Abstract

We describe a compressive snapshot color polarization imager that encodes spatial, spectral, and polarization information using a liquid crystal modulator. We experimentally show that polarization imaging is compressible by multiplexing polarization states and present the reconstruction results. This compressive camera captures the spatial distribution of four polarizations and three color channels. It achieves <0.027° spatial resolution, 103 average extinction ratio, and >30 PSNR.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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  1. W. G. Egan, “Polarization in remote sensing,” Proc. SPIE 1747, 2–48 (1992).
    [Crossref]
  2. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
    [Crossref] [PubMed]
  3. 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] [PubMed]
  4. J. S. Tyo, M. P. Rowe, E. N. Pugh, and N. Engheta, “Target detection in optically scattering media by polarization-difference imaging,” Appl. Opt. 35, 1855–1870 (1996).
    [Crossref] [PubMed]
  5. 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]
  6. J. E. Ahmad and Y. Takakura, “Error analysis for rotating active Stokes-Mueller imaging polarimeters,” Opt. Lett. 31, 2858–2860 (2006).
    [Crossref] [PubMed]
  7. A.-B. Mahler, D. Diner, and R. Chipman, “Analysis of static and time-varying polarization errors in the multiangle spectropolarimetric imager,” Appl Opt,  50, 2080–2087 (2011).
    [Crossref] [PubMed]
  8. J. S. Tyo and H. Wei, “Optimizing imaging polarimeters constructed with imperfect optics,” Appl. Opt. 45, 5497–5503 (2006).
    [Crossref] [PubMed]
  9. B. Bayer, “Color imaging array,” U.S. Patent 4,054,906 (20 July 1976).
  10. 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).
    [Crossref]
  11. 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] [PubMed]
  12. G. Myhre, A. Sayyad, and S. Pau, “Patterned color liquid crystal polymer polarizers,” Opt. Express 18, 27777–27786 (2010).
    [Crossref]
  13. X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “Thin Photo-Patterned Micropolarizer Array for CMOS Image Sensors,” IEEE Circuit. Devic. 21, 805–807 (2009).
  14. 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).
    [Crossref] [PubMed]
  15. J. Guo and D. Brady, “Fabrication of thin-film micropolarizer arrays for visible imaging polarimetry,” Appl. Opt. 39, 1486–1492 (2000).
    [Crossref]
  16. J. Guo and D. Brady, “Fabrication of high-resolution micropolarizer array,” Opt. Eng. 36, 2268–2271 (1997).
    [Crossref]
  17. X. Zhao, X. Pan, X. Fan, P. Xu, A. Bermak, and V. G. Chigrinov, “Patterned dual-layer achromatic micro-quarter-wave-retarder array for active polarization imaging,” Opt. Express 22, 8024–8034 (2014).
    [Crossref] [PubMed]
  18. 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]
  19. J. Kim and M. J. Escuti, “Snapshot imaging spectropolarimeter utilizing polarization gratings,” Proc. SPIE 7086, 708603 (2008).
    [Crossref]
  20. C. Oh and M. J. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett. 33, 2287–2289 (2008).
    [Crossref] [PubMed]
  21. D. J. Brady, Optical imaging and spectroscopy (Wiley-Interscience, 2009).
    [Crossref]
  22. 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).
    [Crossref] [PubMed]
  23. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive Holography,” Opt. Express 17, 13040–13049 (2009).
    [Crossref] [PubMed]
  24. 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]
  25. E. X. Chen, M. Gehm, R. Danell, M. Wells, J. T. Glass, and D. Brady, “Compressive Mass Analysis on Quadrupole Ion Trap Systems,” J. Am. Soc. Mass Spectr. 251295–1307 (2014).
    [Crossref]
  26. P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).
    [Crossref] [PubMed]
  27. T. H. Tsai and D. J. Brady, “Coded aperture snapshot spectral polarization imaging,” Appl. Opt. 52, 2153–2161 (2013).
    [Crossref] [PubMed]
  28. W. Osten and N. Reingand, Optical imaging and metrology advanced technologies (Wiley-VCH, 2012).
    [Crossref]
  29. D. Goldstein, Polarized Light, 2nd ed (Marcel Dekker, 2003).
  30. J. Bioucas-Dias and M. Figueiredo, “A new twist: two-step iterative shrinkage/thresholding for image restoration,” IEEE T. Image Process. 16, 2992–3004 (2007).
    [Crossref]
  31. X. Liao, H. Li, and L. Carin, “Generalized Alternating Projection for Weighted ℓ2,1 Minimization with Applications to Model-based Compressive Sensing,” SIAM J. Imaging Sci. 7(2), 797–823 (2014).
    [Crossref]
  32. X. Yuan, P. Llull, X. Liao, J. Yang, D. Brady, G. Sapiro, and L. Carin, “Low-Cost Compressive Sensing for Color Video and Depth,” Proc. CVPR IEEE, (2014).
  33. X. Yuan, T. H. Tsai, R. Zhu, P. Llull, D. J. Brady, and L. Carin, “Compressive Hyperspectral Imaging with Side Information,” IEEE J. Sel. Top. Signa. (to be published).

