Abstract

Programmable apodizers written on a liquid crystal spatial light modulator (LCSLM) offer the possibility of modifying the point spread function (PSF) of an optical system in monochromatic light with a high degree of flexibility. Extension to polychromatic light has to take into account the liquid crystal response dependence on the wavelength. Proper control of the chromatic properties of the LCSLM in combination with the design of the correct apodizer is necessary for this new range of applications. In this paper we report a successful application of a programmable amplitude apodizer illuminated with polychromatic light. We use an axial apodizing filter to compensate the longitudinal secondary axial color (LSAC) effects of a refractive optical system on the polychromatic PSF. The configuration of the LCSLM has been optimized to obtain a good amplitude transmission in polychromatic light. Agreement between experimental and simulated results shows the feasibility of our proposal.

© 2005 Optical Society of America

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  1. C.S Chung and H.H. Hopkins, “Influence of non-uniform amplitude on PSF,” J. Mod. Opt. 35, 1485–1511 (1988).
    [CrossRef]
  2. C. J. R. Sheppard and Z. S. Hegedus, “Axial behavior of pupil plane filters,” J. Opt. Soc. Am. A,  5, 643–647 (1988).
    [CrossRef]
  3. 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]
  4. D. M. de Juana, J. E. Oti, V. F. Canales, and M. P. Cagigal, “Design of superresolving continuous phase filters,” Opt. Lett. 28, 607–609 (2003).
    [CrossRef] [PubMed]
  5. S. Ledesma, J. Campos, J. C. Escalera, and M. J. Yzuel, “Simple expression for performance parameters of complex filters, with applications to supergaussian phase filters,” Opt. Lett. 29, 932–934 (2004).
    [CrossRef] [PubMed]
  6. J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, “Axially invariant pupil filters,” J. Mod. Opt. 47, 57–68 (2000).
  7. M. J. Yzuel, J. C. Escalera, G. Cansado, and J. Campos, “Illuminance and chromaticity of the image of optical systems with non-uniform transmission filters,” Proc. SPIE 1013, 120–127 (1988).
  8. J. C. Escalera, M. J. Yzuel, and J. Campos, “Control of the polychromatic responses of an optical system through the use of annular color filters,” Appl. Opt. 34, 1655–1663 (1995).
    [CrossRef]
  9. W. J. Smith, Modern Optical Engineering, (McGraw-Hill, 3rd Ed., 2000), 402–412.
  10. M. J. Yzuel and F. Calvo, “A study of the possibility of image optimization by apodization filters with residual aberrations,” Optica Acta 26, 1397–1406 (1979).
    [CrossRef]
  11. J. Campos and M.J. Yzuel, “Axial and extra-axial response in aberrated optical systems with apodizers. Optimization of the Strehl ratio,” J. Mod. Opt. 36, 733–749 (1989).
    [CrossRef]
  12. J. C. Escalera, M. J. Yzuel, and J. Campos, “Influence of amplitude-only filters in optical systems with longitudinal chromatic aberration,” J. Mod. Opt. 38, 1703–1720 (1991).
    [CrossRef]
  13. V. G. Chigrinov, Liquid crystal devices: physics and applications (Artech House, 1999).
  14. J. Campos, A. Márquez, M. J. Yzuel, J. A. Davis, D. M. Cottrell, and I. Moreno, “Fully complex synthetic discriminant functions written onto phase-only modulators,” Appl. Opt. 39, 5965–5970 (2000).
    [CrossRef]
  15. O. Gualdrón, J. A. Davis, J. Nicolás, J. Campos, and M. J. Yzuel, “Complex encoding of rotation invariant filters onto a single phase-only SLM,” Appl. Opt. 42, 1973–1980 (2003)
    [CrossRef] [PubMed]
  16. V. Laude, “Twisted-nematic liquid-crystal pixelated active lens,” Opt. Commun. 153, 134–152 (1998).
    [CrossRef]
  17. M. J. Yzuel, J. Campos, A. Márquez, J. C. Escalera, J. A. Davis, C. Iemmi, and S. Ledesma, “Inherent apodization of lenses encoded on liquid crystal spatial light modulators,” Appl. Opt. 39, 6034–6039 (2000).
    [CrossRef]
  18. J. McOrst, M.D. Sharma, C.J.R. Sheppard, E. West, and K. Matsuda, “Hyperresolving phase-only filters with optically-addressable liquid crystal spatial ligth modulators,” Micron 34, 327–332 (2003).
    [CrossRef]
  19. R. Dou and M. K. Giles, “Closed-loop adaptive optics system with a liquid crystal television as a phase retarder,” Opt. Lett. 20, 1583–1585 (1995).
    [CrossRef] [PubMed]
  20. H.J. Coufal, D. Psaltis, and B.T. Sincerbox, eds., Holographic Data Storage (Springer-Verlag, Berlin, 2000)
  21. J. A. Davis, J. C. Escalera, J. Campos, A. Márquez, M. J. Yzuel, and C. Iemmi, “Programmable axial apodizing and hyperresolving amplitude filters using a liquid crystal spatial light modulator,” Opt. Lett. 24, 628–630 (1999).
    [CrossRef]
  22. A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. 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]
  23. J. L. de Bougrenet de la Tocnaye and L. Dupont, “Complex amplitude modulation by use of liquid-crystal spatial light modulators,” Appl. Opt. 36, 1730–1741 (1997).
    [CrossRef] [PubMed]
  24. A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
    [CrossRef]
  25. 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]
  26. J. Nicolás, J. Campos, and M. J. Yzuel, “Phase and amplitude modulation of elliptic polarization states by non-absorbing anisotropic elements: application to liquid crystal devices,” J. Opt. Soc. Am. A 19, 1013–1020 (2002).
    [CrossRef]
  27. A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, “Characterization of the retardance of a wave plate to increase the robustness of amplitude-only and phase-only modulations of a liquid crystal display,” J. Mod. Opt. 52, 633–650 (2005).
    [CrossRef]

