Abstract

We present a fully transparent, scalable, and flexible color image sensor that consists of stacked thin-film luminescent concentrators (LCs). At each layer, it measures a Radon transform of the corresponding LC’s spectral responses. Color images are then reconstructed through inverse Radon transforms that are obtained using machine learning. A high sampling rate in Radon space allows encoding multiple exposures to cope with under- and overexposed cases in one recording. Thus, our sensor simultaneously measures multiple spectral responses in different LC layers and multiple exposures in different Radon coefficients per layer. We also show that machine learning enables adequate three-channel image reconstruction from the response of only two LC layers.

© 2015 Optical Society of America

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References

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  1. R. Lukac and K. N. Plataniotis, “Color filter arrays: Design and performance analysis,” IEEE T. Consum. Electr. 51(4), 1260–1267 (2005).
    [Crossref]
  2. B. E. Bayer, “Color imaging array,” US Patent3,971,065.
  3. R. W. Schafer and R. M. Mersereau, “Demosaicking: color filter array interpolation,” IEEE Signal Proc. Mag. 22(1), 44–54 (2005).
    [Crossref]
  4. S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7(3), 240–246 (2013).
    [Crossref]
  5. G. Si, Y. Zhao, A. B. Chew, and Y J. Liu, “Plasmonic color filters,” J. Mol. Eng. Mater. 2(2), 1440009 (2014).
    [Crossref]
  6. S. P. Burgos, S. Yokogawa, and H. A. Atwater, “Color imaging via nearest neighbor hole coupling in plasmonic color filters integrated onto a complementary metal-oxide semiconductor image sensor,” ACS Nano 7(11), 10038–10047 (2013).
    [Crossref] [PubMed]
  7. Y. S. Do, J. H. Park, B. Y. Hwang, S-M. Lee, B-K. Ju, and K. C. Choi, “Plasmonic color filter and its fabrication for large-area applications,” Adv. Opt. Mater. 1(2), 133–138 (2013).
    [Crossref]
  8. B. Zeng, Y. Gao, and F. J. Bartoli, “Ultrathin nanostructured metals for highly transmissive plasmonic subtractive color filters,” Sci. Rep. 3, 2840 (2013).
    [Crossref] [PubMed]
  9. Q. Chen, Y. Zhao, and D. R. S. Cumming, “High transmission and low color cross-talk plasmonic color filters using triangular-lattice hole arrays in aluminum films,” Opt. Express 18(13), 14056–14062 (2010).
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  11. H. Park, Y. Dan, K. Seo, Y. J. Yu, P. K. Duane, M. Wober, and K. B. Crozier, “Filter-free image sensor pixels comprising silicon nanowires with selective color absorption,” Nano Lett. 14(4), 1804–1809 (2014).
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  13. D. Knipp, R. A. Street, H. Stiebig, M. Krause, J-P. Lu, S. Ready, and J. Ho, “Vertically integrated thin film color sensor arrays for imaging applications,” Opt. Express 14(8), 3106–3113 (2006).
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  14. A. Bablich, C. Merfort, H. Schäfer-Eberwein, P. Haring-Bolivar, and M. Boehm, “2-in-1 red-/green-/blue sensitive a-SiC:H/a-Si:H/a-SiGeC:H thin film photo detector with an integrated optical filter,” Thin Solid Films 552, 212–217 (2014).
    [Crossref]
  15. H. Seo, S. Aihara, T. Watabe, H. Ohtake, T. Sakai, M. Kubota, N. Egami, T. Hiramatsu, T. Matsuda, M. Furuta, and T. Hirao, “A 128× 96 pixel stack-type color image sensor: stack of individual blue-, green-, and red-sensitive organic photoconductive films integrated with a ZnO thin film transistor readout circuit,” Jpn. J. Appl. Phys. 50(2), 4103 (2011).
    [Crossref]
  16. S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
    [Crossref] [PubMed]
  17. A. Koppelhuber and O. Bimber, “Towards a transparent, flexible, scalable and disposable image sensor using thin-film luminescent concentrators,” Opt. Express 21(4), 4796–4810 (2013).
    [Crossref] [PubMed]
  18. A. Koppelhuber, S. Fanello, C. Birklbauer, D. Schedl, S. Izadi, and O. Bimber, “Enhanced learning-based imaging with thin-film luminescent concentrators,” Opt. Express 22(24), 29531–29543 (2014).
    [Crossref]
  19. A. Koppelhuber, C. Birklbauer, S. Izadi, and O. Bimber, “A transparent thin-film sensor for multi-focal image reconstruction and depth estimation,” Opt. Express 22(8), 8928–8942 (2014).
    [Crossref] [PubMed]
  20. A. Koppelhuber and O. Bimber, “A classification sensor based on compressed optical Radon transform,” Opt. Express 23(7), 9397–9406 (2015).
    [Crossref] [PubMed]
  21. J. S. Batchelder, A. H. Zewail, and T. Cole, “Luminescent solar concentrators. 1: Theory of operation and techniques for performance evaluation,” Appl. Optics 18(18), 3090–3110, (1979).
    [Crossref]
  22. D. J. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12(2), 229–232, (1992).
    [Crossref] [PubMed]
  23. A. Koppelhuber and O. Bimber, “Reconstructions of the test set images,” figshare (2015) [retrieved 16 July 2015], http://dx.doi.org/10.6084/m9.figshare.1485612
  24. T. M. Buzug, Computed Tomography from Photon Statistics to Modern Cone-Beam CT (Springer Verlag, 2008)
  25. A. Kolaman and O. Yadid-Pecht, “Quaternion structural similarity: A new quality index for color images,” IEEE T. Image Process. 21(4), 1526–1536 (2012).
    [Crossref]
  26. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
    [Crossref]
  27. R. H. Inman, G. V. Shcherbatyuk, D. Medvedko, A. Gopinathan, and S. Ghosh, “Cylindrical luminescent solar concentrators with near-infrared quantum dots,” Opt. Express 19(24), 24308–24313 (2011).
    [Crossref] [PubMed]

