Abstract

Dual photoelastic modulator polarimeters can measure light polarization, which is often described as a Stokes vector. By evaluating changes in polarization when light interacts with a sample, the sample Mueller matrix also can be derived, completely describing its interaction with polarized light. The choice of which and how many input Stokes vectors to use for sample investigation is under the experimenter’s control. Previous work has predicted that sets of input Stokes vectors forming the vertices of platonic solids on the Poincaré sphere allow for the most robust Mueller matrix determination. Further, when errors specific to the dual photoelastic modulator polarimeter are considered, simulations revealed that one specific shape and orientation of Stokes vectors (cube on the Poincaré sphere with vertices away from principal sphere axes) allows for the most robust Mueller matrix determination. Here we experimentally validate the optimum input Stokes vectors for dual photoelastic modulator Mueller polarimetry, toward developing a robust polarimetric platform of increasing relevance to biophotonics.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852).
  2. H. Poincaré, Theorié Mathématique de la Lumière (Gauthiers-Villars, 1892).
  3. D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic–Harcourt Brace Jovanovich, 1990).
  4. N. Ghosh and I. A. Vitkin, J. Biomed. Opt. 16, 110801 (2011).
    [CrossRef]
  5. D. Côté and I. A. Vitkin, J. Biomed. Opt. 9, 213 (2004).
    [CrossRef]
  6. N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
    [CrossRef]
  7. M. F. G. Wood, N. Ghosh, M. A. Wallenburg, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biomed. Opt. 15, 047009 (2010).
    [CrossRef]
  8. S. Alali, Y. Wang, and I. A. Vitkin, Biomed. Opt. Express 3, 3250 (2012).
    [CrossRef]
  9. S. Alali, K. J. Aitken, A. Shröder, D. J. Bagli, and I. A. Vitkin, J. Biomed. Opt. 17, 086010 (2012).
    [CrossRef]
  10. A. Pierangelo, A. Nazac, A. Benali, P. Validire, H. Cohen, T. Novikova, B. H. Ibrahim, S. Manhas, C. Fallet, M. R. Antonelli, and A. De Martino, Opt. Express 21, 14120 (2013).
    [CrossRef]
  11. A. Pierangelo, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, Opt. Express 19, 1582 (2011).
    [CrossRef]
  12. P. A. Letnes, I. S. Nerbø, L. M. S. Aas, P. G. Ellingsen, and M. Kildemo, Opt. Express 18, 23095 (2010).
    [CrossRef]
  13. W. Guan, G. A. Jones, Y. Liu, and T. H. Shen, J. Appl. Phys. 103, 043104 (2008).
    [CrossRef]
  14. D. Layden, M. F. G. Wood, and I. A. Vitkin, Opt. Express 20, 20466 (2012).
    [CrossRef]
  15. S. Alali, M. Ahmad, A. J. Kim, M. F. G. Wood, and I. A. Vitkin, J. Biomed. Opt. 17, 045004 (2012).
    [CrossRef]

2013 (1)

2012 (4)

S. Alali, Y. Wang, and I. A. Vitkin, Biomed. Opt. Express 3, 3250 (2012).
[CrossRef]

S. Alali, K. J. Aitken, A. Shröder, D. J. Bagli, and I. A. Vitkin, J. Biomed. Opt. 17, 086010 (2012).
[CrossRef]

D. Layden, M. F. G. Wood, and I. A. Vitkin, Opt. Express 20, 20466 (2012).
[CrossRef]

S. Alali, M. Ahmad, A. J. Kim, M. F. G. Wood, and I. A. Vitkin, J. Biomed. Opt. 17, 045004 (2012).
[CrossRef]

2011 (2)

2010 (2)

P. A. Letnes, I. S. Nerbø, L. M. S. Aas, P. G. Ellingsen, and M. Kildemo, Opt. Express 18, 23095 (2010).
[CrossRef]

M. F. G. Wood, N. Ghosh, M. A. Wallenburg, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biomed. Opt. 15, 047009 (2010).
[CrossRef]

2009 (1)

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

2008 (1)

W. Guan, G. A. Jones, Y. Liu, and T. H. Shen, J. Appl. Phys. 103, 043104 (2008).
[CrossRef]

2004 (1)

D. Côté and I. A. Vitkin, J. Biomed. Opt. 9, 213 (2004).
[CrossRef]

1852 (1)

G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852).

Aas, L. M. S.

Ahmad, M.

S. Alali, M. Ahmad, A. J. Kim, M. F. G. Wood, and I. A. Vitkin, J. Biomed. Opt. 17, 045004 (2012).
[CrossRef]

Aitken, K. J.

S. Alali, K. J. Aitken, A. Shröder, D. J. Bagli, and I. A. Vitkin, J. Biomed. Opt. 17, 086010 (2012).
[CrossRef]

Alali, S.

