Abstract

We show that both a lens and a nonuniform amplitude transmission filter can be encoded simultaneously onto a twisted nematic liquid-crystal spatial light modulator (SLM) working in the phase-only mode. The inherent equivalent apodization that is due to the pixelated structure of the SLM is compensated for. In addition, different types of nonuniform transmission pupil such as transverse apodizing, transverse hyperresolving, and axial hyperresolving (multifocusing) filters are implemented. The excellent agreement between numerical and experimental results shows the capability of this method to encode amplitude apodizers on a phase-only SLM.

© 2001 Optical Society of America

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  1. F. Wyrowsky, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
    [CrossRef]
  2. J. A. Davis, D. M. Cottrell, R. A. Lilly, S. W. Connely, “Multiplexed phase-encoded lenses written on spatial light modulators,” Opt. Lett. 14, 420–422 (1989).
    [CrossRef] [PubMed]
  3. D. M. Cottrell, J. A. Davis, T. R. Hedman, R. A. Lilly, “Multiple imaging phase-encoded optical elements written as programmable spatial light modulators,” Appl. Opt. 29, 2505–2509 (1990).
    [CrossRef] [PubMed]
  4. E. Carcolé, J. Campos, S. Bosch, “Diffraction theory of Fresnel lenses encoded in low-resolution devices,” Appl. Opt. 33, 162–174 (1994).
    [CrossRef] [PubMed]
  5. V. Arrizón, E. Carreón, L. A. González, “Self apodization of low-resolution pixelated lenses,” Appl. Opt. 38, 5073–5077 (1999).
    [CrossRef]
  6. M. J. Yzuel, J. Campos, A. Márquez, J. C. Escalera, J. A. Davis, C. Iemmi, S. Ledesma, “Inherent apodization of lenses encoded on liquid-crystal spatial light modulators,” Appl. Opt. 39, 6034–6039 (2000).
    [CrossRef]
  7. J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
    [CrossRef]
  8. I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
    [CrossRef]
  9. A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M.J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” submitted to Opt. Eng.
  10. A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
    [CrossRef]
  11. R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field. I. Achievement of maximum central irradiance under an energy constraint,” Opt. Acta 27, 587–610 (1980).
    [CrossRef]
  12. C. S. Chung, H. H. Hopkins, “Influence of nonuniform amplitude on the optical transfer function,” Appl. Opt. 28, 1244–1250 (1989).
    [CrossRef] [PubMed]
  13. C. J. R. Sheppard, Z. S. Hegedus, “Axial behavior of pupil-plane filters,” J. Opt. Soc. Am. A 5, 643–647 (1988).
    [CrossRef]
  14. J. Campos, J. C. Escalera, C. J. R. Sheppard, M. J. Yzuel, “Axially invariant pupil filters,” J. Mod. Opt. 47, 57–68 (2000).
  15. J. Ojeda-Castañeda, L. R. Berriel-Valdos, E. Montes, “Ambiguity function as a design tool for high focal depth,” Appl. Opt. 27, 790–795 (1988).
    [CrossRef] [PubMed]
  16. M. J. Yzuel, J. C. Escalera, J. Campos, “Polychromatic axial behaviour of axial apodizing and hyperresolving filters,” Appl. Opt. 29, 1631–1641 (1990).
    [CrossRef] [PubMed]
  17. H. Fukuda, Y. Kobayashi, K. Hama, T. Tawa, S. Okazaki, “Evaluation of pupil-filtering in high-numerical aperture I-line lens,” Jpn. J. Appl. Phys. 32, 5845–5849 (1993).
    [CrossRef]
  18. R. Hild, M. J. Yzuel, J. C. Escalera, “High focal depth imaging of small structures,” Microelectron. Eng. 34, 195–214 (1997).
    [CrossRef]
  19. J. A. Davis, J. C. Escalera, J. Campos, A. Márquez, M. J. Yzuel, C. Iemmi, “Programmable axial apodizing and hyperresolving amplitude filters with a liquid-crystal spatial light modulator,” Opt. Lett. 24, 628–630 (1999).
    [CrossRef]
  20. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
    [CrossRef]
  21. C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
    [CrossRef]
  22. J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
    [CrossRef]
  23. J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
    [CrossRef]

2000

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

J. Campos, J. C. Escalera, C. J. R. Sheppard, M. J. Yzuel, “Axially invariant pupil filters,” J. Mod. Opt. 47, 57–68 (2000).

