Abstract

We develop a photonic crystal filter with a new structure and propose a method to realize a snapshot multispectral polarization camera by mounting the filter on a monochrome imager with no requirement for a specific alignment. The developed filter is based on the Voronoi structure, which forms multilayered photonic crystals with random wave-like structures in each of the Voronoi cells. Because the transmission characteristics of the multilayered photonic crystal can be controlled simply by changing the microstructure, there is no need to change the manufacturing process and materials for each Voronoi cell. Furthermore, the Voronoi cell is randomly distributed so that the filter can be junctioned with the imager at arbitrary positions and angles without the need to position the filter during mounting, although it requires measurement of the camera characteristics and an image restoration process after filter mounting. In this experiment, we evaluated to reconstruct spectra as well as linearly polarized components and RGB images in the visible wavelength range from a single exposure image.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2019 (3)

A. Miyamichi, A. Ono, K. Kagawa, K. Yasutomi, and S. Kawahito, “Plasmonic color filter array with high color purity for cmos image sensors,” Sensors 19(8), 1750 (2019).
[Crossref]

Z. Wang, S. Yi, A. Chen, M. Zhou, T. S. Luk, A. James, J. Nogan, W. Ross, G. Joe, A. Shahsafi, K. X. Wang, M. A. Kats, and Z. Yu, “Single-shot on-chip spectral sensors based on photonic crystal slabs,” Nat. Commun. 10(1), 1020 (2019).
[Crossref]

Y. Ohtera and K. Shinoda, “Nir spectrum estimation utilizing a photonic crystal distributed passband-type multiple filter array,” Appl. Opt. 58(12), 3166–3173 (2019).
[Crossref]

2018 (1)

2017 (4)

X. Tu, L. Jiang, M. Ibn-Elhaj, and S. Pau, “Design, fabrication and testing of achromatic elliptical polarizer,” Opt. Express 25(9), 10355–10367 (2017).
[Crossref]

S. Mihoubi, O. Losson, B. Mathon, and L. Macaire, “Multispectral demosaicing using pseudo-panchromatic image,” IEEE Trans. on Image Process. 3(4), 982–995 (2017).
[Crossref]

A. Ahmed, X. Zhao, V. Gruev, J. Zhang, and A. Bermak, “Residual interpolation for division of focal plane polarization image sensors,” Opt. Express 25(9), 10651–10662 (2017).
[Crossref]

K. Shinoda, Y. Yanagi, Y. Hayasaki, and M. Hasegawa, “Multispectral filter array design without training images,” Opt. Rev. 24(4), 554–571 (2017).
[Crossref]

2016 (5)

J. Zhang, H. Luo, B. Hui, and Z. Chang, “Image interpolation for division of focal plane polarimeters with intensity correlation,” Opt. Express 24(18), 20799–20807 (2016).
[Crossref]

K. Shinoda, T. Hamasaki, M. Kawase, M. Hasegawa, and S. Kato, “Demosaicking for multispectral images based on vectorial total variation,” Opt. Rev. 23(4), 559–570 (2016).
[Crossref]

X. Tu and S. Pau, “Optimized design of n optical filters for color and polarization imaging,” Opt. Express 24(3), 3011–3024 (2016).
[Crossref]

J. Jia, K. J. Barnard, and K. Hirakawa, “Fourier spectral filter array for optimal multispectral imaging,” IEEE Trans. on Image Process. 25(4), 1530–1543 (2016).
[Crossref]

H. K. Aggarwal and A. Majumdar, “Hyperspectral image denoising using spatio-spectral total variation,” IEEE Geosci. Remote Sens. Lett. 13(3), 442–446 (2016).
[Crossref]

2015 (3)

C. Fu, H. Arguello, B. M. Sadler, and G. R. Arce, “Compressive spectral polarization imaging by a pixelized polarizer and colored patterned detector,” J. Opt. Soc. Am. A 32(11), 2178–2188 (2015).
[Crossref]