S. Alali, Y. Wang, and I. A. Vitkin, Biomed. Opt. Express 3, 3250 (2012).
[CrossRef]

S. Alali, K. J. Aitken, A. Shröder, D. J. Bagli, and I. A. Vitkin, J. Biomed. Opt. 17, 086010 (2012).
[CrossRef]

S. Alali, M. Ahmad, A. J. Kim, M. F. G. Wood, and I. A. Vitkin, J. Biomed. Opt. 17, 045004 (2012).
[CrossRef]

Antonelli, M. R.

Bagli, D. J.

S. Alali, K. J. Aitken, A. Shröder, D. J. Bagli, and I. A. Vitkin, J. Biomed. Opt. 17, 086010 (2012).
[CrossRef]

Benali, A.

Cohen, H.

Côté, D.

D. Côté and I. A. Vitkin, J. Biomed. Opt. 9, 213 (2004).
[CrossRef]

De Martino, A.

Ellingsen, P. G.

Fallet, C.

Gayet, B.

Ghosh, N.

N. Ghosh and I. A. Vitkin, J. Biomed. Opt. 16, 110801 (2011).
[CrossRef]

M. F. G. Wood, N. Ghosh, M. A. Wallenburg, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biomed. Opt. 15, 047009 (2010).
[CrossRef]

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

Guan, W.

W. Guan, G. A. Jones, Y. Liu, and T. H. Shen, J. Appl. Phys. 103, 043104 (2008).
[CrossRef]

Ibrahim, B. H.

Jones, G. A.

W. Guan, G. A. Jones, Y. Liu, and T. H. Shen, J. Appl. Phys. 103, 043104 (2008).
[CrossRef]

Kildemo, M.

Kim, A. J.

S. Alali, M. Ahmad, A. J. Kim, M. F. G. Wood, and I. A. Vitkin, J. Biomed. Opt. 17, 045004 (2012).
[CrossRef]

Kliger, D. S.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic–Harcourt Brace Jovanovich, 1990).

Layden, D.

Letnes, P. A.

Lewis, J. W.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic–Harcourt Brace Jovanovich, 1990).

Li, R.-K.

M. F. G. Wood, N. Ghosh, M. A. Wallenburg, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biomed. Opt. 15, 047009 (2010).
[CrossRef]

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

Li, S.

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

Li, S.-H.

M. F. G. Wood, N. Ghosh, M. A. Wallenburg, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biomed. Opt. 15, 047009 (2010).
[CrossRef]

Liu, Y.

W. Guan, G. A. Jones, Y. Liu, and T. H. Shen, J. Appl. Phys. 103, 043104 (2008).
[CrossRef]

Manhas, S.

Nazac, A.

Nerbø, I. S.

Novikova, T.

Pierangelo, A.

Poincaré, H.

H. Poincaré, Theorié Mathématique de la Lumière (Gauthiers-Villars, 1892).

Randall, C. E.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic–Harcourt Brace Jovanovich, 1990).

Shen, T. H.

W. Guan, G. A. Jones, Y. Liu, and T. H. Shen, J. Appl. Phys. 103, 043104 (2008).
[CrossRef]

Shröder, A.

S. Alali, K. J. Aitken, A. Shröder, D. J. Bagli, and I. A. Vitkin, J. Biomed. Opt. 17, 086010 (2012).
[CrossRef]

Stokes, G. G.

G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852).

Validire, P.

Vitkin, I. A.

D. Layden, M. F. G. Wood, and I. A. Vitkin, Opt. Express 20, 20466 (2012).
[CrossRef]

S. Alali, M. Ahmad, A. J. Kim, M. F. G. Wood, and I. A. Vitkin, J. Biomed. Opt. 17, 045004 (2012).
[CrossRef]

S. Alali, K. J. Aitken, A. Shröder, D. J. Bagli, and I. A. Vitkin, J. Biomed. Opt. 17, 086010 (2012).
[CrossRef]

S. Alali, Y. Wang, and I. A. Vitkin, Biomed. Opt. Express 3, 3250 (2012).
[CrossRef]

N. Ghosh and I. A. Vitkin, J. Biomed. Opt. 16, 110801 (2011).
[CrossRef]

M. F. G. Wood, N. Ghosh, M. A. Wallenburg, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biomed. Opt. 15, 047009 (2010).
[CrossRef]

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

D. Côté and I. A. Vitkin, J. Biomed. Opt. 9, 213 (2004).
[CrossRef]

Wallenburg, M. A.

M. F. G. Wood, N. Ghosh, M. A. Wallenburg, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biomed. Opt. 15, 047009 (2010).
[CrossRef]

Wang, Y.

Weisel, R. D.

M. F. G. Wood, N. Ghosh, M. A. Wallenburg, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biomed. Opt. 15, 047009 (2010).
[CrossRef]

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

Wilson, B. C.

M. F. G. Wood, N. Ghosh, M. A. Wallenburg, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biomed. Opt. 15, 047009 (2010).
[CrossRef]

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

Wood, M. F. G.

