Abstract

A combination of several diffractive lenses written onto a single programmable liquid crystal display (LCD) is proposed for increasing the Depth of Focus (DOF) of the imaging system as a whole. The lenses are spatially multiplexed in a random scheme onto the LCD. The axial irradiance distribution produced by each lens overlaps with the next one producing an extended focal depth. To compare the image quality of the multiplexed lenses, the Modulation Transfer Function (MTF) is calculated. Finally we obtain the experimental Point Spread Functions (PSF) for these multiplexed lenses and experimental results in which an extended object is illuminated under spatially incoherent monochromatic light. We compare the images obtained in the focal plane and in some defocused planes with the single lens and with three multiplexed lenses. The experimental results confirm that the multiplexed lenses produce a high increase in the depth of focus.

©2006 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  8. C. J. R. Sheppard and Z. S. Hegedus, “Axial behaviour of pupil-plane filters,” J. Opt. Soc. Am. A 5, 643–647 (1988).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  16. A. Márquez, C. Iemmi, J. Campos, J. C. Escalera, and M. J. Yzuel, “Programmable apodizer to compensate chromatic aberration effects using a liquid crystal spatial light modulator,” Opt. Express 13, 716–730 (2005).
    [Crossref] [PubMed]
  17. A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. Davis, and M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator” Appl. Opt. 40, 2316–2322 (2001).
    [Crossref]
  18. T. R. M Sales and G. M. Morris, “Diffractive superresolution elements,” J. Opt. Soc. Am. A 14, 1637–1646 (1997).
    [Crossref]
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    [Crossref]
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  21. E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-optical extended depth of field imaging system,” J. Opt. A: Pure Appl. Opt. 5, S164–S169 (2003).
    [Crossref]
  22. A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Achromatic diffractive lens written onto a liquid crystal display,” Opt. Lett. 31, 392–394 (2006).
    [Crossref] [PubMed]
  23. A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
    [Crossref]

2006 (1)

2005 (2)

A. Márquez, C. Iemmi, J. Campos, J. C. Escalera, and M. J. Yzuel, “Programmable apodizer to compensate chromatic aberration effects using a liquid crystal spatial light modulator,” Opt. Express 13, 716–730 (2005).
[Crossref] [PubMed]

S. Ledesma, J. C. Escalera, J. Campos, and M. J. Yzuel, “Evolution of the transverse response of an optical system with complex filters,” Opt. Commun. 249, 183–192 (2005).
[Crossref]

2003 (1)

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-optical extended depth of field imaging system,” J. Opt. A: Pure Appl. Opt. 5, S164–S169 (2003).
[Crossref]

2001 (4)

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[Crossref]

W. T Cathey and E. R. Dowski, “New paradigm for imaging systems,” Appl. Opt. 41, 5658–5662 (2001).

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. Davis, and M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator” Appl. Opt. 40, 2316–2322 (2001).
[Crossref]

H. Wang and F. Gan, “High focal depth with a pure-phase apodizer,” Appl. Opt. 40, 5658–5662 (2001).
[Crossref]

1999 (2)

1997 (2)

R. Hild, M. J. Yzuel, and J. C. Escalera, “High focal depth imaging of small structures,” Microelectron. Eng. 34, 195–214 (1997).
[Crossref]

T. R. M Sales and G. M. Morris, “Diffractive superresolution elements,” J. Opt. Soc. Am. A 14, 1637–1646 (1997).
[Crossref]

1995 (1)

1992 (1)

H. Fukuda, “A new pupil filter for annular illumination in optical lithography,” Jpn. J. Appl. Phys. 31, 4126–4130 (1992).
[Crossref]

1990 (2)

1989 (1)

1988 (2)

C. J. R. Sheppard and Z. S. Hegedus, “Axial behaviour of pupil-plane filters,” J. Opt. Soc. Am. A 5, 643–647 (1988).
[Crossref]

C. S. Chung and H. H. Hopkins, “Influence of non-uniform amplitude on PSF,” J. Mod. Opt. 35, 1485–1511 (1988).
[Crossref]

1985 (2)

1984 (1)

1960 (1)

W. T Welford, “Use of annular aperture to increase focal depth,” J. Opt. Soc. Am. A 50, 749–753 (1960).
[Crossref]

Bai, H.

Ben-Eliezer, E.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-optical extended depth of field imaging system,” J. Opt. A: Pure Appl. Opt. 5, S164–S169 (2003).
[Crossref]

Berriel-Valdos, L. R.

Campos, J.

