Abstract

We describe a new setup for a snapshot Mueller matrix polarimeter (SMMP). It relies on the separation and orthogonal polarization of two light beams by a Wollaston prism located at the setup output. The simultaneous treatment of the two spectra allows an enhancement of accuracy for real-time measurements through reduction of the effects caused by random noise and systematic errors. Moreover, it gives insight into the nonuniform spectral response of the medium under study. Experimental results support the feasibility of the proposed technique.

© 2009 Optical Society of America

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References

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  1. R. Ossikovski, E. Garcia-Caurel, and A. De Martino, “Product decompositions of experimentally determined non-depolarizing Mueller matrices,” Phys. Status Solidi C 5, 1059-1063 (2008).
    [CrossRef]
  2. C. Baravian, J. Dillet, F. Caton, and J. P. Decruppe, “Birefringence determination in turbid media,” Phys. Rev. E 75, 032501 (2007).
    [CrossRef]
  3. F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A Pure Appl. Opt. 7, 21-28 (2005).
    [CrossRef]
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    [CrossRef]
  7. K. Oka and T. Kato, “Spectroscopic polarimetry with a channeled spectrum,” Opt. Lett. 24, 1475-1477 (1999).
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  8. N. Hagen, K. Oka, and E. L. Dereniak, “Snapshot Mueller matrix spectropolarimeter,” Opt. Lett. 32, 2100-2102 (2007).
    [CrossRef] [PubMed]
  9. M. Dubreuil, S. Rivet, B. Le Jeune, and J. Cariou, “Snapshot Mueller matrix polarimeter by wavelength polarization coding,” Opt. Express 15, 13660-13668 (2007).
    [CrossRef] [PubMed]
  10. M. Dubreuil, S. Rivet, B. Le Jeune, and J. Cariou, “Systematic errors specific to a snapshot Mueller matrix polarimeter,” Appl. Opt. 48, 1135-1142 (2009).
    [CrossRef]
  11. P. Lemaillet, S. Rivet, and B. Le Jeune, “Optimization of a snapshot Mueller matrix polarimeter,” Opt. Lett. 33, 144-146 (2008).
    [CrossRef] [PubMed]
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  13. F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. 282, 692-704 (2009).
    [CrossRef]

2009 (2)

F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. 282, 692-704 (2009).
[CrossRef]

M. Dubreuil, S. Rivet, B. Le Jeune, and J. Cariou, “Systematic errors specific to a snapshot Mueller matrix polarimeter,” Appl. Opt. 48, 1135-1142 (2009).
[CrossRef]

2008 (2)

P. Lemaillet, S. Rivet, and B. Le Jeune, “Optimization of a snapshot Mueller matrix polarimeter,” Opt. Lett. 33, 144-146 (2008).
[CrossRef] [PubMed]

R. Ossikovski, E. Garcia-Caurel, and A. De Martino, “Product decompositions of experimentally determined non-depolarizing Mueller matrices,” Phys. Status Solidi C 5, 1059-1063 (2008).
[CrossRef]

2007 (3)

2005 (1)

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A Pure Appl. Opt. 7, 21-28 (2005).
[CrossRef]

2004 (1)

E. Garcia-Caurel, A. De Martino, and B. Drévillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

1999 (2)

1997 (1)

1996 (1)

Baravian, C.

C. Baravian, J. Dillet, F. Caton, and J. P. Decruppe, “Birefringence determination in turbid media,” Phys. Rev. E 75, 032501 (2007).
[CrossRef]

Boulbry, B.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A Pure Appl. Opt. 7, 21-28 (2005).
[CrossRef]

Boulvert, F.

F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. 282, 692-704 (2009).
[CrossRef]

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A Pure Appl. Opt. 7, 21-28 (2005).
[CrossRef]

Cariou, J.

F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. 282, 692-704 (2009).
[CrossRef]

M. Dubreuil, S. Rivet, B. Le Jeune, and J. Cariou, “Systematic errors specific to a snapshot Mueller matrix polarimeter,” Appl. Opt. 48, 1135-1142 (2009).
[CrossRef]

M. Dubreuil, S. Rivet, B. Le Jeune, and J. Cariou, “Snapshot Mueller matrix polarimeter by wavelength polarization coding,” Opt. Express 15, 13660-13668 (2007).
[CrossRef] [PubMed]

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A Pure Appl. Opt. 7, 21-28 (2005).
[CrossRef]

Caton, F.

C. Baravian, J. Dillet, F. Caton, and J. P. Decruppe, “Birefringence determination in turbid media,” Phys. Rev. E 75, 032501 (2007).
[CrossRef]

Chipman, R. A.

Collins, R. W.

De Martino, A.

R. Ossikovski, E. Garcia-Caurel, and A. De Martino, “Product decompositions of experimentally determined non-depolarizing Mueller matrices,” Phys. Status Solidi C 5, 1059-1063 (2008).
[CrossRef]

E. Garcia-Caurel, A. De Martino, and B. Drévillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

Decruppe, J. P.

C. Baravian, J. Dillet, F. Caton, and J. P. Decruppe, “Birefringence determination in turbid media,” Phys. Rev. E 75, 032501 (2007).
[CrossRef]

Delplancke, F.

Dereniak, E. L.

Dillet, J.

C. Baravian, J. Dillet, F. Caton, and J. P. Decruppe, “Birefringence determination in turbid media,” Phys. Rev. E 75, 032501 (2007).
[CrossRef]

Drévillon, B.

E. Garcia-Caurel, A. De Martino, and B. Drévillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

Dubreuil, M.

Garcia-Caurel, E.

R. Ossikovski, E. Garcia-Caurel, and A. De Martino, “Product decompositions of experimentally determined non-depolarizing Mueller matrices,” Phys. Status Solidi C 5, 1059-1063 (2008).
[CrossRef]

E. Garcia-Caurel, A. De Martino, and B. Drévillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

Hagen, N.

