Abstract

The paper analyzes the imaging properties of the light sword optical element (LSOE) applied as a contact lens to the presbyopic human eye. We performed our studies with a human eye model based on the Gullstrand parameterization. In order to quantify the discussion concerning imaging with extended depth of focus, we introduced quantitative parameters characterizing output images of optotypes obtained in numerical simulations. The quality of the images formed by the LSOE were compared with those created by a presbyopic human eye, reading glasses and a quartic inverse axicon. Then we complemented the numerical results by an experiment where a 3D scene was imaged by means of the refractive LSOE correcting an artificial eye based on the Gullstrand model. According to performed simulations and experiments the LSOE exhibits abilities for presbyopia correction in a wide range of functional vision distances.

©2011 Optical Society of America

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References

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  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. Z. Zalevsky, “Extended depth of focus imaging: a review,” SPIE Rev. 1(1), 018001 (2010).
    [Crossref]
  5. A. Kołodziejczyk, 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]
  6. K. Petelczyc, J. A. García, S. Bará, Z. Jaroszewicz, K. Kakarenko, A. Kolodziejczyk, and M. Sypek, “Strehl ratios characterizing optical elements designed for presbyopia compensation,” Opt. Express 19(9), 8693–8699 (2011).
    [Crossref] [PubMed]
  7. A. Valberg, Light Vision Color (Wiley, 2005).
  8. H. Gross, F. Blechinger, and B. Achtner, Handbook of Optical Systems, Vol. 4, Survey of Optical Instruments (Wiley-VCH, 2008).
  9. M. Sypek, “Light propagation in the Fresnel region. New numerical approach,” Opt. Commun. 116(1-3), 43–48 (1995).
    [Crossref]
  10. 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]
  11. 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]
  12. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44(8), 592–597 (1954).
    [Crossref]
  13. Z. Jaroszewicz, Axicons: Design and Propagation Properties, Research & Development Treaties, (SPIE Polish Chapter, Warsaw, 1997), Vol. 5.
  14. J. Sochacki, A. Kołodziejczyk, Z. Jaroszewicz, and S. Bará, “Nonparaxial design of generalized axicons,” Appl. Opt. 31(25), 5326–5330 (1992).
    [Crossref] [PubMed]
  15. W. Chi and N. George, “Electronic imaging using a logarithmic asphere,” Opt. Lett. 26(12), 875–877 (2001).
    [Crossref] [PubMed]
  16. J. Ares, R. Flores, S. Bará, and Z. Jaroszewicz, “Presbyopia compensation with a quartic axicon,” Optom. Vis. Sci. 82(12), 1071–1078 (2005).
    [Crossref] [PubMed]
  17. 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]
  18. G. Mikuła, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001(1–7) (2005).
  19. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).
  20. D. Moore, Basic Practice of Statistics, (W. H. Freeman and Company, 2010).
  21. B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001(17pp) (2009).

2011 (1)

2010 (2)

2009 (1)

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001(17pp) (2009).

2008 (1)

2007 (1)

2005 (2)

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

G. Mikuła, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001(1–7) (2005).

2003 (1)

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]

2001 (2)

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]

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

1995 (1)

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

1993 (1)

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

1992 (1)

1990 (1)

A. Kołodziejczyk, 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]

1954 (1)

Ares, J.

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

Ares García, J.

Artal, P.

Asundi, A.

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001(17pp) (2009).

Bara, S.

A. Kołodziejczyk, 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]

Bará, S.

Chi, W.

Croft, M. A.

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]

Flores, R.

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

García, J. A.

George, N.

Glasser, A.

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]

Gomez García, M.

Gorecki, M.

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]

Jaroszewicz, Z.

Kakarenko, K.

Kaufman, P. L.

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]

Kolodziejczyk, A.

Makowski, M.

G. Mikuła, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001(1–7) (2005).

McLeod, J. H.

Mikula, G.

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]

G. Mikuła, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001(1–7) (2005).

Pan, B.

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001(17pp) (2009).

Petelczyc, K.

Pierscionek, B. K.

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

Prokopowicz, C.

G. Mikuła, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001(1–7) (2005).

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]

Qian, K.

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001(17pp) (2009).

Sochacki, J.

Sypek, M.

K. Petelczyc, J. A. García, S. Bará, Z. Jaroszewicz, K. Kakarenko, A. Kolodziejczyk, and M. Sypek, “Strehl ratios characterizing optical elements designed for presbyopia compensation,” Opt. Express 19(9), 8693–8699 (2011).
[Crossref] [PubMed]

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]

G. Mikuła, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001(1–7) (2005).

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]

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

A. Kołodziejczyk, 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]

Tabernero, J.

Xie, H.

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001(17pp) (2009).

Zalevsky, Z.