M. J. Yzuel, J. Campos, A. Márquez, J. C. Escalera, J. A. Davis, C. Iemmi, S. Ledesma, “Inherent apodization of lenses encoded on liquid-crystal spatial light modulators,” Appl. Opt. 39, 6034–6039 (2000).
[CrossRef]

1999

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
[CrossRef]

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

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

V. Arrizón, E. Carreón, L. A. González, “Self apodization of low-resolution pixelated lenses,” Appl. Opt. 38, 5073–5077 (1999).
[CrossRef]

1998

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
[CrossRef]

1997

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

1994

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

E. Carcolé, J. Campos, S. Bosch, “Diffraction theory of Fresnel lenses encoded in low-resolution devices,” Appl. Opt. 33, 162–174 (1994).
[CrossRef] [PubMed]

1993

H. Fukuda, Y. Kobayashi, K. Hama, T. Tawa, S. Okazaki, “Evaluation of pupil-filtering in high-numerical aperture I-line lens,” Jpn. J. Appl. Phys. 32, 5845–5849 (1993).
[CrossRef]

1991

F. Wyrowsky, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

1990

1989

1988

1980

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field. I. Achievement of maximum central irradiance under an energy constraint,” Opt. Acta 27, 587–610 (1980).
[CrossRef]

Allison, D. B.

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

Arrizón, V.

Berriel-Valdos, L. R.

Boivin, A.

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field. I. Achievement of maximum central irradiance under an energy constraint,” Opt. Acta 27, 587–610 (1980).
[CrossRef]

Boivin, R.

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field. I. Achievement of maximum central irradiance under an energy constraint,” Opt. Acta 27, 587–610 (1980).
[CrossRef]

Bosch, S.

Bryngdahl, O.

F. Wyrowsky, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

Campos, J.

M. J. Yzuel, J. Campos, A. Márquez, J. C. Escalera, J. A. Davis, C. Iemmi, S. Ledesma, “Inherent apodization of lenses encoded on liquid-crystal spatial light modulators,” Appl. Opt. 39, 6034–6039 (2000).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

J. Campos, J. C. Escalera, C. J. R. Sheppard, M. J. Yzuel, “Axially invariant pupil filters,” J. Mod. Opt. 47, 57–68 (2000).

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

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
[CrossRef]

E. Carcolé, J. Campos, S. Bosch, “Diffraction theory of Fresnel lenses encoded in low-resolution devices,” Appl. Opt. 33, 162–174 (1994).
[CrossRef] [PubMed]

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

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M.J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” submitted to Opt. Eng.

Carcolé, E.

Carreón, E.

Chung, C. S.

Connely, S. W.

Cottrell, D. M.

D’Nelly, K. G.

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

Davis, J. A.

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

M. J. Yzuel, J. Campos, A. Márquez, J. C. Escalera, J. A. Davis, C. Iemmi, S. Ledesma, “Inherent apodization of lenses encoded on liquid-crystal spatial light modulators,” Appl. Opt. 39, 6034–6039 (2000).
[CrossRef]

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

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

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
[CrossRef]

J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

D. M. Cottrell, J. A. Davis, T. R. Hedman, R. A. Lilly, “Multiple imaging phase-encoded optical elements written as programmable spatial light modulators,” Appl. Opt. 29, 2505–2509 (1990).
[CrossRef] [PubMed]

J. A. Davis, D. M. Cottrell, R. A. Lilly, S. W. Connely, “Multiplexed phase-encoded lenses written on spatial light modulators,” Opt. Lett. 14, 420–422 (1989).
[CrossRef] [PubMed]

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M.J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” submitted to Opt. Eng.

