Abstract

Recently we proposed a novel polarimetric method, based on Stokes polarimetry, enabling the characterization of the linear retardance and its flicker amplitude in electro-optic devices behaving as variable linear retarders. In this work we apply extensively the technique to parallel-aligned liquid crystal on silicon devices (PA-LCoS) under the most typical working conditions. As a previous step we provide some experimental analysis to delimitate the robustness of the technique dealing with its repeatability and its reproducibility. Then we analyze the dependencies of retardance and flicker for different digital sequence formats and for a wide variety of working geometries.

© 2014 Optical Society of America

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References

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    [Crossref]
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  21. A. Lizana, N. Martín, M. Estapé, E. Fernández, I. Moreno, A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the incident angle in the performance of liquid crystal on silicon displays,” Opt. Express 17(10), 8491–8505 (2009).
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2014 (2)

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, and I. Pascual, “Extended linear polarimeter to measure retardance and flicker: application to liquid crystal on silicon devices in two working geometries,” Opt. Eng. 53, 014105 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (3)

2011 (1)

2010 (1)

2009 (2)

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 (2009).
[Crossref]

A. Lizana, N. Martín, M. Estapé, E. Fernández, I. Moreno, A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the incident angle in the performance of liquid crystal on silicon displays,” Opt. Express 17(10), 8491–8505 (2009).
[Crossref] [PubMed]

2008 (4)

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, “Error analysis of a rotating quarter-wave plate Stokes’ polarimeter,” IEEE Trans. Instrum. Meas. 57(4), 731–735 (2008).
[Crossref]

M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion trimming in a reconfigurable wavelength selective switch,” J. Lightwave Technol. 26(1), 73–78 (2008).
[Crossref]

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]

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 (1)

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

2006 (1)

2005 (1)

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

Abakoumov, D.

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 (2009).
[Crossref]

Arias, A.

Baxter, G.

Beléndez, A.

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Classical polarimetric method revisited to analyse the modulation capabilities of parallel aligned liquid crystal on silicon displays,” Proc. SPIE 8498, 84980L (2012).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned LCoS devices,” Opt. Eng. (accepted for publication).

Besse, J.

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, “Error analysis of a rotating quarter-wave plate Stokes’ polarimeter,” IEEE Trans. Instrum. Meas. 57(4), 731–735 (2008).
[Crossref]

Bigo, S.

Bigot-Astruc, M.

Blümel, T.

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

Bolger, J. A.

Boutin, A.

Brindel, P.

Brown, T. G.

Campos, J.

Charlet, G.

Chipman, R. A.

Christmas, J.

Chu, D.

Collings, N.

N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, “The applications and technology of phase-only liquid crystal on silicon devices,” J. Display Technol. 7(3), 112–119 (2011).
[Crossref]

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, B.

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]

Davey, T.

Eggleton, B. J.

Estapé, M.

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.

Flueraru, C.

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, “Error analysis of a rotating quarter-wave plate Stokes’ polarimeter,” IEEE Trans. Instrum. Meas. 57(4), 731–735 (2008).
[Crossref]

Francés, J.

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, and I. Pascual, “Extended linear polarimeter to measure retardance and flicker: application to liquid crystal on silicon devices in two working geometries,” Opt. Eng. 53, 014105 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Classical polarimetric method revisited to analyse the modulation capabilities of parallel aligned liquid crystal on silicon displays,” Proc. SPIE 8498, 84980L (2012).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned LCoS devices,” Opt. Eng. (accepted for publication).

Frisken, S.

Gallego, S.

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, and I. Pascual, “Extended linear polarimeter to measure retardance and flicker: application to liquid crystal on silicon devices in two working geometries,” Opt. Eng. 53, 014105 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Classical polarimetric method revisited to analyse the modulation capabilities of parallel aligned liquid crystal on silicon displays,” Proc. SPIE 8498, 84980L (2012).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned LCoS devices,” Opt. Eng. (accepted for publication).

García-Márquez, J.

González-Vega, A.

Hermerschmidt, A.

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

Iemmi, C.

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]

Karakus, B.

Koebele, C.

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-crystal-based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[Crossref]

Latoui, S.

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, “Error analysis of a rotating quarter-wave plate Stokes’ polarimeter,” IEEE Trans. Instrum. Meas. 57(4), 731–735 (2008).
[Crossref]

Ledesma, S.

Legendre, P.

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, “Error analysis of a rotating quarter-wave plate Stokes’ polarimeter,” IEEE Trans. Instrum. Meas. 57(4), 731–735 (2008).
[Crossref]

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.

López, V.

Mardoyan, H.

Márquez, A.

