Abstract

The description of adjustment of an imaging Stokes polarimeter constructed and tested in our laboratory is presented. Our polarimeter’s operation is based on six fast intensity distribution measurements realized in six different configurations of linear and circular analyzers. Using liquid crystal variable retarders (LCVRs) makes this construction compact and mechanically simple. However, new problems arise with proper azimuthal alignment as well as with proper LCVR voltage adjustment. Three basic steps of the adjustment procedure adapted to the specific construction of our polarimeter are described in detail. Some remarks concerning the critical parameters of the used CCD camera’s parameters are also presented, as well as experimental verifications of the setup’s accuracy acquired due to the proper adjustment process.

© 2011 Optical Society of America

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  1. J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
    [CrossRef]
  2. C. C. Montarou and T. K. Gaylord, “Two-wave-plate compensator for single-point retardation measurement,” Appl. Opt. 43, 6580–6595 (2004).
    [CrossRef]
  3. P. A. Williams, A. H. Rose, and C. M. Wang, “Rotating-polarizer polarimeter for accurate retardance measurement,” Appl. Opt. 36, 6466–6472 (1997).
    [CrossRef]
  4. P. Kurzynowski and W. A. Woźniak, “Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates,” Optik (Jena) 113, 51–53 (2002).
    [CrossRef]
  5. M. Mujat, E. Baleine, and A. Dogariu, “Interferometric imaging polarimeter,” J. Opt. Soc. Am. A 21, 2244–2249 (2004).
    [CrossRef]
  6. J. F. Lin and Y. L. Lo, “The new circular heterodyne interferometer with electro-optic modulation for measurement of the optical linear birefringence,” Opt. Commun. 260, 486–492(2006).
    [CrossRef]
  7. M. Takeda, H. Ina, and H. Kobayashi, “Fourier transform method of fringe-pattern analysis for computer based topography and interferometry,” J. Opt. Soc. Am. 72, 156–159 (1982).
    [CrossRef]
  8. S. Drobczyński, J. M. Bueno, P. Artal, and H. Kasprzak, “Transmission imaging polarimetry for linear birefringent medium using carrier fringe method,” Appl. Opt. 45, 5489–5496 (2006).
    [CrossRef] [PubMed]
  9. P. Kurzynowski, S. Drobczyński, and W. A. Woźniak, “Dynamic polarization states and birefringence distributions measurements in spatial elliptical polariscope using Fourier analysis method,” Opt. Express 17, 10144–10154 (2009).
    [CrossRef] [PubMed]
  10. B. Laude-Boulesteix, A. de Martino, B. Drevillon, and L. Schwartz, “Mueller polarimetric imaging system with liquid crystals,” Appl. Opt. 43, 2824–2832 (2004).
    [CrossRef] [PubMed]
  11. Y. L. Lo, S. Y. Lee, and J. F. Lin, “Polariscope for simultaneous measurement of the principal axis and the phase retardation by use of two phase-locked extractions,” Appl. Opt. 43, 6248–6254 (2004).
    [CrossRef] [PubMed]
  12. S. Drobczyński and P. Kurzynowski, “Imaging polarimeter for linear birefringence measurements using a liquid crystal modulator,” Opt. Eng. 47, 023603 (2008).
    [CrossRef]
  13. T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, “Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plates elements,” Appl. Opt. 46, 4963–4967 (2007).
    [CrossRef] [PubMed]
  14. K. Oka and T. Kaneko, “Compact complete imaging polarimeter using birefringent wedge prisms,” Opt. Express 11, 1510–1519 (2003).
    [CrossRef] [PubMed]
  15. K. Oka and N. Saito, “Snapshot complete imaging polarimeter using Savart plates,” Proc. SPIE 6295, 629508 (2006).
    [CrossRef]
  16. W. A. Woźniak and P. Kurzynowski, “Compact spatial polariscope for light polarization state analysis,” Opt. Express 16, 10471–10479 (2008).
    [CrossRef] [PubMed]
  17. P. A. Williams, “Rotating-wave-plate Stokes polarimeter for differential group delay measurements of polarization-mode dispersion,” Appl. Opt. 38, 6508–6515 (1999).
    [CrossRef]
  18. P. Goudail, P. Terrier, Y. Takakura, L. Bigué, F. Galland, and V. Devlaminck, “Target detection with liquid-crystal-based passive Stokes polarimeter,” Appl. Opt. 43, 274–282(2004).
    [CrossRef] [PubMed]
  19. J. E. Wolfe and R. A. Chipman, “Polarimetric characterization of liquid-crystal-on-silicon panels,” Appl. Opt. 45, 1688–1703 (2006).
    [CrossRef] [PubMed]
  20. J. S. Baba and P. R. Boudreaux, “Wavelength, temperature and voltage dependent calibration of a nematic liquid crystal multispectral polarization generating device,” Appl. Opt. 46, 5539–5544 (2007).
    [CrossRef] [PubMed]
  21. P. Terrier, J. M. Charbois, and V. Devlaminck, “Fast-axis orientation dependence on driving voltage for a Stokes polarimeter based on concrete liquid-crystal variable retarders,” Appl. Opt. 49, 4278–4283 (2010).
    [CrossRef] [PubMed]
  22. P. Yeh and C. Gu, “Optics of Liquid Crystal Displays(Wiley, 2010).