Escalera, J. C.

Fukuda, H.

H. Fukuda, Y. Kobayashi, K. Hama, T. Tawa, S. Okazaki, “Evaluation of pupil-filtering in high-numerical aperture I-line lens,” Jpn. J. Appl. Phys. 32, 5845–5849 (1993).
[CrossRef]

González, L. A.

Hama, K.

H. Fukuda, Y. Kobayashi, K. Hama, T. Tawa, S. Okazaki, “Evaluation of pupil-filtering in high-numerical aperture I-line lens,” Jpn. J. Appl. Phys. 32, 5845–5849 (1993).
[CrossRef]

Hedman, T. R.

Hegedus, Z. S.

Hild, R.

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

Hopkins, H. H.

Iemmi, C.

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

M. J. Yzuel, J. Campos, A. Márquez, J. C. Escalera, J. A. Davis, C. Iemmi, S. Ledesma, “Inherent apodization of lenses encoded on liquid-crystal spatial light modulators,” Appl. Opt. 39, 6034–6039 (2000).
[CrossRef]

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

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M.J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” submitted to Opt. Eng.

Kobayashi, Y.

H. Fukuda, Y. Kobayashi, K. Hama, T. Tawa, S. Okazaki, “Evaluation of pupil-filtering in high-numerical aperture I-line lens,” Jpn. J. Appl. Phys. 32, 5845–5849 (1993).
[CrossRef]

Ledesma, S.

Lilly, R. A.

Lu, K.

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

Márquez, A.

M. J. Yzuel, J. Campos, A. Márquez, J. C. Escalera, J. A. Davis, C. Iemmi, S. Ledesma, “Inherent apodization of lenses encoded on liquid-crystal spatial light modulators,” Appl. Opt. 39, 6034–6039 (2000).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

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

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M.J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” submitted to Opt. Eng.

Montes, E.

Moreno, A.

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

Moreno, I.

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
[CrossRef]

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M.J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” submitted to Opt. Eng.

Ojeda-Castañeda, J.

Okazaki, S.

H. Fukuda, Y. Kobayashi, K. Hama, T. Tawa, S. Okazaki, “Evaluation of pupil-filtering in high-numerical aperture I-line lens,” Jpn. J. Appl. Phys. 32, 5845–5849 (1993).
[CrossRef]

Robert, A.

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

Sheppard, C. J. R.

J. Campos, J. C. Escalera, C. J. R. Sheppard, M. J. Yzuel, “Axially invariant pupil filters,” J. Mod. Opt. 47, 57–68 (2000).

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

Soutar, C.

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

Tawa, T.

H. Fukuda, Y. Kobayashi, K. Hama, T. Tawa, S. Okazaki, “Evaluation of pupil-filtering in high-numerical aperture I-line lens,” Jpn. J. Appl. Phys. 32, 5845–5849 (1993).
[CrossRef]

Tsai, P.

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
[CrossRef]

Wilson, M. L.

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

Wyrowsky, F.

F. Wyrowsky, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

Yzuel, M. J.

Yzuel, M.J.

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M.J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” submitted to Opt. Eng.

Appl. Opt.

D. M. Cottrell, J. A. Davis, T. R. Hedman, R. A. Lilly, “Multiple imaging phase-encoded optical elements written as programmable spatial light modulators,” Appl. Opt. 29, 2505–2509 (1990).
[CrossRef] [PubMed]

E. Carcolé, J. Campos, S. Bosch, “Diffraction theory of Fresnel lenses encoded in low-resolution devices,” Appl. Opt. 33, 162–174 (1994).
[CrossRef] [PubMed]

V. Arrizón, E. Carreón, L. A. González, “Self apodization of low-resolution pixelated lenses,” Appl. Opt. 38, 5073–5077 (1999).
[CrossRef]

