Abstract

A high throughput static channeled interference imaging spectropolarimeter (CIISP) over 480–960nm spectral range is presented. The CIISP system includes two birefringent retarders and a Savart interferometer employing tempo-spatially mixed modulated mode with no internal moving parts, and offers a robust system and a high optical throughput to resist the instrument noise. The optical layout and operation of the CIISP sensor are presented in addition to the radiometric, spectral and improved polarimetric calibration techniques used with the system. The performance of the system is verified through laboratory tests, and the outdoor measurement demonstrates the sensor’s ability for target identification, color measurement, and agriculture monitoring applications.

© 2016 Optical Society of America

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References

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2014 (2)

2013 (1)

2012 (1)

2011 (2)

J. Craven-Jones, M. W. Kudenov, M. G. Stapelbroek, and E. L. Dereniak, “Infrared hyperspectral imaging polarimeter using birefringent prisms,” Appl. Opt. 50(8), 1170–1185 (2011).
[Crossref] [PubMed]

H. W. Gao, C. M. Zhang, and B. C. Zhao, “Relative calibration for a polarization interference imaging spectrometer,” Opt. Commun. 284(12), 2747–2750 (2011).
[Crossref]

2010 (2)

2009 (2)

F. Snik, T. Karalidi, and C. U. Keller, “Spectral modulation for full linear polarimetry,” Appl. Opt. 48(7), 1337–1346 (2009).
[Crossref] [PubMed]

J. M. Craven, M. W. Kudenov, and E. L. Dereniak, “False signature reduction in infrared channeled spectropolarimetry,” Proc. SPIE 7419, 741909 (2009).
[Crossref]

2008 (2)

C. M. Zhang, X. Yan, and B. C. Zhao, “A novel model for obtaining interferogram and spectrum based on the temporarily and spatially mixed modulated polarization interference imaging spectrometer,” Opt. Commun. 281(8), 2050–2056 (2008).
[Crossref]

R. W. Aumiller, C. Vandervlugt, E. L. Dereniak, R. Sampson, and R. W. McMillan, “Snapshot imaging spectropolarimetry in the visible and infrared,” Proc. SPIE 6972, 69720D (2008).
[Crossref]

2007 (1)

2006 (2)

2005 (2)

N. Hagen, E. L. Dereniak, and D. T. Sass, “Visible snapshot imaging spectro-polaimeter,” Proc. SPIE 5888, 588810 (2005).
[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]

2004 (3)

2002 (1)

C. M. Zhang, L. B. Xiang, B. C. Zhao, and X. J. Yuan, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. 203(1–2), 21–26 (2002).
[Crossref]

2001 (2)

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(11), 1245–1248 (2001).
[Crossref] [PubMed]

J. S. Tyo and T. S. Turner., “Variable-retardance, Fourier-transform imaging spectropolarimeters for visible spectrum remote sensing,” Appl. Opt. 40(9), 1450–1458 (2001).
[Crossref] [PubMed]

1999 (2)

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5(10), 1209–1212 (1999).
[Crossref] [PubMed]

K. Oka and T. Kato, “Spectroscopic polarimetry with a channeled spectrum,” Opt. Lett. 24(21), 1475–1477 (1999).
[Crossref] [PubMed]

1993 (1)

1982 (1)

Ahn, J. S.

Asaka, S.

Aumiller, R. W.

R. W. Aumiller, C. Vandervlugt, E. L. Dereniak, R. Sampson, and R. W. McMillan, “Snapshot imaging spectropolarimetry in the visible and infrared,” Proc. SPIE 6972, 69720D (2008).
[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(11), 1245–1248 (2001).
[Crossref] [PubMed]

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(11), 1245–1248 (2001).
[Crossref] [PubMed]

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]

Bouma, G. J.

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5(10), 1209–1212 (1999).
[Crossref] [PubMed]

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]

Craven, J. M.

J. M. Craven, M. W. Kudenov, and E. L. Dereniak, “False signature reduction in infrared channeled spectropolarimetry,” Proc. SPIE 7419, 741909 (2009).
[Crossref]

Craven-Jones, J.

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(11), 1245–1248 (2001).
[Crossref] [PubMed]

Davila, J. M.

T. G. Moran and J. M. Davila, “Three-dimensional polarimetric imaging of coronal mass ejections,” Science 305(5680), 66–70 (2004).
[Crossref] [PubMed]

Dereniak, E. L.