2015 (2)

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

A. Koppelhuber and O. Bimber, “A classification sensor based on compressed optical Radon transform,” Opt. Express 23(7), 9397–9406 (2015).
[Crossref] [PubMed]

2014 (5)

A. Koppelhuber, S. Fanello, C. Birklbauer, D. Schedl, S. Izadi, and O. Bimber, “Enhanced learning-based imaging with thin-film luminescent concentrators,” Opt. Express 22(24), 29531–29543 (2014).
[Crossref]

A. Koppelhuber, C. Birklbauer, S. Izadi, and O. Bimber, “A transparent thin-film sensor for multi-focal image reconstruction and depth estimation,” Opt. Express 22(8), 8928–8942 (2014).
[Crossref] [PubMed]

H. Park, Y. Dan, K. Seo, Y. J. Yu, P. K. Duane, M. Wober, and K. B. Crozier, “Filter-free image sensor pixels comprising silicon nanowires with selective color absorption,” Nano Lett. 14(4), 1804–1809 (2014).
[Crossref] [PubMed]

A. Bablich, C. Merfort, H. Schäfer-Eberwein, P. Haring-Bolivar, and M. Boehm, “2-in-1 red-/green-/blue sensitive a-SiC:H/a-Si:H/a-SiGeC:H thin film photo detector with an integrated optical filter,” Thin Solid Films 552, 212–217 (2014).
[Crossref]

G. Si, Y. Zhao, A. B. Chew, and Y J. Liu, “Plasmonic color filters,” J. Mol. Eng. Mater. 2(2), 1440009 (2014).
[Crossref]

2013 (5)

S. P. Burgos, S. Yokogawa, and H. A. Atwater, “Color imaging via nearest neighbor hole coupling in plasmonic color filters integrated onto a complementary metal-oxide semiconductor image sensor,” ACS Nano 7(11), 10038–10047 (2013).
[Crossref] [PubMed]

Y. S. Do, J. H. Park, B. Y. Hwang, S-M. Lee, B-K. Ju, and K. C. Choi, “Plasmonic color filter and its fabrication for large-area applications,” Adv. Opt. Mater. 1(2), 133–138 (2013).
[Crossref]

B. Zeng, Y. Gao, and F. J. Bartoli, “Ultrathin nanostructured metals for highly transmissive plasmonic subtractive color filters,” Sci. Rep. 3, 2840 (2013).
[Crossref] [PubMed]

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7(3), 240–246 (2013).
[Crossref]

A. Koppelhuber and O. Bimber, “Towards a transparent, flexible, scalable and disposable image sensor using thin-film luminescent concentrators,” Opt. Express 21(4), 4796–4810 (2013).
[Crossref] [PubMed]

2012 (2)

S. Yokogawa, S. P. Burgos, and H. A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12(8), 4349–4354 (2012).
[Crossref] [PubMed]