M. J. Yzuel, J. Campos, A. Márquez, J. C. Escalera, J. A. Davis, C. Iemmi, S. Ledesma, “Inherent apodization of lenses encoded on liquid-crystal spatial light modulators,” Appl. Opt. 39, 6034–6039 (2000).
[CrossRef]

J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
[CrossRef]

J. Ojeda-Castañeda, L. R. Berriel-Valdos, E. Montes, “Ambiguity function as a design tool for high focal depth,” Appl. Opt. 27, 790–795 (1988).
[CrossRef] [PubMed]

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

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
[CrossRef]

C. S. Chung, H. H. Hopkins, “Influence of nonuniform amplitude on the optical transfer function,” Appl. Opt. 28, 1244–1250 (1989).
[CrossRef] [PubMed]

J. Mod. Opt.

J. Campos, J. C. Escalera, C. J. R. Sheppard, M. J. Yzuel, “Axially invariant pupil filters,” J. Mod. Opt. 47, 57–68 (2000).

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

H. Fukuda, Y. Kobayashi, K. Hama, T. Tawa, S. Okazaki, “Evaluation of pupil-filtering in high-numerical aperture I-line lens,” Jpn. J. Appl. Phys. 32, 5845–5849 (1993).
[CrossRef]

Microelectron. Eng.

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

Opt. Acta

R. Boivin, A. Boivin, “Optimized amplitude filtering for superresolution over a restricted field. I. Achievement of maximum central irradiance under an energy constraint,” Opt. Acta 27, 587–610 (1980).
[CrossRef]

Opt. Eng.

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Optical setup: LPs, linear polarizers; WPs, wave plates; MO, microscope objective.

Fig. 2
Fig. 2

Normalized amplitude transmission and phase dephasing for the phase-only configuration of the SLM.

Fig. 3
Fig. 3

Amplitude distribution along the radius of the lens (in millimeters). Theoretical simulation of the apodizing inherent equivalent effect that is due to the pixelated structure of the SLM (continuous curve), experimentally measured values with the annuli masks (squares), and polynomial fitting to the experimental values (dashed curve).

Fig. 4
Fig. 4

1, Transversal apodizing (1 - ρ2); 2, transversal hyperresolving (ρ2); and 3, axial multifocusing (1 - 4ρ2 + 4ρ4) functions: (a) with no inherent apodizing effect and (b) including the inherent apodizing effect. ρ is the normalized radial coordinate in the plane of the lens.

Fig. 5
Fig. 5

Theoretical transverse response in the best image plane obtained with (a) a transversal apodizing filter (1 - ρ2) and (b) a transversal hyperresolving filter (ρ2). Dashed curves, including the inherent equivalent apodizing effect; solid curves, with no inherent apodizing effect. r is the radial coordinate in the image plane.

Fig. 6
Fig. 6

Experimental best plane images for (a1), (a2), transversal apodizing and transversal hyperresolving filters, respectively, without compensation for the inherent apodizing effect; (b1), (b2), the inherent apodizing effect compensated for. The peak intensity values measured in gray levels of the frame grabber are given.

Fig. 7
Fig. 7

Axial multifocusing theoretical axial response.

Fig. 8
Fig. 8

Axial multifocusing optical system in various defocus planes including compensation for the inherent equivalent apodizing effect. Top, experimental images. Bottom, corresponding numerically calculated transverse responses. r is the radial coordinate in the image plane.

Equations (8)

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Z*u, v=exp-i πλfu2+v2.
Gu, v=Tu, vZ*u, v=Tu, vexp-i πλfu2+v2.
GM, φ=n=-n= Gn expinφ,
Gu, v=n=-sincMu, v-n×expinΦu, v-πu2+v2λf.
Ux, y  expiπx2+y2λf×--n=-sincMu, v-nexpinΦu, v-πu2+v2λf expiπu2+v2λf×exp-i2πux+vyλfdudv.
τu, v=sincWu/λfsincWv/λf,
τPρ=1-0.89ρ2+0.27ρ4-0.04ρ6,
TAρ=1-ρ2,THρ=ρ2,TMρ=1-4ρ2+4ρ4,

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