M. W. Kudenov and E. L. Dereniak, “Compact real-time birefringent imaging spectrometer,” Opt. Express 20(16), 17973–17986 (2012).
[Crossref] [PubMed]

J. Craven-Jones, M. W. Kudenov, M. G. Stapelbroek, and E. L. Dereniak, “Infrared hyperspectral imaging polarimeter using birefringent prisms,” Appl. Opt. 50(8), 1170–1185 (2011).
[Crossref] [PubMed]

J. M. Craven, M. W. Kudenov, and E. L. Dereniak, “False signature reduction in infrared channeled spectropolarimetry,” Proc. SPIE 7419, 741909 (2009).
[Crossref]

R. W. Aumiller, C. Vandervlugt, E. L. Dereniak, R. Sampson, and R. W. McMillan, “Snapshot imaging spectropolarimetry in the visible and infrared,” Proc. SPIE 6972, 69720D (2008).
[Crossref]

M. W. Kudenov, N. A. Hagen, E. L. Dereniak, and G. R. Gerhart, “Fourier transform channeled spectropolarimetry in the MWIR,” Opt. Express 15(20), 12792–12805 (2007).
[Crossref] [PubMed]

N. Hagen, E. L. Dereniak, and D. T. Sass, “Visible snapshot imaging spectro-polaimeter,” Proc. SPIE 5888, 588810 (2005).
[Crossref]

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]

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(11), 1245–1248 (2001).
[Crossref] [PubMed]

Fletcher-Holmes, D.

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]

Gao, B.

Gao, H. W.

H. W. Gao, C. M. Zhang, and B. C. Zhao, “Relative calibration for a polarization interference imaging spectrometer,” Opt. Commun. 284(12), 2747–2750 (2011).
[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(11), 1245–1248 (2001).
[Crossref] [PubMed]

Gerhart, G. R.

Goldstein, D. L.

Groner, W.

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5(10), 1209–1212 (1999).
[Crossref] [PubMed]

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(11), 1245–1248 (2001).
[Crossref] [PubMed]

Hagen, N.

N. Hagen, E. L. Dereniak, and D. T. Sass, “Visible snapshot imaging spectro-polaimeter,” Proc. SPIE 5888, 588810 (2005).
[Crossref]

Hagen, N. A.

Harris, A. G.

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5(10), 1209–1212 (1999).
[Crossref] [PubMed]

Harvey, A.

Hayakawa, M.

Hou, X.

Iannarilli, F.

Ince, C.

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5(10), 1209–1212 (1999).
[Crossref] [PubMed]

Itoh, K.

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(11), 1245–1248 (2001).
[Crossref] [PubMed]

Jian, X.

Jones, S.

Karalidi, T.

Kato, T.

Kebabian, P.

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]

Keller, C. U.

Kitagawa, T.

Kudenov, M. W.

Li, J.

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]

McMillan, R. W.

R. W. Aumiller, C. Vandervlugt, E. L. Dereniak, R. Sampson, and R. W. McMillan, “Snapshot imaging spectropolarimetry in the visible and infrared,” Proc. SPIE 6972, 69720D (2008).
[Crossref]

Meng, X.

Messmer, K.

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5(10), 1209–1212 (1999).
[Crossref] [PubMed]

Moran, T. G.

T. G. Moran and J. M. Davila, “Three-dimensional polarimetric imaging of coronal mass ejections,” Science 305(5680), 66–70 (2004).
[Crossref] [PubMed]

Nadeau, R. G.

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5(10), 1209–1212 (1999).
[Crossref] [PubMed]

Oka, K.

Okabe, H.

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(11), 1245–1248 (2001).
[Crossref] [PubMed]

Qi, C.

Sampson, R.

R. W. Aumiller, C. Vandervlugt, E. L. Dereniak, R. Sampson, and R. W. McMillan, “Snapshot imaging spectropolarimetry in the visible and infrared,” Proc. SPIE 6972, 69720D (2008).
[Crossref]

Sass, D. T.

N. Hagen, E. L. Dereniak, and D. T. Sass, “Visible snapshot imaging spectro-polaimeter,” Proc. SPIE 5888, 588810 (2005).
[Crossref]

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.

Snik, F.

Song, H.

Stapelbroek, M. G.

Takahashi, S.

Taniguchi, A.

Turner, T. S.

Tyo, J. S.

Vandervlugt, C.