A. Kolaman and O. Yadid-Pecht, “Quaternion structural similarity: A new quality index for color images,” IEEE T. Image Process. 21(4), 1526–1536 (2012).
[Crossref]

2011 (2)

R. H. Inman, G. V. Shcherbatyuk, D. Medvedko, A. Gopinathan, and S. Ghosh, “Cylindrical luminescent solar concentrators with near-infrared quantum dots,” Opt. Express 19(24), 24308–24313 (2011).
[Crossref] [PubMed]

H. Seo, S. Aihara, T. Watabe, H. Ohtake, T. Sakai, M. Kubota, N. Egami, T. Hiramatsu, T. Matsuda, M. Furuta, and T. Hirao, “A 128× 96 pixel stack-type color image sensor: stack of individual blue-, green-, and red-sensitive organic photoconductive films integrated with a ZnO thin film transistor readout circuit,” Jpn. J. Appl. Phys. 50(2), 4103 (2011).
[Crossref]

2010 (1)

2006 (1)

2005 (2)

R. Lukac and K. N. Plataniotis, “Color filter arrays: Design and performance analysis,” IEEE T. Consum. Electr. 51(4), 1260–1267 (2005).
[Crossref]

R. W. Schafer and R. M. Mersereau, “Demosaicking: color filter array interpolation,” IEEE Signal Proc. Mag. 22(1), 44–54 (2005).
[Crossref]

2004 (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

1992 (1)

D. J. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12(2), 229–232, (1992).
[Crossref] [PubMed]

1979 (1)

J. S. Batchelder, A. H. Zewail, and T. Cole, “Luminescent solar concentrators. 1: Theory of operation and techniques for performance evaluation,” Appl. Optics 18(18), 3090–3110, (1979).
[Crossref]

Aihara, S.

H. Seo, S. Aihara, T. Watabe, H. Ohtake, T. Sakai, M. Kubota, N. Egami, T. Hiramatsu, T. Matsuda, M. Furuta, and T. Hirao, “A 128× 96 pixel stack-type color image sensor: stack of individual blue-, green-, and red-sensitive organic photoconductive films integrated with a ZnO thin film transistor readout circuit,” Jpn. J. Appl. Phys. 50(2), 4103 (2011).
[Crossref]

Atwater, H. A.

S. P. Burgos, S. Yokogawa, and H. A. Atwater, “Color imaging via nearest neighbor hole coupling in plasmonic color filters integrated onto a complementary metal-oxide semiconductor image sensor,” ACS Nano 7(11), 10038–10047 (2013).
[Crossref] [PubMed]

S. Yokogawa, S. P. Burgos, and H. A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12(8), 4349–4354 (2012).
[Crossref] [PubMed]

Bablich, A.

A. Bablich, C. Merfort, H. Schäfer-Eberwein, P. Haring-Bolivar, and M. Boehm, “2-in-1 red-/green-/blue sensitive a-SiC:H/a-Si:H/a-SiGeC:H thin film photo detector with an integrated optical filter,” Thin Solid Films 552, 212–217 (2014).
[Crossref]

Bartoli, F. J.

B. Zeng, Y. Gao, and F. J. Bartoli, “Ultrathin nanostructured metals for highly transmissive plasmonic subtractive color filters,” Sci. Rep. 3, 2840 (2013).
[Crossref] [PubMed]

Batchelder, J. S.

J. S. Batchelder, A. H. Zewail, and T. Cole, “Luminescent solar concentrators. 1: Theory of operation and techniques for performance evaluation,” Appl. Optics 18(18), 3090–3110, (1979).
[Crossref]

Bayer, B. E.

B. E. Bayer, “Color imaging array,” US Patent3,971,065.

Bimber, O.

Birklbauer, C.

Boehm, M.

A. Bablich, C. Merfort, H. Schäfer-Eberwein, P. Haring-Bolivar, and M. Boehm, “2-in-1 red-/green-/blue sensitive a-SiC:H/a-Si:H/a-SiGeC:H thin film photo detector with an integrated optical filter,” Thin Solid Films 552, 212–217 (2014).
[Crossref]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

Bulliard, X.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Burgos, S. P.

S. P. Burgos, S. Yokogawa, and H. A. Atwater, “Color imaging via nearest neighbor hole coupling in plasmonic color filters integrated onto a complementary metal-oxide semiconductor image sensor,” ACS Nano 7(11), 10038–10047 (2013).
[Crossref] [PubMed]

S. Yokogawa, S. P. Burgos, and H. A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12(8), 4349–4354 (2012).
[Crossref] [PubMed]

Buzug, T. M.

