Abstract

Digital addressing of the electrical signal in spatial light modulators, as it is the case in present liquid crystal on silicon (LCoS) displays, may lead to temporal phase fluctuations in the optical beam. In diffractive optics applications a reduction in the modulation diffraction efficiency may be expected. Experimental work is done characterizing the fluctuations amplitude and phase depth for three different digital addressing sequences. We propose a diffractive model to evaluate the modulation diffraction efficiency of phase diffractive optical elements (DOEs) in the presence of phase fluctuations. Best results are obtained for the most stable electrical sequence even though its phase depth is as small as 280°. The results show good agreement with the numerical calculation given by the model.

© 2010 OSA

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2009

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the temporal fluctuations phenomena on the ECB LCoS performance,” Proc. SPIE 7442, 74420G–1 (2009).
[CrossRef]

2008

A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. Eur. Opt. Soc. – Rapid Pub . 3, 08011 1–6 (2008).

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photon. Technol. Lett. 20(1), 60–62 (2008).
[CrossRef]

A. Márquez, I. Moreno, C. Iemmi, A. Lizana, J. Campos, and M. J. Yzuel, “Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization,” Opt. Express 16(3), 1669–1685 (2008).
[CrossRef] [PubMed]

P. Clemente, V. Durán, L. Martínez-León, V. Climent, E. Tajahuerce, and J. Lancis, “Use of polar decomposition of Mueller matrices for optimizing the phase response of a liquid-crystal-on-silicon display,” Opt. Express 16(3), 1965–1974 (2008).
[CrossRef] [PubMed]

I. Moreno, A. Lizana, J. Campos, A. Márquez, C. Iemmi, and M. J. Yzuel, “Combined Mueller and Jones matrix method for the evaluation of the complex modulation in a liquid-crystal-on-silicon display,” Opt. Lett. 33(6), 627–629 (2008).
[CrossRef] [PubMed]

A. Lizana, I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, “Time-resolved Mueller matrix analysis of a liquid crystal on silicon display,” Appl. Opt. 47(23), 4267–4274 (2008).
[CrossRef] [PubMed]

I. Moreno, A. Lizana, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16(21), 16711–16722 (2008).
[CrossRef] [PubMed]

2007

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystalbased micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[CrossRef]

2006

2005

2004

2001

R. D. Juday, “Generality of matched filtering and minimum Euclidean distance projection for optical pattern recognition,” J. Opt. Soc. Am. A 18(8), 1882–1896 (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(11), 2558–2564 (2001).
[CrossRef]

1998

1996

1995

A. Bergeron, J. Gauvin, F. Gagnon, D. Gingras, H. H. Arsenault, and M. Doucet, “Phase calibration and applications of a liquid crystal spatial light modulator,” Appl. Opt. 34(23), 5133–5139 (1995).
[CrossRef] [PubMed]

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34, 6423–6432 (1995).
[CrossRef]

1994

C. Soutar, S. E. Monroe, and J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33(4), 1061–1069 (1994).
[CrossRef]

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal television,” Opt. Eng. 33(9), 3018–3022 (1994).
[CrossRef]

1993

1990

K. Lu and B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29(3), 240–246 (1990).
[CrossRef]

Also, E.

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the temporal fluctuations phenomena on the ECB LCoS performance,” Proc. SPIE 7442, 74420G–1 (2009).
[CrossRef]

Arsenault, H. H.

Bengtsson, J.

Bergeron, A.

Blümel, T.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystalbased micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[CrossRef]

Campos, J.

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the temporal fluctuations phenomena on the ECB LCoS performance,” Proc. SPIE 7442, 74420G–1 (2009).
[CrossRef]

I. Moreno, A. Lizana, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16(21), 16711–16722 (2008).
[CrossRef] [PubMed]

A. Márquez, I. Moreno, C. Iemmi, A. Lizana, J. Campos, and M. J. Yzuel, “Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization,” Opt. Express 16(3), 1669–1685 (2008).
[CrossRef] [PubMed]

A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. Eur. Opt. Soc. – Rapid Pub . 3, 08011 1–6 (2008).

