Abstract

The ophthalmic applications of a diffractive trifocal lens design with adjustable add powers and light distribution in the foci are investigated. Axial PSFs of the trifocal lenses are calculated and analyzed as a function of the design parameters and the eye pupil size. The optical performance in actual eyes is also simulated by including the measured ocular wave aberration functions of human eyes in the calculation of transverse and axial PSFs, and Strehl ratio axial variation. The effect of the polychromatic character of natural light has also been considered. The calculus and simulation method of this paper can be applied for the design and analysis of any other kind of diffractive or refractive multifocal contact or intraocular lens.

© 2005 Optical Society of America

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References

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  1. A. L. Cohen, �??Practical design of a bifocal hologram contact lens or intraocular lens,�?? Appl. Opt. 31, 3750-3754 (1992).
    [CrossRef] [PubMed]
  2. A. L. Cohen, �??Diffractive bifocal lens designs,�?? Optom. Vis. Sci. 70, 461-468 (1993).
    [CrossRef] [PubMed]
  3. S. A. Klein, �??Understanding the diffractive bifocal contact lens,�?? Optom. Vis. Sci. 70, 439-460 (1993).
    [CrossRef] [PubMed]
  4. G. M. Morris and L. T. Nordan, �??Phakic intraocular lenses,�?? Opt. Photon News, 15 nº 9, 26-31 (2004). <a href="http://www.osa- pn.org/abstract.cfm?URI=OPN-15-9-26.">http://www.osa- pn.org/abstract.cfm?URI=OPN-15-9-26</a>
    [CrossRef]
  5. N. Chateau and D. Baude, �??Simulated in situ optical performance of bifocal contact lenses,�?? Optom. Vis. Sci. 74, 532-539 (1997).
    [CrossRef] [PubMed]
  6. M. Larsson, C. Beckman, A. Nyström, S. Hård, and J. Sjöstrand, �??Optical properties of diffractive, bifocal, intraocular lenses,�?? Appl. Opt. 31, 2377-84 (1992).
    [CrossRef] [PubMed]
  7. M. J. Simpson, �??Diffractive multifocal intraocular lens image quality,�?? Appl. Opt. 31, 3621-3626 (1992).
    [CrossRef] [PubMed]
  8. D. A. Atchison and L. N. Thibos, �??Diffractive properties of the Diffrax bifocal contact lens,�?? Ophthalmic Physiol. Opt. 13, 186-188 (1993).
    [CrossRef] [PubMed]
  9. S. Pieh , P. Marvan, B. Lackner, G. Hanselmayer, G. Schmidinder, 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]
  10. J. L. Alió, M. Tovalato, F. de la Hoz, P. Claramonte, J.-L. Rodríguez-Prats, and A. Galal, �??Near vision restoration with refractive lens exchange and pseudoaccommodating and multifocal refractive and diffractive intraocular lenses,�?? J. Cataract Refract. Surg. 30, 2494-2503 (2004).
    [CrossRef] [PubMed]
  11. M. Golub and I. Grossinger, �??Diffractive optical elements for biomedical applications.�?? <a href="http://www.holoor.co.il/data/ready2/publications/Biospape.pdf.">http://www.holoor.co.il/data/ready2/publications/Biospape.pdf</a>
  12. Basics and Clinical Science Course Section 3: Optics, Refraction, and Contact Lenses, (American Academy of Ophthalmology, San Francisco, 2002).
  13. M. W. Farn and W. B. Veldkamp, �??Binary Optics�?? in Handbook of Optics Vol. II, M. Bass, ed. (McGraw-Hill, New York, 1995), pp. 8.1-8.19.
  14. M. Born and E. Wolf, Principles of Optics (University Press, Cambridge, UK, 1999).
  15. L. N. Thibos, R. A. Applegate, J. T. Schweigerling, R. Webb, and VSIA Standards Taskforce members, Standards for Reporting the Optical Aberration of Eyes, Vol 35 of OSA Topics in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp.232-244.
  16. J. A. Martin and A. Roorda, �??Predicting and assessing visual performance with multizone bifocal contact lenses,�?? Optom. Vis. Sci. 80, 812-819 (2003).
    [CrossRef] [PubMed]
  17. M. P. Cagigal, V. F. Canales, J. F. Castejón-Mochón, P. M. Prieto, N. López-Gil, and P. Artal, �??Statistical description of wave-front aberration in the human eye,�?? Opt. Lett. 27, 37-39 (2002).
    [CrossRef]
  18. L. N. Thibos, X. Hong, A. Bradley, and R. A: Applegate, �??Accuracy and precision of objective refraction from wavefront aberrations,�?? J. Vis. 4, 329-351 (2004). <a href="http://journalofvision.org/4/4/9/. ">http://journalofvision.org/4/4/9/.</a>
    [CrossRef] [PubMed]
  19. J. D. Marsack, L. N. Thibos, and R. A. Applegate, �??Metrics of optical quality derived from wave aberrations predict visual performance,�?? J. Vis. 4, 322-328 (2004). <a href="http://journalofvision.org/4/4/8/."> http://journalofvision.org/4/4/8/</a>
    [CrossRef] [PubMed]
  20. R. Navarro, M. Ferro, P. Artal, and I. Miranda, �??Modulation transfer functions of eye implanted with intraocular lens,�?? Appl. Opt. 32, 6359-6367 (1993).
    [CrossRef] [PubMed]
  21. L. N. Thibos, Y. Ming, 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]