2010 (1)

2009 (1)

2008 (2)

S. Drobczyński and P. Kurzynowski, “Imaging polarimeter for linear birefringence measurements using a liquid crystal modulator,” Opt. Eng. 47, 023603 (2008).
[CrossRef]

W. A. Woźniak and P. Kurzynowski, “Compact spatial polariscope for light polarization state analysis,” Opt. Express 16, 10471–10479 (2008).
[CrossRef] [PubMed]

2007 (2)

2006 (4)

J. E. Wolfe and R. A. Chipman, “Polarimetric characterization of liquid-crystal-on-silicon panels,” Appl. Opt. 45, 1688–1703 (2006).
[CrossRef] [PubMed]

K. Oka and N. Saito, “Snapshot complete imaging polarimeter using Savart plates,” Proc. SPIE 6295, 629508 (2006).
[CrossRef]

J. F. Lin and Y. L. Lo, “The new circular heterodyne interferometer with electro-optic modulation for measurement of the optical linear birefringence,” Opt. Commun. 260, 486–492(2006).
[CrossRef]

S. Drobczyński, J. M. Bueno, P. Artal, and H. Kasprzak, “Transmission imaging polarimetry for linear birefringent medium using carrier fringe method,” Appl. Opt. 45, 5489–5496 (2006).
[CrossRef] [PubMed]

2004 (5)

2003 (1)

2002 (1)

P. Kurzynowski and W. A. Woźniak, “Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates,” Optik (Jena) 113, 51–53 (2002).
[CrossRef]

1999 (1)

1997 (1)

1995 (1)

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

1982 (1)

Araki, T.

Artal, P.

Baba, J. S.

Baleine, E.

Bigué, L.

Boudreaux, P. R.

Bueno, J. M.

Charbois, J. M.

Chipman, R. A.

de Martino, A.

Devlaminck, V.

Dogariu, A.

Drevillon, B.

Drobczynski, S.

Galland, F.

Gaylord, T. K.

Goudail, P.

Gu, C.

P. Yeh and C. Gu, “Optics of Liquid Crystal Displays(Wiley, 2010).

Ina, H.

Kaneko, T.

Kasprzak, H.

Kawakami, S.

Kobayashi, H.

Kurzynowski, P.

P. Kurzynowski, S. Drobczyński, and W. A. Woźniak, “Dynamic polarization states and birefringence distributions measurements in spatial elliptical polariscope using Fourier analysis method,” Opt. Express 17, 10144–10154 (2009).
[CrossRef] [PubMed]

S. Drobczyński and P. Kurzynowski, “Imaging polarimeter for linear birefringence measurements using a liquid crystal modulator,” Opt. Eng. 47, 023603 (2008).
[CrossRef]

W. A. Woźniak and P. Kurzynowski, “Compact spatial polariscope for light polarization state analysis,” Opt. Express 16, 10471–10479 (2008).
[CrossRef] [PubMed]

P. Kurzynowski and W. A. Woźniak, “Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates,” Optik (Jena) 113, 51–53 (2002).
[CrossRef]

Laude-Boulesteix, B.