2005 (1)

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, “Characterization of the retardance of a wave plate to increase the robustness of amplitude-only and phase-only modulations of a liquid crystal display,” J. Mod. Opt. 52, 633–650 (2005).
[CrossRef]

2004 (1)

2003 (3)

2002 (1)

2001 (2)

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]

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. 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]

2000 (4)

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

J. Campos, A. Márquez, M. J. Yzuel, J. A. Davis, D. M. Cottrell, and I. Moreno, “Fully complex synthetic discriminant functions written onto phase-only modulators,” Appl. Opt. 39, 5965–5970 (2000).
[CrossRef]

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

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

1999 (1)

1998 (1)

V. Laude, “Twisted-nematic liquid-crystal pixelated active lens,” Opt. Commun. 153, 134–152 (1998).
[CrossRef]

1997 (1)

1995 (2)

1991 (1)

J. C. Escalera, M. J. Yzuel, and J. Campos, “Influence of amplitude-only filters in optical systems with longitudinal chromatic aberration,” J. Mod. Opt. 38, 1703–1720 (1991).
[CrossRef]

1990 (1)

1989 (1)

J. Campos and M.J. Yzuel, “Axial and extra-axial response in aberrated optical systems with apodizers. Optimization of the Strehl ratio,” J. Mod. Opt. 36, 733–749 (1989).
[CrossRef]

1988 (3)

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

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

M. J. Yzuel, J. C. Escalera, G. Cansado, and J. Campos, “Illuminance and chromaticity of the image of optical systems with non-uniform transmission filters,” Proc. SPIE 1013, 120–127 (1988).

1979 (1)

M. J. Yzuel and F. Calvo, “A study of the possibility of image optimization by apodization filters with residual aberrations,” Optica Acta 26, 1397–1406 (1979).
[CrossRef]

Cagigal, M. P.

Calvo, F.

M. J. Yzuel and F. Calvo, “A study of the possibility of image optimization by apodization filters with residual aberrations,” Optica Acta 26, 1397–1406 (1979).
[CrossRef]

Campos, J.