2014 (3)

X. Zhao, X. Pan, X. Fan, P. Xu, A. Bermak, and V. G. Chigrinov, “Patterned dual-layer achromatic micro-quarter-wave-retarder array for active polarization imaging,” Opt. Express 22, 8024–8034 (2014).
[Crossref] [PubMed]

E. X. Chen, M. Gehm, R. Danell, M. Wells, J. T. Glass, and D. Brady, “Compressive Mass Analysis on Quadrupole Ion Trap Systems,” J. Am. Soc. Mass Spectr. 251295–1307 (2014).
[Crossref]

X. Liao, H. Li, and L. Carin, “Generalized Alternating Projection for Weighted ℓ2,1 Minimization with Applications to Model-based Compressive Sensing,” SIAM J. Imaging Sci. 7(2), 797–823 (2014).
[Crossref]

2013 (2)

2012 (2)

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]

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).
[Crossref]

2011 (2)

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] [PubMed]

A.-B. Mahler, D. Diner, and R. Chipman, “Analysis of static and time-varying polarization errors in the multiangle spectropolarimetric imager,” Appl Opt,  50, 2080–2087 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (2)

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “Thin Photo-Patterned Micropolarizer Array for CMOS Image Sensors,” IEEE Circuit. Devic. 21, 805–807 (2009).

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

2008 (2)

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] [PubMed]

2007 (3)

2006 (3)

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 (1)

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]

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] [PubMed]

1997 (1)

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

1996 (1)

1992 (1)

W. G. Egan, “Polarization in remote sensing,” Proc. SPIE 1747, 2–48 (1992).
[Crossref]

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).
[Crossref]

Bayer, B.

B. Bayer, “Color imaging array,” U.S. Patent 4,054,906 (20 July 1976).

Bermak, A.

Bioucas-Dias, J.

J. Bioucas-Dias and M. Figueiredo, “A new twist: two-step iterative shrinkage/thresholding for image restoration,” IEEE T. Image Process. 16, 2992–3004 (2007).
[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] [PubMed]

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] [PubMed]

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “Thin Photo-Patterned Micropolarizer Array for CMOS Image Sensors,” IEEE Circuit. Devic. 21, 805–807 (2009).

Brady, D.

E. X. Chen, M. Gehm, R. Danell, M. Wells, J. T. Glass, and D. Brady, “Compressive Mass Analysis on Quadrupole Ion Trap Systems,” J. Am. Soc. Mass Spectr. 251295–1307 (2014).
[Crossref]

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]

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]

X. Yuan, P. Llull, X. Liao, J. Yang, D. Brady, G. Sapiro, and L. Carin, “Low-Cost Compressive Sensing for Color Video and Depth,” Proc. CVPR IEEE, (2014).

Brady, D. J.

Carin, L.

X. Liao, H. Li, and L. Carin, “Generalized Alternating Projection for Weighted ℓ2,1 Minimization with Applications to Model-based Compressive Sensing,” SIAM J. Imaging Sci. 7(2), 797–823 (2014).
[Crossref]

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).
[Crossref] [PubMed]

X. Yuan, P. Llull, X. Liao, J. Yang, D. Brady, G. Sapiro, and L. Carin, “Low-Cost Compressive Sensing for Color Video and Depth,” Proc. CVPR IEEE, (2014).

X. Yuan, T. H. Tsai, R. Zhu, P. Llull, D. J. Brady, and L. Carin, “Compressive Hyperspectral Imaging with Side Information,” IEEE J. Sel. Top. Signa. (to be published).

Chawla, A.

Chen, E. X.

E. X. Chen, M. Gehm, R. Danell, M. Wells, J. T. Glass, and D. Brady, “Compressive Mass Analysis on Quadrupole Ion Trap Systems,” J. Am. Soc. Mass Spectr. 251295–1307 (2014).
[Crossref]

Chenault, D. B.

