L. Gobin, J. Cataract. Refract. Surg. 37, 2060 (2011).
[CrossRef]

Prieto, P. M.

Raveh, I.

A. Zlotnik, I. Raveh, S. Ben Yaish, O. Yehezkel, M. Belkin, and Z. Zalevsky, Proc. SPIE 7550, 75500A (2010).
[CrossRef]

Robert Iskander, D.

F. Yi, D. Robert Iskander, and M. Collins, Vis. Res. 51, 1648 (2011).
[CrossRef]

Roorda, A.

J. A. Martin and A. Roorda, Optom. Vis. Sci. 80, 812 (2003).
[CrossRef]

Rootman, D. S.

A. Lichtinger and D. S. Rootman, Curr. Opin. Ophthalmol. 23, 40 (2012).
[CrossRef]

Sawides, L.

L. Sawides, P. de Gracia, C. Dorronsoro, M. A. Webster, and S. Marcos, PLoS ONE 6, e27031 (2011).
[CrossRef]

Thibos, L. N.

J. D. Marsack, L. N. Thibos, and R. A. Applegate, J. Vis. 4(4), 8 (2004).
[CrossRef]

X. Cheng, A. Bradley, and L. N. Thibos, J. Vis. 4(4), 310 (2004).

Webster, M. A.

L. Sawides, P. de Gracia, C. Dorronsoro, M. A. Webster, and S. Marcos, PLoS ONE 6, e27031 (2011).
[CrossRef]

Yehezkel, O.

A. Zlotnik, I. Raveh, S. Ben Yaish, O. Yehezkel, M. Belkin, and Z. Zalevsky, Proc. SPIE 7550, 75500A (2010).
[CrossRef]

Yi, F.

F. Yi, D. Robert Iskander, and M. Collins, Vis. Res. 51, 1648 (2011).
[CrossRef]

Yuan, X. C.

Zalevsky, Z.

A. Zlotnik, I. Raveh, S. Ben Yaish, O. Yehezkel, M. Belkin, and Z. Zalevsky, Proc. SPIE 7550, 75500A (2010).
[CrossRef]

Zlotnik, A.

A. Zlotnik, I. Raveh, S. Ben Yaish, O. Yehezkel, M. Belkin, and Z. Zalevsky, Proc. SPIE 7550, 75500A (2010).
[CrossRef]

Curr. Opin. Ophthalmol. (1)

A. Lichtinger and D. S. Rootman, Curr. Opin. Ophthalmol. 23, 40 (2012).
[CrossRef]

Int. Ophthalmol. Clin. (1)

A. Glasser, M. A. Croft, and P. L. Kaufman, Int. Ophthalmol. Clin. 41, 1 (2001).
[CrossRef]

J. Cataract. Refract. Surg. (1)

D. Gatinel, C. Pagnoulle, Y. Houbrechts, and L. Gobin, J. Cataract. Refract. Surg. 37, 2060 (2011).
[CrossRef]

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

J. Vis. (3)

P. de Gracia, C. Dorronsoro, G. Marin, M. Hernández, and S. Marcos, J. Vis. 11(2), 5 (2011).
[CrossRef]

X. Cheng, A. Bradley, and L. N. Thibos, J. Vis. 4(4), 310 (2004).

J. D. Marsack, L. N. Thibos, and R. A. Applegate, J. Vis. 4(4), 8 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Optom. Vis. Sci. (4)

D. R. Iskander, Optom. Vis. Sci. 83, 57 (2006).
[CrossRef]

J. A. Martin and A. Roorda, Optom. Vis. Sci. 80, 812 (2003).
[CrossRef]

S. A. Klein and B. A. Barsky, Optom. Vis. Sci. 72, 816 (1995).
[CrossRef]

C. Dorronsoro, S. Barbero, L. Llorente, and S. Marcos, Optom. Vis. Sci. 80, 115 (2003).
[CrossRef]

PLoS ONE (1)

L. Sawides, P. de Gracia, C. Dorronsoro, M. A. Webster, and S. Marcos, PLoS ONE 6, e27031 (2011).
[CrossRef]

Proc. SPIE (1)

A. Zlotnik, I. Raveh, S. Ben Yaish, O. Yehezkel, M. Belkin, and Z. Zalevsky, Proc. SPIE 7550, 75500A (2010).
[CrossRef]

Vis. Res. (3)

F. Yi, D. Robert Iskander, and M. Collins, Vis. Res. 51, 1648 (2011).
[CrossRef]

P. de Gracia, C. Dorronsoro, E. Gambra, G. Marin, M. Hernández, and S. Marcos, Vis. Res. 50, 2008 (2010).
[CrossRef]

Y. Benard, N. Lopez-Gil, and R. Legras, Vis. Res. 51, 2471 (2011).
[CrossRef]

Other (4)

W. Fiala and M. Gerlach, “Multifocal lens,” U.S. patent application20130050640 (October28, 2012).

B. F. M. W. Angerlo and B. J. W. Arnhem, “Ophthalmic lens with optical sectors,” U.S. patent application20120029631 A1 (May9, 2012).

M. Bass, ed., Handbook of Optics, 3rd ed. (Optical Society of America, 1995), Vol. 3, Chap. 21.

D. Fernández, S. Barbero, C. Dorronsoro, and S. Marcos, “Multifocal intraocular lens providing improved,” Spanish patentP201232043 (December27, 2012).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

WT for different numbers of angular (top row) and radial (lower row) zones. Maps are represented considering only defocus in angular and radial designs. Values of [n1,n2,Φ] are shown for each pattern.

Fig. 2.
Fig. 2.

DOF versus area under the visual Strehl through-focus curves, for phase patterns with N angular (blue circles) and radial (red triangles) zones (N ranges from 1 to 50). The labels next to each spot stand for the number of zones of the corresponding design. Area under the visual Strehl is normalized by the area of the bifocal angular design. Data are for 4 mm pupil diameter.

Fig. 3.
Fig. 3.

Visual Strehl value as a function of defocus for phase patterns generated with 2, 3, 4, 5, 10, 20, 30, 40, and 50 zones. Left panel: phase patterns with angular zones. Right panel: phase patterns with radial zones and C04=0.4μm. Data are for 4 mm pupil diameter.

Fig. 4.
Fig. 4.

Left column: Zernike coefficients of the wave aberration in each zone for each of the six multifocal phase patterns. Right column: multifocal phase patterns generated by the combination of high- and low-order aberrations. Data are for 4 mm pupil diameters.

Fig. 5.
Fig. 5.

(A) Through-focus visual Strehl for the six different multifocal designs described in Fig. 4 (corresponding colors) with multiple zones and different combinations of aberrations in each zone. The gray line represents values for a 1-zone multifocal pattern with spherical aberration (0.22 μm). (B) DOF versus area under the visual Strehl through-focus curves for the six designs described in Fig. 4. Area is normalized by that of the bifocal angular design. Data are for 4 mm pupil diameters.

Equations (4)

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

Di=Df+(DnDfN)(i1),
WT=i=1Nwi(Di)*σjl,
σjl(ρ,θ)=1ρ[ρmln1,ρm(l+1)n1],0otherwise,
σjl(ρ,θ)=1θ[2πjn2,2π(j+1)n2]+Φ,0otherwise

Metrics