T. M. Buzug, Computed Tomography from Photon Statistics to Modern Cone-Beam CT (Springer Verlag, 2008)

Chao, T.

D. J. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12(2), 229–232, (1992).
[Crossref] [PubMed]

Chen, Q.

Chew, A. B.

G. Si, Y. Zhao, A. B. Chew, and Y J. Liu, “Plasmonic color filters,” J. Mol. Eng. Mater. 2(2), 1440009 (2014).
[Crossref]

Choi, K. C.

Y. S. Do, J. H. Park, B. Y. Hwang, S-M. Lee, B-K. Ju, and K. C. Choi, “Plasmonic color filter and its fabrication for large-area applications,” Adv. Opt. Mater. 1(2), 133–138 (2013).
[Crossref]

Cole, T.

J. S. Batchelder, A. H. Zewail, and T. Cole, “Luminescent solar concentrators. 1: Theory of operation and techniques for performance evaluation,” Appl. Optics 18(18), 3090–3110, (1979).
[Crossref]

Crozier, K. B.

H. Park, Y. Dan, K. Seo, Y. J. Yu, P. K. Duane, M. Wober, and K. B. Crozier, “Filter-free image sensor pixels comprising silicon nanowires with selective color absorption,” Nano Lett. 14(4), 1804–1809 (2014).
[Crossref] [PubMed]

Cumming, D. R. S.

Dan, Y.

H. Park, Y. Dan, K. Seo, Y. J. Yu, P. K. Duane, M. Wober, and K. B. Crozier, “Filter-free image sensor pixels comprising silicon nanowires with selective color absorption,” Nano Lett. 14(4), 1804–1809 (2014).
[Crossref] [PubMed]

Do, Y. S.

Y. S. Do, J. H. Park, B. Y. Hwang, S-M. Lee, B-K. Ju, and K. C. Choi, “Plasmonic color filter and its fabrication for large-area applications,” Adv. Opt. Mater. 1(2), 133–138 (2013).
[Crossref]

Duane, P. K.

H. Park, Y. Dan, K. Seo, Y. J. Yu, P. K. Duane, M. Wober, and K. B. Crozier, “Filter-free image sensor pixels comprising silicon nanowires with selective color absorption,” Nano Lett. 14(4), 1804–1809 (2014).
[Crossref] [PubMed]

Egami, N.

H. Seo, S. Aihara, T. Watabe, H. Ohtake, T. Sakai, M. Kubota, N. Egami, T. Hiramatsu, T. Matsuda, M. Furuta, and T. Hirao, “A 128× 96 pixel stack-type color image sensor: stack of individual blue-, green-, and red-sensitive organic photoconductive films integrated with a ZnO thin film transistor readout circuit,” Jpn. J. Appl. Phys. 50(2), 4103 (2011).
[Crossref]

Fanello, S.

Fujii, T.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7(3), 240–246 (2013).
[Crossref]

Furuta, M.

H. Seo, S. Aihara, T. Watabe, H. Ohtake, T. Sakai, M. Kubota, N. Egami, T. Hiramatsu, T. Matsuda, M. Furuta, and T. Hirao, “A 128× 96 pixel stack-type color image sensor: stack of individual blue-, green-, and red-sensitive organic photoconductive films integrated with a ZnO thin film transistor readout circuit,” Jpn. J. Appl. Phys. 50(2), 4103 (2011).
[Crossref]

Gao, Y.

B. Zeng, Y. Gao, and F. J. Bartoli, “Ultrathin nanostructured metals for highly transmissive plasmonic subtractive color filters,” Sci. Rep. 3, 2840 (2013).
[Crossref] [PubMed]

Ghosh, S.

Gopinathan, A.

Han, M. G.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Haring-Bolivar, P.

A. Bablich, C. Merfort, H. Schäfer-Eberwein, P. Haring-Bolivar, and M. Boehm, “2-in-1 red-/green-/blue sensitive a-SiC:H/a-Si:H/a-SiGeC:H thin film photo detector with an integrated optical filter,” Thin Solid Films 552, 212–217 (2014).
[Crossref]

Heo, C-J.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Hiramatsu, T.

