Abstract

The aim of this paper is to compare the properties of four different profiles which can be used as multifocal intraocular lens. The Hankel transform based on the theory of scalar diffraction is applied to a binary profile, a parabolic one, a parabolic profile with holes, and finally a sinusoidal one. This enables to study the various distributions of the diffractive efficiencies and the axial chromatism. The image quality is evaluated by means of simulations of the MTFs with Zemax®. Finally we propose a new way to graphically synthesize all the properties of these lenses, using a radar graph.

© 2010 OSA

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References

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  1. J. A. Davison and M. J. Simpson, “History and development of the apodized diffractive intraocular lens,” J. Cataract Refract. Surg. 32(5), 849–858 (2006).
    [CrossRef] [PubMed]
  2. A. L. Cohen, “Diffractive bifocal lens designs,” Optom. Vis. Sci. 6, 461–468 (1993).
    [CrossRef]
  3. V. Moreno, J. F. Roman, and J. R. Salguerio, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65(6), 556–562 (1997).
    [CrossRef]
  4. B. Kress, and P. Meyrueis, Digital Diffractive Optics: An introduction to planar diffractive optics and related technology (John Wiley and Sons, 2000).
  5. D. Baude, PhD-thesis, “Caractérisation, optimisation et réalisation de composants optiques multifocaux diffractifs et réfractifs,” Université Paris-Sud, centre d’Orsay, France (1990).
  6. A. L. Cohen, “Progressive intensity phase bifocal,” US patent application 438,320 (November 1989).
  7. M. Guizar-Sicairos and J. C. Gutiérrez-Vega, “Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields,” J. Opt. Soc. Am. A 21(1), 53 (2004).
    [CrossRef]
  8. A. Lang and V. Portney, “Interpreting multifocal intraocular lens modulation transfer functions,” J. Cataract Refract. Surg. 19(4), 505–512 (1993).
    [PubMed]
  9. A. L. Cohen, “Diffraction bifocal with adjusted chromaticity,” US patent application 553,336 (July 1990).
  10. A. L. Cohen, “Diffractive multifocal optical device,” US patent application 456,226 (December 1989).
  11. 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(19), 3594–3600 (1992).
    [CrossRef] [PubMed]

2006 (1)

J. A. Davison and M. J. Simpson, “History and development of the apodized diffractive intraocular lens,” J. Cataract Refract. Surg. 32(5), 849–858 (2006).
[CrossRef] [PubMed]

2004 (1)

1997 (1)

V. Moreno, J. F. Roman, and J. R. Salguerio, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65(6), 556–562 (1997).
[CrossRef]

1993 (2)

A. Lang and V. Portney, “Interpreting multifocal intraocular lens modulation transfer functions,” J. Cataract Refract. Surg. 19(4), 505–512 (1993).
[PubMed]

A. L. Cohen, “Diffractive bifocal lens designs,” Optom. Vis. Sci. 6, 461–468 (1993).
[CrossRef]

1992 (1)

Bradley, A.

Cohen, A. L.

A. L. Cohen, “Diffractive bifocal lens designs,” Optom. Vis. Sci. 6, 461–468 (1993).
[CrossRef]

Davison, J. A.

J. A. Davison and M. J. Simpson, “History and development of the apodized diffractive intraocular lens,” J. Cataract Refract. Surg. 32(5), 849–858 (2006).
[CrossRef] [PubMed]

Guizar-Sicairos, M.

Gutiérrez-Vega, J. C.

Lang, A.

A. Lang and V. Portney, “Interpreting multifocal intraocular lens modulation transfer functions,” J. Cataract Refract. Surg. 19(4), 505–512 (1993).
[PubMed]

Moreno, V.

V. Moreno, J. F. Roman, and J. R. Salguerio, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65(6), 556–562 (1997).
[CrossRef]

Portney, V.

A. Lang and V. Portney, “Interpreting multifocal intraocular lens modulation transfer functions,” J. Cataract Refract. Surg. 19(4), 505–512 (1993).
[PubMed]

Roman, J. F.

V. Moreno, J. F. Roman, and J. R. Salguerio, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65(6), 556–562 (1997).
[CrossRef]

Salguerio, J. R.

V. Moreno, J. F. Roman, and J. R. Salguerio, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65(6), 556–562 (1997).
[CrossRef]

Simpson, M. J.

