Abstract

We describe a spectral Stokesmeter: a device for fast simultaneous measurement of the four Stokes parameters of light. It consists of an original optical part, a four-channel scanning optoelectronic system, and a controlling computer system. The original optical scheme was first proposed by us. It is based on two holographic gratings, one of which is a special type of polarization grating. It allows an easy calibration of the device comprising wavelength and sensitivity calibration. The spectral range of the present implementation of the spectral Stokesmeter is 520750nm, and the error in the measurement of the normalized Stokes parameters is 0.05.

© 2007 Optical Society of America

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References

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  1. R. M. A. Azzam, "Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light," Opt. Acta 29, 685-689 (1982).
    [CrossRef]
  2. R. M. A. Azzam, "Beam-splitters for the division-of-amplitude photopolarimeter," Opt. Acta 32, 1407-1412 (1985).
    [CrossRef]
  3. R. M. A. Azzam, "Arrangement of four photodetectors for measuring the state of polarization of light," Opt. Lett. 10, 309-311 (1985).
    [CrossRef] [PubMed]
  4. K. Brudzewski, "Static Stokes ellipsometer: general analysis and optimization," J. Mod. Opt. 38, 889-896 (1991).
    [CrossRef]
  5. T. Todorov and L. Nikolova, "Spectrophotopolarometer: fast simultaneous real-time measurement of light parameters," Opt. Lett. 17, 358-359 (1992).
    [CrossRef] [PubMed]
  6. L. Nikolova, M. Ivanov, T. Todorov, and S. Stoyanov, "Spectrophotopolarimeter: a simplified version for real-time measurement at selected wavelengths," Bulg. J. Phys. 20, 46-54 (1993).
  7. L. Nikolova, T. Todorov, M. Ivanov, F. Andruzzi, S. Hilsted, and P. S. Ramanujam, "Photoinduced circular anisotropy in side-chain azobenzene polyesters," Opt. Mater. 8, 255-258 (1997).
    [CrossRef]
  8. M. Ivanov, I. Naydenova, T. Todorov, L. Nikolova, T. Petrova, N. Tomova, and V. Dragostinova, "Light-induced optical activity in optically ordered amorphous side-chain azobenzene containing polymer," J. Mod. Opt. 47, 861-867 (2000).
  9. I. Naydenova, L. Nikolova, P. S. Ramanujam, and S. Hvilsted, "Light-induced circular birefringence in cyanoazobenzene side-chain liquid-crystalline polyester films," J. Opt. A , Pure Appl. Opt. 1, 438-441 (1999).
    [CrossRef]
  10. C. Provenzano, G. Cipparrone, and A. Mazzulla, "Photopolarimeter based on two gratings recorded in thin organic films," Appl. Opt. 45, 3929-3934 (2006).
    [CrossRef] [PubMed]
  11. F. Gori, "Measuring Stokes parameters by means of a polarization grating," Opt. Lett. 24, 584-586 (1999).
    [CrossRef]
  12. D. B. Chenault and R. A. Chipman, "Measurement of linear diattenuation and linear retardance spectra with a rotating sample spectropolarimeter," Appl. Opt. 32, 3513-3519 (1993).
    [CrossRef] [PubMed]
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    [CrossRef]
  14. J.-K. Lee, J. T. Shen, A. Heifetz, R. Tripathi, and M. S. Shariar, "Demonstration of a thick holographic Stokesmeter," Opt. Commun. 259, 484-487 (2006).
    [CrossRef]
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  16. J. M. Bueno, "Polarimetry using liquid-crystal variable retarders: theory and calibration," J. Opt. A , Pure Appl. Opt. 2, 216-222 (2000).
    [CrossRef]
  17. N. Gupta, L. J. Denes, M. Gottlieb, D. R. Suhre, B. Maminsky, and P. Metes, "Object detection with field-portable spectropolarimetric imager," Appl. Opt. 40, 6626-6632 (2001).
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    [CrossRef] [PubMed]
  20. D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, and R. W. McMillan, "Snapshot imaging spectropolarimeter," Opt. Eng. 41, 1048-1054 (2002).
    [CrossRef]
  21. D. Sabatke, A. M. Locke, E. L. Dereniak, and R. W. McMillan, "Linear calibration and reconstruction techniques for channeled spectropolarimetry," Opt. Expess 11, 2940-2952 (2003).
    [CrossRef]
  22. L. Nikolova and T. Todorov, "Diffraction efficiency and selectivity of polarization diffraction grating," Opt. Acta 31, 579-588 (1984).
    [CrossRef]
  23. T. Todorov, P. Markovski, M. Mazakova, M. Miteva, V. Razsolkov, and M. Pancheva, "Spectral characteristic of thick phase holographic gratings," Opt. Acta 28, 379-388 (1981).
    [CrossRef]
  24. M. Mazakova, M. Pancheva, P. Sharlandjiev, and G. Spasov, "Electron-donors and heat treatment: their effects on the diffraction efficiency of DCG holograms," Appl. Opt. 14, 2156-2160 (1985).
    [CrossRef]

