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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 9 — Apr. 25, 2011
  • pp: 8693–8699
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Strehl ratios characterizing optical elements designed for presbyopia compensation

K. Petelczyc, J. Ares García, S. Bará, Z. Jaroszewicz, K. Kakarenko, A. Kolodziejczyk, and M. Sypek  »View Author Affiliations


Optics Express, Vol. 19, Issue 9, pp. 8693-8699 (2011)
http://dx.doi.org/10.1364/OE.19.008693


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Abstract

We present results of numerical analysis of the Strehl ratio characteristics for the light sword optical element (LSOE). For comparison there were analyzed other optical imaging elements proposed for compensation of presbyopia such as the bifocal lens, the trifocal lens, the stenopeic contact lens, and elements with extended depth of focus (EDOF), such as the logarithmic and quartic axicons. The simulations were based on a human eye’s model being a simplified version of the Gullstrand model. The results obtained allow to state that the LSOE exhibits much more uniform characteristics of the Strehl ratio comparing with other known hitherto elements and therefore it could be a promising aid to compensate for the insufficient accommodation range of the human eye.

© 2011 OSA

1. Introduction

2. Eye model

The schematic eye model, which will be used for simulations, on one hand must be sufficiently simple, whereas on the other one it should offer adequate simulation’s accuracy. Our starting point was the Gullstrand eye model without accomodation [26

26. A. Valberg, Light Vision Color (John Wiley & Sons, 2005).

], [27

27. H. Gross, F. Blechinger, and B. Achtner, Handbook of Optical Systems, Vol. 4, Survey of Optical Instruments (Wiley-VCH, 2008).

].

In our analysis we limit our attention to the foveal region. It allows to relieve the computational effort of the simulation and to use the paraxial approximation for the optical elements composing the model. Our assumption is justified because this retina’s area allows to obtain vision of highest resolution and quality.

Our approximation allows also to simplify the presbyopic eye’s model to the set-up shown in Fig. 1
Fig. 1 Eye model assumed in the modeling and its parameters. Gullstrand unaccommodated eye geometry in a background.
, where the cornea is represented by a lens of 43 D placed 5.38 mm in front of the second lens substituting a presbyopic eye with optical power equal to 19.2 D. The distance between the retinal plane and the second lens is assumed to be 18.76 mm. The refraction index value of the liquid between the cornea, the lens and the retina is taken as 1.336. The pupil and the contact lens representing the optical element compensating presbyopia are placed in front of the first lens substituting the cornea.

3. Presbyopia compensating elements

Δl(r,θ)=Cr2+Dθr2,whereC=1/2f1D=14π(1f11f1+Δf),
(2)

The shape of the LSOE and aLSOE elements together with their focusing geometry is shown in Fig. 2
Fig. 2 Shape of the LSOE and aLSOE elements and their scheme of imaging. The infinitesimal angular sector of the element images object from different distance (a). Element has a sharp step in geometrical profile (b) equal to shape’s maximum difference between 0D and 4D lens(c).
. Every infinitesimal sector of these elements is supposed to focus light into the corresponding point situated within the focal segment. However, focusing is approximate only and in reality instead of point focus we observe a small focal segment perpendicular to the optical axis [24

24. J. Ares García, S. Bará, M. Gomez García, Z. Jaroszewicz, A. Kolodziejczyk, and K. Petelczyc, “Imaging with extended focal depth by means of the refractive light sword optical element,” Opt. Express 16(22), 18371–18378 (2008). [CrossRef] [PubMed]

].

Distributions of dioptric powers of all elements compared in this work are shown in Fig. 3
Fig. 3 Optical elements used in simulation. Their diameter was assumed to be equal to 8 mm. The used abbreviations were explained in the text. The optical power corresponding to different areas is marked with the color bar.
.

3. Results of simulation

In order to compare the performance of the elements intended for presbyopia compensation, the Strehl ratio was chosen. It can range from 0 to 1 and is defined as the ratio of the peak intensity of the eye’s PSF IMax,Φ to that of a diffraction limited PSF IMax,Φ=0 for an aberration-free eye (i.e., for Φ=0) with the same pupil size [34

34. V. Mahajan, Aberration theory made simple, (SPIE Press, 1991).

]:

S=IMax,Φ/IMax,Φ=0
(3)

The results were obtained by using the numerical software for diffraction simulation [28

28. M. Sypek, “Light propagation in the Fresnel region. New numerical approach,” Opt. Commun. 116(1-3), 43–48 (1995). [CrossRef]

