Abstract

We describe a single-shot polarization spectral imager that combines two birefringent crystals with a binary coded aperture to encode the spatial, spectral and polarization data cube for compressive sampling on a two-dimensional (2D) detector array. We use a total variation prior to reconstruct the four-dimensional (4D) data cube from the single 2D measurement. The 4D data cube includes 1500×1240pixels in the spatial domain, 19 wavelength channels between 400 and 680 nm and two Stokes parameters.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. C. F. LaCasse, R. A. Chipman, and J. S. Tyo, “Band limited data reconstruction in modulated polarimeters,” Opt. Express 19, 14976–14989 (2011).
    [CrossRef]
  6. M. Gehm, R. John, D. J. Brady, R. Willett, and T. Schulz, “Single-shot compressive spectral imaging with a dual-disperser architecture,” Opt. Express 15, 14013–14027 (2007).
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  7. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049 (2009).
    [CrossRef]
  8. K. MacCabe, K. Krishnamurthy, A. Chawla, D. Marks, E. Samei, and D. Brady, “Pencil beam coded aperture x-ray scatter imaging,” Opt. Express 20, 16310–16320 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. A. Wagadarikar, R. John, R. Willett, and D. J. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (2008).
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    [CrossRef]
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  23. X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “High-resolution thin guest-host micropolarizer arrays for visible imaging polarimetry,” Opt. Express 19, 5565–5573 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  26. V. Gruev, A. Ortu, N. Lazarus, J. Van der Spiegel, and N. Engheta, “Fabrication of a dual-tier thin film micropolarization array,” Opt. Express 15, 4994–5007 (2007).
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  27. J. Guo and D. Brady, “Fabrication of thin-film micropolarizer arrays for visible imaging polarimetry,” Appl. Opt. 39, 1486–1492 (2000).
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    [CrossRef]
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    [CrossRef]

2012 (4)

2011 (3)

2010 (2)

2009 (3)

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049 (2009).
[CrossRef]

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “Thin photo-patterned micropolarizer array for CMOS image sensors,” IEEE Photon. Technol. Lett. 21, 805–807 (2009).
[CrossRef]

J. M. Eichenholz, and J. Dougherty, “Ultracompact fully integrated megapixel multispectral imager,” Proc. SPIE 7218, 721814 (2009).
[CrossRef]

2008 (3)

2007 (2)

2006 (2)

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)

W. Smith, D. Zhou, F. Harrison, H. Revercomb, A. Larar, A. Huang, and B. Huang, “Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft,” Proc. SPIE 4151, 94–102 (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 (1)

1999 (1)

R. G. Nadeau, W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, and K. Messmer, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[CrossRef]

1997 (2)

Ahmad, J. E.

Bachman, K. A.

J. J. Peltzer, K. A. Bachman, J. W. Rose, P. D. Flammer, T. E. Furtak, R. T. Collins, and R. E. Hollingsworth, “Ultracompact fully integrated megapixel multispectral imager,” Proc. SPIE 8364, 83640O (2012).

Bayer, B.

B. Bayer, “Color imaging array,” U.S. patent 4,054,906 (20July1976).

Bermak, A.

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “High-resolution thin guest-host micropolarizer arrays for visible imaging polarimetry,” Opt. Express 19, 5565–5573 (2011).
[CrossRef]

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “Thin photo-patterned micropolarizer array for CMOS image sensors,” IEEE Photon. Technol. Lett. 21, 805–807 (2009).
[CrossRef]

Bouma, G. J.

R. G. Nadeau, W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, and K. Messmer, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[CrossRef]

Boussaid, F.

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “High-resolution thin guest-host micropolarizer arrays for visible imaging polarimetry,” Opt. Express 19, 5565–5573 (2011).
[CrossRef]

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “Thin photo-patterned micropolarizer array for CMOS image sensors,” IEEE Photon. Technol. Lett. 21, 805–807 (2009).
[CrossRef]

Brady, D.

Brady, D. J.

Chawla, A.

Chenault, D. B.

Chigrinov, V. G.

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “High-resolution thin guest-host micropolarizer arrays for visible imaging polarimetry,” Opt. Express 19, 5565–5573 (2011).
[CrossRef]

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “Thin photo-patterned micropolarizer array for CMOS image sensors,” IEEE Photon. Technol. Lett. 21, 805–807 (2009).
[CrossRef]

Chipman, R.