H. Seo, S. Aihara, T. Watabe, H. Ohtake, T. Sakai, M. Kubota, N. Egami, T. Hiramatsu, T. Matsuda, M. Furuta, and T. Hirao, “A 128× 96 pixel stack-type color image sensor: stack of individual blue-, green-, and red-sensitive organic photoconductive films integrated with a ZnO thin film transistor readout circuit,” Jpn. J. Appl. Phys. 50(2), 4103 (2011).
[Crossref]

Hiramoto, M.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7(3), 240–246 (2013).
[Crossref]

Hirao, T.

H. Seo, S. Aihara, T. Watabe, H. Ohtake, T. Sakai, M. Kubota, N. Egami, T. Hiramatsu, T. Matsuda, M. Furuta, and T. Hirao, “A 128× 96 pixel stack-type color image sensor: stack of individual blue-, green-, and red-sensitive organic photoconductive films integrated with a ZnO thin film transistor readout circuit,” Jpn. J. Appl. Phys. 50(2), 4103 (2011).
[Crossref]

Ho, J.

Hwang, B. Y.

Y. S. Do, J. H. Park, B. Y. Hwang, S-M. Lee, B-K. Ju, and K. C. Choi, “Plasmonic color filter and its fabrication for large-area applications,” Adv. Opt. Mater. 1(2), 133–138 (2013).
[Crossref]

Im, D.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Inman, R. H.

Izadi, S.

Jin, Y. W.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Ju, B-K.

Y. S. Do, J. H. Park, B. Y. Hwang, S-M. Lee, B-K. Ju, and K. C. Choi, “Plasmonic color filter and its fabrication for large-area applications,” Adv. Opt. Mater. 1(2), 133–138 (2013).
[Crossref]

Jung, J.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Kim, K-S.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Knipp, D.

Kolaman, A.

A. Kolaman and O. Yadid-Pecht, “Quaternion structural similarity: A new quality index for color images,” IEEE T. Image Process. 21(4), 1526–1536 (2012).
[Crossref]

Koppelhuber, A.

Krause, M.

Kubota, M.

H. Seo, S. Aihara, T. Watabe, H. Ohtake, T. Sakai, M. Kubota, N. Egami, T. Hiramatsu, T. Matsuda, M. Furuta, and T. Hirao, “A 128× 96 pixel stack-type color image sensor: stack of individual blue-, green-, and red-sensitive organic photoconductive films integrated with a ZnO thin film transistor readout circuit,” Jpn. J. Appl. Phys. 50(2), 4103 (2011).
[Crossref]

Lee, G. H.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Lee, K-H.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Lee, M.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Lee, S.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Lee, S-M.

Y. S. Do, J. H. Park, B. Y. Hwang, S-M. Lee, B-K. Ju, and K. C. Choi, “Plasmonic color filter and its fabrication for large-area applications,” Adv. Opt. Mater. 1(2), 133–138 (2013).
[Crossref]

Lee, T-Y.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Leem, D-S.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Lim, S-J.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Liu, Y J.

G. Si, Y. Zhao, A. B. Chew, and Y J. Liu, “Plasmonic color filters,” J. Mol. Eng. Mater. 2(2), 1440009 (2014).
[Crossref]

Lu, J-P.

Lukac, R.

R. Lukac and K. N. Plataniotis, “Color filter arrays: Design and performance analysis,” IEEE T. Consum. Electr. 51(4), 1260–1267 (2005).
[Crossref]

Matsuda, T.

H. Seo, S. Aihara, T. Watabe, H. Ohtake, T. Sakai, M. Kubota, N. Egami, T. Hiramatsu, T. Matsuda, M. Furuta, and T. Hirao, “A 128× 96 pixel stack-type color image sensor: stack of individual blue-, green-, and red-sensitive organic photoconductive films integrated with a ZnO thin film transistor readout circuit,” Jpn. J. Appl. Phys. 50(2), 4103 (2011).
[Crossref]

Medvedko, D.

Merfort, C.

A. Bablich, C. Merfort, H. Schäfer-Eberwein, P. Haring-Bolivar, and M. Boehm, “2-in-1 red-/green-/blue sensitive a-SiC:H/a-Si:H/a-SiGeC:H thin film photo detector with an integrated optical filter,” Thin Solid Films 552, 212–217 (2014).
[Crossref]

Merrill, R. B.

R. B. Merrill, “Color separation in an active pixel cell imaging array using a triple-well structure,” US Patent5,965,875.

Mersereau, R. M.