Y. Monno, S. Kikuchi, M. Tanaka, and M. Okutomi, “A practical one-shot multispectral imaging system using a single image sensor,” IEEE Trans. on Image Process. 24(10), 3048–3059 (2015).
[Crossref]

Y. Q. Zhao and J. Yang, “Hyperspectral image denoising via sparse representation and low-rank constraint,” IEEE T. Geosci. Remote Sens. 53(1), 296–308 (2015).
[Crossref]

2014 (1)

H. Zhang, W. He, L. Zhang, H. Shen, and Q. Yuan, “Hyperspectral image restoration using low-rank matrix recovery,” IEEE T. Geosci. Remote Sens. 52(8), 4729–4743 (2014).
[Crossref]

2013 (2)

2012 (4)

2011 (1)

2010 (2)

2009 (3)

Y. Zhao, L. Zhang, D. Zhang, and Q. Pana, “Object separation by polarimetric and spectral imagery fusion,” Comput. Vis. Image Underst. 113(8), 855–866 (2009).
[Crossref]

G. Shambat, M. S. Mirotznik, G. W. Euliss, V. Smolski, E. G. Johnson, and R. A. Athale, “Photonic crystal filters for multi-band optical filtering on a monolithic substrate,” J. Nanophotonics 3(1), 031506 (2009).
[Crossref]

Y. Murakami, M. Yamaguchi, and N. Ohyama, “Piecewise wiener estimation for reconstruction of spectral reflectance image by multipoint spectral measurements,” Appl. Opt. 48(11), 2188–2202 (2009).
[Crossref]

2007 (1)

2006 (1)

L. Miao, H. Qi, R. Ramanath, and W. E. Snyder, “Binary tree-based generic demosaicking algorithm for multispectral filter arrays,” IEEE Trans. on Image Process. 15(11), 3550–3558 (2006).
[Crossref]

2000 (1)

T. Kawashima, K. Miura, T. Sato, and S. Kawakami, “Self-healing effects in the fabrication processes of photonic crystals,” Appl. Phys. Lett. 77(16), 2613–2615 (2000).
[Crossref]

1991 (1)

F. Aurenhammer, “Voronoi diagrams – a survey of a fundamental geometric data structure,” ACM Comput. Surv. 23(3), 345–405 (1991).
[Crossref]

Aggarwal, H. K.

H. K. Aggarwal and A. Majumdar, “Hyperspectral image denoising using spatio-spectral total variation,” IEEE Geosci. Remote Sens. Lett. 13(3), 442–446 (2016).
[Crossref]

Ahmed, A.

Arce, G. R.

Arguello, H.

Athale, R. A.

G. Shambat, M. S. Mirotznik, G. W. Euliss, V. Smolski, E. G. Johnson, and R. A. Athale, “Photonic crystal filters for multi-band optical filtering on a monolithic substrate,” J. Nanophotonics 3(1), 031506 (2009).
[Crossref]

Aurenhammer, F.

F. Aurenhammer, “Voronoi diagrams – a survey of a fundamental geometric data structure,” ACM Comput. Surv. 23(3), 345–405 (1991).
[Crossref]

Barnard, K. J.

J. Jia, K. J. Barnard, and K. Hirakawa, “Fourier spectral filter array for optimal multispectral imaging,” IEEE Trans. on Image Process. 25(4), 1530–1543 (2016).
[Crossref]

Barrière, C.

Bermak, A.

Brock, N.

Bryan, K. M.

Chang, Z.

Chen, A.

Z. Wang, S. Yi, A. Chen, M. Zhou, T. S. Luk, A. James, J. Nogan, W. Ross, G. Joe, A. Shahsafi, K. X. Wang, M. A. Kats, and Z. Yu, “Single-shot on-chip spectral sensors based on photonic crystal slabs,” Nat. Commun. 10(1), 1020 (2019).
[Crossref]

Chen, Y.