Chigrinov, V. G.

Chipman, R.

A.-B. Mahler, D. Diner, and R. Chipman, “Analysis of static and time-varying polarization errors in the multiangle spectropolarimetric imager,” Appl Opt,  50, 2080–2087 (2011).
[Crossref] [PubMed]

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).
[Crossref]

Danell, R.

E. X. Chen, M. Gehm, R. Danell, M. Wells, J. T. Glass, and D. Brady, “Compressive Mass Analysis on Quadrupole Ion Trap Systems,” J. Am. Soc. Mass Spectr. 251295–1307 (2014).
[Crossref]

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]

Diner, D.

A.-B. Mahler, D. Diner, and R. Chipman, “Analysis of static and time-varying polarization errors in the multiangle spectropolarimetric imager,” Appl Opt,  50, 2080–2087 (2011).
[Crossref] [PubMed]

Egan, W. G.

W. G. Egan, “Polarization in remote sensing,” Proc. SPIE 1747, 2–48 (1992).
[Crossref]

Engheta, N.

Escuti, M. J.

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

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

Fan, X.

Figueiredo, M.

J. Bioucas-Dias and M. Figueiredo, “A new twist: two-step iterative shrinkage/thresholding for image restoration,” IEEE T. Image Process. 16, 2992–3004 (2007).
[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).
[Crossref]

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).
[Crossref]

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.

E. X. Chen, M. Gehm, R. Danell, M. Wells, J. T. Glass, and D. Brady, “Compressive Mass Analysis on Quadrupole Ion Trap Systems,” J. Am. Soc. Mass Spectr. 251295–1307 (2014).
[Crossref]

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).
[Crossref] [PubMed]

Glass, J. T.

E. X. Chen, M. Gehm, R. Danell, M. Wells, J. T. Glass, and D. Brady, “Compressive Mass Analysis on Quadrupole Ion Trap Systems,” J. Am. Soc. Mass Spectr. 251295–1307 (2014).
[Crossref]

Goldstein, D.

D. Goldstein, Polarized Light, 2nd ed (Marcel 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] [PubMed]

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] [PubMed]

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).
[Crossref]

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] [PubMed]

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.

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.

Li, H.

X. Liao, H. Li, and L. Carin, “Generalized Alternating Projection for Weighted ℓ2,1 Minimization with Applications to Model-based Compressive Sensing,” SIAM J. Imaging Sci. 7(2), 797–823 (2014).
[Crossref]

Liao, X.

X. Liao, H. Li, and L. Carin, “Generalized Alternating Projection for Weighted ℓ2,1 Minimization with Applications to Model-based Compressive Sensing,” SIAM J. Imaging Sci. 7(2), 797–823 (2014).
[Crossref]

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).
[Crossref] [PubMed]

X. Yuan, P. Llull, X. Liao, J. Yang, D. Brady, G. Sapiro, and L. Carin, “Low-Cost Compressive Sensing for Color Video and Depth,” Proc. CVPR IEEE, (2014).

Lim, S.

Llull, P.

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).
[Crossref] [PubMed]

X. Yuan, P. Llull, X. Liao, J. Yang, D. Brady, G. Sapiro, and L. Carin, “Low-Cost Compressive Sensing for Color Video and Depth,” Proc. CVPR IEEE, (2014).

X. Yuan, T. H. Tsai, R. Zhu, P. Llull, D. J. Brady, and L. Carin, “Compressive Hyperspectral Imaging with Side Information,” IEEE J. Sel. Top. Signa. (to be published).

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.

A.-B. Mahler, D. Diner, and R. Chipman, “Analysis of static and time-varying polarization errors in the multiangle spectropolarimetric imager,” Appl Opt,  50, 2080–2087 (2011).
[Crossref] [PubMed]

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] [PubMed]

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] [PubMed]

Oh, C.

Ortu, A.

Osten, W.

W. Osten and N. Reingand, Optical imaging and metrology advanced technologies (Wiley-VCH, 2012).
[Crossref]

Pan, X.

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).
[Crossref]

Pugh, E. N.

Reingand, N.

W. Osten and N. Reingand, Optical imaging and metrology advanced technologies (Wiley-VCH, 2012).
[Crossref]

Revercomb, H.

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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).
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Rowe, M. P.

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.

Sapiro, G.

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).
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X. Yuan, P. Llull, X. Liao, J. Yang, D. Brady, G. Sapiro, and L. Carin, “Low-Cost Compressive Sensing for Color Video and Depth,” Proc. CVPR IEEE, (2014).

