Abstract

A new method to measure the light polarization state and the birefringent media parameters is proposed. We have used the setup described previously, consisting of two pairs of the linear Wollaston and circular compensators which form a set of two spatially modulated elliptical compensators. We have modified this setup introducing some carrier frequencies in all compensators and assuming that the second linear one would introduce the frequency which is a multiplicity of the basis frequency of the first linear compensator. Both of these modifications allow calculating all polarization parameters of polarized light or birefringent medium from only one measured intensity distribution of the light outcoming the described setup. They allow measuring not only the parameters of homogeneous beams/mediums but also x,y-distributions of all desired parameters, like azimuth and ellipticity angles of the light or first medium eigenvector and the phase difference introduced by this medium. The proposed calculation method comprises of Fourier analysis of obtained intensity distribution with some manipulation of coordinate system and filtration of obtained data. This method is claimed to be simple and fast enough to be treated as a real-time method.

©2009 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  8. Y. L. Lo and P. F. Hsu, “Birefringence measurements by an electro-optic modulator using a new heterodyne scheme,” Opt. Eng. 41, 2764–2767 (2002).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

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]

2006 (3)

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]

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]

K. Oka and N. Saito, “Snapshot complete imaging polarimeter using Savart plates,” Proc. SPIE6295–6299,  1 (2006).

2004 (5)

2003 (1)

2002 (3)

B. Zuccarello and G. Tripoli, “Photoelastic stress pattern analysis Fourier transform with carrier fringes: influence of quarter wave plate error,” Opt. Lasers Eng. 37, 401–416 (2002).
[Crossref]

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

Y. L. Lo and P. F. Hsu, “Birefringence measurements by an electro-optic modulator using a new heterodyne scheme,” Opt. Eng. 41, 2764–2767 (2002).
[Crossref]

2001 (1)

2000 (1)

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

1999 (1)

B. Wang and T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
[Crossref]

1997 (1)

1992 (1)

1983 (1)

J. Kobayashi and Y. Uesu, “A new optical method and apparatus ‘HAUP’ for measuring simultaneously optical activity and birefringence of crystals. I. Principles and construction,” J. Appl. Crystallogr. 16, 204–211 (1983).
[Crossref]

1982 (1)

Artal, P.

Baleine, E.

Berezhna, S. Y.

Berezhnyy, I. V.

Bueno, J. M.

de Martino, A.

Dogariu, A.

Drevillon, B.

Drobczynski, S.

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

Gaylord, T. K.

Goldstein, D. H.

Hashimoto, N.

T. Sato, Y. Sasaki, N. Hashimoto, and S. Kawakami, “Novel scheme of ellipsometry utilizing parallel processing with arrayed photonic crystal,” Photon. Nanostruct. Fundam. Appl. 2, 149–154 (2004).
[Crossref]

Hsu, P. F.

Ina, H.

Kaneko, T.

Kasprzak, H.

Kawakami, S.

T. Sato, Y. Sasaki, N. Hashimoto, and S. Kawakami, “Novel scheme of ellipsometry utilizing parallel processing with arrayed photonic crystal,” Photon. Nanostruct. Fundam. Appl. 2, 149–154 (2004).
[Crossref]

Kobayashi, H.

Kobayashi, J.

J. Kobayashi and Y. Uesu, “A new optical method and apparatus ‘HAUP’ for measuring simultaneously optical activity and birefringence of crystals. I. Principles and construction,” J. Appl. Crystallogr. 16, 204–211 (1983).
[Crossref]

Kurzynowski, P.

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 113, 51–53 (2002).
[Crossref]

Lai, C. H.

Laude-Boulesteix, B.

Lin, J. F.

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]

Lo, Y. L.

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]

Montarou, C. C.

Mujat, M.

Oakberg, T. C.

B. Wang and T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
[Crossref]

Oka, K.

K. Oka and N. Saito, “Snapshot complete imaging polarimeter using Savart plates,” Proc. SPIE6295–6299,  1 (2006).

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

Rose, A. H.

Saito, N.

K. Oka and N. Saito, “Snapshot complete imaging polarimeter using Savart plates,” Proc. SPIE6295–6299,  1 (2006).

Sasaki, Y.

T. Sato, Y. Sasaki, N. Hashimoto, and S. Kawakami, “Novel scheme of ellipsometry utilizing parallel processing with arrayed photonic crystal,” Photon. Nanostruct. Fundam. Appl. 2, 149–154 (2004).
[Crossref]

Sato, T.

T. Sato, Y. Sasaki, N. Hashimoto, and S. Kawakami, “Novel scheme of ellipsometry utilizing parallel processing with arrayed photonic crystal,” Photon. Nanostruct. Fundam. Appl. 2, 149–154 (2004).
[Crossref]

Schwartz, L.

Takashi, M.

Takeda, M.

Tripoli, G.

B. Zuccarello and G. Tripoli, “Photoelastic stress pattern analysis Fourier transform with carrier fringes: influence of quarter wave plate error,” Opt. Lasers Eng. 37, 401–416 (2002).
[Crossref]

Uesu, Y.