Lee, S. Y.

Lin, J. F.

J. F. Lin and Y. L. Lo, “The new circular heterodyne interferometer with electro-optic modulation for measurement of the optical linear birefringence,” Opt. Commun. 260, 486–492(2006).
[CrossRef]

Y. L. Lo, S. Y. Lee, and J. F. Lin, “Polariscope for simultaneous measurement of the principal axis and the phase retardation by use of two phase-locked extractions,” Appl. Opt. 43, 6248–6254 (2004).
[CrossRef] [PubMed]

Lo, Y. L.

J. F. Lin and Y. L. Lo, “The new circular heterodyne interferometer with electro-optic modulation for measurement of the optical linear birefringence,” Opt. Commun. 260, 486–492(2006).
[CrossRef]

Y. L. Lo, S. Y. Lee, and J. F. Lin, “Polariscope for simultaneous measurement of the principal axis and the phase retardation by use of two phase-locked extractions,” Appl. Opt. 43, 6248–6254 (2004).
[CrossRef] [PubMed]

Montarou, C. C.

Mujat, M.

Oka, K.

K. Oka and N. Saito, “Snapshot complete imaging polarimeter using Savart plates,” Proc. SPIE 6295, 629508 (2006).
[CrossRef]

K. Oka and T. Kaneko, “Compact complete imaging polarimeter using birefringent wedge prisms,” Opt. Express 11, 1510–1519 (2003).
[CrossRef] [PubMed]

Pezzaniti, J. L.

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

Rose, A. H.

Saito, N.

K. Oka and N. Saito, “Snapshot complete imaging polarimeter using Savart plates,” Proc. SPIE 6295, 629508 (2006).
[CrossRef]

Sasaki, Y.

Sato, T.

Schwartz, L.

Tadokoro, T.

Takakura, Y.

Takeda, M.

Terrier, P.

Tsuru, T.

Wang, C. M.

Williams, P. A.

Wolfe, J. E.

Wozniak, W. A.

Yeh, P.

P. Yeh and C. Gu, “Optics of Liquid Crystal Displays(Wiley, 2010).

Appl. Opt. (11)

C. C. Montarou and T. K. Gaylord, “Two-wave-plate compensator for single-point retardation measurement,” Appl. Opt. 43, 6580–6595 (2004).
[CrossRef]

P. A. Williams, A. H. Rose, and C. M. Wang, “Rotating-polarizer polarimeter for accurate retardance measurement,” Appl. Opt. 36, 6466–6472 (1997).
[CrossRef]

S. Drobczyński, J. M. Bueno, P. Artal, and H. Kasprzak, “Transmission imaging polarimetry for linear birefringent medium using carrier fringe method,” Appl. Opt. 45, 5489–5496 (2006).
[CrossRef] [PubMed]

B. Laude-Boulesteix, A. de Martino, B. Drevillon, and L. Schwartz, “Mueller polarimetric imaging system with liquid crystals,” Appl. Opt. 43, 2824–2832 (2004).
[CrossRef] [PubMed]

Y. L. Lo, S. Y. Lee, and J. F. Lin, “Polariscope for simultaneous measurement of the principal axis and the phase retardation by use of two phase-locked extractions,” Appl. Opt. 43, 6248–6254 (2004).
[CrossRef] [PubMed]

T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, “Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plates elements,” Appl. Opt. 46, 4963–4967 (2007).
[CrossRef] [PubMed]

P. A. Williams, “Rotating-wave-plate Stokes polarimeter for differential group delay measurements of polarization-mode dispersion,” Appl. Opt. 38, 6508–6515 (1999).
[CrossRef]

P. Goudail, P. Terrier, Y. Takakura, L. Bigué, F. Galland, and V. Devlaminck, “Target detection with liquid-crystal-based passive Stokes polarimeter,” Appl. Opt. 43, 274–282(2004).
[CrossRef] [PubMed]

J. E. Wolfe and R. A. Chipman, “Polarimetric characterization of liquid-crystal-on-silicon panels,” Appl. Opt. 45, 1688–1703 (2006).
[CrossRef] [PubMed]