A. Lizana, I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, “Time-resolved Mueller matrix analysis of a liquid crystal on silicon display,” Appl. Opt. 47(23), 4267–4274 (2008).
[CrossRef] [PubMed]

I. Moreno, A. Lizana, J. Campos, A. Márquez, C. Iemmi, and M. J. Yzuel, “Combined Mueller and Jones matrix method for the evaluation of the complex modulation in a liquid-crystal-on-silicon display,” Opt. Lett. 33(6), 627–629 (2008).
[CrossRef] [PubMed]

A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Achromatic diffractive lens written onto a liquid crystal display,” Opt. Lett. 31(3), 392–394 (2006).
[CrossRef] [PubMed]

A. Márquez, C. Iemmi, I. Moreno, J. Campos, and M. J. Yzuel, “Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays. Optimization of the modulation diffraction efficiency,” Opt. Express 13(6), 2111–2119 (2005).
[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(3), 716–730 (2005).
[CrossRef] [PubMed]

I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, “Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display,” Appl. Opt. 43(34), 6278–6284 (2004).
[CrossRef] [PubMed]

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(11), 2558–2564 (2001).
[CrossRef]

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34, 6423–6432 (1995).
[CrossRef]

Chipman, R. A.

Clemente, P.

Climent, V.

Collings, N.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photon. Technol. Lett. 20(1), 60–62 (2008).
[CrossRef]

Crossland, W. A.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photon. Technol. Lett. 20(1), 60–62 (2008).
[CrossRef]

Davey, A. B.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photon. Technol. Lett. 20(1), 60–62 (2008).
[CrossRef]

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(11), 2558–2564 (2001).
[CrossRef]

J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37(5), 937–945 (1998).
[CrossRef]

Doucet, M.

Durán, V.

Engström, D.

Escalera, J. C.

Evans, M.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photon. Technol. Lett. 20(1), 60–62 (2008).
[CrossRef]

Fernández, E.

Gagnon, F.

Galt, S.

Gauvin, J.

Gingras, D.

Gorecki, C.

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34, 6423–6432 (1995).
[CrossRef]

Hermerschmidt, A.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystalbased micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[CrossRef]

Iemmi, C.

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the temporal fluctuations phenomena on the ECB LCoS performance,” Proc. SPIE 7442, 74420G–1 (2009).
[CrossRef]

I. Moreno, A. Lizana, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16(21), 16711–16722 (2008).
[CrossRef] [PubMed]

A. Márquez, I. Moreno, C. Iemmi, A. Lizana, J. Campos, and M. J. Yzuel, “Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization,” Opt. Express 16(3), 1669–1685 (2008).
[CrossRef] [PubMed]

A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. Eur. Opt. Soc. – Rapid Pub . 3, 08011 1–6 (2008).

A. Lizana, I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, “Time-resolved Mueller matrix analysis of a liquid crystal on silicon display,” Appl. Opt. 47(23), 4267–4274 (2008).
[CrossRef] [PubMed]

I. Moreno, A. Lizana, J. Campos, A. Márquez, C. Iemmi, and M. J. Yzuel, “Combined Mueller and Jones matrix method for the evaluation of the complex modulation in a liquid-crystal-on-silicon display,” Opt. Lett. 33(6), 627–629 (2008).
[CrossRef] [PubMed]

A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Achromatic diffractive lens written onto a liquid crystal display,” Opt. Lett. 31(3), 392–394 (2006).
[CrossRef] [PubMed]

A. Márquez, C. Iemmi, I. Moreno, J. Campos, and M. J. Yzuel, “Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays. Optimization of the modulation diffraction efficiency,” Opt. Express 13(6), 2111–2119 (2005).
[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(3), 716–730 (2005).
[CrossRef] [PubMed]

I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, “Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display,” Appl. Opt. 43(34), 6278–6284 (2004).
[CrossRef] [PubMed]

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(11), 2558–2564 (2001).
[CrossRef]

Jeziorska, A. M.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photon. Technol. Lett. 20(1), 60–62 (2008).
[CrossRef]

Juday, R. D.

Knopp, J.

C. Soutar, S. E. Monroe, and J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33(4), 1061–1069 (1994).
[CrossRef]

Kohler, C.

W. Osten, C. Kohler, and J. Liesener, “Evaluation and application of spatial light modulators for optical metrology,” Opt. Pura Apl. 38, 71–81 (2005).

Komarcevic, M.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photon. Technol. Lett. 20(1), 60–62 (2008).
[CrossRef]

Krüger, S.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystalbased micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[CrossRef]

Lancis, J.

Liesener, J.

W. Osten, C. Kohler, and J. Liesener, “Evaluation and application of spatial light modulators for optical metrology,” Opt. Pura Apl. 38, 71–81 (2005).

Lizana, A.

Lu, G.