R. W. Schafer and R. M. Mersereau, “Demosaicking: color filter array interpolation,” IEEE Signal Proc. Mag. 22(1), 44–54 (2005).
[Crossref]

Na, K.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Nakamura, T.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7(3), 240–246 (2013).
[Crossref]

Nishiwaki, S.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7(3), 240–246 (2013).
[Crossref]

Ohtake, H.

H. Seo, S. Aihara, T. Watabe, H. Ohtake, T. Sakai, M. Kubota, N. Egami, T. Hiramatsu, T. Matsuda, M. Furuta, and T. Hirao, “A 128× 96 pixel stack-type color image sensor: stack of individual blue-, green-, and red-sensitive organic photoconductive films integrated with a ZnO thin film transistor readout circuit,” Jpn. J. Appl. Phys. 50(2), 4103 (2011).
[Crossref]

Park, H.

H. Park, Y. Dan, K. Seo, Y. J. Yu, P. K. Duane, M. Wober, and K. B. Crozier, “Filter-free image sensor pixels comprising silicon nanowires with selective color absorption,” Nano Lett. 14(4), 1804–1809 (2014).
[Crossref] [PubMed]

Park, J. H.

Y. S. Do, J. H. Park, B. Y. Hwang, S-M. Lee, B-K. Ju, and K. C. Choi, “Plasmonic color filter and its fabrication for large-area applications,” Adv. Opt. Mater. 1(2), 133–138 (2013).
[Crossref]

Park, K-B.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Plataniotis, K. N.

R. Lukac and K. N. Plataniotis, “Color filter arrays: Design and performance analysis,” IEEE T. Consum. Electr. 51(4), 1260–1267 (2005).
[Crossref]

Ready, S.

Ro, T.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Sakai, T.

H. Seo, S. Aihara, T. Watabe, H. Ohtake, T. Sakai, M. Kubota, N. Egami, T. Hiramatsu, T. Matsuda, M. Furuta, and T. Hirao, “A 128× 96 pixel stack-type color image sensor: stack of individual blue-, green-, and red-sensitive organic photoconductive films integrated with a ZnO thin film transistor readout circuit,” Jpn. J. Appl. Phys. 50(2), 4103 (2011).
[Crossref]

Satoh, R-I.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Schafer, R. W.

R. W. Schafer and R. M. Mersereau, “Demosaicking: color filter array interpolation,” IEEE Signal Proc. Mag. 22(1), 44–54 (2005).
[Crossref]

Schäfer-Eberwein, H.

A. Bablich, C. Merfort, H. Schäfer-Eberwein, P. Haring-Bolivar, and M. Boehm, “2-in-1 red-/green-/blue sensitive a-SiC:H/a-Si:H/a-SiGeC:H thin film photo detector with an integrated optical filter,” Thin Solid Films 552, 212–217 (2014).
[Crossref]

Schedl, D.

Seo, H.

H. Seo, S. Aihara, T. Watabe, H. Ohtake, T. Sakai, M. Kubota, N. Egami, T. Hiramatsu, T. Matsuda, M. Furuta, and T. Hirao, “A 128× 96 pixel stack-type color image sensor: stack of individual blue-, green-, and red-sensitive organic photoconductive films integrated with a ZnO thin film transistor readout circuit,” Jpn. J. Appl. Phys. 50(2), 4103 (2011).
[Crossref]

Seo, K.

H. Park, Y. Dan, K. Seo, Y. J. Yu, P. K. Duane, M. Wober, and K. B. Crozier, “Filter-free image sensor pixels comprising silicon nanowires with selective color absorption,” Nano Lett. 14(4), 1804–1809 (2014).
[Crossref] [PubMed]

Shcherbatyuk, G. V.

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

Si, G.

G. Si, Y. Zhao, A. B. Chew, and Y J. Liu, “Plasmonic color filters,” J. Mol. Eng. Mater. 2(2), 1440009 (2014).
[Crossref]

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

Stiebig, H.

Street, R. A.

Sul, S.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Suzuki, M.

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7(3), 240–246 (2013).
[Crossref]

Tadmor, Y.

D. J. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12(2), 229–232, (1992).
[Crossref] [PubMed]

Tolhurst, D. J.

D. J. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12(2), 229–232, (1992).
[Crossref] [PubMed]

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

Watabe, T.

H. Seo, S. Aihara, T. Watabe, H. Ohtake, T. Sakai, M. Kubota, N. Egami, T. Hiramatsu, T. Matsuda, M. Furuta, and T. Hirao, “A 128× 96 pixel stack-type color image sensor: stack of individual blue-, green-, and red-sensitive organic photoconductive films integrated with a ZnO thin film transistor readout circuit,” Jpn. J. Appl. Phys. 50(2), 4103 (2011).
[Crossref]

Wober, M.

