Abstract

We present a new, to the best of our knowledge, experimental configuration of Mueller matrix polarimeter based on wavelength polarization coding. This is a compact and fast technique to study polarization phenomena. Our theoretical approach, the necessity to correct systematic errors and our experimental results are presented. The feasibility of the technique is tested on vacuum and on a linear polarizer.

© 2007 Optical Society of America

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References

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  1. B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, "Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range," Opt. Express 9, 225-235 (2001).
    [CrossRef] [PubMed]
  2. B. Boulbry, T. A. Germer, and J. C. Ramella-Roman, "A novel hemispherical spectro-polarimetric scattering instrument for skin lesion imaging," Proc. SPIE 6078, 128-134 (2006).
  3. C. Baravian, J. Dillet, F. Caton, and J. P. Decruppe, "Birefringence determination in turbid media," Phys. Rev. E. 75, 032501 (2007).
    [CrossRef]
  4. 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]
  5. S. Guyot, M. Anastasiadou, E. Deléchelle, and A. De Martino, "Registration scheme suitable to Mueller matrix imaging for biomedical applications," Opt. Express 15, 7393-7400 (2007).
    [CrossRef] [PubMed]
  6. J. W. Evans, "Solc biregringent filter," J. Opt. Soc. Am. 48, 142-146 (1958).
    [CrossRef]
  7. K. Oka and T. Kato, "Spectroscopic polarimetry with a channeled spectrum," Opt. Lett. 24, 1475-1477 (1999).
    [CrossRef]
  8. N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, W. W. Chen, E. L. Dereniak, and D. T. Sass, "Compact methods for measuring stress birefringence," Proc. SPIE 5158, 45-53 (2003).
    [CrossRef]
  9. N. Hagen, K. Oka, and E. L. Dereniak, "Snapshot Mueller matrix spectropolarimeter," Opt. Lett. 32, 2100-2102 (2007).
    [CrossRef] [PubMed]
  10. G. Ghosh, "Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals," Opt. Commun. 163, 95-102 (1999).
    [CrossRef]

2007 (3)

2006 (1)

B. Boulbry, T. A. Germer, and J. C. Ramella-Roman, "A novel hemispherical spectro-polarimetric scattering instrument for skin lesion imaging," Proc. SPIE 6078, 128-134 (2006).

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]

2003 (1)

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, W. W. Chen, E. L. Dereniak, and D. T. Sass, "Compact methods for measuring stress birefringence," Proc. SPIE 5158, 45-53 (2003).
[CrossRef]

2001 (1)

1999 (2)

G. Ghosh, "Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals," Opt. Commun. 163, 95-102 (1999).
[CrossRef]

K. Oka and T. Kato, "Spectroscopic polarimetry with a channeled spectrum," Opt. Lett. 24, 1475-1477 (1999).
[CrossRef]

1958 (1)

Anastasiadou, M.

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.

B. Boulbry, T. A. Germer, and J. C. Ramella-Roman, "A novel hemispherical spectro-polarimetric scattering instrument for skin lesion imaging," Proc. SPIE 6078, 128-134 (2006).

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]

B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, "Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range," Opt. Express 9, 225-235 (2001).
[CrossRef] [PubMed]

Boulvert, F.

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]

Bousquet, B.

Cariou, J.

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]

Chen, W. W.

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, W. W. Chen, E. L. Dereniak, and D. T. Sass, "Compact methods for measuring stress birefringence," Proc. SPIE 5158, 45-53 (2003).
[CrossRef]

De Martino, A.

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]

Deléchelle, E.

Dereniak, E. L.

N. Hagen, K. Oka, and E. L. Dereniak, "Snapshot Mueller matrix spectropolarimeter," Opt. Lett. 32, 2100-2102 (2007).
[CrossRef] [PubMed]

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, W. W. Chen, E. L. Dereniak, and D. T. Sass, "Compact methods for measuring stress birefringence," Proc. SPIE 5158, 45-53 (2003).
[CrossRef]

Dillet, J.

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

Evans, J. W.

Germer, T. A.

B. Boulbry, T. A. Germer, and J. C. Ramella-Roman, "A novel hemispherical spectro-polarimetric scattering instrument for skin lesion imaging," Proc. SPIE 6078, 128-134 (2006).

Ghosh, G.

G. Ghosh, "Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals," Opt. Commun. 163, 95-102 (1999).
[CrossRef]

Guern, Y.

Guyot, S.

Hagen, N.

Hagen, N. A.

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, W. W. Chen, E. L. Dereniak, and D. T. Sass, "Compact methods for measuring stress birefringence," Proc. SPIE 5158, 45-53 (2003).
[CrossRef]

Jansson, P. A.

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, W. W. Chen, E. L. Dereniak, and D. T. Sass, "Compact methods for measuring stress birefringence," Proc. SPIE 5158, 45-53 (2003).
[CrossRef]

Kato, T.

Le Brun, G.

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.

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]

B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, "Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range," Opt. Express 9, 225-235 (2001).
[CrossRef] [PubMed]

Lotrian, J.

Oka, K.

Ramella-Roman, J. C.

B. Boulbry, T. A. Germer, and J. C. Ramella-Roman, "A novel hemispherical spectro-polarimetric scattering instrument for skin lesion imaging," Proc. SPIE 6078, 128-134 (2006).

Rivet, S.

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]

Sabatke, D. S.

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, W. W. Chen, E. L. Dereniak, and D. T. Sass, "Compact methods for measuring stress birefringence," Proc. SPIE 5158, 45-53 (2003).
[CrossRef]

Sass, D. T.

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, W. W. Chen, E. L. Dereniak, and D. T. Sass, "Compact methods for measuring stress birefringence," Proc. SPIE 5158, 45-53 (2003).
[CrossRef]

Scholl, J. F.