A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Achromatic diffractive lens written onto a liquid crystal display,” Opt. Lett. 31, 392–394 (2006).
[Crossref] [PubMed]

A. Márquez, C. Iemmi, J. Campos, J. C. Escalera, and M. J. Yzuel, “Programmable apodizer to compensate chromatic aberration effects using a liquid crystal spatial light modulator,” Opt. Express 13, 716–730 (2005).
[Crossref] [PubMed]

S. Ledesma, J. C. Escalera, J. Campos, and M. J. Yzuel, “Evolution of the transverse response of an optical system with complex filters,” Opt. Commun. 249, 183–192 (2005).
[Crossref]

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. Davis, and M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator” Appl. Opt. 40, 2316–2322 (2001).
[Crossref]

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[Crossref]

J. Davis, J. C. Escalera, J. Campos, A. Márquez, M. J. Yzuel, and C. Iemmi, “Programmable axial apodizing and hyperrsolving amplitude filters with a liquid-crystal spatial light modulator” Opt. Lett. 24, 628–630 (1999).
[Crossref]

J. C. Escalera, M. J. Yzuel, and J. Campos, “Control of the polychromatic response of an optical system through the use of annular color filters,” Appl. Opt. 34, 1655–1663 (1995).
[Crossref] [PubMed]

M. J. Yzuel, J. C. Escalera, and J. Campos, “Polychromatic axial behavior of axial apodizing and hyperresolving filters,” Appl. Opt. 29, 1631–1641 (1990).
[Crossref] [PubMed]

Cathey, W. T

W. T Cathey and E. R. Dowski, “New paradigm for imaging systems,” Appl. Opt. 41, 5658–5662 (2001).

Chung, C. S.

C. S. Chung and H. H. Hopkins, “Influence of non-uniform amplitude on PSF,” J. Mod. Opt. 35, 1485–1511 (1988).
[Crossref]

Davis, J.

Davis, J. A.

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[Crossref]

Díaz, A.

Dowski, E. R.

W. T Cathey and E. R. Dowski, “New paradigm for imaging systems,” Appl. Opt. 41, 5658–5662 (2001).

Escalera, J. C.

Fukuda, H.

H. Fukuda, “A new pupil filter for annular illumination in optical lithography,” Jpn. J. Appl. Phys. 31, 4126–4130 (1992).
[Crossref]

Gan, F.

Hegedus, Z. S

Z. S Hegedus, “Annular pupil arrays. Application to confocal scanning,” Opt. Acta. 32, 815–826 (1985).
[Crossref]

Hegedus, Z. S.

Hild, R.

R. Hild, M. J. Yzuel, and J. C. Escalera, “High focal depth imaging of small structures,” Microelectron. Eng. 34, 195–214 (1997).
[Crossref]

Hopkins, H. H.

C. S. Chung and H. H. Hopkins, “Influence of non-uniform amplitude on PSF,” J. Mod. Opt. 35, 1485–1511 (1988).
[Crossref]

Iemmi, C.

Indebetow, G.

Konforti, N.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-optical extended depth of field imaging system,” J. Opt. A: Pure Appl. Opt. 5, S164–S169 (2003).
[Crossref]

Ledesma, S.

S. Ledesma, J. C. Escalera, J. Campos, and M. J. Yzuel, “Evolution of the transverse response of an optical system with complex filters,” Opt. Commun. 249, 183–192 (2005).
[Crossref]

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. Davis, and M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator” Appl. Opt. 40, 2316–2322 (2001).
[Crossref]

Marom, E.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-optical extended depth of field imaging system,” J. Opt. A: Pure Appl. Opt. 5, S164–S169 (2003).
[Crossref]

Márquez, A.

Montes, E.

Moreno, I.

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[Crossref]

Morris, G. M.

Ojeda-Castañeda, J.

Sales, T. R. M

Sheppard, C. J. R.

Tepichin, E.

Valdos, L. R. Berriel

Wang, H.

Welford, W. T

W. T Welford, “Use of annular aperture to increase focal depth,” J. Opt. Soc. Am. A 50, 749–753 (1960).
[Crossref]

Yang, G. G.

G. G. Yang, “An optical pickup using a diffractive optical element for a high-density optical disc,” Opt. Commun. 159, 19–22 (1999).
[Crossref]

Yzuel, M. J.