Y. Chen, W. He, N. Yokoya, and T. Huang, “Weighted group sparsity regularized low-rank tensor decomposition for hyperspectral image restoration,” in IEEE International Geoscience and Remote Sensing Symposium, (2019), pp. 234–237.

Cheng, W.

Chipman, R. A.

Cox, M. P.

Edrees, H. M.

Elson, D. S.

Englund, D.

X. Gan, N. Pervez, I. Kymissis, F. Hatami, and D. Englund, “A high-resolution spectrometer based on a compact planar two dimensional photonic crystal cavity array,” Appl. Phys. Lett. 100(23), 231104 (2012).
[Crossref]

Euliss, G. W.

G. Shambat, M. S. Mirotznik, G. W. Euliss, V. Smolski, E. G. Johnson, and R. A. Athale, “Photonic crystal filters for multi-band optical filtering on a monolithic substrate,” J. Nanophotonics 3(1), 031506 (2009).
[Crossref]

Fu, C.

Gan, X.

X. Gan, N. Pervez, I. Kymissis, F. Hatami, and D. Englund, “A high-resolution spectrometer based on a compact planar two dimensional photonic crystal cavity array,” Appl. Phys. Lett. 100(23), 231104 (2012).
[Crossref]

Gao, S.

Gazes, M. J.

Gruev, V.

Hamasaki, T.

K. Shinoda, T. Hamasaki, M. Kawase, M. Hasegawa, and S. Kato, “Demosaicking for multispectral images based on vectorial total variation,” Opt. Rev. 23(4), 559–570 (2016).
[Crossref]

Hasegawa, M.

K. Shinoda, Y. Ohtera, and M. Hasegawa, “Snapshot multispectral polarization imaging using a photonic crystal filter array,” Opt. Express 26(12), 15948–15961 (2018).
[Crossref]

K. Shinoda, Y. Yanagi, Y. Hayasaki, and M. Hasegawa, “Multispectral filter array design without training images,” Opt. Rev. 24(4), 554–571 (2017).
[Crossref]

K. Shinoda, T. Hamasaki, M. Kawase, M. Hasegawa, and S. Kato, “Demosaicking for multispectral images based on vectorial total variation,” Opt. Rev. 23(4), 559–570 (2016).
[Crossref]

Hatami, F.

X. Gan, N. Pervez, I. Kymissis, F. Hatami, and D. Englund, “A high-resolution spectrometer based on a compact planar two dimensional photonic crystal cavity array,” Appl. Phys. Lett. 100(23), 231104 (2012).
[Crossref]

Hayasaki, Y.

K. Shinoda, Y. Yanagi, Y. Hayasaki, and M. Hasegawa, “Multispectral filter array design without training images,” Opt. Rev. 24(4), 554–571 (2017).
[Crossref]

He, W.

H. Zhang, W. He, L. Zhang, H. Shen, and Q. Yuan, “Hyperspectral image restoration using low-rank matrix recovery,” IEEE T. Geosci. Remote Sens. 52(8), 4729–4743 (2014).
[Crossref]

Y. Chen, W. He, N. Yokoya, and T. Huang, “Weighted group sparsity regularized low-rank tensor decomposition for hyperspectral image restoration,” in IEEE International Geoscience and Remote Sensing Symposium, (2019), pp. 234–237.

Hirakawa, K.

J. Jia, K. J. Barnard, and K. Hirakawa, “Fourier spectral filter array for optimal multispectral imaging,” IEEE Trans. on Image Process. 25(4), 1530–1543 (2016).
[Crossref]

Hsu, W.-L.

Huang, T.

Y. Chen, W. He, N. Yokoya, and T. Huang, “Weighted group sparsity regularized low-rank tensor decomposition for hyperspectral image restoration,” in IEEE International Geoscience and Remote Sensing Symposium, (2019), pp. 234–237.

Hui, B.

Ibn-Elhaj, M.

Inoue, Y.

James, A.