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal television,” Opt. Eng. 33(9), 3018–3022 (1994).
[CrossRef]

Lu, K.

K. Lu and B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29(3), 240–246 (1990).
[CrossRef]

Lu, S.-Y.

Márquez, A.

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the temporal fluctuations phenomena on the ECB LCoS performance,” Proc. SPIE 7442, 74420G–1 (2009).
[CrossRef]

A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. Eur. Opt. Soc. – Rapid Pub . 3, 08011 1–6 (2008).

A. Márquez, I. Moreno, C. Iemmi, A. Lizana, J. Campos, and M. J. Yzuel, “Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization,” Opt. Express 16(3), 1669–1685 (2008).
[CrossRef] [PubMed]

I. Moreno, A. Lizana, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16(21), 16711–16722 (2008).
[CrossRef] [PubMed]

A. Lizana, I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, “Time-resolved Mueller matrix analysis of a liquid crystal on silicon display,” Appl. Opt. 47(23), 4267–4274 (2008).
[CrossRef] [PubMed]

I. Moreno, A. Lizana, J. Campos, A. Márquez, C. Iemmi, and M. J. Yzuel, “Combined Mueller and Jones matrix method for the evaluation of the complex modulation in a liquid-crystal-on-silicon display,” Opt. Lett. 33(6), 627–629 (2008).
[CrossRef] [PubMed]

A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Achromatic diffractive lens written onto a liquid crystal display,” Opt. Lett. 31(3), 392–394 (2006).
[CrossRef] [PubMed]

A. Márquez, C. Iemmi, I. Moreno, J. Campos, and M. J. Yzuel, “Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays. Optimization of the modulation diffraction efficiency,” Opt. Express 13(6), 2111–2119 (2005).
[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(3), 716–730 (2005).
[CrossRef] [PubMed]

I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, “Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display,” Appl. Opt. 43(34), 6278–6284 (2004).
[CrossRef] [PubMed]

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(11), 2558–2564 (2001).
[CrossRef]

Martínez-León, L.

Milewski, G.

Millán, M. S.

Monroe, S. E.

C. Soutar, S. E. Monroe, and J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33(4), 1061–1069 (1994).
[CrossRef]

Moore, J. R.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photon. Technol. Lett. 20(1), 60–62 (2008).
[CrossRef]

Moreno, I.

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the temporal fluctuations phenomena on the ECB LCoS performance,” Proc. SPIE 7442, 74420G–1 (2009).
[CrossRef]

I. Moreno, A. Lizana, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16(21), 16711–16722 (2008).
[CrossRef] [PubMed]

A. Márquez, I. Moreno, C. Iemmi, A. Lizana, J. Campos, and M. J. Yzuel, “Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization,” Opt. Express 16(3), 1669–1685 (2008).
[CrossRef] [PubMed]

A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. Eur. Opt. Soc. – Rapid Pub . 3, 08011 1–6 (2008).

I. Moreno, A. Lizana, J. Campos, A. Márquez, C. Iemmi, and M. J. Yzuel, “Combined Mueller and Jones matrix method for the evaluation of the complex modulation in a liquid-crystal-on-silicon display,” Opt. Lett. 33(6), 627–629 (2008).
[CrossRef] [PubMed]

A. Lizana, I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, “Time-resolved Mueller matrix analysis of a liquid crystal on silicon display,” Appl. Opt. 47(23), 4267–4274 (2008).
[CrossRef] [PubMed]

A. Márquez, C. Iemmi, I. Moreno, J. Campos, and M. J. Yzuel, “Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays. Optimization of the modulation diffraction efficiency,” Opt. Express 13(6), 2111–2119 (2005).
[CrossRef] [PubMed]

I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, “Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display,” Appl. Opt. 43(34), 6278–6284 (2004).
[CrossRef] [PubMed]

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(11), 2558–2564 (2001).
[CrossRef]

J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37(5), 937–945 (1998).
[CrossRef]

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34, 6423–6432 (1995).
[CrossRef]

Osten, S.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystalbased micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[CrossRef]

Osten, W.

W. Osten, C. Kohler, and J. Liesener, “Evaluation and application of spatial light modulators for optical metrology,” Opt. Pura Apl. 38, 71–81 (2005).

Otón, J.

Parker, R. J.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photon. Technol. Lett. 20(1), 60–62 (2008).
[CrossRef]

Pérez-Cabré, E.

Pezzaniti, J. L.

Saleh, B. E. A.