Sayyad, A.

Schulz, T.

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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.

Tsai, T. H.

T. H. Tsai and D. J. Brady, “Coded aperture snapshot spectral polarization imaging,” Appl. Opt. 52, 2153–2161 (2013).
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X. Yuan, T. H. Tsai, R. Zhu, P. Llull, D. J. Brady, and L. Carin, “Compressive Hyperspectral Imaging with Side Information,” IEEE J. Sel. Top. Signa. (to be published).

Tyo, J. S.

Van der Spiegel, J.

Wei, H.

Wells, M.

E. X. Chen, M. Gehm, R. Danell, M. Wells, J. T. Glass, and D. Brady, “Compressive Mass Analysis on Quadrupole Ion Trap Systems,” J. Am. Soc. Mass Spectr. 251295–1307 (2014).
[Crossref]

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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).
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P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).
[Crossref] [PubMed]

X. Yuan, P. Llull, X. Liao, J. Yang, D. Brady, G. Sapiro, and L. Carin, “Low-Cost Compressive Sensing for Color Video and Depth,” Proc. CVPR IEEE, (2014).

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P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).
[Crossref] [PubMed]

X. Yuan, T. H. Tsai, R. Zhu, P. Llull, D. J. Brady, and L. Carin, “Compressive Hyperspectral Imaging with Side Information,” IEEE J. Sel. Top. Signa. (to be published).

X. Yuan, P. Llull, X. Liao, J. Yang, D. Brady, G. Sapiro, and L. Carin, “Low-Cost Compressive Sensing for Color Video and Depth,” Proc. CVPR IEEE, (2014).

Zhao, X.

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]

Zhu, R.

X. Yuan, T. H. Tsai, R. Zhu, P. Llull, D. J. Brady, and L. Carin, “Compressive Hyperspectral Imaging with Side Information,” IEEE J. Sel. Top. Signa. (to be published).

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E. X. Chen, M. Gehm, R. Danell, M. Wells, J. T. Glass, and D. Brady, “Compressive Mass Analysis on Quadrupole Ion Trap Systems,” J. Am. Soc. Mass Spectr. 251295–1307 (2014).
[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).
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[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).
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X. Yuan, P. Llull, X. Liao, J. Yang, D. Brady, G. Sapiro, and L. Carin, “Low-Cost Compressive Sensing for Color Video and Depth,” Proc. CVPR IEEE, (2014).

X. Yuan, T. H. Tsai, R. Zhu, P. Llull, D. J. Brady, and L. Carin, “Compressive Hyperspectral Imaging with Side Information,” IEEE J. Sel. Top. Signa. (to be published).

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Figures (11)