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, “Characterization of the retardance of a wave plate to increase the robustness of amplitude-only and phase-only modulations of a liquid crystal display,” J. Mod. Opt. 52, 633–650 (2005).
[CrossRef]

S. Ledesma, J. Campos, J. C. Escalera, and M. J. Yzuel, “Simple expression for performance parameters of complex filters, with applications to supergaussian phase filters,” Opt. Lett. 29, 932–934 (2004).
[CrossRef] [PubMed]

O. Gualdrón, J. A. Davis, J. Nicolás, J. Campos, and M. J. Yzuel, “Complex encoding of rotation invariant filters onto a single phase-only SLM,” Appl. Opt. 42, 1973–1980 (2003)
[CrossRef] [PubMed]

J. Nicolás, J. Campos, and M. J. Yzuel, “Phase and amplitude modulation of elliptic polarization states by non-absorbing anisotropic elements: application to liquid crystal devices,” J. Opt. Soc. Am. A 19, 1013–1020 (2002).
[CrossRef]

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. 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]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, and 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, and M. J. Yzuel, “Axially invariant pupil filters,” J. Mod. Opt. 47, 57–68 (2000).

J. Campos, A. Márquez, M. J. Yzuel, J. A. Davis, D. M. Cottrell, and I. Moreno, “Fully complex synthetic discriminant functions written onto phase-only modulators,” Appl. Opt. 39, 5965–5970 (2000).
[CrossRef]

M. J. Yzuel, J. Campos, A. Márquez, J. C. Escalera, J. A. Davis, C. Iemmi, and 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, and C. Iemmi, “Programmable axial apodizing and hyperresolving amplitude filters using 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 responses of an optical system through the use of annular color filters,” Appl. Opt. 34, 1655–1663 (1995).
[CrossRef]

J. C. Escalera, M. J. Yzuel, and J. Campos, “Influence of amplitude-only filters in optical systems with longitudinal chromatic aberration,” J. Mod. Opt. 38, 1703–1720 (1991).
[CrossRef]

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]

J. Campos and M.J. Yzuel, “Axial and extra-axial response in aberrated optical systems with apodizers. Optimization of the Strehl ratio,” J. Mod. Opt. 36, 733–749 (1989).
[CrossRef]

M. J. Yzuel, J. C. Escalera, G. Cansado, and J. Campos, “Illuminance and chromaticity of the image of optical systems with non-uniform transmission filters,” Proc. SPIE 1013, 120–127 (1988).

Canales, V. F.

Cansado, G.

M. J. Yzuel, J. C. Escalera, G. Cansado, and J. Campos, “Illuminance and chromaticity of the image of optical systems with non-uniform transmission filters,” Proc. SPIE 1013, 120–127 (1988).

Cazorla, C.

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, “Characterization of the retardance of a wave plate to increase the robustness of amplitude-only and phase-only modulations of a liquid crystal display,” J. Mod. Opt. 52, 633–650 (2005).
[CrossRef]

Chigrinov, V. G.

V. G. Chigrinov, Liquid crystal devices: physics and applications (Artech House, 1999).

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]

Cottrell, D. M.

Davis, J. A.

O. Gualdrón, J. A. Davis, J. Nicolás, J. Campos, and M. J. Yzuel, “Complex encoding of rotation invariant filters onto a single phase-only SLM,” Appl. Opt. 42, 1973–1980 (2003)
[CrossRef] [PubMed]

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. 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. Campos, A. Márquez, M. J. Yzuel, J. A. Davis, D. M. Cottrell, and I. Moreno, “Fully complex synthetic discriminant functions written onto phase-only modulators,” Appl. Opt. 39, 5965–5970 (2000).
[CrossRef]

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

de Bougrenet de la Tocnaye, J. L.

de Juana, D. M.

Dou, R.

Dupont, L.

Escalera, J. C.

S. Ledesma, J. Campos, J. C. Escalera, and M. J. Yzuel, “Simple expression for performance parameters of complex filters, with applications to supergaussian phase filters,” Opt. Lett. 29, 932–934 (2004).
[CrossRef] [PubMed]

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. 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]

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

J. Campos, J. C. Escalera, C. J. R. Sheppard, and 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, and C. Iemmi, “Programmable axial apodizing and hyperresolving amplitude filters using 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 responses of an optical system through the use of annular color filters,” Appl. Opt. 34, 1655–1663 (1995).
[CrossRef]

J. C. Escalera, M. J. Yzuel, and J. Campos, “Influence of amplitude-only filters in optical systems with longitudinal chromatic aberration,” J. Mod. Opt. 38, 1703–1720 (1991).
[CrossRef]

M. J. Yzuel, J. C. Escalera, G. Cansado, and J. Campos, “Illuminance and chromaticity of the image of optical systems with non-uniform transmission filters,” Proc. SPIE 1013, 120–127 (1988).