Appl. Opt.

Arch. Ophthalmol.

S. Pieh , P. Marvan, B. Lackner, G. Hanselmayer, G. Schmidinder, 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. Cataract Refract. Surg.

J. L. Alió, M. Tovalato, F. de la Hoz, P. Claramonte, J.-L. Rodríguez-Prats, and A. Galal, �??Near vision restoration with refractive lens exchange and pseudoaccommodating and multifocal refractive and diffractive intraocular lenses,�?? J. Cataract Refract. Surg. 30, 2494-2503 (2004).
[CrossRef] [PubMed]

J. Vis.

L. N. Thibos, X. Hong, A. Bradley, and R. A: Applegate, �??Accuracy and precision of objective refraction from wavefront aberrations,�?? J. Vis. 4, 329-351 (2004). <a href="http://journalofvision.org/4/4/9/. ">http://journalofvision.org/4/4/9/.</a>
[CrossRef] [PubMed]

J. D. Marsack, L. N. Thibos, and R. A. Applegate, �??Metrics of optical quality derived from wave aberrations predict visual performance,�?? J. Vis. 4, 322-328 (2004). <a href="http://journalofvision.org/4/4/8/."> http://journalofvision.org/4/4/8/</a>
[CrossRef] [PubMed]

Ophthalmic Physiol. Opt.

D. A. Atchison and L. N. Thibos, �??Diffractive properties of the Diffrax bifocal contact lens,�?? Ophthalmic Physiol. Opt. 13, 186-188 (1993).
[CrossRef] [PubMed]

Opt. Lett.

Opt. Photon News

G. M. Morris and L. T. Nordan, �??Phakic intraocular lenses,�?? Opt. Photon News, 15 nº 9, 26-31 (2004). <a href="http://www.osa- pn.org/abstract.cfm?URI=OPN-15-9-26.">http://www.osa- pn.org/abstract.cfm?URI=OPN-15-9-26</a>
[CrossRef]

Optom. Vis. Sci.

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

A. L. Cohen, �??Diffractive bifocal lens designs,�?? Optom. Vis. Sci. 70, 461-468 (1993).
[CrossRef] [PubMed]

S. A. Klein, �??Understanding the diffractive bifocal contact lens,�?? Optom. Vis. Sci. 70, 439-460 (1993).
[CrossRef] [PubMed]

J. A. Martin and A. Roorda, �??Predicting and assessing visual performance with multizone bifocal contact lenses,�?? Optom. Vis. Sci. 80, 812-819 (2003).
[CrossRef] [PubMed]

OSA Topics in Optics and Photonics Serie

L. N. Thibos, R. A. Applegate, J. T. Schweigerling, R. Webb, and VSIA Standards Taskforce members, Standards for Reporting the Optical Aberration of Eyes, Vol 35 of OSA Topics in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp.232-244.

Other

M. Golub and I. Grossinger, �??Diffractive optical elements for biomedical applications.�?? <a href="http://www.holoor.co.il/data/ready2/publications/Biospape.pdf.">http://www.holoor.co.il/data/ready2/publications/Biospape.pdf</a>

Basics and Clinical Science Course Section 3: Optics, Refraction, and Contact Lenses, (American Academy of Ophthalmology, San Francisco, 2002).

M. W. Farn and W. B. Veldkamp, �??Binary Optics�?? in Handbook of Optics Vol. II, M. Bass, ed. (McGraw-Hill, New York, 1995), pp. 8.1-8.19.