R. W. Aumiller, C. Vandervlugt, E. L. Dereniak, R. Sampson, and R. W. McMillan, “Snapshot imaging spectropolarimetry in the visible and infrared,” Proc. SPIE 6972, 69720D (2008).
[Crossref]

Winkelman, J. W.

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5(10), 1209–1212 (1999).
[Crossref] [PubMed]

Wu, H.

Xiang, L. B.

C. M. Zhang, L. B. Xiang, B. C. Zhao, and X. J. Yuan, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. 203(1–2), 21–26 (2002).
[Crossref]

Yan, X.

C. M. Zhang, X. Yan, and B. C. Zhao, “A novel model for obtaining interferogram and spectrum based on the temporarily and spatially mixed modulated polarization interference imaging spectrometer,” Opt. Commun. 281(8), 2050–2056 (2008).
[Crossref]

Yuan, X. J.

C. M. Zhang, L. B. Xiang, B. C. Zhao, and X. J. Yuan, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. 203(1–2), 21–26 (2002).
[Crossref]

Zhang, C.

Zhang, C. M.

H. W. Gao, C. M. Zhang, and B. C. Zhao, “Relative calibration for a polarization interference imaging spectrometer,” Opt. Commun. 284(12), 2747–2750 (2011).
[Crossref]

C. M. Zhang, X. Yan, and B. C. Zhao, “A novel model for obtaining interferogram and spectrum based on the temporarily and spatially mixed modulated polarization interference imaging spectrometer,” Opt. Commun. 281(8), 2050–2056 (2008).
[Crossref]

C. M. Zhang, L. B. Xiang, B. C. Zhao, and X. J. Yuan, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. 203(1–2), 21–26 (2002).
[Crossref]

Zhang, L.

Zhao, B.

Zhao, B. C.

H. W. Gao, C. M. Zhang, and B. C. Zhao, “Relative calibration for a polarization interference imaging spectrometer,” Opt. Commun. 284(12), 2747–2750 (2011).
[Crossref]

C. M. Zhang, X. Yan, and B. C. Zhao, “A novel model for obtaining interferogram and spectrum based on the temporarily and spatially mixed modulated polarization interference imaging spectrometer,” Opt. Commun. 281(8), 2050–2056 (2008).
[Crossref]

C. M. Zhang, L. B. Xiang, B. C. Zhao, and X. J. Yuan, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. 203(1–2), 21–26 (2002).
[Crossref]

Zhu, J.

Zhu, R.

Appl. Opt. (6)

Appl. Spectrosc. (1)

Nat. Med. (2)

W. Groner, J. W. Winkelman, A. G. Harris, C. Ince, G. J. Bouma, K. Messmer, and R. G. Nadeau, “Orthogonal polarization spectral imaging: a new method for study of the microcirculation,” Nat. Med. 5(10), 1209–1212 (1999).
[Crossref] [PubMed]

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(11), 1245–1248 (2001).
[Crossref] [PubMed]

Opt. Commun. (3)

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C. M. Zhang, L. B. Xiang, B. C. Zhao, and X. J. Yuan, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. 203(1–2), 21–26 (2002).
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Proc. SPIE (4)

J. M. Craven, M. W. Kudenov, and E. L. Dereniak, “False signature reduction in infrared channeled spectropolarimetry,” Proc. SPIE 7419, 741909 (2009).
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R. W. Aumiller, C. Vandervlugt, E. L. Dereniak, R. Sampson, and R. W. McMillan, “Snapshot imaging spectropolarimetry in the visible and infrared,” Proc. SPIE 6972, 69720D (2008).
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Figures (20)