Escalera, J.C.

Giles, M. K.

Gualdrón, O.

Hegedus, Z. S.

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.

Laude, V.

V. Laude, “Twisted-nematic liquid-crystal pixelated active lens,” Opt. Commun. 153, 134–152 (1998).
[CrossRef]

Ledesma, S.

Márquez, A.

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, “Characterization of the retardance of a wave plate to increase the robustness of amplitude-only and phase-only modulations of a liquid crystal display,” J. Mod. Opt. 52, 633–650 (2005).
[CrossRef]

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. 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]

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

J. Campos, A. Márquez, M. J. Yzuel, J. A. Davis, D. M. Cottrell, and I. Moreno, “Fully complex synthetic discriminant functions written onto phase-only modulators,” Appl. Opt. 39, 5965–5970 (2000).
[CrossRef]

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

Matsuda, K.

J. McOrst, M.D. Sharma, C.J.R. Sheppard, E. West, and K. Matsuda, “Hyperresolving phase-only filters with optically-addressable liquid crystal spatial ligth modulators,” Micron 34, 327–332 (2003).
[CrossRef]

McOrst, J.

J. McOrst, M.D. Sharma, C.J.R. Sheppard, E. West, and K. Matsuda, “Hyperresolving phase-only filters with optically-addressable liquid crystal spatial ligth modulators,” Micron 34, 327–332 (2003).
[CrossRef]

Moreno, A.

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

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]

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

J. Campos, A. Márquez, M. J. Yzuel, J. A. Davis, D. M. Cottrell, and I. Moreno, “Fully complex synthetic discriminant functions written onto phase-only modulators,” Appl. Opt. 39, 5965–5970 (2000).
[CrossRef]

Nicolás, J.

Oti, J. E.

Robert, A.

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

Sharma, M.D.

J. McOrst, M.D. Sharma, C.J.R. Sheppard, E. West, and K. Matsuda, “Hyperresolving phase-only filters with optically-addressable liquid crystal spatial ligth modulators,” Micron 34, 327–332 (2003).
[CrossRef]

Sheppard, C. J. R.

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

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

Sheppard, C.J.R.

J. McOrst, M.D. Sharma, C.J.R. Sheppard, E. West, and K. Matsuda, “Hyperresolving phase-only filters with optically-addressable liquid crystal spatial ligth modulators,” Micron 34, 327–332 (2003).
[CrossRef]

Smith, W. J.

W. J. Smith, Modern Optical Engineering, (McGraw-Hill, 3rd Ed., 2000), 402–412.

West, E.

J. McOrst, M.D. Sharma, C.J.R. Sheppard, E. West, and K. Matsuda, “Hyperresolving phase-only filters with optically-addressable liquid crystal spatial ligth modulators,” Micron 34, 327–332 (2003).
[CrossRef]

Yzuel, M. J.

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, “Characterization of the retardance of a wave plate to increase the robustness of amplitude-only and phase-only modulations of a liquid crystal display,” J. Mod. Opt. 52, 633–650 (2005).
[CrossRef]

S. Ledesma, J. Campos, J. C. Escalera, and M. J. Yzuel, “Simple expression for performance parameters of complex filters, with applications to supergaussian phase filters,” Opt. Lett. 29, 932–934 (2004).
[CrossRef] [PubMed]

O. Gualdrón, J. A. Davis, J. Nicolás, J. Campos, and M. J. Yzuel, “Complex encoding of rotation invariant filters onto a single phase-only SLM,” Appl. Opt. 42, 1973–1980 (2003)
[CrossRef] [PubMed]

J. Nicolás, J. Campos, and M. J. Yzuel, “Phase and amplitude modulation of elliptic polarization states by non-absorbing anisotropic elements: application to liquid crystal devices,” J. Opt. Soc. Am. A 19, 1013–1020 (2002).
[CrossRef]

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. 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]