J. Kobayashi and Y. Uesu, “A new optical method and apparatus ‘HAUP’ for measuring simultaneously optical activity and birefringence of crystals. I. Principles and construction,” J. Appl. Crystallogr. 16, 204–211 (1983).
[Crossref]

Wang, B.

B. Wang and T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
[Crossref]

Wang, C. M.

Williams, P. A.

Wozniak, W. A.

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 113, 51–53 (2002).
[Crossref]

Zuccarello, B.

B. Zuccarello and G. Tripoli, “Photoelastic stress pattern analysis Fourier transform with carrier fringes: influence of quarter wave plate error,” Opt. Lasers Eng. 37, 401–416 (2002).
[Crossref]

Appl. Opt. (6)

J. Appl. Crystallogr. (1)

J. Kobayashi and Y. Uesu, “A new optical method and apparatus ‘HAUP’ for measuring simultaneously optical activity and birefringence of crystals. I. Principles and construction,” J. Appl. Crystallogr. 16, 204–211 (1983).
[Crossref]

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

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

J. Opt. Soc. Am. (1)

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

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)

Y. L. Lo and P. F. Hsu, “Birefringence measurements by an electro-optic modulator using a new heterodyne scheme,” Opt. Eng. 41, 2764–2767 (2002).
[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 (2)

Opt. Lasers Eng. (1)

B. Zuccarello and G. Tripoli, “Photoelastic stress pattern analysis Fourier transform with carrier fringes: influence of quarter wave plate error,” Opt. Lasers Eng. 37, 401–416 (2002).
[Crossref]

Optik (1)

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

Photon. Nanostruct. Fundam. Appl. (1)

T. Sato, Y. Sasaki, N. Hashimoto, and S. Kawakami, “Novel scheme of ellipsometry utilizing parallel processing with arrayed photonic crystal,” Photon. Nanostruct. Fundam. Appl. 2, 149–154 (2004).
[Crossref]

Proc. SPIE (1)

K. Oka and N. Saito, “Snapshot complete imaging polarimeter using Savart plates,” Proc. SPIE6295–6299,  1 (2006).

Rev. Sci. Instrum. (1)

B. Wang and T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. The scheme of spatial elliptical polariscope. PL1C1 - all polarization state spatial generator, C2L2A - polarization state spatial analyzer, CCD - a CCD camera.
Fig. 2.
Fig. 2. Positions of A m,n coefficients in u,v-Fourier plane; see description in text.
Fig. 3.
Fig. 3. Positions of A m,n coefficients in u,v-Fourier plane in the case of elliptical spatial polarimeter with different carrier frequencies of the both linear compensators.
Fig. 4.
Fig. 4. The numerical simulations of proposed method: a) the assumed input contaminated Gaussian beam; b) the calculated output intensity distribution; c) the Fourier transform of this distribution with marked area used in following computations.
Fig. 5.
Fig. 5. The azimuth angle α(x, y) distributions: (a) assumed; (b) calculated; (c) the difference between calculated and assumed distributions.
Fig. 6.
Fig. 6. The ellipticity angle ϑ(x, y) distributions: (a) assumed; (b) calculated; (c) the difference between calculated and assumed distributions.
Fig. 7.
Fig. 7. The phase shift γ (x, y) distributions: (a) assumed; (b) calculated; (c) the difference between calculated and assumed distributions.

Equations (23)

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fi=1Λi=2Δnitanαiλ ,
δL1,L2=2 π fL1,L2 x ,
δC1,C2=2πfC1,C2y.
VPLC=[sinδC1cosδL1cosδC1cosδL1sinδL1],
VCLA=[sinδC2cosδL2cosδC2cosδL2sinδL2].
V=[sin(2α)cos(2ϑ)cos(2α)cos(2ϑ)sin(2ϑ)],
I(x,y)=I0 (x,y)T2 (1+VCLA·V) ,
I(x,y)=m,nam,nexp[2πi(fmx+fny)]+c. c . ,
am,n(x,y)=f (α,ϑ;I0T2) ,
a1,0=iI0 T2 sin2 ϑ ,
a1,1=12I0 T2 cos2 ϑ exp (2iα) ,
tan2α(x,y)=Im(a1,1)Re(a1,1) ,
sin2ϑ(x,y)=ia1,0a1,02+2a1,12.
Vf=[sin(2αf)cos(2ϑf)cos(2αf)cos(2ϑf)sin(2ϑf)],
II0T2=1+Z(VCLA·Vf)(VPLC·Vf)+X(VCLA·VPLC)+Y[Vf·(VCLA×VPLC)] ,
X=cosγ , Y=sinγ , Z=1cosγ
I(x,y)=m,nam,nexp[2πi(fmx+fny)]+c.c,
a1,1=I0T2 cos2 ϑf exp (2iaf) sinγ ,
a1,2=a3,2=14I0T2 cos2 2 ϑf exp (4iαf)(1cosγ),
a3,1=12I0T2 sin4 ϑf exp (2iαf)(1cosγ).
tan2αf=Im(a1,1)Re(a1,1),
tan2ϑf=a3,1a1,2=a3,1a3,2,
tan2 γ2=a3,1a1,12+4a3,2a1,12=a3,1a1,12+4a1,2a1,12.

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