], [29

29. M. Sypek, C. Prokopowicz, and M. Gorecki, “Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation,” Opt. Eng. 42(11), 3158–3164 (2003). [CrossRef]

] with use of monochromatic light of wavelenghth 555 nm coresponding to maximum sensitivity of photopic vision [26

26. A. Valberg, Light Vision Color (John Wiley & Sons, 2005).

]. Images of the point sources placed at distances corresponding to values of defocus from 0 till 4 D were calculated at the retinal plane after passing the compensating element and two lenses located as it was shown in Fig. 1. The whole procedure of Strehl ratio determination was as follows: generation of diverging spherical wave corresponding to the defocus value of the plot, multiplication by the transmittance of the element correcting the presbyopia, multiplication by the transmittance of cornea and an amplitude distribution equal to exp(−0.053r2) corresponding to the Stiles-Crawford effect, propagation by a distance of 5,4 mm in a medium with refraction index equal to 1,336, multiplication by the transmittance of the eye lens, and propagation to the retina by a distance of 18,76 mm. Then the Strehl ratio was obtained by finding the maximum value of the PSF obtained in the above way and its division by the analogous value for PSF obtained without correcting element and with zero defocus.

4. Conclusions

Acknowledgment

This work was supported by the Polish Ministry of Science and Higher Education under grants N N 514 149038 and N N 518 378237 as well as by the European Social Fund implemented under the Human Capital Operational Programme (POKL), project: “Preparation and Realization of Medical Physics Specialty” with complementary support from the Spanish Ministerio de Ciencia e Innovación (MICINN) grant FIS2008-03884.

References and links

1.

P. Artal and J. Tabernero, “Optics of human eye: 400 years of exploration from Galileo’s time,” Appl. Opt. 49(16), D123–D130 (2010). [CrossRef] [PubMed]

2.

B. K. Pierscionek, “What we know and understand about presbyopia,” Clin. Exp. Optom. 76(3), 83–90 (1993). [CrossRef]

3.

A. Glasser, M. A. Croft, and P. L. Kaufman, “Aging of the human crystalline lens and presbyopia,” Int. Ophthalmol. Clin. 41(2), 1–15 (2001). [CrossRef] [PubMed]

4.

A. W. Lohmann and D. P. Paris, “Variable Fresnel zone pattern,” Appl. Opt. 6(9), 1567–1570 (1967). [CrossRef] [PubMed]

5.

A. Kolodziejczyk and Z. Jaroszewicz, “Diffractive elements of variable optical power and high diffraction efficiency,” Appl. Opt. 32(23), 4317–4322 (1993). [CrossRef] [PubMed]

6.

A. N. Simonov, G. Vdovin, and M. C. Rombach, “Cubic optical elements for an accommodative intraocular lens,” Opt. Express 14(17), 7757–7775 (2006). [CrossRef] [PubMed]

7.

A. N. Simonov, G. Vdovin, and M. Loktev, “Liquid-crystal intraocular adaptive lens with wireless control,” Opt. Express 15(12), 7468–7478 (2007). [CrossRef] [PubMed]

8.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006). [CrossRef] [PubMed]

9.

G. Li, P. Valley, P. Äyräs, D. L. Mathine, S. Honkanen, and N. Peyghambarian, “High-efficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures,” Appl. Phys. Lett. 90(11), 111105 (2007). [CrossRef]

10.

R. Menapace, O. Findl, K. Kriechbaum, and Ch. Leydolt-Koeppl, “Accommodating intraocular lenses: a critical review of present and future concepts,” Graefes Arch. Clin. Exp. Ophthalmol. 245(4), 473–489 (2007). [CrossRef]

11.

W. Zhang, K. Aljasem, H. Zappe, and A. Seifert, “Completely integrated, thermo-pneumatically tunable microlens,” Opt. Express 19(3), 2347–2362 (2011). [CrossRef] [PubMed]

12.

W. Qiao, D. Johnson, F. S. Tsai, S. H. Cho, and Y.-H. Lo, “Bio-inspired accommodating fluidic intraocular lens,” Opt. Lett. 34(20), 3214–3216 (2009). [CrossRef] [PubMed]

13.

H. Lesiewska-Junk and J. Kałuzny, “Intraocular lens movement and accommodation in eyes of young patients,” J. Cataract Refract. Surg. 26(4), 562–565 (2000). [CrossRef] [PubMed]

14.