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

J. Campos, A. Márquez, M. J. Yzuel, J. A. Davis, D. M. Cottrell, and I. Moreno, “Fully complex synthetic discriminant functions written onto phase-only modulators,” Appl. Opt. 39, 5965–5970 (2000).
[CrossRef]

J. A. Davis, J. C. Escalera, J. Campos, A. Márquez, M. J. Yzuel, and C. Iemmi, “Programmable axial apodizing and hyperresolving amplitude filters using 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 responses of an optical system through the use of annular color filters,” Appl. Opt. 34, 1655–1663 (1995).
[CrossRef]

J. C. Escalera, M. J. Yzuel, and J. Campos, “Influence of amplitude-only filters in optical systems with longitudinal chromatic aberration,” J. Mod. Opt. 38, 1703–1720 (1991).
[CrossRef]

M. J. Yzuel, J. C. Escalera, G. Cansado, and J. Campos, “Illuminance and chromaticity of the image of optical systems with non-uniform transmission filters,” Proc. SPIE 1013, 120–127 (1988).

M. J. Yzuel and F. Calvo, “A study of the possibility of image optimization by apodization filters with residual aberrations,” Optica Acta 26, 1397–1406 (1979).
[CrossRef]

Yzuel, M.J.

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]

J. Campos and M.J. Yzuel, “Axial and extra-axial response in aberrated optical systems with apodizers. Optimization of the Strehl ratio,” J. Mod. Opt. 36, 733–749 (1989).
[CrossRef]

Appl. Opt. (7)

J. Mod. Opt. (5)

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, “Characterization of the retardance of a wave plate to increase the robustness of amplitude-only and phase-only modulations of a liquid crystal display,” J. Mod. Opt. 52, 633–650 (2005).
[CrossRef]

J. Campos and M.J. Yzuel, “Axial and extra-axial response in aberrated optical systems with apodizers. Optimization of the Strehl ratio,” J. Mod. Opt. 36, 733–749 (1989).
[CrossRef]

J. C. Escalera, M. J. Yzuel, and J. Campos, “Influence of amplitude-only filters in optical systems with longitudinal chromatic aberration,” J. Mod. Opt. 38, 1703–1720 (1991).
[CrossRef]

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

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

J. Opt. Soc. Am. A (2)

Micron (1)

J. McOrst, M.D. Sharma, C.J.R. Sheppard, E. West, and K. Matsuda, “Hyperresolving phase-only filters with optically-addressable liquid crystal spatial ligth modulators,” Micron 34, 327–332 (2003).
[CrossRef]

Opt. Commun. (1)

V. Laude, “Twisted-nematic liquid-crystal pixelated active lens,” Opt. Commun. 153, 134–152 (1998).
[CrossRef]

Opt. Eng. (2)

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

Opt. Lett. (4)

Optica Acta (1)

M. J. Yzuel and F. Calvo, “A study of the possibility of image optimization by apodization filters with residual aberrations,” Optica Acta 26, 1397–1406 (1979).
[CrossRef]

Proc. SPIE (1)

M. J. Yzuel, J. C. Escalera, G. Cansado, and J. Campos, “Illuminance and chromaticity of the image of optical systems with non-uniform transmission filters,” Proc. SPIE 1013, 120–127 (1988).

Other (3)

W. J. Smith, Modern Optical Engineering, (McGraw-Hill, 3rd Ed., 2000), 402–412.

H.J. Coufal, D. Psaltis, and B.T. Sincerbox, eds., Holographic Data Storage (Springer-Verlag, Berlin, 2000)

V. G. Chigrinov, Liquid crystal devices: physics and applications (Artech House, 1999).

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Figures (11)

Fig. 1.
Fig. 1.

(a) Scheme of the imaging system. The pupil is located behind the optical system. (b) Longitudinal chromatic aberration for the imaging system expressed with respect to the BIP for the green (514 nm) and the blue (488 nm).

Fig. 2.
Fig. 2.

Simulated results for the 3-D PSF considering the exit pupil with no filter. Plots (b), (c) and (d) are in lab coordinates: (a) Amplitude transmission along the exit pupil with no filter. The transmission is equal to one for the three wavelengths; (b) Intensity along the axis. We note the defocus between the various wavelengths; Intensity at the BIP for (c) the green (z=0 mm) and (d) the red (z=3.16 mm).