Z. Wang, S. Yi, A. Chen, M. Zhou, T. S. Luk, A. James, J. Nogan, W. Ross, G. Joe, A. Shahsafi, K. X. Wang, M. A. Kats, and Z. Yu, “Single-shot on-chip spectral sensors based on photonic crystal slabs,” Nat. Commun. 10(1), 1020 (2019).
[Crossref]

Jia, J.

J. Jia, K. J. Barnard, and K. Hirakawa, “Fourier spectral filter array for optimal multispectral imaging,” IEEE Trans. on Image Process. 25(4), 1530–1543 (2016).
[Crossref]

Jia, Z.

Jiang, L.

Joe, G.

Z. Wang, S. Yi, A. Chen, M. Zhou, T. S. Luk, A. James, J. Nogan, W. Ross, G. Joe, A. Shahsafi, K. X. Wang, M. A. Kats, and Z. Yu, “Single-shot on-chip spectral sensors based on photonic crystal slabs,” Nat. Commun. 10(1), 1020 (2019).
[Crossref]

Johnson, E. G.

G. Shambat, M. S. Mirotznik, G. W. Euliss, V. Smolski, E. G. Johnson, and R. A. Athale, “Photonic crystal filters for multi-band optical filtering on a monolithic substrate,” J. Nanophotonics 3(1), 031506 (2009).
[Crossref]

Junger, S.

S. Junger, W. Tschekalinskij, N. Verwaal, and N. Weber, “Polarization and spectral filter arrays based on sub-wavelength structures in cmos,” in SENSOR+TEST Conferences, (2011), pp. 161–165.

Kagawa, K.

A. Miyamichi, A. Ono, K. Kagawa, K. Yasutomi, and S. Kawahito, “Plasmonic color filter array with high color purity for cmos image sensors,” Sensors 19(8), 1750 (2019).
[Crossref]

Kato, S.

K. Shinoda, T. Hamasaki, M. Kawase, M. Hasegawa, and S. Kato, “Demosaicking for multispectral images based on vectorial total variation,” Opt. Rev. 23(4), 559–570 (2016).
[Crossref]

Kats, M. A.

Z. Wang, S. Yi, A. Chen, M. Zhou, T. S. Luk, A. James, J. Nogan, W. Ross, G. Joe, A. Shahsafi, K. X. Wang, M. A. Kats, and Z. Yu, “Single-shot on-chip spectral sensors based on photonic crystal slabs,” Nat. Commun. 10(1), 1020 (2019).
[Crossref]

Kawahito, S.

A. Miyamichi, A. Ono, K. Kagawa, K. Yasutomi, and S. Kawahito, “Plasmonic color filter array with high color purity for cmos image sensors,” Sensors 19(8), 1750 (2019).
[Crossref]

Kawakami, S.

Y. Ohtera, T. Onuki, Y. Inoue, and S. Kawakami, “Multichannel photonic crystal wavelength filter array for near-infrared wavelengths,” J. Lightwave Technol. 25(2), 499–503 (2007).
[Crossref]

T. Kawashima, K. Miura, T. Sato, and S. Kawakami, “Self-healing effects in the fabrication processes of photonic crystals,” Appl. Phys. Lett. 77(16), 2613–2615 (2000).
[Crossref]

Kawase, M.

K. Shinoda, T. Hamasaki, M. Kawase, M. Hasegawa, and S. Kato, “Demosaicking for multispectral images based on vectorial total variation,” Opt. Rev. 23(4), 559–570 (2016).
[Crossref]

Kawashima, T.

T. Kawashima, K. Miura, T. Sato, and S. Kawakami, “Self-healing effects in the fabrication processes of photonic crystals,” Appl. Phys. Lett. 77(16), 2613–2615 (2000).
[Crossref]

Kikuchi, S.

Y. Monno, S. Kikuchi, M. Tanaka, and M. Okutomi, “A practical one-shot multispectral imaging system using a single image sensor,” IEEE Trans. on Image Process. 24(10), 3048–3059 (2015).
[Crossref]

Kulkarni, M.