K. Lu and B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29(3), 240–246 (1990).
[CrossRef]

Soutar, C.

C. Soutar, S. E. Monroe, and J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33(4), 1061–1069 (1994).
[CrossRef]

Tajahuerce, E.

Tsai, P.

Wilkinson, T. D.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photon. Technol. Lett. 20(1), 60–62 (2008).
[CrossRef]

Wolfe, J. E.

Xu, H.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photon. Technol. Lett. 20(1), 60–62 (2008).
[CrossRef]

Yu, F. T. S.

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal television,” Opt. Eng. 33(9), 3018–3022 (1994).
[CrossRef]

Yzuel, M. J.

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the temporal fluctuations phenomena on the ECB LCoS performance,” Proc. SPIE 7442, 74420G–1 (2009).
[CrossRef]

I. Moreno, A. Lizana, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16(21), 16711–16722 (2008).
[CrossRef] [PubMed]

A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. Eur. Opt. Soc. – Rapid Pub . 3, 08011 1–6 (2008).

A. Márquez, I. Moreno, C. Iemmi, A. Lizana, J. Campos, and M. J. Yzuel, “Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization,” Opt. Express 16(3), 1669–1685 (2008).
[CrossRef] [PubMed]

A. Lizana, I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, “Time-resolved Mueller matrix analysis of a liquid crystal on silicon display,” Appl. Opt. 47(23), 4267–4274 (2008).
[CrossRef] [PubMed]

I. Moreno, A. Lizana, J. Campos, A. Márquez, C. Iemmi, and M. J. Yzuel, “Combined Mueller and Jones matrix method for the evaluation of the complex modulation in a liquid-crystal-on-silicon display,” Opt. Lett. 33(6), 627–629 (2008).
[CrossRef] [PubMed]

A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Achromatic diffractive lens written onto a liquid crystal display,” Opt. Lett. 31(3), 392–394 (2006).
[CrossRef] [PubMed]

A. Márquez, C. Iemmi, I. Moreno, J. Campos, and M. J. Yzuel, “Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays. Optimization of the modulation diffraction efficiency,” Opt. Express 13(6), 2111–2119 (2005).
[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(3), 716–730 (2005).
[CrossRef] [PubMed]

I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, “Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display,” Appl. Opt. 43(34), 6278–6284 (2004).
[CrossRef] [PubMed]

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(11), 2558–2564 (2001).
[CrossRef]

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34, 6423–6432 (1995).
[CrossRef]

Zhang, Z.

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal television,” Opt. Eng. 33(9), 3018–3022 (1994).
[CrossRef]

Appl. Opt.

IEEE Photon. Technol. Lett.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photon. Technol. Lett. 20(1), 60–62 (2008).
[CrossRef]

J. Eur. Opt. Soc. – Rapid Pub

A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. Eur. Opt. Soc. – Rapid Pub . 3, 08011 1–6 (2008).

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. 34, 6423–6432 (1995).
[CrossRef]

Opt. Eng.

C. Soutar, S. E. Monroe, and J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33(4), 1061–1069 (1994).
[CrossRef]

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal television,” Opt. Eng. 33(9), 3018–3022 (1994).
[CrossRef]

K. Lu and B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29(3), 240–246 (1990).
[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(11), 2558–2564 (2001).
[CrossRef]

Opt. Express

M. S. Millán, J. Otón, and E. Pérez-Cabré, “Chromatic compensation of programmable Fresnel lenses,” Opt. Express 14(13), 6226–6242 (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(3), 716–730 (2005).
[CrossRef] [PubMed]

A. Márquez, C. Iemmi, I. Moreno, J. Campos, and M. J. Yzuel, “Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays. Optimization of the modulation diffraction efficiency,” Opt. Express 13(6), 2111–2119 (2005).
[CrossRef] [PubMed]

I. Moreno, A. Lizana, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16(21), 16711–16722 (2008).
[CrossRef] [PubMed]

M. S. Millán, J. Otón, and E. Pérez-Cabré, “Dynamic compensation of chromatic aberration in a programmable diffractive lens,” Opt. Express 14(20), 9103–9112 (2006).
[CrossRef] [PubMed]

A. Márquez, I. Moreno, C. Iemmi, A. Lizana, J. Campos, and M. J. Yzuel, “Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization,” Opt. Express 16(3), 1669–1685 (2008).
[CrossRef] [PubMed]

P. Clemente, V. Durán, L. Martínez-León, V. Climent, E. Tajahuerce, and J. Lancis, “Use of polar decomposition of Mueller matrices for optimizing the phase response of a liquid-crystal-on-silicon display,” Opt. Express 16(3), 1965–1974 (2008).
[CrossRef] [PubMed]

Opt. Lett.