H. Park, Y. Dan, K. Seo, Y. J. Yu, P. K. Duane, M. Wober, and K. B. Crozier, “Filter-free image sensor pixels comprising silicon nanowires with selective color absorption,” Nano Lett. 14(4), 1804–1809 (2014).
[Crossref] [PubMed]

Yadid-Pecht, O.

A. Kolaman and O. Yadid-Pecht, “Quaternion structural similarity: A new quality index for color images,” IEEE T. Image Process. 21(4), 1526–1536 (2012).
[Crossref]

Yagi, T.

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

Yokogawa, S.

S. P. Burgos, S. Yokogawa, and H. A. Atwater, “Color imaging via nearest neighbor hole coupling in plasmonic color filters integrated onto a complementary metal-oxide semiconductor image sensor,” ACS Nano 7(11), 10038–10047 (2013).
[Crossref] [PubMed]

S. Yokogawa, S. P. Burgos, and H. A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12(8), 4349–4354 (2012).
[Crossref] [PubMed]

Yu, Y. J.

H. Park, Y. Dan, K. Seo, Y. J. Yu, P. K. Duane, M. Wober, and K. B. Crozier, “Filter-free image sensor pixels comprising silicon nanowires with selective color absorption,” Nano Lett. 14(4), 1804–1809 (2014).
[Crossref] [PubMed]

Zeng, B.

B. Zeng, Y. Gao, and F. J. Bartoli, “Ultrathin nanostructured metals for highly transmissive plasmonic subtractive color filters,” Sci. Rep. 3, 2840 (2013).
[Crossref] [PubMed]

Zewail, A. H.

J. S. Batchelder, A. H. Zewail, and T. Cole, “Luminescent solar concentrators. 1: Theory of operation and techniques for performance evaluation,” Appl. Optics 18(18), 3090–3110, (1979).
[Crossref]

Zhao, Y.

ACS Nano (1)

S. P. Burgos, S. Yokogawa, and H. A. Atwater, “Color imaging via nearest neighbor hole coupling in plasmonic color filters integrated onto a complementary metal-oxide semiconductor image sensor,” ACS Nano 7(11), 10038–10047 (2013).
[Crossref] [PubMed]

Adv. Opt. Mater. (1)

Y. S. Do, J. H. Park, B. Y. Hwang, S-M. Lee, B-K. Ju, and K. C. Choi, “Plasmonic color filter and its fabrication for large-area applications,” Adv. Opt. Mater. 1(2), 133–138 (2013).
[Crossref]

Appl. Optics (1)

J. S. Batchelder, A. H. Zewail, and T. Cole, “Luminescent solar concentrators. 1: Theory of operation and techniques for performance evaluation,” Appl. Optics 18(18), 3090–3110, (1979).
[Crossref]

IEEE Signal Proc. Mag. (1)

R. W. Schafer and R. M. Mersereau, “Demosaicking: color filter array interpolation,” IEEE Signal Proc. Mag. 22(1), 44–54 (2005).
[Crossref]

IEEE T. Consum. Electr. (1)

R. Lukac and K. N. Plataniotis, “Color filter arrays: Design and performance analysis,” IEEE T. Consum. Electr. 51(4), 1260–1267 (2005).
[Crossref]

IEEE T. Image Process. (2)

A. Kolaman and O. Yadid-Pecht, “Quaternion structural similarity: A new quality index for color images,” IEEE T. Image Process. 21(4), 1526–1536 (2012).
[Crossref]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

J. Mol. Eng. Mater. (1)

G. Si, Y. Zhao, A. B. Chew, and Y J. Liu, “Plasmonic color filters,” J. Mol. Eng. Mater. 2(2), 1440009 (2014).
[Crossref]

Jpn. J. Appl. Phys. (1)

H. Seo, S. Aihara, T. Watabe, H. Ohtake, T. Sakai, M. Kubota, N. Egami, T. Hiramatsu, T. Matsuda, M. Furuta, and T. Hirao, “A 128× 96 pixel stack-type color image sensor: stack of individual blue-, green-, and red-sensitive organic photoconductive films integrated with a ZnO thin film transistor readout circuit,” Jpn. J. Appl. Phys. 50(2), 4103 (2011).
[Crossref]

Nano Lett. (2)