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, and I. Pascual, “Extended linear polarimeter to measure retardance and flicker: application to liquid crystal on silicon devices in two working geometries,” Opt. Eng. 53, 014105 (2014).
[Crossref]

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Classical polarimetric method revisited to analyse the modulation capabilities of parallel aligned liquid crystal on silicon displays,” Proc. SPIE 8498, 84980L (2012).
[Crossref]

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 (2009).
[Crossref]

A. Lizana, N. Martín, M. Estapé, E. Fernández, I. Moreno, A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the incident angle in the performance of liquid crystal on silicon displays,” Opt. Express 17(10), 8491–8505 (2009).
[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]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned LCoS devices,” Opt. Eng. (accepted for publication).

Martín, N.

Martínez, F. J.

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, and I. Pascual, “Extended linear polarimeter to measure retardance and flicker: application to liquid crystal on silicon devices in two working geometries,” Opt. Eng. 53, 014105 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Classical polarimetric method revisited to analyse the modulation capabilities of parallel aligned liquid crystal on silicon displays,” Proc. SPIE 8498, 84980L (2012).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned LCoS devices,” Opt. Eng. (accepted for publication).

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.

Neves, L.

Noé, E.

Ortuño, M.

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Classical polarimetric method revisited to analyse the modulation capabilities of parallel aligned liquid crystal on silicon displays,” Proc. SPIE 8498, 84980L (2012).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned LCoS devices,” Opt. Eng. (accepted for publication).

Osten, S.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal-based 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).

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]

Pascual, I.

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, and I. Pascual, “Extended linear polarimeter to measure retardance and flicker: application to liquid crystal on silicon devices in two working geometries,” Opt. Eng. 53, 014105 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Classical polarimetric method revisited to analyse the modulation capabilities of parallel aligned liquid crystal on silicon displays,” Proc. SPIE 8498, 84980L (2012).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned LCoS devices,” Opt. Eng. (accepted for publication).

Poole, S.

Provost, L.

Ramirez, C.

Rebón, L.

Roelens, M. A. F.

Salsi, M.

Sillard, P.

Solís-Prosser, M. A.

Sperti, D.

Tran, P.

Varga, J. J. M.

Verluise, F.

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]

Yzuel, M. J.

Zhan, Q.

Appl. Opt. (1)

IEEE Photon. Technol. Lett. (1)

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Figures (9)

Fig. 1
Fig. 1 Experimental setup used to measure linear retardance and flicker with the averaging Stokes polarimetric technique and for the two generic working geometries: (a) with a beam-splitter, and (b) without.
Fig. 2
Fig. 2 Experimental values for the: (a) Stokes parameters; (b) the DoP. For input SOP linear at + 45°, λ = 633nm, and for sequences “18-6 633 2pi linear” (dashed) and “5-5 633 2pi linear” (continuous). For working geometry with a cube beam-splitter in front of the PA-LCoS.
Fig. 3
Fig. 3 Calculated values for the average retardance and the fluctuation amplitude for λ = 633nm, and for sequences “18-6 633 2pi linear” (dashed) and “5-5 633 2pi linear” (continuous). For working geometry with a cube beam-splitter in front of the PA-LCoS.
Fig. 4
Fig. 4 Experimental setup for the extended linear polarimeter [18], which further enables to measure instantaneous values. For working geometry with a cube beam-splitter.
Fig. 5
Fig. 5 Evaluation of the repeatability. (a) Average retardance (10 curves), and (b) its associated standard deviation. (c) Fluctuation amplitude (10 curves), and (d) its associated standard deviation. For λ = 633nm, sequence “5-5 633 2pi linear”, and incidence at 3°.
Fig. 6
Fig. 6 Evaluation of the reproducibility. (a) Average retardance and (b) fluctuation amplitude results. The setup has been rebuilt from scratch in each case. For λ = 633nm, sequence “5-5 633 2pi linear”, and incidence at 3°.
Fig. 7
Fig. 7 Stokes parameter S1 for the two sequences and the 4 geometries: (a) Sequence “18-6 2pi linear 633nm”, (b) Sequence “5-5 2pi linear 633nm”.
Fig. 8
Fig. 8 Results for the 4 geometries and for the sequence “18-6 2pi linear 633nm”: (a) Average retardance, (b) Fluctuation amplitude.
Fig. 9
Fig. 9 Results for the 4 geometries and for the sequence “5-5 2pi linear 633nm”: (a) Average retardance, (b) Fluctuation amplitude.

Tables (1)

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Table 1 Average retardance and fluctuation amplitude obtained with the average Stokes polarimetric method (columns 3 and 4) and with the instantaneous measurements (colums 5 and 6).

Equations (6)

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M R ( Γ )=( 1 0 0 0 0 1 0 0 0 0 cosΓ sinΓ 0 0 sinΓ cosΓ )
M R ( Γ ¯ ,a) =( 1 0 0 0 0 1 0 0 0 0 ( sina /a )cos Γ ¯ ( sina /a )sin Γ ¯ 0 0 ( sina /a )sin Γ ¯ ( sina /a )cos Γ ¯ )
Inv=( 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 )
S out =Inv M R ( Γ ¯ ,a) S in
S out =( 1 0 ( sina /a )cos Γ ¯ ( sina /a )sin Γ ¯ )
DoP=( sina /a )

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