Kato, T.

Koh, J.

Le Brun, G.

F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. 282, 692-704 (2009).
[CrossRef]

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A Pure Appl. Opt. 7, 21-28 (2005).
[CrossRef]

Le Jeune, B.

Lemaillet, P.

Lu, S.-Y.

Martin, L.

F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. 282, 692-704 (2009).
[CrossRef]

Oka, K.

Ossikovski, R.

R. Ossikovski, E. Garcia-Caurel, and A. De Martino, “Product decompositions of experimentally determined non-depolarizing Mueller matrices,” Phys. Status Solidi C 5, 1059-1063 (2008).
[CrossRef]

Rivet, S.

Appl. Opt. (2)

J. Opt. A Pure Appl. Opt. (1)

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A Pure Appl. Opt. 7, 21-28 (2005).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. 282, 692-704 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. E (1)

C. Baravian, J. Dillet, F. Caton, and J. P. Decruppe, “Birefringence determination in turbid media,” Phys. Rev. E 75, 032501 (2007).
[CrossRef]

Phys. Status Solidi C (1)

R. Ossikovski, E. Garcia-Caurel, and A. De Martino, “Product decompositions of experimentally determined non-depolarizing Mueller matrices,” Phys. Status Solidi C 5, 1059-1063 (2008).
[CrossRef]

Thin Solid Films (1)

E. Garcia-Caurel, A. De Martino, and B. Drévillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for a two-channel SMMP in the ( e , e , 5 e , 5 e ) configuration. A single-channel SMMP gives access to only I ( λ ) .

Fig. 2
Fig. 2

Simulations of the impact by systematic errors in the cases of a single-channel SMMP (continuous line) and a two-channel-SMMP (squares). The medium under study was a quarter-wave plate oriented at 120 ° . The inaccuracy of the window phase, Δ ϕ w , is expressed in radians. The setup used in the simulations consisted of four calcite plates ( Δ n = 0.166 ) of thicknesses e = 2.08 mm for plates 1 and 2, and 5 e = 10.4 mm for plates 3 and 4. The source had a broadband spectrum with λ 0 = 829 nm , and the analysis window of the detection system was Δ λ = 10 nm sampled with 512 pixels. The thickness error inaccuracies, Δ e 2 , Δ e 3 , and Δ e 4 , are expressed in units of wavelengths; the misalignment errors, Δ α 1 , Δ α 2 , Δ α 3 , and Δ α 4 , are given in degrees. The term used to quantify the measurement errors is the Frobenius norm, Δ M F = i j | m i j errors m i j ideal | 2 ; it corresponds to the difference between the Mueller matrix with systematic errors ( m i j errors ) and the ideal one ( m i j ideal ). All of the m i j coefficients are normalized by m 00 .

Fig. 3
Fig. 3

Experimental spectra: (a) vacuum (source shape) and (b) quartz wave plate (multiple-reflection interference signal).

Tables (1)

Tables Icon

Table 1 Experimental Mueller Matrices for a Quarter-Wave Plate with its Fast Axis Oriented at 120 ° with Either the Single Channel SMMP or the Two-Channel SMMP

Equations (14)

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I ( λ ) = [ 1 0 0 0 ] T [ P o l ( π / 2 ) ] · [ B ( 5 ϕ , π / 4 ) ] · [ B ( 5 ϕ , 0 ) ] · [ M ] · [ B ( ϕ , 0 ) ] · [ B ( ϕ , π / 4 ) ] · [ P o l ( 0 ) ] · S i ,
I ( λ ) = [ 1 0 0 0 ] T [ P o l ( 0 ) ] · [ B ( 5 ϕ , π / 4 ) ] · [ B ( 5 ϕ , 0 ) ] · [ M ] · [ B ( ϕ , 0 ) ] · [ B ( ϕ , π / 4 ) ] · [ P o l ( 0 ) ] · S i ,
I ( λ ) = s ( λ ) · Re [ g 0 + n = 1 12 ( g n + i h n ) · e i ( n f 0 λ + ϕ w ) ] ,
I ( λ ) = s ( λ ) · Re [ g 0 + n = 1 12 ( g n + i h n ) · e i ( n f 0 λ + ϕ w ) ] ,
EWV = k = 1 16 Var ( m ) k = k = 1 16 1 μ k 2 .
I ( λ ) + I ( λ ) = s ( λ ) · f ( λ ) ,
64 f ( λ ) = 32 m 00 + 16 m 02 + 32 m 01 cos ( f 0 λ ) 16 m 02 cos ( 2 f 0 λ ) 16 m 03 sin ( 2 f 0 λ ) .
Δ M F = i j | m i j exp m i j th | 2 ,
[ M 1 ] = [ M ] [ P o l ( 0 ) ] · [ B ( π , 0 ) ] ,
[ M 2 ] = [ M ] [ P o l ( 0 ) ] · [ B ( π , π / 4 ) ] .
[ M tot ] = [ M ] · ( 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ) = ( m 00 + m 01 0 0 0 m 10 + m 11 0 0 0 m 20 + m 21 0 0 0 m 30 + m 31 0 0 0 ) .
I tot = I 1 ( λ ) + I 1 ( λ ) + I 2 ( λ ) + I 2 ( λ ) = s ( λ ) · f ( λ ) ,
[ 1.000 0.010 0.002 0.005 0.007 0.259 0.444 0.865 0.000 0.423 0.753 0.509 0.002 0.878 0.483 0.006 ]
[ 1.000 0.000 0.000 0.000 0.006 0.258 0.445 0.864 0.003 0.435 0.746 0.512 0.001 0.868 0.485 0.002 ]

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