Abstract

A Fourier-transform imaging spectropolarimeter is presented and demonstrated. It is composed of a time-division polarization modulator and a high radiation throughput Fourier-transform spectrometer. Four polarization states of the input light are generated by rotating the retarder. Then, the polarized light enters the Fourier-transform spectrometer to create four sets of interferometric images, where we can recover four polarization spectra and calculate the full-Stokes vector in various wavenumber frequency. The method has good performance to resist instrument noise and has the advantage of high spatial resolution. The laboratory setup is described and the noise source is analyzed. Two proven experiments have been carried out in visible light.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2013

2012

H. Dong, P. Shum, Y. Gong, and Q. Sun, “Measurement errors induced by retardance deviation in a rotatable retarder fixed polarizer Stokes polarimeter,” Opt. Eng. 51, 033001 (2012).
[CrossRef]

T. Mu, C. Zhang, C. Jia, and W. Ren, “Static hyperspectral imaging polarimeter for full linear Stokes parameters,” Opt. Express 20, 18194–18201 (2012).
[CrossRef]

2011

2010

2007

2006

2005

D. J. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Food, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

R. G. Sellar and G. D. Boreman, “Comparison of relative signal-to-noise ratios of different classes of imaging spectrometer,” Appl. Opt. 44, 1614–1624 (2005).
[CrossRef]

2004

2001

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef]

J. S. Tyo and T. S. Turner, “Variable-retardance, Fourier-transform imaging spectropolarimeters for visible spectrum remote sensing,” Appl. Opt. 40, 1450–1458 (2001).
[CrossRef]

2000

1999

1996

M. Lavi, U. Milman, D. Cabib, Y. Garini, A. Gil, T. Juta, and M. Adel, “A new compact design interferometer based spectral imaging system for bio-medical applications,” Proc. SPIE 3261, 313–321 (1996).
[CrossRef]

1994

1993

A. Dutt and V. Rokhlin, “Fast Fourier-transforms for nonequispaced data,” Siam J. Sci. Comput. 14, 1368–1393 (1993).
[CrossRef]

1983

J. O. Stenflo, D. Twerenbold, J. W. Harvey, and J. W. Brault, “Coherent scattering in the solar spectrum: survey of linear polarization in the range 4200–9950  Å,” Astron. Astrophys. Suppl. Ser. 54, 505–514 (1983).

Adel, M.

M. Lavi, U. Milman, D. Cabib, Y. Garini, A. Gil, T. Juta, and M. Adel, “A new compact design interferometer based spectral imaging system for bio-medical applications,” Proc. SPIE 3261, 313–321 (1996).
[CrossRef]

Backman, V.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef]

Badizadegan, K.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef]

Barducci, A.

Beaudry, N.

D. J. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Food, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Bergstralh, J.

Boreman, G. D.

Brault, J. W.

J. O. Stenflo, D. Twerenbold, J. W. Harvey, and J. W. Brault, “Coherent scattering in the solar spectrum: survey of linear polarization in the range 4200–9950  Å,” Astron. Astrophys. Suppl. Ser. 54, 505–514 (1983).

Cabib, D.

M. Lavi, U. Milman, D. Cabib, Y. Garini, A. Gil, T. Juta, and M. Adel, “A new compact design interferometer based spectral imaging system for bio-medical applications,” Proc. SPIE 3261, 313–321 (1996).
[CrossRef]

Cairns, B.

D. J. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Food, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Chenault, D. B.

Chipman, R. A.

D. J. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Food, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Christophe, C.

Clark, D.

D. Clark and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, 1971).

Cunningham, T. J.

D. J. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Food, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Dasari, R. R.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef]

Dereniak, E. L.

Diner, D. J.

D. J. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Food, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Dong, H.

H. Dong, P. Shum, Y. Gong, and Q. Sun, “Measurement errors induced by retardance deviation in a rotatable retarder fixed polarizer Stokes polarimeter,” Opt. Eng. 51, 033001 (2012).
[CrossRef]

Dutt, A.

A. Dutt and V. Rokhlin, “Fast Fourier-transforms for nonequispaced data,” Siam J. Sci. Comput. 14, 1368–1393 (1993).
[CrossRef]

Feld, M. S.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef]

Food, L. D.

D. J. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Food, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Garini, Y.

M. Lavi, U. Milman, D. Cabib, Y. Garini, A. Gil, T. Juta, and M. Adel, “A new compact design interferometer based spectral imaging system for bio-medical applications,” Proc. SPIE 3261, 313–321 (1996).
[CrossRef]

Georgakoudi, I.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef]

Gerhart, G. R.

Gil, A.