O. Findl, B. Kiss, V. Petternel, R. Menapace, M. Georgopoulos, G. Rainer, and W. Drexler, “Intraocular lens movement caused by ciliary muscle contraction,” J. Cataract Refract. Surg. 29(4), 669–676 (2003). [CrossRef] [PubMed]

15.

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]

16.

B. Żelichowska, M. Rękas, A. Stankiewicz, A. Cerviño, and R. Montés-Micó, “Apodized diffractive versus refractive multifocal intraocular lenses: optical and visual evaluation,” J. Cataract Refract. Surg. 34(12), 2036–2042 (2008). [CrossRef] [PubMed]

17.

P. J. Valle, J. E. Oti, V. F. Canales, and M. P. Cagigal, “Visual axial PSF of diffractive trifocal lenses,” Opt. Express 13(7), 2782–2792 (2005). [CrossRef] [PubMed]

18.

J. Sochacki, A. Kołodziejczyk, Z. Jaroszewicz, and S. Bara, “Nonparaxial design of generalized axicons,” Appl. Opt. 31(25), 5326–5330 (1992). [CrossRef] [PubMed]

19.

W. Chi and N. George, “Electronic imaging using a logarithmic asphere,” Opt. Lett. 26(12), 875–877 (2001). [CrossRef]

20.

J. Ares, R. Flores, S. Bara, and Z. Jaroszewicz, “Presbyopia compensation with a quartic axicon,” Optom. Vis. Sci. 82(12), 1071–1078 (2005). [CrossRef] [PubMed]

21.

E. R. Dowski, Jr., andW. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34(11), 1859–1866 (1995). [CrossRef] [PubMed]

22.

A. Kolodziejczyk, S. Bara, Z. Jaroszewicz, and M. Sypek, “The light sword optical element – a new diffraction structure with extended depth of focus,” J. Mod. Opt. 37(8), 1283–1286 (1990). [CrossRef]

23.

G. Mikuła, Z. Jaroszewicz, A. Kolodziejczyk, K. Petelczyc, and M. Sypek, “Imaging with extended focal depth by means of lenses with radial and angular modulation,” Opt. Express 15(15), 9184–9193 (2007). [CrossRef] [PubMed]

24.

J. Ares García, S. Bará, M. Gomez García, Z. Jaroszewicz, A. Kolodziejczyk, and K. Petelczyc, “Imaging with extended focal depth by means of the refractive light sword optical element,” Opt. Express 16(22), 18371–18378 (2008). [CrossRef] [PubMed]

25.

K. Petelczyc, J. Ares Garcia, S. Bará, Z. Jaroszewicz, A. Kolodziejczyk, and M. Sypek, “Presbyopia compensation with a light sword optical element of a variable diameter,” Phot. Lett. Poland 1, 55–57 (2009).

26.

A. Valberg, Light Vision Color (John Wiley & Sons, 2005).

27.

H. Gross, F. Blechinger, and B. Achtner, Handbook of Optical Systems, Vol. 4, Survey of Optical Instruments (Wiley-VCH, 2008).

28.

M. Sypek, “Light propagation in the Fresnel region. New numerical approach,” Opt. Commun. 116(1-3), 43–48 (1995). [CrossRef]

29.

M. Sypek, C. Prokopowicz, and M. Gorecki, “Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation,” Opt. Eng. 42(11), 3158–3164 (2003). [CrossRef]

30.

S. Wittenberg, “Pinhole eyewear systems: a special report,” J. Am. Optom. Assoc. 64(2), 112–116 (1993). [PubMed]

31.

J. L. Breger, “Pinhole presbyopic contact lenses,” US Patent 6,283,595 (April 04 2001).

32.

J. T. De Carle, “Bifocal contact lenses,” US Patent 4,704,016 (March 11 1987).

33.

J. H. Roffman, T. R. Poling, and M. Guillon, “Pupil-tuned multifocal ophthalmic lens,” US Patent 5,448,312 (May 09 1995).

34.

V. Mahajan, Aberration theory made simple, (SPIE Press, 1991).

35.

B. W. Wang and K. J. Ciuffreda, “Depth-of-focus of the human eye: theory and clinical implications,” Surv. Ophthalmol. 51(1), 75–85 (2006). [CrossRef] [PubMed]

36.

D. R. Williams, G. Y. Yoon, A. Guirao, H. Hofer, and J. Porter, “How far can we extend the limits of human vision,” in Customized corneal ablation: the quest for super vision, S.M. MacRae, R.R. Krueger, and R.A. Applegate, eds. (Slack, 2001), pp.11–32.