S. Yokogawa, S. P. Burgos, and H. A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12(8), 4349–4354 (2012).
[Crossref] [PubMed]

H. Park, Y. Dan, K. Seo, Y. J. Yu, P. K. Duane, M. Wober, and K. B. Crozier, “Filter-free image sensor pixels comprising silicon nanowires with selective color absorption,” Nano Lett. 14(4), 1804–1809 (2014).
[Crossref] [PubMed]

Nat. Photonics (1)

S. Nishiwaki, T. Nakamura, M. Hiramoto, T. Fujii, and M. Suzuki, “Efficient colour splitters for high-pixel-density image sensors,” Nat. Photonics 7(3), 240–246 (2013).
[Crossref]

Ophthalmic Physiol. Opt. (1)

D. J. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12(2), 229–232, (1992).
[Crossref] [PubMed]

Opt. Express (7)

Sci. Rep. (2)

S-J. Lim, D-S. Leem, K-B. Park, K-S. Kim, S. Sul, K. Na, G. H. Lee, C-J. Heo, K-H. Lee, X. Bulliard, R-I. Satoh, T. Yagi, T. Ro, D. Im, J. Jung, M. Lee, T-Y. Lee, M. G. Han, Y. W. Jin, and S. Lee, “Organic-on-silicon complementary metal-oxide-semiconductor colour image sensors,” Sci. Rep. 5, 7708 (2015).
[Crossref] [PubMed]

B. Zeng, Y. Gao, and F. J. Bartoli, “Ultrathin nanostructured metals for highly transmissive plasmonic subtractive color filters,” Sci. Rep. 3, 2840 (2013).
[Crossref] [PubMed]

Thin Solid Films (1)

A. Bablich, C. Merfort, H. Schäfer-Eberwein, P. Haring-Bolivar, and M. Boehm, “2-in-1 red-/green-/blue sensitive a-SiC:H/a-Si:H/a-SiGeC:H thin film photo detector with an integrated optical filter,” Thin Solid Films 552, 212–217 (2014).
[Crossref]

Other (4)

A. Koppelhuber and O. Bimber, “Reconstructions of the test set images,” figshare (2015) [retrieved 16 July 2015], http://dx.doi.org/10.6084/m9.figshare.1485612

T. M. Buzug, Computed Tomography from Photon Statistics to Modern Cone-Beam CT (Springer Verlag, 2008)

R. B. Merrill, “Color separation in an active pixel cell imaging array using a triple-well structure,” US Patent5,965,875.

B. E. Bayer, “Color imaging array,” US Patent3,971,065.

Supplementary Material (1)

NameDescription
» Dataset 1       Reconstructions of the test set images

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Figures (4)

Fig. 1
Fig. 1 Multi-layer Radon sensor: (a) Stacked LISA green and LISA red LC films. (b) Illustration of the sensor’s underlying principle. (c) Implementation of a two-layer sensor prototype.

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Fig. 2
Fig. 2 RGB color image reconstruction with two LC layers. The numbers indicate the structural similarity (SSIM) between reconstruction and ground truth. We apply the method in [25] to compute the SSIM between RGB images, and the one in [26] to compute the SSIM between single color channels. All 4,000 reconstructions of the test set and their SSIM values are available in Dataset 1, [23].

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Fig. 3
Fig. 3 Coded exposure imaging: (a) Coded exposure imaging vs. single-exposure imaging for two sample images. The SSIM indicates the difference from the ground truth, and the blue boxes indicate the optimal single exposures for the two samples. (b) Sinogram of exposure codes determined for the LISA green layer, color-coded and plotted at x,ϕ-coordinates (ϕ = 45° − 225°: calibrated, ϕ = 225°− 45°: simulated). (c) Coded exposure imaging vs. single-exposure imaging statistics over 4,000 test images.

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Fig. 4
Fig. 4 Physical light measurements vs. image reconstructions: (a) Absorption-emission spectra of LISA green and LISA red LC films. (b) Structural similarity histograms of reconstructions compared to the ground truth (red/green/blue: separate color channels, dashed black: RGB). (c) Integration behavior of a single aperture triangle.

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Equations (6)

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

P ⊤ = T − 1 L ⊤ .
P = L T − ⊤ ,
T − 1 = [ ( L ⊤ L ) − 1 L ⊤ P ] ⊤ .
p = T − 1 l ,
[ P r P g P b ] = [ L 1 L 2 L 3 ] T − T ,
[ P r P g P b ] = [ L 1 L 2 ] T − T ,

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