2006 (2)

J.-K. Lee, J. T. Shen, A. Heifetz, R. Tripathi, and M. S. Shariar, "Demonstration of a thick holographic Stokesmeter," Opt. Commun. 259, 484-487 (2006).
[CrossRef]

C. Provenzano, G. Cipparrone, and A. Mazzulla, "Photopolarimeter based on two gratings recorded in thin organic films," Appl. Opt. 45, 3929-3934 (2006).
[CrossRef] [PubMed]

2004 (3)

2003 (1)

D. Sabatke, A. M. Locke, E. L. Dereniak, and R. W. McMillan, "Linear calibration and reconstruction techniques for channeled spectropolarimetry," Opt. Expess 11, 2940-2952 (2003).
[CrossRef]

2002 (1)

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, and R. W. McMillan, "Snapshot imaging spectropolarimeter," Opt. Eng. 41, 1048-1054 (2002).
[CrossRef]

2001 (2)

2000 (2)

J. M. Bueno, "Polarimetry using liquid-crystal variable retarders: theory and calibration," J. Opt. A , Pure Appl. Opt. 2, 216-222 (2000).
[CrossRef]

M. Ivanov, I. Naydenova, T. Todorov, L. Nikolova, T. Petrova, N. Tomova, and V. Dragostinova, "Light-induced optical activity in optically ordered amorphous side-chain azobenzene containing polymer," J. Mod. Opt. 47, 861-867 (2000).

1999 (2)

I. Naydenova, L. Nikolova, P. S. Ramanujam, and S. Hvilsted, "Light-induced circular birefringence in cyanoazobenzene side-chain liquid-crystalline polyester films," J. Opt. A , Pure Appl. Opt. 1, 438-441 (1999).
[CrossRef]

F. Gori, "Measuring Stokes parameters by means of a polarization grating," Opt. Lett. 24, 584-586 (1999).
[CrossRef]

1997 (1)

L. Nikolova, T. Todorov, M. Ivanov, F. Andruzzi, S. Hilsted, and P. S. Ramanujam, "Photoinduced circular anisotropy in side-chain azobenzene polyesters," Opt. Mater. 8, 255-258 (1997).
[CrossRef]

1993 (2)

D. B. Chenault and R. A. Chipman, "Measurement of linear diattenuation and linear retardance spectra with a rotating sample spectropolarimeter," Appl. Opt. 32, 3513-3519 (1993).
[CrossRef] [PubMed]

L. Nikolova, M. Ivanov, T. Todorov, and S. Stoyanov, "Spectrophotopolarimeter: a simplified version for real-time measurement at selected wavelengths," Bulg. J. Phys. 20, 46-54 (1993).