M. Born and E. Wolf, Principles of Optics (University Press, Cambridge, UK, 1999).

Supplementary Material (3)

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Figures (11)

Fig. 1.
Fig. 1.

Geometry and coordinates of the focusing problem.

Fig. 2.
Fig. 2.

Axial PSF of a trifocal lens with 2D add power (pbase =0). The zero position corresponds to the eye focal point and the z axis is expressed in added diopters (Eq. (7)), so increasing z coordinate corresponds to decreasing add power. PSF normalization has been done by setting the PSF maximum of the eye without diffractive lens equals to one.

Fig. 3.
Fig. 3.

Trifocal lens phase profile radial cross-section following Eq. 6 (a=1.724 mm-2, b=0.127µm, pbase =0, and R=3.5 mm). Phase is in π units.

Fig. 4.
Fig. 4.

Axial PSF of a trifocal lens (2D add power, pbase =0) for three eye pupil diameters: 7 (green), 5 (red), and 3 (blue) mm. Each PSF is normalized with the corresponding PSF for the same pupil size without lens.

Fig. 5.
Fig. 5.

Axial PSF of a trifocal lens with 2D add power and pbase =2D (a=1.724 mm-2, b=0.127µm, R=3.5 mm).

Fig. 6.
Fig. 6.

Movie representation of axial PSFs of trifocal lenses with foci distance in the range 0.5 to 3 diopters (parameter a is in the range 0.445 to 2.531 mm-2, b=0.127 µm, and R=3.5 mm) (84KB).

Fig. 7.
Fig. 7.

Movie representation of axial PSFs of trifocal lenses with parameter b in the range 0.103 to 0.149 µm (a=1.724 mm-2 and R=3.5 mm), (24KB).

Fig. 8.
Fig. 8.

(Blue line) Axial PSF calculated from measured aberration function of an actual eye. (a) uncorrected eye and (b) astigmatism corrected eye. For comparison, ideal aberration-free axial PSF is drawn with red line. (Pupil radius 3.5 mm and focal length 22.6 mm).

Fig. 9.
Fig. 9.

Calculated Strehl ratio of the same eye as in Fig. 8(b) but while wearing a trifocal lens of 2D add power and pbase =1.25D (a=1.724 mm-2, b=0.127µm, and R=3.5 mm).

Fig. 10.
Fig. 10.

Transverse PSF calculated from measured aberration function of an actual eye. (left) focal plane of the naked eye, (right) axial variation of the eye with a 2D add power trifocal diffractive lens. u is the axial coordinate and SR the Strehl ratio of each transverse PSF. [Media 3]

Fig. 11.
Fig. 11.

Axial PSF of the same trifocal lens (a=1.724 mm-2, h 0=0.104µm, pbase =2D, and R=3.5 mm) for three different wavelengths, 450 nm (blue), 540 nm (green), and 580 nm (yellow/red).

Equations (12)

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A ( ν , φ , u ) = A 0 1 2 π 0 2 π 0 1 P ( ρ , θ ) exp [ i k ( ν ρ cos ( θ φ ) + 1 2 u ρ 2 ) ] 2 ρ d ρ d θ ,
A ( u ) = A 0 1 2 π 0 1 { 0 2 π P ( ρ , θ ) d θ } exp [ i k 1 2 u ρ 2 ] 2 ρ d ρ .
h ( ρ ) = h 0 cos ( 2 π a R 2 ρ 2 ) ,
h opt ( ρ ) = ( n 2 n 1 ) h 0 cos ( 2 π a R 2 ρ 2 ) = b cos ( 2 π a R 2 ρ 2 ) ,
P lens ( ρ ) = exp [ i Φ lens ( ρ ) ] ,
Φ lens ( ρ ) = k [ b cos ( 2 π a R 2 ρ 2 ) p base ( R 2 ρ 2 2 ) ] .
p a = ( f + Δ f ) 1 ( f ) 1 ,
p a = u R 2 + f u .
Φ eye ( ρ , θ ) = k j c j Z j ( ρ , θ ) ,
P eye ( ρ , θ ) = exp [ i Φ eye ( ρ , θ ) ] and P ( ρ , θ ) = P lens ( ρ ) P eye ( ρ , θ ) .
A ( ν , u f ) = A 0 0 1 P lens ( ρ ) J 0 ( k ν ρ ) exp [ i k 1 2 u f ρ 2 ) ] 2 ρ d ρ ,
a = p a 2 λ ( 1 + f p a ) p a 2 λ .

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