Fig. 1
Fig. 1 The amplitude modulation tests for three color channels and two orthogonal decompositions. The horizontal axis represents the 8-bit applied voltage address on the SLM. The vertical axis is the average pixel count. (a), (b), and (c) are the response of linear horizontal and linear vertical of red, green, and blue channels, respectively. (d), (e), and (f) are the response of linear 45° and linear 135°.The spectral band of the red, green, and blue channels is 580 nm to 680 nm, 490 nm to 580 nm, and 400 nm to 490 nm, respectively.
Fig. 2
Fig. 2 The schematic of the compressive color polarization camera.
Fig. 3
Fig. 3 Experimental prototype of the compressive spectral polarization camera.
Fig. 4
Fig. 4 The detector measurement of a negative 1951 resolution chart which is under a linear vertical polarized illumination. The phase retardation generated by the SLM provided a polarization and wavelength dependent transmission pattern to the scene.
Fig. 5
Fig. 5 The spectral and polarization reconstruction of the compressive sampling. The reconstruction includes red, green and blue colors combined with linear horizontal (0°), linear vertical (90°), linear 45(45°), and linear 135(135°) polarization channels. Their brightness follows the normalized irradiance. The color representations are using Matlab generated pseudo-color.
Fig. 6
Fig. 6 The S1 Stokes parameter reconstructions of the green channel under different incident polarization states. The azimuth angles of the polarizer are 0°[(a) upper left, S1 = 1], 30°[(b) upper middle, S1 = 0.5], 45°[(c) upper right, S1 = 0], 60°[(d) bottom left, S1 = −0.5], 90°[(e) bottom middle, S1 = −1], and 135 [(f) bottom middle, S1 = 0]. The average value: 0.79, 0.31, 0, −0.35, −0.82, and −0.04, which corresponding to S1 = 1, 0.5, 0, −0.5, −1, and 0, respectively.
Fig. 7
Fig. 7 The S2 Stokes parameter reconstructions of the green channel under different incident polarization states. The azimuth angles of the polarizer are 0°[(a) upper left, S2 = 0], 30°[(b) upper middle, S2 = 0.87], 45 [(c) upper right, S2 = 1], 60°[(d) bottom left, S2 = 0.87], 90°[(e) bottom middle, S2 = 0], and 135°[(f) bottom middle, S2 = −1]. The average value: 0.03, 0.67, 0.84, 0.64, 0.01, and −0.69, which corresponding to S2 = 0, 0.87, 1, 0.87, 0, and −1, respectively.
Fig. 8
Fig. 8 The measurement, the references, and the reconstruction of toys which is filtered by two orthogonal sheet polarizers. (a) The azimuth angle of two sheet polarizers. The left polarizer is vertical and the right polarizer is horizontal. (b) An un-polarized reference of the scene. (c) The compressed measurement. (d), (e), and (f) are the references of linear horizontal, linear vertical, and linear 45° polarized color images measured by the same detector with a rotatable polarizer. (g), (h), and (i) are the reconstructed images of linear horizontal, linear vertical, and linear 45° polarized color images. Notice that the left side of the image is linear vertically polarized and the right side is linear horizontally polarized.
Fig. 9
Fig. 9 The measurement, the references, and the reconstruction of the scene in a parking lot. (a) An un-polarized reference of the scene. (b) The compressed measurement. (c), (d), (e), and (f) are the reference images of linear horizontal, linear vertical, linear 45°, and linear −45° polarized color images measured by a color camera with a sheet polarizer. (g), (h), (i), and (j) are the reconstructed images of linear horizontal, linear vertical, linear 45°, and linear 135° polarized color images. Notice that the reflections on the windows and on the rear screen of cars are polarized.
Fig. 10
Fig. 10 The spatial resolution test. The test target is a negative USAF 1951 resolution chart which was illuminated by vertically polarized light. (a) The reference image which is recorded by the same camera without modulation. (b) The reconstructed image in the linear vertical channel. The finest resolvable line pairs are group 2 element 6 and group 2 element 5 in (a) and (b), respectively. The corresponding angular resolution is 0.024° in unmodulated reference image; and 0.027° in reconstructed compressive measurement. Both images have a 60×60 pixels spatial resolution.
Fig. 11
Fig. 11 The PSNR for the reconstruction stability. The object is a stationary resolution chart illuminated by vertically polarized light. Each point represents the average PSNR in each reconstructed frame. The mean PSNR are 32.5, 38.0, 33.8, and 33.7 for linear horizontal, linear vertical, linear 45° and linear 135°, respectively.

Equations (13)

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S 0 = ( I 0 + I 90 + I 45 + I 135 ) / 4
S 1 = I 0 I 90
S 2 = I 45 I 135 ,
I = 1 2 ( S 0 S 1 cos ( 2 β ( λ ) ) + S 2 sin ( 2 β ( λ ) ) ) ,
g ( x , y , λ ) = f ( x , y , λ ) T ( x , y , λ ) + f ( x , y , λ ) T ( x , y , λ ) ,
g m n = [ f ( x , y , λ ) T ( x , y , λ ) + f ( x , y , λ ) T ( x , y , λ ) ] rect ( x Δ m , y Δ n ) d x d y d λ + w m n .
g m n = k = 1 4 p = 1 4 f m n k p T m n k p + w m n .
f ^ = argmin f { 1 2 g H f 2 2 + τ H TV ( f ) } ,
H TV ( f ) = l i , j | [ f ( i + 1 , j , l ) f ( i , j , l ) ] 2 + [ f ( i , j + 1 , l ) f ( i , j , l ) ] 2 | ,
( v ( t ) , θ ( t ) ) = arg min w , θ v θ 2 2 + λ ( t ) θ 2 , 1 𝒢 β subject to Φ v = y ,
v ( t ) = θ ( t 1 ) + Φ T ( Φ Φ T ) 1 ( y Φ θ ( t 1 ) ) ,
θ 𝒢 k ( t ) = v 𝒢 k ( t ) max { 1 λ ( t ) β k w 𝒢 k ( t ) 2 , 0 } , k = 1 , , m
where λ ( t ) = v 𝒢 j m + 1 ( t ) ( t ) 2 β j m + 1 ( t ) 1 , m < m

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