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, W. W. Chen, E. L. Dereniak, and D. T. Sass, "Compact methods for measuring stress birefringence," Proc. SPIE 5158, 45-53 (2003).
[CrossRef]

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. (1)

Opt. Commun. (1)

G. Ghosh, "Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals," Opt. Commun. 163, 95-102 (1999).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

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]

Proc. SPIE (2)

N. A. Hagen, D. S. Sabatke, J. F. Scholl, P. A. Jansson, W. W. Chen, E. L. Dereniak, and D. T. Sass, "Compact methods for measuring stress birefringence," Proc. SPIE 5158, 45-53 (2003).
[CrossRef]

B. Boulbry, T. A. Germer, and J. C. Ramella-Roman, "A novel hemispherical spectro-polarimetric scattering instrument for skin lesion imaging," Proc. SPIE 6078, 128-134 (2006).

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Figures (6)

Fig. 1.
Fig. 1.

Snapshot Mueller polarimeter for the configuration (e, e, 5e, 5e).

Fig. 2.
Fig. 2.

Theoretical (a) and experimental (b) signals given by the snapshot Mueller polarimeter. The experimental signal is split into 5 zones for which the instantaneous frequency will be studied.

Fig. 3.
Fig. 3.

Theoretical (black) and experimental (red) absolute values of the Fourier transform for vacuum. The inset graph shows the experimental response of the detection from the vacuum signal.

Fig. 4.
Fig. 4.

Relative evolution of the instantaneous frequency fi in each zone defined in Fig. 2. b.

Fig. 5.
Fig. 5.

Fourier transform of the experimental signal of vacuum. (a) Real Part. (b) Imaginary Part.

Fig. 6.
Fig. 6.

(a) The analysis window, whose length is Δ, is positioned at the pixel x for vaccum. (b) According to the analysis window position, the imaginary parts of the 6f0-frequency peak (red points) and of the 7f0-frequency peak (black asterisks) are measured. For vacuum, we expect the snapshot Mueller polarimeter to get a 6f0 -frequency peak and no 7f0 -frequency peak.

Tables (3)

Tables Icon

Table 1. Magnitude of Real and Imaginary Peaks According to mij Coefficients.

Tables Icon

Table 2. Experimental Mueller Matrix for Vacuum Obtained from a Single Acquisition of 1 ms with and without Corrections.

Tables Icon

Table 3. Experimental Mueller Matrix (1ms) for Different Positions of a Linear Polarizer after Corrections : Response of the Detector + Phase Error Correction + Noise Filter.

Equations (19)

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S o = [ P ( π 2 ) ] . [ B ( 5 ϕ , π 4 ) ] . [ B 5 ϕ 0 ] . [ M ] . [ B ( ϕ , 0 ) ] . [ B ( ϕ , π 4 ) ] . [ P ( 0 ) ] . S i ,
ϕ = 2 π Δ n ( λ ) e λ ,
ϕ ϕ 0 + f 0 λ ,
32 I ( λ ) = 8 m 00 + 4 m 02 4 m 20 2 m 22 + ( 8 m 01 4 m 21 ) cos ( f 0 λ )
( 4 m 02 2 m 22 ) cos ( 2 f 0 λ ) + 2 m 12 cos ( 3 f 0 λ ) 4 m 11 cos ( 4 f 0 λ )
( 8 m 10 4 m 12 ) cos ( 5 f 0 λ ) 4 m 11 cos ( 6 f 0 λ ) + 2 m 12 cos ( 7 f 0 λ )
( m 22 m 33 ) cos ( 8 f 0 λ ) + 2 m 21 cos ( 9 f 0 λ ) + ( 4 m 20 + 2 m 22 ) cos ( 10 f 0 λ )
+ 2 m 21 cos ( 11 f 0 λ ) ( m 22 + m 33 ) cos ( 12 f 0 λ ) ( 4 m 03 2 m 23 ) sin ( 2 f 0 λ )
2 m 13 sin ( 3 f 0 λ ) + 2 m 13 sin ( 7 f 0 λ ) + ( m 23 + m 32 ) sin ( 8 f 0 λ ) 2 m 13 sin ( 9 f 0 λ )
( 4 m 30 + 2 m 32 ) sin ( 10 f 0 λ ) 2 m 31 sin ( 11 f 0 λ ) ( m 23 m 32 ) sin ( 12 f 0 λ ) ,
V = [ V 0 Re V 1 Re V 2 Re V 12 Re V 1 Im V 2 Im V 12 Im ] T ,
X = [ m 00 m 01 m 02 m 03 m 30 m 31 m 32 m 33 ] T .
V = [ P ] . X ,
X = ( [ P ] T . [ P ] ) 1 . [ P ] T . V .
S o = [ P ( π 2 ) ] . [ B ( + ϕ 4 , π 4 ) ] . [ B ( + ϕ 3 , 0 ) ] . [ M ]
. [ B ( ϕ + ϕ 2 , 0 ) ] . [ B ( ϕ , π 4 ) ] . [ P ( 0 ) ] . S i .
16 I ( λ ) = 3 + cos [ 2 ( ϕ w + f 0 λ ) + ϕ 2 + ϕ 3 ϕ 4 ] 2 cos [ 4 ( ϕ w + f 0 λ ) + ϕ 4 ]
2 cos [ 6 ( ϕ w + f 0 λ ) + ϕ 4 ] + cos [ 10 ( ϕ w + f 0 λ ) + ϕ 2 + ϕ 3 + ϕ 4 ]
cos [ 12 ( ϕ w + f 0 λ ) + ϕ 2 + ϕ 3 + ϕ 4 ] ,

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