Opt. Pura Apl.

W. Osten, C. Kohler, and J. Liesener, “Evaluation and application of spatial light modulators for optical metrology,” Opt. Pura Apl. 38, 71–81 (2005).

Proc. SPIE

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the temporal fluctuations phenomena on the ECB LCoS performance,” Proc. SPIE 7442, 74420G–1 (2009).
[CrossRef]

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystalbased micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[CrossRef]

Other

S. T. Wu, and D. K. Yang, Reflective Liquid Crystal Displays, (John Wiley and Sons Inc., Chichester, 2005).

J. Turunen and F. Wyrowski eds., Diffractive Optics for Industrial and Commercial Applications, (Akademie Verlag, Berlin, 1997).

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

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Figures (5)

Fig. 1
Fig. 1

Phase modulation values corresponding to the ECB LCoS display working as a phase-only device for 633 nm, and for the three electrical signal sequences. (a) Average phase. (b-d) Instantaneous phase for the sequences: (b) #1, (c) #2, and (d) #3.

Fig. 2
Fig. 2

Mapping scheme for the implementation of the linear mismatching encoding (Model 1) and the saturation mismatching encoding (Model 2).

Fig. 3
Fig. 3

Simulation for the energy for the first term α = 1 and for the two mismatching encoding strategies: in (a) as a function of the phase depth and in (b) as a function of the fluctuation amplitude.

Fig. 4
Fig. 4

Energy for the first term α = 1 calculated for the values of the phase parameters corresponding to the three digital electrical sequences. We plot the energy values corresponding to a phase depth of 360° (continuous red curve) as a function of the fluctuation amplitude. In this curve the points with fluctuation amplitude values of 50% and 120%, indicated by the vertical lines, correspond to sequences #1 and #2. The two horizontal lines correspond respectively to the energy values obtained when applying the linear (long-short dash) and the saturated (short dash) encodings for the sequence #3, having a phase depth of 280° and a fluctuation amplitude of 30%.

Fig. 5
Fig. 5

Normalized intensity for the zero and first orders obtained when addressing a blazed grating and the following sequences and phase encoding schemes. (a) sequence #1, (b) sequence #2, (c) sequence #3 with linear mismatch, and (d) sequence #3 with saturated mismatch. The ECB LCoS is in the phase-only regime and it is illuminated with the wavelength 633 nm.

Tables (2)

Tables Icon

Table 1 Values for the parameters characterizing the instantaneous phase signals shown in Figs. 1(b-d), measured with the diffractive-based method and for the three electrical sequences.

Tables Icon

Table 2 Values for the parameters characterizing the instantaneous normalized intensities for the zero and the first diffracted orders produced by the blazed grating. Both experimental and numerical values are given.

Equations (17)

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

M(φ)=A(φ)exp(iφ')=αGα   exp(iαφ)
p(t)=p¯+Kp¯(12+tT),
ε(t)=ε¯+Kε¯(12+tT),
m(ϕ,t)=exp[iε(t)2πϕ],
Gα(ε¯,K,t)=Exp[i(ε¯2πα+Kε¯2π(12+tT))π]
×   sinc((ε¯2πα+Kε¯2π(12+tT))),
ηα(ε¯,K)=1T0T|Gα(ε¯,K,t)|2dt,
ηα(ε¯)=sinc2(ε¯2πα)
p(ϕ,t)={ϕ(t)0<ϕε¯ε(t)ε¯<ϕ(2π+ε¯)/20(2π+ε¯)/2<ϕ2π
ϕ(t)=ϕ+Kϕ(12+tT).
Gα(ε¯,K,t)=Exp[i(1α+K(12+tT))ε¯2]sin((1α+K(12+tT))ε¯2)π(1α+K(12+tT))
+Exp[i(1α2+K(12+tT))ε¯](1)αExp[iαε¯2]iα2π
+1(1)αExp[iαε¯2]iα2π.
Gα(ε¯,K=0,t)=Exp[i(1α)ε¯2]ε¯2πsinc((1α)ε¯2π)
+Exp[i(1α2)ε¯](1)αExp[iαε¯2]iα2π
+1(1)αExp[iαε¯2]iα2π,
η1(ε¯)={ε¯2π+sin(ε¯/2)π}2

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