J. S. Baba and P. R. Boudreaux, “Wavelength, temperature and voltage dependent calibration of a nematic liquid crystal multispectral polarization generating device,” Appl. Opt. 46, 5539–5544 (2007).
[CrossRef] [PubMed]

P. Terrier, J. M. Charbois, and V. Devlaminck, “Fast-axis orientation dependence on driving voltage for a Stokes polarimeter based on concrete liquid-crystal variable retarders,” Appl. Opt. 49, 4278–4283 (2010).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

J. F. Lin and Y. L. Lo, “The new circular heterodyne interferometer with electro-optic modulation for measurement of the optical linear birefringence,” Opt. Commun. 260, 486–492(2006).
[CrossRef]

Opt. Eng. (2)

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

S. Drobczyński and P. Kurzynowski, “Imaging polarimeter for linear birefringence measurements using a liquid crystal modulator,” Opt. Eng. 47, 023603 (2008).
[CrossRef]

Opt. Express (3)

Optik (Jena) (1)

P. Kurzynowski and W. A. Woźniak, “Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates,” Optik (Jena) 113, 51–53 (2002).
[CrossRef]

Proc. SPIE (1)

K. Oka and N. Saito, “Snapshot complete imaging polarimeter using Savart plates,” Proc. SPIE 6295, 629508 (2006).
[CrossRef]

Other (1)

P. Yeh and C. Gu, “Optics of Liquid Crystal Displays(Wiley, 2010).

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Figures (8)

Fig. 1
Fig. 1

Scheme of the optical system of the proposed Stokes polarimeter: LCVR1, LCVR2, liquid crystal modulators; A, linear analyzer; CCD, camera.

Fig. 2
Fig. 2

Cross sections of the measured intensities I 0 , I 90 , I 45 , I 45 , I R , and I L for the specific input light (see description in the text).

Fig. 3
Fig. 3

Dependence of the polarization degree on the background intensity level I BG .

Fig. 4
Fig. 4

Dependence of the calculated mean standard deviations of the azimuth angle δ α versus the measured light maximum intensity I max .

Fig. 5
Fig. 5

Histograms of measured polarization degree distributions p for two CCD cameras: (a) inaccurate camera characteristics I = f ( P ) , (b) correct camera characteristics I = f ( P ) , (c) p-histogram for inaccurate camera, and (d) p-histogram for correct camera.

Fig. 6
Fig. 6

Histograms of calculated light polarization state parameters: (a) azimuth angle α, (b) ellipticity angle ϑ, and (c) degree of polarization p—all for the assumed light polarization state α = 20 ° , ϑ = 20 ° .

Fig. 7
Fig. 7

Calculated polarization state of light passing through the Wollaston compensator: (a) the azimuth angle α distribution, (b) the ellipticity angle ϑ distribution, (c) mean profile of the azimuth angle α along the x-axis, and (d) the mean profile of the ellipticity angle ϑ along the x axis.

Fig. 8
Fig. 8

Calculated polarization state of the light passing through the “circular Wollaston compensator:” (a) the azimuth angle α distribution, (b) the ellipticity angle ϑ distribution, (c) mean profile of the azimuth angle α along the x axis, and (d) the mean profile of the ellipticity angle ϑ along the x axis.

Tables (2)

Tables Icon

Table 1 Sequence of Retardations γ LCVR 1 and γ LCVR 2 Introduced by Both LCVRs for the Chosen Set of Analyzer

Tables Icon

Table 2 Parameters (α, ϑ, p) of Generated Uniform Light Polarization States and Obtained Experimental Results

Equations (8)

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

V 1 = I 0 + I 90 = I 45 + I 45 = I R + I L ,
V 2 = I 0 I 90 I 0 + I 90 ,
V 3 = I 45 I 45 I 45 + I 45
V 4 = I R I L I R + I L .
I ( x , y ) V 1 = I 0 + I 90 = I 45 + I 45 = I R + I L ,
p ( x , y ) = V 2 2 + V 3 2 + V 4 2 ,
α ( x , y ) = 0.5 · arctan ( V 3 V 2 ) ,
ϑ ( x , y ) = 0.5 · arcsin ( V 4 ) .

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