Kurniatan, D.

Kymissis, I.

LaCasse, C.

Losson, O.

S. Mihoubi, O. Losson, B. Mathon, and L. Macaire, “Multispectral demosaicing using pseudo-panchromatic image,” IEEE Trans. on Image Process. 3(4), 982–995 (2017).
[Crossref]

Luk, T. S.

Z. Wang, S. Yi, A. Chen, M. Zhou, T. S. Luk, A. James, J. Nogan, W. Ross, G. Joe, A. Shahsafi, K. X. Wang, M. A. Kats, and Z. Yu, “Single-shot on-chip spectral sensors based on photonic crystal slabs,” Nat. Commun. 10(1), 1020 (2019).
[Crossref]

Luo, H.

Macaire, L.

S. Mihoubi, O. Losson, B. Mathon, and L. Macaire, “Multispectral demosaicing using pseudo-panchromatic image,” IEEE Trans. on Image Process. 3(4), 982–995 (2017).
[Crossref]

Majumdar, A.

H. K. Aggarwal and A. Majumdar, “Hyperspectral image denoising using spatio-spectral total variation,” IEEE Geosci. Remote Sens. Lett. 13(3), 442–446 (2016).
[Crossref]

Mathon, B.

S. Mihoubi, O. Losson, B. Mathon, and L. Macaire, “Multispectral demosaicing using pseudo-panchromatic image,” IEEE Trans. on Image Process. 3(4), 982–995 (2017).
[Crossref]

Miao, L.

L. Miao, H. Qi, R. Ramanath, and W. E. Snyder, “Binary tree-based generic demosaicking algorithm for multispectral filter arrays,” IEEE Trans. on Image Process. 15(11), 3550–3558 (2006).
[Crossref]

Mihoubi, S.

S. Mihoubi, O. Losson, B. Mathon, and L. Macaire, “Multispectral demosaicing using pseudo-panchromatic image,” IEEE Trans. on Image Process. 3(4), 982–995 (2017).
[Crossref]

Mirotznik, M. S.

G. Shambat, M. S. Mirotznik, G. W. Euliss, V. Smolski, E. G. Johnson, and R. A. Athale, “Photonic crystal filters for multi-band optical filtering on a monolithic substrate,” J. Nanophotonics 3(1), 031506 (2009).
[Crossref]

Miura, K.

T. Kawashima, K. Miura, T. Sato, and S. Kawakami, “Self-healing effects in the fabrication processes of photonic crystals,” Appl. Phys. Lett. 77(16), 2613–2615 (2000).
[Crossref]

Miyamichi, A.

A. Miyamichi, A. Ono, K. Kagawa, K. Yasutomi, and S. Kawahito, “Plasmonic color filter array with high color purity for cmos image sensors,” Sensors 19(8), 1750 (2019).
[Crossref]

Monno, Y.

Y. Monno, S. Kikuchi, M. Tanaka, and M. Okutomi, “A practical one-shot multispectral imaging system using a single image sensor,” IEEE Trans. on Image Process. 24(10), 3048–3059 (2015).
[Crossref]

Murakami, Y.

Myhre, G.

Nogan, J.

Z. Wang, S. Yi, A. Chen, M. Zhou, T. S. Luk, A. James, J. Nogan, W. Ross, G. Joe, A. Shahsafi, K. X. Wang, M. A. Kats, and Z. Yu, “Single-shot on-chip spectral sensors based on photonic crystal slabs,” Nat. Commun. 10(1), 1020 (2019).
[Crossref]

Ohtera, Y.

Ohyama, N.

Okutomi, M.

Y. Monno, S. Kikuchi, M. Tanaka, and M. Okutomi, “A practical one-shot multispectral imaging system using a single image sensor,” IEEE Trans. on Image Process. 24(10), 3048–3059 (2015).
[Crossref]

Ono, A.

