Abstract

A polarimetric method for the measurement of linear retardance in the presence of phase fluctuations is presented. This can be applied to electro-optic devices behaving as variable linear retarders. The method is based on an extended Mueller matrix model for the linear retarder containing the time-averaged effects of the instabilities. As a result, an averaged Stokes polarimetry technique is proposed to characterize both the retardance and its flicker magnitude. Predictive capability of the approach is experimentally demonstrated, validating the model and the calibration technique. The approach is applied to liquid crystal on silicon displays (LCoS) using a commercial Stokes polarimeter. Both the magnitude of the average retardance and the amplitude of its fluctuation are obtained for each gray level value addressed, thus enabling a complete phase characterization of the LCoS.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Goldstein, Polarized Light (Marcel Dekker, 2003).
  2. A. De Martino, Y. K. Kim, E. Garcia-Caurel, B. Laude, and B. Drévillon, Opt. Lett. 28, 616 (2003).
    [CrossRef]
  3. A. Peinado, A. Lizana, J. Vidal, C. Iemmi, and J. Campos, Opt. Express 18, 9815 (2010).
    [CrossRef]
  4. S. T. Wu and D. K. Yang, Reflective Liquid Crystal Displays (Wiley, 2005).
  5. N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, J. Disp. Technol. 7, 112 (2011).
    [CrossRef]
  6. C. Ramirez, E. Otón, C. Iemmi, I. Moreno, N. Bennis, J. M. Otón, and J. Campos, Opt. Express 21, 8116 (2013).
    [CrossRef]
  7. A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, J. Mod. Opt. 52, 633 (2005).
    [CrossRef]
  8. J. E. Wolfe and R. A. Chipman, Appl. Opt. 45, 1688 (2006).
    [CrossRef]
  9. A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, Proc. SPIE 6584, 65840E (2007).
    [CrossRef]
  10. 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, IEEE Photon. Technol. Lett. 20, 60 (2008).
    [CrossRef]
  11. A. Lizana, I. Moreno, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, Opt. Express 16, 16711 (2008).
    [CrossRef]
  12. A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, Proc. SPIE 7442, 74420G-1 (2009).
  13. J. García-Márquez, V. López, A. González-Vega, and E. Noé, Opt. Express 20, 8431 (2012).
    [CrossRef]
  14. A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, Proc. SPIE 8498, 84980L (2012).
    [CrossRef]
  15. C. Ramirez, B. Karakus, A. Lizana, and J. Campos, Opt. Express 21, 3182 (2013).
    [CrossRef]
  16. C. Flueraru, S. Latoui, J. Besse, and P. Legendre, IEEE Trans. Instrum. Meas. 57, 731 (2008).
    [CrossRef]
  17. T. G. Brown and Q. Zhan, Opt. Express 18, 10775 (2010).
    [CrossRef]

2013 (2)

2012 (2)

J. García-Márquez, V. López, A. González-Vega, and E. Noé, Opt. Express 20, 8431 (2012).
[CrossRef]

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, Proc. SPIE 8498, 84980L (2012).
[CrossRef]

2011 (1)

N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, J. Disp. Technol. 7, 112 (2011).
[CrossRef]

2010 (2)

2009 (1)

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, Proc. SPIE 7442, 74420G-1 (2009).

2008 (3)

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, IEEE Trans. Instrum. Meas. 57, 731 (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, IEEE Photon. Technol. Lett. 20, 60 (2008).
[CrossRef]

A. Lizana, I. Moreno, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, Opt. Express 16, 16711 (2008).
[CrossRef]

2007 (1)

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, Proc. SPIE 6584, 65840E (2007).
[CrossRef]

2006 (1)

2005 (1)

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, J. Mod. Opt. 52, 633 (2005).
[CrossRef]

2003 (1)

Also, E.

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, Proc. SPIE 7442, 74420G-1 (2009).

Beléndez, A.

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, Proc. SPIE 8498, 84980L (2012).
[CrossRef]

Bennis, N.

Besse, J.

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, IEEE Trans. Instrum. Meas. 57, 731 (2008).
[CrossRef]

Blümel, T.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, Proc. SPIE 6584, 65840E (2007).
[CrossRef]

Brown, T. G.

Campos, J.

Cazorla, C.

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, J. Mod. Opt. 52, 633 (2005).
[CrossRef]

Chipman, R. A.

Christmas, J.

N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, J. Disp. Technol. 7, 112 (2011).
[CrossRef]

Chu, D.

N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, J. Disp. Technol. 7, 112 (2011).
[CrossRef]

Collings, N.

N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, J. Disp. Technol. 7, 112 (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, IEEE Photon. Technol. Lett. 20, 60 (2008).
[CrossRef]

Crossland, B.

N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, J. Disp. Technol. 7, 112 (2011).
[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, IEEE Photon. Technol. Lett. 20, 60 (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, IEEE Photon. Technol. Lett. 20, 60 (2008).
[CrossRef]

Davey, T.

N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, J. Disp. Technol. 7, 112 (2011).
[CrossRef]

De Martino, A.

Drévillon, B.

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, IEEE Photon. Technol. Lett. 20, 60 (2008).
[CrossRef]

Fernández, E.

Flueraru, C.

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, IEEE Trans. Instrum. Meas. 57, 731 (2008).
[CrossRef]

Francés, J.

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, Proc. SPIE 8498, 84980L (2012).
[CrossRef]

Gallego, S.