1992 (1)

1991 (1)

K. Brudzewski, "Static Stokes ellipsometer: general analysis and optimization," J. Mod. Opt. 38, 889-896 (1991).
[CrossRef]

1985 (3)

R. M. A. Azzam, "Beam-splitters for the division-of-amplitude photopolarimeter," Opt. Acta 32, 1407-1412 (1985).
[CrossRef]

M. Mazakova, M. Pancheva, P. Sharlandjiev, and G. Spasov, "Electron-donors and heat treatment: their effects on the diffraction efficiency of DCG holograms," Appl. Opt. 14, 2156-2160 (1985).
[CrossRef]

R. M. A. Azzam, "Arrangement of four photodetectors for measuring the state of polarization of light," Opt. Lett. 10, 309-311 (1985).
[CrossRef] [PubMed]

1984 (1)

L. Nikolova and T. Todorov, "Diffraction efficiency and selectivity of polarization diffraction grating," Opt. Acta 31, 579-588 (1984).
[CrossRef]

1982 (1)

R. M. A. Azzam, "Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light," Opt. Acta 29, 685-689 (1982).
[CrossRef]

1981 (1)

T. Todorov, P. Markovski, M. Mazakova, M. Miteva, V. Razsolkov, and M. Pancheva, "Spectral characteristic of thick phase holographic gratings," Opt. Acta 28, 379-388 (1981).
[CrossRef]

Appl. Opt. (6)

Bulg. J. Phys. (1)

L. Nikolova, M. Ivanov, T. Todorov, and S. Stoyanov, "Spectrophotopolarimeter: a simplified version for real-time measurement at selected wavelengths," Bulg. J. Phys. 20, 46-54 (1993).

J. Mod. Opt. (2)

M. Ivanov, I. Naydenova, T. Todorov, L. Nikolova, T. Petrova, N. Tomova, and V. Dragostinova, "Light-induced optical activity in optically ordered amorphous side-chain azobenzene containing polymer," J. Mod. Opt. 47, 861-867 (2000).

K. Brudzewski, "Static Stokes ellipsometer: general analysis and optimization," J. Mod. Opt. 38, 889-896 (1991).
[CrossRef]

J. Opt. A (2)

I. Naydenova, L. Nikolova, P. S. Ramanujam, and S. Hvilsted, "Light-induced circular birefringence in cyanoazobenzene side-chain liquid-crystalline polyester films," J. Opt. A , Pure Appl. Opt. 1, 438-441 (1999).
[CrossRef]

J. M. Bueno, "Polarimetry using liquid-crystal variable retarders: theory and calibration," J. Opt. A , Pure Appl. Opt. 2, 216-222 (2000).
[CrossRef]

Opt. Acta (4)

R. M. A. Azzam, "Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light," Opt. Acta 29, 685-689 (1982).
[CrossRef]

R. M. A. Azzam, "Beam-splitters for the division-of-amplitude photopolarimeter," Opt. Acta 32, 1407-1412 (1985).
[CrossRef]

L. Nikolova and T. Todorov, "Diffraction efficiency and selectivity of polarization diffraction grating," Opt. Acta 31, 579-588 (1984).
[CrossRef]

T. Todorov, P. Markovski, M. Mazakova, M. Miteva, V. Razsolkov, and M. Pancheva, "Spectral characteristic of thick phase holographic gratings," Opt. Acta 28, 379-388 (1981).
[CrossRef]

Opt. Commun. (1)

J.-K. Lee, J. T. Shen, A. Heifetz, R. Tripathi, and M. S. Shariar, "Demonstration of a thick holographic Stokesmeter," Opt. Commun. 259, 484-487 (2006).
[CrossRef]

Opt. Eng. (1)

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, and R. W. McMillan, "Snapshot imaging spectropolarimeter," Opt. Eng. 41, 1048-1054 (2002).
[CrossRef]

Opt. Expess (1)

D. Sabatke, A. M. Locke, E. L. Dereniak, and R. W. McMillan, "Linear calibration and reconstruction techniques for channeled spectropolarimetry," Opt. Expess 11, 2940-2952 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Opt. Mater. (1)

L. Nikolova, T. Todorov, M. Ivanov, F. Andruzzi, S. Hilsted, and P. S. Ramanujam, "Photoinduced circular anisotropy in side-chain azobenzene polyesters," Opt. Mater. 8, 255-258 (1997).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Principal scheme of the SS. PDG, polarization diffraction grating; DG, conventional diffraction grating; A, linear polarizers oriented at 0° and 45°; LIS, linear image sensors; L 0 , the measured light beam; L 1 , L 2 , L 3 , and L 4 , the four measured spectra; L, the beam transmitted after the PDG.