Chipman, R. A.

Choi, K.

Collins, R. T.

J. J. Peltzer, K. A. Bachman, J. W. Rose, P. D. Flammer, T. E. Furtak, R. T. Collins, and R. E. Hollingsworth, “Ultracompact fully integrated megapixel multispectral imager,” Proc. SPIE 8364, 83640O (2012).

Dereniak, E.

Dereniak, E. L.

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]

Descour, M.

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]

M. Descour, C. Volin, E. Dereniak, K. Thorne, A. Schumacher, D. Wilson, and P. Maker, “Demonstration of a high-speed nonscanning imaging spectrometer,” Opt. Lett. 22, 1271–1273 (1997).
[CrossRef]

Diner, D.

Dougherty, J.

J. M. Eichenholz, and J. Dougherty, “Ultracompact fully integrated megapixel multispectral imager,” Proc. SPIE 7218, 721814 (2009).
[CrossRef]

Eichenholz, J. M.

J. M. Eichenholz, and J. Dougherty, “Ultracompact fully integrated megapixel multispectral imager,” Proc. SPIE 7218, 721814 (2009).
[CrossRef]

Engheta, N.

Escuti, M. J.

J. Kim and M. J. Escuti, “Snapshot imaging spectropolarimeter utilizing polarization gratings,” Proc. SPIE 7086, 708603 (2008).
[CrossRef]

C. Oh, and M. J. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett. 33, 2287–2289 (2008).
[CrossRef]

Flammer, P. D.

J. J. Peltzer, K. A. Bachman, J. W. Rose, P. D. Flammer, T. E. Furtak, R. T. Collins, and R. E. Hollingsworth, “Ultracompact fully integrated megapixel multispectral imager,” Proc. SPIE 8364, 83640O (2012).

Furtak, T. E.

J. J. Peltzer, K. A. Bachman, J. W. Rose, P. D. Flammer, T. E. Furtak, R. T. Collins, and R. E. Hollingsworth, “Ultracompact fully integrated megapixel multispectral imager,” Proc. SPIE 8364, 83640O (2012).

Garcia, J.

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]

Gehm, M.

Goldstein, D.

D. Goldstein, Polarized Light, 2nd ed. (Dekker, 2003).

Goldstein, D. L.

Groner, W.

R. G. Nadeau, W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, and K. Messmer, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[CrossRef]

Gruev, V.

Guo, J.

J. Guo and D. Brady, “Fabrication of thin-film micropolarizer arrays for visible imaging polarimetry,” Appl. Opt. 39, 1486–1492 (2000).
[CrossRef]

J. Guo and D. Brady, “Fabrication of high-resolution micropolarizer array,” Opt. Eng. 36, 2268–2271 (1997).
[CrossRef]

Hamilton, T.

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]

Harris, A. G.

R. G. Nadeau, W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, and K. Messmer, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[CrossRef]

Harrison, F.

W. Smith, D. Zhou, F. Harrison, H. Revercomb, A. Larar, A. Huang, and B. Huang, “Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft,” Proc. SPIE 4151, 94–102 (2001).
[CrossRef]

Hollingsworth, R. E.

J. J. Peltzer, K. A. Bachman, J. W. Rose, P. D. Flammer, T. E. Furtak, R. T. Collins, and R. E. Hollingsworth, “Ultracompact fully integrated megapixel multispectral imager,” Proc. SPIE 8364, 83640O (2012).

Horisaki, R.

Huang, A.

W. Smith, D. Zhou, F. Harrison, H. Revercomb, A. Larar, A. Huang, and B. Huang, “Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft,” Proc. SPIE 4151, 94–102 (2001).
[CrossRef]

Huang, B.

W. Smith, D. Zhou, F. Harrison, H. Revercomb, A. Larar, A. Huang, and B. Huang, “Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft,” Proc. SPIE 4151, 94–102 (2001).
[CrossRef]

Ince, C.

R. G. Nadeau, W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, and K. Messmer, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[CrossRef]

Jia, C.

John, R.

Kim, J.

J. Kim and M. J. Escuti, “Snapshot imaging spectropolarimeter utilizing polarization gratings,” Proc. SPIE 7086, 708603 (2008).
[CrossRef]

Kittle, D.