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, Proc. SPIE 8498, 84980L (2012).
[CrossRef]

Garcia-Caurel, E.

García-Márquez, J.

Goldstein, G.

G. Goldstein, Polarized Light (Marcel Dekker, 2003).

González-Vega, A.

Hermerschmidt, A.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, 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, IEEE Photon. Technol. Lett. 20, 60 (2008).
[CrossRef]

Karakus, B.

Kim, Y. K.

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, IEEE Photon. Technol. Lett. 20, 60 (2008).
[CrossRef]

Krüger, S.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, Proc. SPIE 6584, 65840E (2007).
[CrossRef]

Latoui, S.

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, IEEE Trans. Instrum. Meas. 57, 731 (2008).
[CrossRef]

Laude, B.

Legendre, P.

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, IEEE Trans. Instrum. Meas. 57, 731 (2008).
[CrossRef]

Lizana, A.

López, V.

Márquez, A.

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, Proc. SPIE 8498, 84980L (2012).
[CrossRef]

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, Proc. SPIE 7442, 74420G-1 (2009).

A. Lizana, I. Moreno, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, Opt. Express 16, 16711 (2008).
[CrossRef]

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, J. Mod. Opt. 52, 633 (2005).
[CrossRef]

Martínez, F. J.

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, Proc. SPIE 8498, 84980L (2012).
[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, IEEE Photon. Technol. Lett. 20, 60 (2008).
[CrossRef]

Moreno, I.

Noé, E.

Ortuño, M.

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, Proc. SPIE 8498, 84980L (2012).
[CrossRef]

Osten, S.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, Proc. SPIE 6584, 65840E (2007).
[CrossRef]

Otón, E.

Otón, J. M.

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, IEEE Photon. Technol. Lett. 20, 60 (2008).
[CrossRef]

Pascual, I.

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, Proc. SPIE 8498, 84980L (2012).
[CrossRef]

Peinado, A.

Ramirez, C.

Vidal, J.

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, IEEE Photon. Technol. Lett. 20, 60 (2008).
[CrossRef]

Wolfe, J. E.

Wu, S. T.

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

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, IEEE Photon. Technol. Lett. 20, 60 (2008).
[CrossRef]

Yang, D. K.

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

Yzuel, M. J.

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, Proc. SPIE 7442, 74420G-1 (2009).

A. Lizana, I. Moreno, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, Opt. Express 16, 16711 (2008).
[CrossRef]

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, J. Mod. Opt. 52, 633 (2005).
[CrossRef]

Zhan, Q.

Appl. Opt. (1)

IEEE Photon. Technol. Lett. (1)

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, IEEE Photon. Technol. Lett. 20, 60 (2008).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

C. Flueraru, S. Latoui, J. Besse, and P. Legendre, IEEE Trans. Instrum. Meas. 57, 731 (2008).
[CrossRef]

J. Disp. Technol. (1)

N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, J. Disp. Technol. 7, 112 (2011).
[CrossRef]

J. Mod. Opt. (1)

A. Márquez, C. Cazorla, M. J. Yzuel, and J. Campos, J. Mod. Opt. 52, 633 (2005).
[CrossRef]

Opt. Express (6)

Opt. Lett. (1)

Proc. SPIE (3)

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, Proc. SPIE 7442, 74420G-1 (2009).

A. Márquez, F. J. Martínez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, Proc. SPIE 8498, 84980L (2012).
[CrossRef]

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, Proc. SPIE 6584, 65840E (2007).
[CrossRef]

Other (2)

G. Goldstein, Polarized Light (Marcel Dekker, 2003).

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

Cited By

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

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Experimental values for the Stokes parameters and DoP, for input SOP linear at +45° and λ=633nm.

Fig. 2.
Fig. 2.

Calculated values for the average retardance and the fluctuation amplitude for λ=633nm.

Fig. 3.
Fig. 3.

Experimental and simulated values for the Stokes parameters, for input SOP linear at +15° and λ=633nm.

Fig. 4.
Fig. 4.

Experimental and simulated DoP, for input SOP linear at +15° and λ=633nm.

Fig. 5.
Fig. 5.

Experimental and simulated values for the Stokes parameters, for input SOP right-handed circular and λ=633nm.

Fig. 6.
Fig. 6.

Experimental and simulated DoP at output, for input SOP right-handed circular and λ=633nm.

Equations (12)

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

MR(Γ)=(1000010000cosΓsinΓ00sinΓcosΓ).
Γ(t)={Γ¯a+2aT/2t0t<T/2Γ¯+3a2aT/2tT/2t<T,
cosΓ(t)=(sina/a)cos(Γ¯),
sinΓ(t)=(sina/a)sin(Γ¯).
MR(Γ¯,a)=(1000010000(sina/a)cosΓ¯(sina/a)sinΓ¯00(sina/a)sinΓ¯(sina/a)cosΓ¯).
Inv=(1000010000100001).
Sout=Inv·MR(Γ¯,a)·Sin.
Sout=(S0S1±(sina/a)(S2cosΓ¯+S3sinΓ¯)±(sina/a)(S2sinΓ¯+S3cosΓ¯)),
DoP=(S1)2+(sina/a)2((S2)2+(S3)2)/S0.
Sout=(10(sina/a)cosΓ¯(sina/a)sinΓ¯),
DoP=(sina/a).
Sout=(10(sina/a)sinΓ¯(sina/a)cosΓ¯).

Metrics