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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Fukuda, "A new pupil filter for annular illumination in optical lithography," Jpn. J. Appl. Phys. 31, 4126-4130 (1992).
    [CrossRef]
  2. R. Hild, M. J. Yzuel and J. C. Escalera, "High focal depth imaging of small structures," Microelectron. Eng. 34, 195-214 (1997).
    [CrossRef]
  3. G. G. Yang, "An optical pickup using a diffractive optical element for a high-density optical disc," Opt. Commun. 159, 19-22 (1999).
    [CrossRef]
  4. H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl. Opt. 40, 5658-5662 (2001).
    [CrossRef]
  5. W. T Welford, "Use of annular aperture to increase focal depth," J. Opt. Soc. Am. A 50, 749-753 (1960).
    [CrossRef]
  6. Z. S Hegedus, "Annular pupil arrays. Application to confocal scanning," Opt. Acta. 32, 815-826 (1985).
    [CrossRef]
  7. 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]
  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]
  9. C. S. Chung and H. H. Hopkins, "Influence of non-uniform amplitude on PSF," J. Mod. Opt. 35, 1485-1511 (1988).
    [CrossRef]
  10. J. Ojeda-Castañeda, E. Tepichin and A. Díaz, "Arbitrarily high focal depth with quasioptimum real and positive transmittance apodizer," Appl. Opt. 28, 2666-2670 (1989).
    [CrossRef] [PubMed]
  11. J. Ojeda-Castañeda, L. R. Berriel Valdos and E. Montes, "Spatial filter for increasing the depth of focus" Opt. Lett. 10, 520-522 (1985).
    [CrossRef] [PubMed]
  12. 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]
  13. J. Ojeda-Castañeda and L. R. Berriel-Valdos, "Zone plate for arbitrarily high focal depth," Appl. Opt. 29, 994-996 (1990).
    [CrossRef] [PubMed]
  14. G. Indebetow and H. Bai, "Imaging with Fresnel zone pupil masks: extended depth of field," Appl. Opt. 23, 4299-4302 (1984).
    [CrossRef]
  15. 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]
  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]
  19. 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]
  20. W. T Cathey, E. R. Dowski, "New paradigm for imaging systems," Appl. Opt. 41, 5658-5662 (2001).
  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, 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.

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, 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, 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.

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)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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.

Fig. 2.
Fig. 2.

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

Fig. 3.
Fig. 3.

MTF of the single lens in three planes

Fig. 4.
Fig. 4.

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

Fig. 5.
Fig. 5.

MTF of the nine multiplexed lens in three planes

Fig. 6.
Fig. 6.

MTF of the 33 multiplexed lens in three planes

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.

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)

Fig. 9.
Fig. 9.

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

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

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.

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.

Metrics