M. Lavi, U. Milman, D. Cabib, Y. Garini, A. Gil, T. Juta, and M. Adel, “A new compact design interferometer based spectral imaging system for bio-medical applications,” Proc. SPIE 3261, 313–321 (1996).
[CrossRef]

Glenar, D. A.

Goldstein, D. L.

Gong, Y.

H. Dong, P. Shum, Y. Gong, and Q. Sun, “Measurement errors induced by retardance deviation in a rotatable retarder fixed polarizer Stokes polarimeter,” Opt. Eng. 51, 033001 (2012).
[CrossRef]

Grainger, J. F.

D. Clark and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, 1971).

Gurjar, R. S.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef]

Guzzi, D.

Hagen, N. A.

Harvey, J. W.

J. O. Stenflo, D. Twerenbold, J. W. Harvey, and J. W. Brault, “Coherent scattering in the solar spectrum: survey of linear polarization in the range 4200–9950  Å,” Astron. Astrophys. Suppl. Ser. 54, 505–514 (1983).

Herve, S.

Hillman, J. J.

Iannarilli, F. J.

Itzkan, I.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef]

Jean, T.

Jerome, P.

Jia, C.

Joel, D.

Jones, S. H.

Juta, T.

M. Lavi, U. Milman, D. Cabib, Y. Garini, A. Gil, T. Juta, and M. Adel, “A new compact design interferometer based spectral imaging system for bio-medical applications,” Proc. SPIE 3261, 313–321 (1996).
[CrossRef]

Kato, T.

Kebabian, P. L.

Keller, C.

D. J. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Food, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Kudenov, M. W.

Lastri, C.

Lavi, M.

M. Lavi, U. Milman, D. Cabib, Y. Garini, A. Gil, T. Juta, and M. Adel, “A new compact design interferometer based spectral imaging system for bio-medical applications,” Proc. SPIE 3261, 313–321 (1996).
[CrossRef]

Li, J.

X. Meng, J. Li, Y. Zhang, and R. Zhu, “Full-Stokes imaging polarimetry using a combination of a retarder and a polarizer,” Proc. SPIE 8908, 890829 (2013).
[CrossRef]

X. Meng, J. Li, T. Xu, D. Liu, and R. Zhu, “High throughput full Stokes Fourier-transform imaging spectropolarimetry,” Opt. Express 21, 32071–32085 (2013).
[CrossRef]

X. Meng, J. Li, D. Liu, and R. Zhu, “Fourier-transform imaging spectropolarimeter using simultaneous polarization modulation,” Opt. Lett. 38, 778–780 (2013).
[CrossRef]

J. Li, W. Zhou, X. Meng, D. Liu, and R. Zhu, “Fourier-transform imaging spectrometry using Sagnac interferometer,” Proc. SPIE 8910, 89101Y (2013).
[CrossRef]

C. Zhang, H. Wu, and J. Li, “Fourier-transform hyperspectrral imaging polarimeter for remote sensing,” Opt. Eng. 50, 066201 (2011).
[CrossRef]

J. Li, J. Zhu, and H. Wu, “Compact static Fourier-transform imaging spectropolarimeter based on channeled polarimetry,” Opt. Lett. 35, 3784–3786 (2010).
[CrossRef]

Li, Q.

Liu, D.

Macenka, S. A.

D. J. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Food, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Marcoionni, P.

Meng, X.

J. Li, W. Zhou, X. Meng, D. Liu, and R. Zhu, “Fourier-transform imaging spectrometry using Sagnac interferometer,” Proc. SPIE 8910, 89101Y (2013).
[CrossRef]

X. Meng, J. Li, Y. Zhang, and R. Zhu, “Full-Stokes imaging polarimetry using a combination of a retarder and a polarizer,” Proc. SPIE 8908, 890829 (2013).
[CrossRef]

X. Meng, J. Li, T. Xu, D. Liu, and R. Zhu, “High throughput full Stokes Fourier-transform imaging spectropolarimetry,” Opt. Express 21, 32071–32085 (2013).
[CrossRef]

X. Meng, J. Li, D. Liu, and R. Zhu, “Fourier-transform imaging spectropolarimeter using simultaneous polarization modulation,” Opt. Lett. 38, 778–780 (2013).
[CrossRef]

Milman, U.

M. Lavi, U. Milman, D. Cabib, Y. Garini, A. Gil, T. Juta, and M. Adel, “A new compact design interferometer based spectral imaging system for bio-medical applications,” Proc. SPIE 3261, 313–321 (1996).
[CrossRef]

Mu, T.

Nardino, V.

Oka, K.

Perelman, L. T.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef]

Pierre, C.

Pierre, F.

Pippi, I.

Pust, N. J.