Fig. 2
Fig. 2

Diffraction of an elliptically polarized light beam from the PDG. The intensities of light diffracted in the + 1 ( I + 1 ) and 1 ( I 1 ) orders are proportional to the left and right circularly polarized components of the incident light beam L 0 . The transmitted light beam with intensity I has the polarization of the beam L 0 .

Fig. 3
Fig. 3

Spectrum of the diffraction efficiency of the PDG.

Fig. 4
Fig. 4

Optical scheme of the SS. 1, head objective; 2, slit; 3, collimating objective; 4, PDG; 5 and 9, objectives; 6, LISs; 7, DG; 8, linear polarizers.

Fig. 5
Fig. 5

Electrical scheme of the SS. 1, LISs; 2, video amplifier; 3, MX; 4, ADC; 5, digital pulse generator; 6, buffers; and 7, PC.

Fig. 6
Fig. 6

Optical scheme used for the testing of the SS. S, white light source; O, collimating objective; P, linear polarizer, oriented at 0°; TO, test object.

Fig. 7
Fig. 7

Normalized spectra of the Stokes parameters S i of the calibrating light beam, polarized at 0°.

Fig. 8
Fig. 8

Spectrum of the light transmitted after an interference filter with λ max = 655 nm , Δ λ half = 12 nm .

Fig. 9
Fig. 9

Spectra of the Stokes parameters S i of light transmitted through a linear polarizer for different orientation φ of the transmission axis: (a) φ = 44 ° , (b) φ = 55 ° .

Fig. 10
Fig. 10

Dependencies of the Stokes parameters (a) S 0 , (b) S 1 , (c) S 2 , and (d) S 3 on the orientation of the transmission axis of a linear polarizer measured at 630 nm: calculated curves, solid lines, and experimentally measured values 0, dots.

Fig. 11
Fig. 11

Dependencies of the Stokes parameters (a) S 0 , (b) S 1 , (c) S 2 , and (d) S 3 on the orientation of the azimuth of a 560 nm quarter-wave plate measured at 560 nm : solid curves, calculated curves; and solid circles, experimentally measured values 0.

Tables (1)

Tables Icon

Table 1 Wavelengths of Maximum Transmittance of the Filters

Equations (21)

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T = | cos Δ φ + i sin Δ φ cos ( 2 δ ) i sin Δ φ cos ( 2 δ ) i sin Δ φ cos ( 2 δ ) cos Δ φ i sin Δ φ cos ( 2 δ ) | ,
E i n = | E x E y exp ( i ψ ) | ,
E + 1 = i sin Δ φ 2 | E x + i E y exp ( i ψ ) i ( E x + i E y exp ( i ψ ) ) | ,
E 1 = i sin Δ φ 2 | E x i E y exp ( i ψ ) i ( E x i E y exp ( i ψ ) ) | .
I 3 I l , I 4 I r .
I 3 S 0 + S 3 , I 4 S 0 S 3 .
E j = | E x j E y j exp ( ψ j ) | .
l 1 j = ( E x j ) 2 / k 1 j ,
l 2 j = [ ( E x j ) 2 + ( E y j ) 2 + 2 E x E y cos ψ j ] / 2 k 2 j ,
l 3 j = ( E left j ) 2 / k 3 j ,  
l 4 j = ( E right j ) 2 / k 4 j ,
( E x j ) 2 = l c a l j , ( E y j ) 2 = 0 ,
( E left j ) 2 = l c a l j / 2 , ( E right j ) 2 = l c a l j / 2 ,
S 0 j = k 3 j l 3 j + k 4 j l 4 j ,
S 1 j = 2 k 1 j l 1 j k 3 j l 3 j k 4 j l 4 j ,
S 2 j = 2 k 2 j l 2 j k 3 j l 3 j k 4 j l 4 j ,
S 3 j = k 3 j l 3 j k 4 j l 4 j .
S 0 = cos 2 α , S 1 = cos 2 α cos 2 α ,
S 2 = cos 2 α sin 2 α , S 3 = 0 .
S 0 = 1 , S 1 = 0.5 sin 4 α ,
S 2 = cos 2 2 α , S 3 = sin 2 α .

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