Z. Zalevsky, “Extended depth of focus imaging: a review,” SPIE Rev. 1(1), 018001 (2010).
[Crossref]

Appl. Opt. (2)

Clin. Exp. Optom. (1)

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

Int. Ophthalmol. Clin. (1)

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]

J. Mod. Opt. (1)

A. Kołodziejczyk, 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]

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (1)

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001(17pp) (2009).

Opt. Commun. (1)

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

Opt. Eng. (2)

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]

G. Mikuła, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. 44, 058001(1–7) (2005).

Opt. Express (3)

Opt. Lett. (1)

Optom. Vis. Sci. (1)

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

SPIE Rev. (1)

Z. Zalevsky, “Extended depth of focus imaging: a review,” SPIE Rev. 1(1), 018001 (2010).
[Crossref]

Other (5)

A. Valberg, Light Vision Color (Wiley, 2005).

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

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

D. Moore, Basic Practice of Statistics, (W. H. Freeman and Company, 2010).

Z. Jaroszewicz, Axicons: Design and Propagation Properties, Research & Development Treaties, (SPIE Polish Chapter, Warsaw, 1997), Vol. 5.

Supplementary Material (3)

» Media 1: PDF (3612 KB)     
» Media 2: PDF (3609 KB)     
» Media 3: PDF (3608 KB)     

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Figures (14)

Fig. 1
Fig. 1 A scheme of the presbyopic human eye model based on the Gullstrand parameterization.

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Fig. 2
Fig. 2 An ideal image of the Snellen E and the Landolt C obtained in the central fragment of the imaging plane with dimensions 33 μm x 33 μm. Presented units denote the angular size in minutes of arc in the retinal space.

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Fig. 3
Fig. 3 Images of optotypes formed by the presbyopic eye. Defocus powers and related object distances are given in the left side. Each individual image corresponds to a square retinal region with dimensions 200 μmx200 μm. Other notations are explained in the text.

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Fig. 6
Fig. 6 Images of optotypes formed by the presbyopic eye compensated by a light sword optical element. Defocus powers and related object distances are given in the left side. Each individual image corresponds to a square retinal region with dimensions 200 μmx200 μm. Other notations are explained in the text.

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Fig. 7
Fig. 7 Quantitative parameters of images of the Snellen E optotype formed by a presbyopic eye without correction (EYE) and after correction with compensating elements (RG, IQAX, LSOE). Results correspond to iris diameters 3mm and 5 mm. Other notations are explained in text.

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Fig. 4
Fig. 4 Images of optotypes formed by the presbyopic eye compensated by reading glasses. Defocus powers and related object distances are given in the left side. Each individual image corresponds to a square retinal region with dimensions 200 μmx200 μm. Other notations are explained in the text.

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Fig. 5
Fig. 5 Images of optotypes formed by the presbyopic eye compensated by an inverse quartic axicon. Defocus powers and related object distances are given in the left side. Each individual image corresponds to a square retinal region with dimensions 200 μmx200 μm. Other notations are explained in the text.

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Fig. 8
Fig. 8 A scheme of the artificial presbyopic eye with indicated dimensions and distances.

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Fig. 9
Fig. 9 A photograph of the artificial presbyopic eye. Blue inscriptions denote parts of human eye and black ones indicate corresponding elements in the constructed model.

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Fig. 10
Fig. 10 The refractive LSOE (left) and its interferogram (center) obtained in a Mach-Zehnder interferometer with a use of monochromatic light with λ = 632,8 nm. The right image shows the numerical interferogram of the ideal phase transmittance

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Fig. 11
Fig. 11 Arrangement of the 3 D scene used in the experiment. Black numbers denote object distances and orange numbers indicate dimensions of particular elements. All letter bricks have in reality the same size.

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Fig. 12
Fig. 12 The 3 D scene imaged by the artificial eye (Media 1).

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Fig. 14
Fig. 14 The 3 D scene imaged by the artificial eye compensated by the LSOE (Media 3).

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Fig. 13
Fig. 13 The 3 D scene imaged by the artificial eye compensated by the monofocal lens (Media 2).

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Equations (5)

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

Δl( r )=A r 4 , A=− Add 4 R 2 for r≤R, A=0 for r>R,
Δl( r,θ )=− r 2 2( f 1 + Δfθ 2π ) ,
W= ∬ [ I( x,y )− I id ( x,y ) ] 2 dxdy ∬ dxdy ,
K= ∬ [ I( x,y )− I m ] [ I id ( x,y )− I idm ]dxdy ∬ [ I( x,y )− I m ] 2 dxdy ∬ [ I id ( x,y )− I idm ] 2 dxdy ,
I m = ∬ I( x,y )dxdy ∬ dxdy , I idm = ∬ I id ( x,y )dxdy ∬ dxdy .

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