37.

P. Artal, “Aging effects on the optics of the eye,” in Age-Related Changes of the Human Eye (Aging Medicine), C.A.P. Cavallotti and L. Cerulli, eds. (Humana Press Inc., 2008), pp.35–44.

OCIS Codes
(080.2740) Geometric optics : Geometric optical design
(100.6890) Image processing : Three-dimensional image processing
(110.2990) Imaging systems : Image formation theory
(220.3620) Optical design and fabrication : Lens system design
(330.4060) Vision, color, and visual optics : Vision modeling
(330.7323) Vision, color, and visual optics : Visual optics, aging changes

ToC Category:
Vision, Color, and Visual Optics

History
Original Manuscript: February 16, 2011
Revised Manuscript: March 11, 2011
Manuscript Accepted: April 4, 2011
Published: April 19, 2011

Virtual Issues
Vol. 6, Iss. 5 Virtual Journal for Biomedical Optics

Citation
K. Petelczyc, J. Ares García, S. Bará, Z. Jaroszewicz, K. Kakarenko, A. Kolodziejczyk, and M. Sypek, "Strehl ratios characterizing optical elements designed for presbyopia compensation," Opt. Express 19, 8693-8699 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8693


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References

  1. P. Artal and J. Tabernero, “Optics of human eye: 400 years of exploration from Galileo’s time,” Appl. Opt. 49(16), D123–D130 (2010). [CrossRef] [PubMed]
  2. B. K. Pierscionek, “What we know and understand about presbyopia,” Clin. Exp. Optom. 76(3), 83–90 (1993). [CrossRef]
  3. A. Glasser, M. A. Croft, and P. L. Kaufman, “Aging of the human crystalline lens and presbyopia,” Int. Ophthalmol. Clin. 41(2), 1–15 (2001). [CrossRef] [PubMed]
  4. A. W. Lohmann and D. P. Paris, “Variable Fresnel zone pattern,” Appl. Opt. 6(9), 1567–1570 (1967). [CrossRef] [PubMed]
  5. A. Kolodziejczyk and Z. Jaroszewicz, “Diffractive elements of variable optical power and high diffraction efficiency,” Appl. Opt. 32(23), 4317–4322 (1993). [CrossRef] [PubMed]
  6. A. N. Simonov, G. Vdovin, and M. C. Rombach, “Cubic optical elements for an accommodative intraocular lens,” Opt. Express 14(17), 7757–7775 (2006). [CrossRef] [PubMed]
  7. A. N. Simonov, G. Vdovin, and M. Loktev, “Liquid-crystal intraocular adaptive lens with wireless control,” Opt. Express 15(12), 7468–7478 (2007). [CrossRef] [PubMed]
  8. G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006). [CrossRef] [PubMed]
  9. G. Li, P. Valley, P. Äyräs, D. L. Mathine, S. Honkanen, and N. Peyghambarian, “High-efficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures,” Appl. Phys. Lett. 90(11), 111105 (2007). [CrossRef]
  10. R. Menapace, O. Findl, K. Kriechbaum, and Ch. Leydolt-Koeppl, “Accommodating intraocular lenses: a critical review of present and future concepts,” Graefes Arch. Clin. Exp. Ophthalmol. 245(4), 473–489 (2007). [CrossRef]
  11. W. Zhang, K. Aljasem, H. Zappe, and A. Seifert, “Completely integrated, thermo-pneumatically tunable microlens,” Opt. Express 19(3), 2347–2362 (2011). [CrossRef] [PubMed]
  12. W. Qiao, D. Johnson, F. S. Tsai, S. H. Cho, and Y.-H. Lo, “Bio-inspired accommodating fluidic intraocular lens,” Opt. Lett. 34(20), 3214–3216 (2009). [CrossRef] [PubMed]
  13. H. Lesiewska-Junk and J. Kałuzny, “Intraocular lens movement and accommodation in eyes of young patients,” J. Cataract Refract. Surg. 26(4), 562–565 (2000). [CrossRef] [PubMed]
  14. O. Findl, B. Kiss, V. Petternel, R. Menapace, M. Georgopoulos, G. Rainer, and W. Drexler, “Intraocular lens movement caused by ciliary muscle contraction,” J. Cataract Refract. Surg. 29(4), 669–676 (2003). [CrossRef] [PubMed]
  15. 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]