Krishnamurthy, K.

LaCasse, C. F.

Larar, A.

W. Smith, D. Zhou, F. Harrison, H. Revercomb, A. Larar, A. Huang, and B. Huang, “Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft,” Proc. SPIE 4151, 94–102 (2001).
[CrossRef]

Lazarus, N.

Lim, S.

Locke, A.

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]

MacCabe, K.

Mahler, A. B.

Maker, P.

Marks, D.

Marks, D. L.

McMillan, R. W.

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]

Messmer, K.

R. G. Nadeau, W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, and K. Messmer, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[CrossRef]

Mu, T.

Myhre, G.

Nadeau, R. G.

R. G. Nadeau, W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, and K. Messmer, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[CrossRef]

Oh, C.

Ortu, A.

Pau, S.

Peltzer, J. J.

J. J. Peltzer, K. A. Bachman, J. W. Rose, P. D. Flammer, T. E. Furtak, R. T. Collins, and R. E. Hollingsworth, “Ultracompact fully integrated megapixel multispectral imager,” Proc. SPIE 8364, 83640O (2012).

Ren, W.

Revercomb, H.

W. Smith, D. Zhou, F. Harrison, H. Revercomb, A. Larar, A. Huang, and B. Huang, “Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft,” Proc. SPIE 4151, 94–102 (2001).
[CrossRef]

Rose, J. W.

J. J. Peltzer, K. A. Bachman, J. W. Rose, P. D. Flammer, T. E. Furtak, R. T. Collins, and R. E. Hollingsworth, “Ultracompact fully integrated megapixel multispectral imager,” Proc. SPIE 8364, 83640O (2012).

Sabatke, D.

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]

Samei, E.

Sayyad, A.

Schulz, T.

Schumacher, A.

Shaw, J. A.

Smith, W.

W. Smith, D. Zhou, F. Harrison, H. Revercomb, A. Larar, A. Huang, and B. Huang, “Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft,” Proc. SPIE 4151, 94–102 (2001).
[CrossRef]

Takakura, Y.

Thorne, K.

Turner, T. S.

Tyo, J. S.

Van der Spiegel, J.

Volin, C.

Wagadarikar, A.

Willett, R.

Wilson, D.

Winkelman, J. W.

R. G. Nadeau, W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, and K. Messmer, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[CrossRef]

Zhang, C.

Zhao, X.

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “High-resolution thin guest-host micropolarizer arrays for visible imaging polarimetry,” Opt. Express 19, 5565–5573 (2011).
[CrossRef]

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “Thin photo-patterned micropolarizer array for CMOS image sensors,” IEEE Photon. Technol. Lett. 21, 805–807 (2009).
[CrossRef]

Zhou, D.

W. Smith, D. Zhou, F. Harrison, H. Revercomb, A. Larar, A. Huang, and B. Huang, “Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft,” Proc. SPIE 4151, 94–102 (2001).
[CrossRef]

Appl. Opt. (6)

IEEE Photon. Technol. Lett. (1)

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “Thin photo-patterned micropolarizer array for CMOS image sensors,” IEEE Photon. Technol. Lett. 21, 805–807 (2009).
[CrossRef]

Nat. Med. (1)

R. G. Nadeau, W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, and K. Messmer, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5, 1209–1212 (1999).
[CrossRef]

Opt. Eng. (2)

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]

J. Guo and D. Brady, “Fabrication of high-resolution micropolarizer array,” Opt. Eng. 36, 2268–2271 (1997).
[CrossRef]

Opt. Express (8)

Opt. Lett. (4)

Proc. SPIE (4)

J. Kim and M. J. Escuti, “Snapshot imaging spectropolarimeter utilizing polarization gratings,” Proc. SPIE 7086, 708603 (2008).
[CrossRef]

J. M. Eichenholz, and J. Dougherty, “Ultracompact fully integrated megapixel multispectral imager,” Proc. SPIE 7218, 721814 (2009).
[CrossRef]

J. J. Peltzer, K. A. Bachman, J. W. Rose, P. D. Flammer, T. E. Furtak, R. T. Collins, and R. E. Hollingsworth, “Ultracompact fully integrated megapixel multispectral imager,” Proc. SPIE 8364, 83640O (2012).