Ren, W.

Rokhlin, V.

A. Dutt and V. Rokhlin, “Fast Fourier-transforms for nonequispaced data,” Siam J. Sci. Comput. 14, 1368–1393 (1993).
[CrossRef]

Saif, B.

Sellar, R. G.

Seshadri, S.

D. J. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Food, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Shaw, J. A.

Shum, P.

H. Dong, P. Shum, Y. Gong, and Q. Sun, “Measurement errors induced by retardance deviation in a rotatable retarder fixed polarizer Stokes polarimeter,” Opt. Eng. 51, 033001 (2012).
[CrossRef]

Stenflo, J. O.

J. O. Stenflo, D. Twerenbold, J. W. Harvey, and J. W. Brault, “Coherent scattering in the solar spectrum: survey of linear polarization in the range 4200–9950  Å,” Astron. Astrophys. Suppl. Ser. 54, 505–514 (1983).

Sun, Q.

H. Dong, P. Shum, Y. Gong, and Q. Sun, “Measurement errors induced by retardance deviation in a rotatable retarder fixed polarizer Stokes polarimeter,” Opt. Eng. 51, 033001 (2012).
[CrossRef]

Turner, T. S.

Twerenbold, D.

J. O. Stenflo, D. Twerenbold, J. W. Harvey, and J. W. Brault, “Coherent scattering in the solar spectrum: survey of linear polarization in the range 4200–9950  Å,” Astron. Astrophys. Suppl. Ser. 54, 505–514 (1983).

Tyo, J. S.

Wu, H.

C. Zhang, H. Wu, and J. Li, “Fourier-transform hyperspectrral imaging polarimeter for remote sensing,” Opt. Eng. 50, 066201 (2011).
[CrossRef]

J. Li, J. Zhu, and H. Wu, “Compact static Fourier-transform imaging spectropolarimeter based on channeled polarimetry,” Opt. Lett. 35, 3784–3786 (2010).
[CrossRef]

Xu, T.

Yann, F.

Zhang, C.

Zhang, L.

Zhang, Y.

X. Meng, J. Li, Y. Zhang, and R. Zhu, “Full-Stokes imaging polarimetry using a combination of a retarder and a polarizer,” Proc. SPIE 8908, 890829 (2013).
[CrossRef]

Zhou, W.

J. Li, W. Zhou, X. Meng, D. Liu, and R. Zhu, “Fourier-transform imaging spectrometry using Sagnac interferometer,” Proc. SPIE 8910, 89101Y (2013).
[CrossRef]

Zhu, J.

Zhu, R.

X. Meng, J. Li, D. Liu, and R. Zhu, “Fourier-transform imaging spectropolarimeter using simultaneous polarization modulation,” Opt. Lett. 38, 778–780 (2013).
[CrossRef]

X. Meng, J. Li, T. Xu, D. Liu, and R. Zhu, “High throughput full Stokes Fourier-transform imaging spectropolarimetry,” Opt. Express 21, 32071–32085 (2013).
[CrossRef]

X. Meng, J. Li, Y. Zhang, and R. Zhu, “Full-Stokes imaging polarimetry using a combination of a retarder and a polarizer,” Proc. SPIE 8908, 890829 (2013).
[CrossRef]

J. Li, W. Zhou, X. Meng, D. Liu, and R. Zhu, “Fourier-transform imaging spectrometry using Sagnac interferometer,” Proc. SPIE 8910, 89101Y (2013).
[CrossRef]

Appl. Opt.

Astron. Astrophys. Suppl. Ser.

J. O. Stenflo, D. Twerenbold, J. W. Harvey, and J. W. Brault, “Coherent scattering in the solar spectrum: survey of linear polarization in the range 4200–9950  Å,” Astron. Astrophys. Suppl. Ser. 54, 505–514 (1983).

Nat. Med.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[CrossRef]

Opt. Eng.

C. Zhang, H. Wu, and J. Li, “Fourier-transform hyperspectrral imaging polarimeter for remote sensing,” Opt. Eng. 50, 066201 (2011).
[CrossRef]

H. Dong, P. Shum, Y. Gong, and Q. Sun, “Measurement errors induced by retardance deviation in a rotatable retarder fixed polarizer Stokes polarimeter,” Opt. Eng. 51, 033001 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

M. Lavi, U. Milman, D. Cabib, Y. Garini, A. Gil, T. Juta, and M. Adel, “A new compact design interferometer based spectral imaging system for bio-medical applications,” Proc. SPIE 3261, 313–321 (1996).
[CrossRef]

J. Li, W. Zhou, X. Meng, D. Liu, and R. Zhu, “Fourier-transform imaging spectrometry using Sagnac interferometer,” Proc. SPIE 8910, 89101Y (2013).
[CrossRef]

X. Meng, J. Li, Y. Zhang, and R. Zhu, “Full-Stokes imaging polarimetry using a combination of a retarder and a polarizer,” Proc. SPIE 8908, 890829 (2013).
[CrossRef]

D. J. Diner, R. A. Chipman, N. Beaudry, B. Cairns, L. D. Food, S. A. Macenka, T. J. Cunningham, S. Seshadri, and C. Keller, “An integrated multiangle, multispectral, and polarimetric imaging concept for aerosol remote sensing from space,” Proc. SPIE 5659, 88–96 (2005).
[CrossRef]

Siam J. Sci. Comput.