  16. B. Żelichowska, M. Rękas, A. Stankiewicz, A. Cerviño, and R. Montés-Micó, “Apodized diffractive versus refractive multifocal intraocular lenses: optical and visual evaluation,” J. Cataract Refract. Surg. 34(12), 2036–2042 (2008). [CrossRef] [PubMed]
  17. P. J. Valle, J. E. Oti, V. F. Canales, and M. P. Cagigal, “Visual axial PSF of diffractive trifocal lenses,” Opt. Express 13(7), 2782–2792 (2005). [CrossRef] [PubMed]
  18. J. Sochacki, A. Kołodziejczyk, Z. Jaroszewicz, and S. Bara, “Nonparaxial design of generalized axicons,” Appl. Opt. 31(25), 5326–5330 (1992). [CrossRef] [PubMed]
  19. W. Chi and N. George, “Electronic imaging using a logarithmic asphere,” Opt. Lett. 26(12), 875–877 (2001). [CrossRef]
  20. J. Ares, R. Flores, S. Bara, and Z. Jaroszewicz, “Presbyopia compensation with a quartic axicon,” Optom. Vis. Sci. 82(12), 1071–1078 (2005). [CrossRef] [PubMed]
  21. E. R. Dowski, Jr., andW. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34(11), 1859–1866 (1995). [CrossRef] [PubMed]
  22. A. Kolodziejczyk, S. Bara, Z. Jaroszewicz, and M. Sypek, “The light sword optical element – a new diffraction structure with extended depth of focus,” J. Mod. Opt. 37(8), 1283–1286 (1990). [CrossRef]
  23. G. Mikuła, Z. Jaroszewicz, A. Kolodziejczyk, K. Petelczyc, and M. Sypek, “Imaging with extended focal depth by means of lenses with radial and angular modulation,” Opt. Express 15(15), 9184–9193 (2007). [CrossRef] [PubMed]
  24. J. Ares García, S. Bará, M. Gomez García, Z. Jaroszewicz, A. Kolodziejczyk, and K. Petelczyc, “Imaging with extended focal depth by means of the refractive light sword optical element,” Opt. Express 16(22), 18371–18378 (2008). [CrossRef] [PubMed]
  25. K. Petelczyc, J. Ares Garcia, S. Bará, Z. Jaroszewicz, A. Kolodziejczyk, and M. Sypek, “Presbyopia compensation with a light sword optical element of a variable diameter,” Phot. Lett. Poland 1, 55–57 (2009).
  26. A. Valberg, Light Vision Color (John Wiley & Sons, 2005).
  27. H. Gross, F. Blechinger, and B. Achtner, Handbook of Optical Systems, Vol. 4, Survey of Optical Instruments (Wiley-VCH, 2008).
  28. M. Sypek, “Light propagation in the Fresnel region. New numerical approach,” Opt. Commun. 116(1-3), 43–48 (1995). [CrossRef]
  29. M. Sypek, C. Prokopowicz, and M. Gorecki, “Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation,” Opt. Eng. 42(11), 3158–3164 (2003). [CrossRef]
  30. S. Wittenberg, “Pinhole eyewear systems: a special report,” J. Am. Optom. Assoc. 64(2), 112–116 (1993). [PubMed]
  31. J. L. Breger, “Pinhole presbyopic contact lenses,” US Patent 6,283,595 (April 04 2001).
  32. J. T. De Carle, “Bifocal contact lenses,” US Patent 4,704,016 (March 11 1987).
  33. J. H. Roffman, T. R. Poling, and M. Guillon, “Pupil-tuned multifocal ophthalmic lens,” US Patent 5,448,312 (May 09 1995).
  34. V. Mahajan, Aberration theory made simple, (SPIE Press, 1991).
  35. B. W. Wang and K. J. Ciuffreda, “Depth-of-focus of the human eye: theory and clinical implications,” Surv. Ophthalmol. 51(1), 75–85 (2006). [CrossRef] [PubMed]
  36. D. R. Williams, G. Y. Yoon, A. Guirao, H. Hofer, and J. Porter, “How far can we extend the limits of human vision,” in Customized corneal ablation: the quest for super vision, S.M. MacRae, R.R. Krueger, and R.A. Applegate, eds. (Slack, 2001), pp.11–32.
  37. P. Artal, “Aging effects on the optics of the eye,” in Age-Related Changes of the Human Eye (Aging Medicine), C.A.P. Cavallotti and L. Cerulli, eds. (Humana Press Inc., 2008), pp.35–44.

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