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Z. Wang, S. Yi, A. Chen, M. Zhou, T. S. Luk, A. James, J. Nogan, W. Ross, G. Joe, A. Shahsafi, K. X. Wang, M. A. Kats, and Z. Yu, “Single-shot on-chip spectral sensors based on photonic crystal slabs,” Nat. Commun. 10(1), 1020 (2019).
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Y. Zhao, L. Zhang, D. Zhang, and Q. Pana, “Object separation by polarimetric and spectral imagery fusion,” Comput. Vis. Image Underst. 113(8), 855–866 (2009).
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H. Zhang, W. He, L. Zhang, H. Shen, and Q. Yuan, “Hyperspectral image restoration using low-rank matrix recovery,” IEEE T. Geosci. Remote Sens. 52(8), 4729–4743 (2014).
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Z. Wang, S. Yi, A. Chen, M. Zhou, T. S. Luk, A. James, J. Nogan, W. Ross, G. Joe, A. Shahsafi, K. X. Wang, M. A. Kats, and Z. Yu, “Single-shot on-chip spectral sensors based on photonic crystal slabs,” Nat. Commun. 10(1), 1020 (2019).
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X. Gan, N. Pervez, I. Kymissis, F. Hatami, and D. Englund, “A high-resolution spectrometer based on a compact planar two dimensional photonic crystal cavity array,” Appl. Phys. Lett. 100(23), 231104 (2012).
[Crossref]

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Biomed. Opt. Express (1)

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J. Opt. Soc. Am. A (1)

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Z. Wang, S. Yi, A. Chen, M. Zhou, T. S. Luk, A. James, J. Nogan, W. Ross, G. Joe, A. Shahsafi, K. X. Wang, M. A. Kats, and Z. Yu, “Single-shot on-chip spectral sensors based on photonic crystal slabs,” Nat. Commun. 10(1), 1020 (2019).
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Opt. Rev. (2)

K. Shinoda, T. Hamasaki, M. Kawase, M. Hasegawa, and S. Kato, “Demosaicking for multispectral images based on vectorial total variation,” Opt. Rev. 23(4), 559–570 (2016).
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Sensors (1)

A. Miyamichi, A. Ono, K. Kagawa, K. Yasutomi, and S. Kawahito, “Plasmonic color filter array with high color purity for cmos image sensors,” Sensors 19(8), 1750 (2019).
[Crossref]

Other (3)

S. Junger, W. Tschekalinskij, N. Verwaal, and N. Weber, “Polarization and spectral filter arrays based on sub-wavelength structures in cmos,” in SENSOR+TEST Conferences, (2011), pp. 161–165.

Y. Chen, W. He, N. Yokoya, and T. Huang, “Weighted group sparsity regularized low-rank tensor decomposition for hyperspectral image restoration,” in IEEE International Geoscience and Remote Sensing Symposium, (2019), pp. 234–237.

W. K. Pratt, Digital Image Processing (Wiley, 1978).

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Figures (14)
Fig. 1.
Fig. 1. Conceptual diagram of a multilayer photonic crystal. a, Overview of the multilayer structure. b, Transmittance example for different lattice pitches (265, 280, 290, 305 nm). The layer thickness is about 4 $\mu m$. c, Transmittance example in the TE and TM modes.

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Fig. 2.
Fig. 2. Conceptual diagram of a Voronoi-like random photonic crystal filter.

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Fig. 3.
Fig. 3. Conceptual diagram of filter equivalence relations. a, Top view of the lattice pattern. b, Visual color example mounted on a $5 \times 5$ pixel imager. Each Voronoi cell appears as a different color indicating a different lattice pitch, and each pixel contains various Voronoi cells. c, Filter array pattern equivalent to b for $5 \times 5$ pixels. The arrows represent the reference axis of the polarization.

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Fig. 4.
Fig. 4. Overview of the fabrication process of a Voronoi-like random photonic crystal filter.