W. Smith, D. Zhou, F. Harrison, H. Revercomb, A. Larar, A. Huang, and B. Huang, “Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft,” Proc. SPIE 4151, 94–102 (2001).
[CrossRef]

Other (3)

D. Goldstein, Polarized Light, 2nd ed. (Dekker, 2003).

D. J. Brady, Optical Imaging and Spectroscopy (Wiley-Interscience, 2009).

B. Bayer, “Color imaging array,” U.S. patent 4,054,906 (20July1976).

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of the CASSPI. The objective images the scene onto the coded aperture. The relay optics relay the encoded image from the plane of the coded aperture to the detector plane through the birefringent crystals.

Fig. 2.
Fig. 2.

Experimental prototype of the CASSPI system.

Fig. 3.
Fig. 3.

Design of the birefringent crystals.

Fig. 4.
Fig. 4.

Dispersion relation caused by the birefringent crystals.

Fig. 5.
Fig. 5.

Measured data of the scene including a negative 1951 USAF resolution test chart. Given the splitting and dispersion by the birefringent crystal, this measurement consists of spectral–spatial and polarization–spatial overlap of the coded modulated image of the test chart.

Fig. 6.
Fig. 6.

Spectral and polarization reconstruction in each of 19 wavelength channels between 400 and 680 nm in irradiance terms.

Fig. 7.
Fig. 7.

Spectral and polarization reconstruction in each of 19 wavelength channels between 400 and 680 nm in polarization difference terms.

Fig. 8.
Fig. 8.

Reconstructed spectral intensity (S0(λ)) of the resolution test chart illuminated by tungsten light. Spectrum from an Ocean Optics nonimaging reference spectrometer is shown for comparison.

Fig. 9.
Fig. 9.

Reconstructed difference in spectral intensity (S1(λ)) of the resolution test chart illuminated by tungsten light. Spectrum from an Ocean Optics nonimaging reference spectrometer is shown for comparison.

Fig. 10.
Fig. 10.

Reconstruction at 611 nm with different polarization states. (a) The upper left is the irradiance. The azimuth angles of the polarizer are 0° [(b) upper middle, S1=1], 30° [(c) upper right, S1=0.5], 45° [(d) bottom left, S1=0], 60° [(e) bottom middle, S1=0.5], and 90° [(f) bottom right, S1=1]. The average S1/S0 value: 0.935, 0.473, 0.033, 0.314 and 0.625, which corresponds to S1=1, 0.5, 0, 0.5, and 1, respectively.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

f0(x,y;λ)={S0(x,y;λ)S1(x,y;λ),
f1(x,y;λ)=T(x,y)f0(x,y;λ).
f2(x,y;λ)=δ(xx+ds)δ(yy+d(λλc))T(x,y)[S0(x,y;λ)+S1(x,y;λ)]dxdy+δ(xx+d(λλc))δ(yy+ds)T(x,y)[S0(x,y;λ)S1(x,y;λ)]dxdy;f2(x,y;λ)=T(x+ds,y+d(λλc))[S0(x,y;λ)+S1(x,y;λ)]+T(x+d(λλc),y+ds)[S0(x,y;λ)S1(x,y;λ)].
g(x,y)=f2(x,y;λ)dλ.
gnm=g(x,y)rect(xΔm,yΔn)dxdy.
T(x,y)=n,mtn,mrect(xqΔm,yqΔn),
gnm=n,mtn,m{rect(x+dsqΔm,y+d(λλc)qΔn)×[S0(x+ds,y+d(λλc);λ)+S1(x+ds,y+d(λλc);λ)]+rect(x+d(λλc)qΔm,y+dsqΔn)×[S0((x+d(λλc,y+ds;λ)S1(x+d(λλc,y+ds);λ)]}×rect(xΔm,yΔn)dxdydλ.
gnm=k[S0(i+ds)(j+k1)kt(i+ds)(j+k1)+S1(i+k1)(j+ds)kt(i+k1)(j+ds)]=(Hf)nm.
f^=argminf{12gHf22+τHTV(f)},
HTV(f)=ki,j|[f(i+1,j,k)f(i,j,k)]2+[f(i,j+1,k)f(i,j,k)]2|.
d(λ)=L·(1no(λ)2ne(λ)2)·tanθ1+no(λ)2ne(λ)2tan2θ,

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