Fig. 1
Fig. 1 Optical layout of the CIISP based on a Savart polariscope.
Fig. 2
Fig. 2 Data acquisition model of the CIISP system.
Fig. 3
Fig. 3 Photograph of the core optics.
Fig. 4
Fig. 4 Interferogram of the CIISP for a 22.5° linear incident polarization state. The 7 channels in interferogram are separated in OPD space by the retardations φ 1 and φ 2 . Spacing between each channel is for a 2:1 thickness ratio ( d 2 : d 1 ) using our setup.
Fig. 5
Fig. 5 The spectropolarimetric hypercube acquired by the CIISP system.
Fig. 6
Fig. 6 (Left) Raw interferogram image of an unpolarized polychromatic light with 5ms exposure time. (Right) Image data after relative radiometric calibration.
Fig. 7
Fig. 7 DN value of pixels in column 200 (the upper) and row 200 (the lower) from the two images.
Fig. 8
Fig. 8 (a) Interference fringes are slanted to the right in large-OPD area in the right part of the scene. (b) The distribution of total OPD in each pixel calculated at the calibration laser’s wavenumber.
Fig. 9
Fig. 9 Spectral calibration results of four monochromatic laser lights in short wavelength band with selected rows (the upper), and the polychromatic xenon light (the lower).
Fig. 10
Fig. 10 Normalized spectral responsivity of the instrument.
Fig. 11
Fig. 11 (a) Effect of the linear fitting with all 15 points. (b) Spectrum from the CIISP sensor (blue line) and standard spectral radiation meter (red line). The spectral resolution of the CIISP system is approximately 81.3cm−1 (1.9nm) for the cutoff wavelength of 480nm.
Fig. 12
Fig. 12 Contour plots of the reconstructed results for the normalized Stokes parameters S1, S2 (a), and S3 (b) using the improved method.
Fig. 13
Fig. 13 Experiment setup for laboratory testing of the CIISP. The uniaxial turntable is not shown.
Fig. 14
Fig. 14 Recorded channeled Interferograms for 0° (a) and 45° (b) linear polarization states after scanning and data preprocessing. The background (red line) was removed using the least squares method.
Fig. 15
Fig. 15 Four spectral images of the scene at 520, 570, 620, and 670nm, respectively.
Fig. 16
Fig. 16 (a) Spectrum of point A (row, column) = (410, 275) with Stokes parameter S0. (b) Normalized Stokes parameters.
Fig. 17
Fig. 17 Normalized Stokes parameter images at 620nm.
Fig. 18
Fig. 18 (a) Spectral images of the scene at 882nm. (b) Normalized Stokes parameters of point B (row, column) = (209, 350).
Fig. 19
Fig. 19 Band integrated DoP spatial images of 0° (left) and 45° (right) linear polarization states.
Fig. 20
Fig. 20 Outdoor tests results. (a) S0, band integrated data. (b) Spectra recovered at two selected pixels across the scene. (c) DoP, band integrated data.

Equations (19)

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S out = M P 2 M SP M P 1 M R 2 M R 1 S in
I CCD (z) (1+cos φ Z (σ)) 4 [ S 0 (σ)+ S 1 (σ)cos( φ 2 (σ)) + S 2 (σ)sin( φ 1 (σ))sin( φ 2 (σ)) S 3 (σ)sin( φ 1 (σ))cos( φ 2 (σ))]dσ
φ Z (σ)=2πΔzσ
φ 1 (σ)=2π L 1 σ
φ 2 (σ)=2π L 2 σ
I CCD (z) (1+cos φ Z ) 2 [ S 0 + S 1 2 e i φ 2 + S 1 2 e i φ 2 + S 2 +i S 3 4 e i( φ 1 φ 2 ) + S 2 i S 3 4 e i( φ 1 φ 2 ) + S 2 +i S 3 4 e i( φ 1 + φ 2 ) + S 2 i S 3 4 e i( φ 1 + φ 2 ) ]dσ
{ C 0 }= 1 2 S 0 (σ)
{ C 1 }= 1 4 | S 1 (σ)|exp{i[ φ 2 (σ )+arg{S 1 (σ)}]}
{ C 2 }= 1 8 | S 23 (σ)|exp{i[ φ 2 (σ) φ 1 (σ)+ arg{S 23 (σ)}]}
K i,j t (L)= R i,j t N i,j t (L)+ O i,j t
OP D ref (x,y)= 2 t n o 2 n e 2 n o 2 + n e 2 x f + t 2 n o n e n o 2 n e 2 ( n o 2 + n e 2 ) 3/2 2xy f 2
OP D i =OP D ref,i B( σ 1,i ) B( σ ref )
σ offset,i = σ 1,i B( σ ref ) B( σ 1,i )
L k = E k M k + F k
S 1,sample (σ)=cos2θRe| ( C 1,sample ) ( C 1,reference,θ )/ S 0,reference ,θ |
φ 2all =arctan{ Im[{ C 1,reference,θ }] Re[{ C 1,reference,θ }] }
S 1,sample (σ)={ C 1,sample }exp[i φ 2 (σ)]
S 23,sample (σ)={ C 2,sample }exp{ i[ φ 1 (σ) φ 2 (σ)] }
DoP(σ)= S 1 (σ) 2 + S 2 (σ) 2 + S 3 (σ) 2 S 0 (σ)

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