S. Alali, M. Ahmad, A. J. Kim, M. F. G. Wood, and I. A. Vitkin, J. Biomed. Opt. 17, 045004 (2012).
[CrossRef]

D. Layden, M. F. G. Wood, and I. A. Vitkin, Opt. Express 20, 20466 (2012).
[CrossRef]

M. F. G. Wood, N. Ghosh, M. A. Wallenburg, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biomed. Opt. 15, 047009 (2010).
[CrossRef]

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

Biomed. Opt. Express (1)

J. Appl. Phys. (1)

W. Guan, G. A. Jones, Y. Liu, and T. H. Shen, J. Appl. Phys. 103, 043104 (2008).
[CrossRef]

J. Biomed. Opt. (5)

M. F. G. Wood, N. Ghosh, M. A. Wallenburg, S.-H. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biomed. Opt. 15, 047009 (2010).
[CrossRef]

S. Alali, M. Ahmad, A. J. Kim, M. F. G. Wood, and I. A. Vitkin, J. Biomed. Opt. 17, 045004 (2012).
[CrossRef]

S. Alali, K. J. Aitken, A. Shröder, D. J. Bagli, and I. A. Vitkin, J. Biomed. Opt. 17, 086010 (2012).
[CrossRef]

N. Ghosh and I. A. Vitkin, J. Biomed. Opt. 16, 110801 (2011).
[CrossRef]

D. Côté and I. A. Vitkin, J. Biomed. Opt. 9, 213 (2004).
[CrossRef]

J. Biophoton. (1)

N. Ghosh, M. F. G. Wood, S. Li, R. D. Weisel, B. C. Wilson, R.-K. Li, and I. A. Vitkin, J. Biophoton. 2, 145 (2009).
[CrossRef]

Opt. Express (4)

Trans. Cambridge Philos. Soc. (1)

G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852).

Other (2)

H. Poincaré, Theorié Mathématique de la Lumière (Gauthiers-Villars, 1892).

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic–Harcourt Brace Jovanovich, 1990).

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 (4)

Fig. 1.
Fig. 1.

Dual PEM polarimeter. Polarized light of a suitable input state is produced by the polarization state generator (PSG). This light interacts with a sample, and the output polarization is analyzed by passing through two PEMs (45° and 0° above horizontal) and a linear polarizer (22.5° above horizontal). The modulation frequencies, f1 and f2, of the PEMs are used as references for lock-in amplifiers, which recover Q, U, and V of light reaching the detector, via synchronous detection. The I component is recovered by a lock-in using the beam chopper frequency, fc, as a reference.

Fig. 2.
Fig. 2.

Sets of input vectors forming Platonic solids (namely, a cube) when plotted on the Poincaré sphere. The sphere equator represents linear polarizations, and the poles represent circular polarizations. Phase-error regions, where Q, U, or V=0, are shown with red circles. (a) The Optimum set contains Stokes vectors that from vertices of a cube, maximally distant from the phase-error regions. (b) The Rotated-Optimum set also forms a cube, but with vertices rotated into the phase-error regions. Column (i) gives 3D views; column (ii) shows the front face of the Poincaré sphere; column (iii) shows the back face.

Fig. 3.
Fig. 3.

Random sets of input Stokes vectors plotted on the Poincaré sphere. Sets differ in mean separation angle and proximity to phase-error regions: (a) Random1; (b) Random2; (c) Random3. Column (i) gives 3D views; column (ii) shows the front face of the Poincaré sphere; column (iii) shows the back face.

Fig. 4.
Fig. 4.

Mueller matrix error associated with different sets of input Stokes vectors. Error bars show standard error. Differences between all sets were significant, as determined by two-tailed unpaired t-tests (p<0.05), except between Rotated-Optimum and Random1. Optimum allows the most robust Mueller matrix determination, since its vectors are evenly spread about the Poincaré sphere and are maximally distant from phase-error regions.

Tables (1)

Tables Icon

Table 1. Characteristics of Input Polarization Sets

Equations (13)

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

Sout=MSin.
Sout=MSin.
M=Sout(Sin)1,
M=Sout(Sin)+,
δMn1/22(δSout+4MδSin)(Sin)+,
(Sin)+min(n)=(10n)1/2.
δM(52)1/2(δSout+4MδSin).
S(opt)in=[S(1)inS(8)in]whereS(1)in=[10.580.580.58];S(2)in=[10.580.580.58];S(3)in=[10.580.580.58];S(4)in=[10.580.580.58];S(5)in=[10.580.580.58];S(6)in=[10.580.580.58];S(7)in=[10.580.580.58];S(8)in=[10.580.580.58].
M(0)=[1.0000.00000.00000.00000.00760.41470.00110.00050.00500.00040.43550.00070.00370.00320.00160.8220].
S(iavg)=j=110S(ij)10.
δM(k)=M(k)M(0),
δM(k)=(M(k)M(0))(M(k)M(0))¯.
δM=k=1160δM(k)160.

Metrics