J. A. Davison and M. J. Simpson, “History and development of the apodized diffractive intraocular lens,” J. Cataract Refract. Surg. 32(5), 849–858 (2006).
[CrossRef] [PubMed]

Thibos, L. N.

Ye, M.

Zhang, X.

Am. J. Phys. (1)

V. Moreno, J. F. Roman, and J. R. Salguerio, “High efficiency diffractive lenses: Deduction of kinoform profile,” Am. J. Phys. 65(6), 556–562 (1997).
[CrossRef]

Appl. Opt. (1)

J. Cataract Refract. Surg. (2)

J. A. Davison and M. J. Simpson, “History and development of the apodized diffractive intraocular lens,” J. Cataract Refract. Surg. 32(5), 849–858 (2006).
[CrossRef] [PubMed]

A. Lang and V. Portney, “Interpreting multifocal intraocular lens modulation transfer functions,” J. Cataract Refract. Surg. 19(4), 505–512 (1993).
[PubMed]

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

Optom. Vis. Sci. (1)

A. L. Cohen, “Diffractive bifocal lens designs,” Optom. Vis. Sci. 6, 461–468 (1993).
[CrossRef]

Other (5)

A. L. Cohen, “Diffraction bifocal with adjusted chromaticity,” US patent application 553,336 (July 1990).

A. L. Cohen, “Diffractive multifocal optical device,” US patent application 456,226 (December 1989).

B. Kress, and P. Meyrueis, Digital Diffractive Optics: An introduction to planar diffractive optics and related technology (John Wiley and Sons, 2000).

D. Baude, PhD-thesis, “Caractérisation, optimisation et réalisation de composants optiques multifocaux diffractifs et réfractifs,” Université Paris-Sud, centre d’Orsay, France (1990).

A. L. Cohen, “Progressive intensity phase bifocal,” US patent application 438,320 (November 1989).

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Figures (8)

Fig. 1
Fig. 1

the four diffractive profiles studied in this paper. (A) Binary profile; (B) Parabolic profile; (C) Parabolic profile with holes; (D) Sinusoidal profile.

Fig. 2
Fig. 2

Distribution of the diffractive efficiencies at 550 nm for the four different lenses. (A) Parabolic profile; (B) Parabolic profile with holes; (C) Sinusoidal profile; (D) Binary profile

Fig. 3
Fig. 3

Optical system used in the simulation of the MTF with Zemax® for near and far objects.

Fig. 4
Fig. 4

MTF of the four profiles at 550 nm, for near (A) and far object (B).

Fig. 5
Fig. 5

Variations of the diffractive efficiencies versus λ

Fig. 6
Fig. 6

MTFs for the near and far vision, at 440 nm and 640 nm.

Fig. 7
Fig. 7

radar graphs for the four different profiles.

Fig. 8
Fig. 8

Superimposition of the radar graphs for the four different profiles.

Tables (1)

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Table 1 Variation of the convergent focal length with wavelength.

Equations (14)

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R ( k ) = 2 k f λ
R ' ( k ) = k f λ , k o d d
h max = 0.5 λ Δ n
h ' max = 0.415 λ Δ n
h ( r ) = { h max i f R ' ( k ) < r < R ' ( k + 1 ) , k e v e n 0 i f R ' ( k + 1 ) < r < R ' ( k + 2 ) , k e v e n
h ( r ) = h max k h max r 2 R ( 1 ) 2 , k Ν
h ( r ) = { h max ( k 1 + α ² α ² ) h max r 2 α ² R ( 1 ) 2 i f R ' ( k ) < r < R ' ( k + 1 ) , k e v e n , α ² = 0.5 0 i f R ' ( k + 1 ) < r < R ' ( k + 2 ) , k e v e n
h ( r ) = h ' max 2 { 1 ( 1 ) k cos ( π r 2 R ( 1 ) 2 ) }
t ( r ) = p Z C p exp ( 2 i π p . r ² R ( 1 ) ² )
C p = 1 R ( 1 ) ² 0 R ( 1 ) ² t ( r ) exp ( 2 i π p u R ( 1 ) ² ) d u
η p = | C p ² |
d λ λ = 640 440 550 = 0.364
d Δ n Δ n = [ n ( 640 ) n a i r ] [ n ( 440 ) n a i r ] [ n ( 550 ) n a i r ] = ( 1.581 1.610 ) 1.590 1 = 0.049
P = P 0 λ λ 0 Δ P = Δ λ λ P

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