A. Dutt and V. Rokhlin, “Fast Fourier-transforms for nonequispaced data,” Siam J. Sci. Comput. 14, 1368–1393 (1993).
[CrossRef]

Other

D. Clark and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, 1971).

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Figures (12)

Fig. 1.
Fig. 1.

Schematic layout of the Fourier-transform ISP.

Fig. 2.
Fig. 2.

Absolute error of the realistic OPD minus the calculated linear OPD.

Fig. 3.
Fig. 3.

Maximum OPDs for a variety of wavelengths with different beam splitter thicknesses.

Fig. 4.
Fig. 4.

Experimental setup consists of a time-division polarization modulator and a Sagnac Fourier-transform spectrometer, without a slit.

Fig. 5.
Fig. 5.

(a) Phase retardance of the achromatic quarter-wave plate measured by the ellipsometer. (b) Condition number of the polarization modulator at various wavelengths.

Fig. 6.
Fig. 6.

Errors of the recovered Stokes parameters with different initial relative angular orientation errors.

Fig. 7.
Fig. 7.

Schematic layout of the calibration system to calculate the relative angle of the fast axis of the retarder with respect to the transmission axis of the fixed polarizer.

Fig. 8.
Fig. 8.

Recovered values of S0 parameter in the repetition experiments to test the time-division polarization modulator.

Fig. 9.
Fig. 9.

(a) Four polarized fringe pattern of a point on the white plate. (b) Normalized Stokes parameters spectra of the point. The dashed line is the theory value and the solid curve denotes the recovered spectra.

Fig. 10.
Fig. 10.

(a) Scene of the target. (b) Four interferometric images with different polarization states.

Fig. 11.
Fig. 11.

(a) Four spectral images of the scene at 510, 540, 570, and 600 nm, respectively. (b) Normalized Stokes parameter images at 540 nm.

Fig. 12.
Fig. 12.

(a) Spectra of point A. (b) Normalized Stokes parameters spectra of point A.

Equations (19)

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Sout=MLP(0°)MR(θ,δ(σ))Sin(S0,S1,S2,S3)T,
MLP(0°)=12[1100110000000000],
MR(θ,δ(σ))=[10000cos22θ+sin22θcosδsin2θcos2θ(1cosδ)sin2θsinδ0sin2θcos2θ(1cosδ)sin22θ+cos22θcosδcos2θsinδ0sin2θsinδcos2θsinδcosδ],
I(Δ)=0σM14(1+cos2πσΔ)(Sout0(σ))dσ=0σM18(1+cos2πσΔ)(m0S0(σ)+m1S1(σ)+m2S2(σ)+m3S3(σ))dσ,
m0nS0+m1nS1+m2nS2+m3nS3=Bn(σ)=RI1(In(Δ)),
A·Sin=B,
A=[m00m10m20m30m01m11m21m31m02m12m22m32m03m13m23m33],B=[B0B1B2B3].
[S0S1S2S3]=[1cos(δ(σ))0sin(δ(σ))1100114+34cos(δ(σ))34(1cos(δ(σ)))32sin(δ(σ))114+34cos(δ(σ))34(1cos(δ(σ)))32sin(δ(σ))]1·[B0B1B2B3].
Δ=dsinβ,
Δ=(22h(tan(β+45°)w1+cot(β+45°)w2)+d0)sinβ,
w1=1sin(β+45°)n2(σ)sin2(β+45°),
w2=1sin(β+45°)n2(σ)cos2(β+45°),
SNR=Se(Np+Ni),
ωmax=2arctan(H2f1),
I(α)=S0+S0cos22θ0cos2α+S0sin2θ0cos2θ0sin2α,
S0·cos22θ0=1πα0α0+2πI(α)cos2αdα,
S0·sin2θ0cos2θ0=1πα0α0+2πI(α)sin2αdα,
tan2θ0=α0α0+2πI(α)sin2αdαα0α0+2πI(α)cos2αdα.
Sin=S0(1,0.5,0.866,0).

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