Fig. 3.
Fig. 3.

Simulated results for the 3-D PSF considering the exit pupil with the supergaussian filter Ω=0.17, α=1, t0=0.5. Plots (b), (c) and (d) are in lab coordinates: (a) Amplitude transmission along the exit pupil; (b) Intensity along the axis. We note that the depth of focus has increased for the various wavelengths; Intensity at the BIP for (c) the green (z=0 mm) and (d) the red (z=3.16 mm).

Fig. 4.
Fig. 4.

Modulation response of the LCSLM for the three wavelengths used in this work. Symbols correspond to the experimental measurements and continuous lines to the theoretical predictions. (a) Intensity transmission and (b) phase shift.

Fig. 5.
Fig. 5.

Simulated results for the 3-D PSF considering the exit pupil with the supergaussian filter Ω=0.17, α=1, t0=0.5 together with the transmission curve of the LCSLM for each of the wavelengths. Plots (c) and (d) are in lab coordinates: (a) Amplitude transmission and (b) coupled phase profile along the exit pupil for the three wavelengths; Intensity along the axis considering that (c) there is no coupled phase, and (d) considering the coupled phase.

Fig. 6.
Fig. 6.

Simulated results for the 3-D PSF considering the exit pupil with the supergaussian filter Ω=0.17, α=1, t0=0.5 together with the amplitude transmission and coupled phase given by the LCSLM for each of the wavelengths. Intensity at the BIP (a) for the green (z=0 mm) and (b) for the red (z=3.16 mm). Plots are in lab coordinates.

Fig. 7.
Fig. 7.

Scheme of the imaging set-up with the optical system under analysis. The aperture of the LCSLM (16.52 mm of diameter) determines the exit pupil of the system. P1 and P2 are the polarizers; MO is the microscope objective. The distance d from the exit pupil to the image plane is about 50 cm; the distance dMO is fixed to capture magnified images with the same magnification.

Fig. 8.
Fig. 8.

PSF obtained with the system without filter. The first and the second rows correspond to the BIP for the green (z=0 mm) and for the red (z=3.16 mm) respectively. The first three columns are the monochromatic PSF for the 633 nm, 514 nm and 458 nm wavelengths. The last column is a pseudocolored image obtained from the three monochromatic ones.

Fig. 9.
Fig. 9.

PSF obtained with the supergaussian filter Ω=0.17, α=1, t0=0.5. The first and the second rows correspond to the BIP for the green (z=0 mm) and for the red (z=3.16 mm) respectively. The first three columns are the monochromatic PSF for the 633 nm, 514 nm and 458 nm wavelengths. The last column is a pseudocolored image obtained from the three monochromatic ones.

Fig. 10.
Fig. 10.

Pseudocolored images of the PSF obtained in the BIP for the green, z=0 mm (first row), and for the red, z=3.16 mm (second row), for the system without filter (column 1), and with supergaussian filters (columns 2, 3 and 4) centered at the same position t0=0.4 and for different widths given by Ω. In all cases the degree of the supergaussian is α=1.

Fig. 11.
Fig. 11.

Pseudocolored images of the PSF obtained in the BIP for the green, z=0 mm (first row), and for the red, z=3.16 mm (second row), for the system without filter (column 1), and with supergaussian filters (columns 2, 3 and 4) of the same width Ω=0.17 and centered in different positions given by t0. In all cases the degree of the supergaussian is α=1.

Equations (7)

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G λ ( ρ ) = ( 1 λ ) 2 F λ ( ρ ) 2 ,
F λ ( ρ ) = A f λ ( r ) J 0 ( 2 π r ρ ) r dr ,
f λ ( r ) = { τ λ ( r ) exp [ i 2 π W λ ( r ) ] within A 0 outside ,
G λ ( ρ , W 20 ) = ( 1 λ ) 2 F λ ( ρ , W 20 ) 2 ,
F λ ( ρ , W 20 ) = A f λ ( r ) exp ( i 2 π W 20 r 2 ) J 0 ( 2 π r ρ ) r dr .
s = λ NA ρ , z = 2 λ NA 2 W 20 ,
τ ( t ) = K exp [ ( t t 0 Ω ) 2 α ]

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