A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Achromatic diffractive lens written onto a liquid crystal display,” Opt. Lett. 31, 392–394 (2006).
[Crossref] [PubMed]

S. Ledesma, J. C. Escalera, J. Campos, and M. J. Yzuel, “Evolution of the transverse response of an optical system with complex filters,” Opt. Commun. 249, 183–192 (2005).
[Crossref]

A. Márquez, C. Iemmi, J. Campos, J. C. Escalera, and M. J. Yzuel, “Programmable apodizer to compensate chromatic aberration effects using a liquid crystal spatial light modulator,” Opt. Express 13, 716–730 (2005).
[Crossref] [PubMed]

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. Davis, and M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator” Appl. Opt. 40, 2316–2322 (2001).
[Crossref]

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[Crossref]

J. Davis, J. C. Escalera, J. Campos, A. Márquez, M. J. Yzuel, and C. Iemmi, “Programmable axial apodizing and hyperrsolving amplitude filters with a liquid-crystal spatial light modulator” Opt. Lett. 24, 628–630 (1999).
[Crossref]

R. Hild, M. J. Yzuel, and J. C. Escalera, “High focal depth imaging of small structures,” Microelectron. Eng. 34, 195–214 (1997).
[Crossref]

J. C. Escalera, M. J. Yzuel, and J. Campos, “Control of the polychromatic response of an optical system through the use of annular color filters,” Appl. Opt. 34, 1655–1663 (1995).
[Crossref] [PubMed]

M. J. Yzuel, J. C. Escalera, and J. Campos, “Polychromatic axial behavior of axial apodizing and hyperresolving filters,” Appl. Opt. 29, 1631–1641 (1990).
[Crossref] [PubMed]

Zalevsky, Z.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-optical extended depth of field imaging system,” J. Opt. A: Pure Appl. Opt. 5, S164–S169 (2003).
[Crossref]

Appl. Opt. (8)

J. Mod. Opt. (1)

C. S. Chung and H. H. Hopkins, “Influence of non-uniform amplitude on PSF,” J. Mod. Opt. 35, 1485–1511 (1988).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, “All-optical extended depth of field imaging system,” J. Opt. A: Pure Appl. Opt. 5, S164–S169 (2003).
[Crossref]

J. Opt. Soc. Am. A (3)

Jpn. J. Appl. Phys. (1)

H. Fukuda, “A new pupil filter for annular illumination in optical lithography,” Jpn. J. Appl. Phys. 31, 4126–4130 (1992).
[Crossref]

Microelectron. Eng. (1)

R. Hild, M. J. Yzuel, and J. C. Escalera, “High focal depth imaging of small structures,” Microelectron. Eng. 34, 195–214 (1997).
[Crossref]

Opt. Acta. (1)

Z. S Hegedus, “Annular pupil arrays. Application to confocal scanning,” Opt. Acta. 32, 815–826 (1985).
[Crossref]

Opt. Commun. (2)

G. G. Yang, “An optical pickup using a diffractive optical element for a high-density optical disc,” Opt. Commun. 159, 19–22 (1999).
[Crossref]

S. Ledesma, J. C. Escalera, J. Campos, and M. J. Yzuel, “Evolution of the transverse response of an optical system with complex filters,” Opt. Commun. 249, 183–192 (2005).
[Crossref]

Opt. Eng. (1)

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

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Figures (12)
Fig. 1.
Fig. 1. Random multiplexing scheme. For each sub aperture a lens is chosen randomly and the transmission of its pixels assigned to the multiplexed lens.

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Fig. 2.
Fig. 2. (a) a single diffractive lens, (b) 9 lenses multiplexed and (c) 33 lenses multiplexed.

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Fig. 3.
Fig. 3. MTF of the single lens in three planes

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Fig. 4.
Fig. 4. MTF of the single lens in three planes (zoom of the region of interest)

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Fig. 5.
Fig. 5. MTF of the nine multiplexed lens in three planes

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Fig. 6.
Fig. 6. MTF of the 33 multiplexed lens in three planes

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Fig. 7.
Fig. 7. Scheme of the imaging set-up for extended objects. D is a rotating diffuser, C a condenser, O is the object placed in the focal plane of lens L. P1 and P2 are polarizers, WP1 and WP2 are wave plates that together with the liquid crystal display LCD conform the pure phase modulator used to display the diffractive lenses. An image of O is captured by a CCD camera.

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Fig. 8.
Fig. 8. Intensity profile of the PSF along the axis for SL, M9, M17 and M33 lenses (a); and for just M9, M17 and M33 lenses (b). Position Z=0 corresponds to Best Image Plane (BIP)

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Fig. 9.
Fig. 9. PSF of the simple and multiplexed lenses, captured at three different planes.

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Fig. 10.
Fig. 10. Images of an enlarged portion of the Siemens star and the resolution test captured at Z = 0 plane when 9 multiplexed lenses and 33 multiplexed lenses are used

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Fig. 11.
Fig. 11. Images of the Siemens star captured at the best image plane (Z = 0) and defocused planes (Z = -6 cm and Z = -10 cm) when a single lens and a multiplexed lens (M33) are used.

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Fig. 12.
Fig. 12. Images of the resolution target captured at the best image plane (Z = 0) and defocused planes (Z = -6 cm and Z = -10 cm) when a single lens and a multiplexed lens (M33) are used.

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