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Fig. 5.
Fig. 5. Prototype camera and filter. a, Camera overview (commercial monochrome camera, ARTRAY, ARTCAM-150P5-WOM). b, Frontal view of the camera. The fabricated Voronoi-like random photonic crystal filter is mounted on the monochrome imager (SONY, ICX205AL) and is covered with a cover glass. c, Optical image of the fabricated and mounted filter. The Voronoi-like random pattern is $232.5 \mu m \times 232.5 \mu m$ ($50 \times 50$ pixels in the imager). For a visual comparison, a regular filter array pattern ($4.65 \mu m$ / pitch) is also deposited next to the Voronoi pattern.

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Fig. 6.
Fig. 6. Fabrication test of Voronoi-like random pattern. a, Lattice pattern data for lithography. b, Scanning electron microscope (SEM) image of the surface of the fabricated filter. The area is about $18.6 \times 18.6 \mu m$ (corresponding to $4\times 4$ pixels) and is captured from a tilted angle.

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Fig. 7.
Fig. 7. Experimental set-up for measuring the transmission spectra at various angles. The transmitted wavelength is controlled by a liquid crystal tunable filter, and the transmitted polarization is controlled by the angle of the liquid crystal tunable filter to the optical axis.

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Fig. 8.
Fig. 8. Spectral transmittance of a fabricated filter. a, b, Transmittance vs. angle and wavelength at pixel positions of $(x, y) = (25, 25)$ and $(26, 26)$. c, d Transmittance vs. angle in a and b, showing 31 plots for different wavelengths.

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Fig. 9.
Fig. 9. Spectral transmittance for 0$^{\circ }$ and 90$^{\circ }$, shown as red and blue lines. The horizontal axis is wavelength (nm) and the vertical axis is spectral transmittance. Each graph corresponds to the transmittance in one pixel. Pixel positions from $(24, 24)$ to $(27, 27)$ ($4 \times 4$ from the center of $50 \times 50$ pixels) are shown.

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Fig. 10.
Fig. 10. Visual comparison of RGB images of a color chart (x-rite, ColorChecker Classic). a, RGB reproduction of color chart from original spectrum. b, RGB reproduction of color chart from demosaicked image.

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Fig. 11.
Fig. 11. Spectrum comparison of color chart. The red line is the original and the blue line is the average spectrum of the demosaicked $50 \times 50$ image. Each graph corresponds to patches 1 to 24 from left-top to right-bottom.

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Fig. 12.
Fig. 12. Average spectrum of polarized white light. The red line is 0$^{\circ }$ and the blue line is 90$^{\circ }$.

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Fig. 13.
Fig. 13. Demosaicked RGB image of 0$^{\circ }$ polarized white light. a, Demosaicked 0$^{\circ }$ polarized RGB image. b, Demosaicked 90$^{\circ }$ polarized RGB image.

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Fig. 14.
Fig. 14. Multispectral-polarization-RGB-imaging demonstration using a mobile phone. a, Overview of the captured object. This image is captured by a general RGB camera, and not by our camera. b, Snapshot monochrome image captured by the proposed camera. The pixel size is $50\times 50$. c,d,e,f, RGB, 450, 550, 650 nm of 0$^{\circ }$ image recovered from b. g,h,i,j, RGB, 450, 550, 650 nm of 90$^{\circ }$ image recovered from b.

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Equations (24)

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

r e g ( p s ) = ∩ p q ∈ S − { p s } d o m ( p s , p q ) ,
d o m ( p s , p q ) = { p ∈ R 2 | δ ( p , p s ) ≤ δ ( p , p q ) } ,
s = P ′ I ,
P ′ = [ 1 0 1 1 0 − 1 − 1 2 − 1 ] .
g = a R − θ M R θ s ,
g = 1 2 [ q + r ( q − r ) cos ⁡ 2 θ ( q − r ) sin ⁡ 2 θ ] T s ,
g = 1 2 ∑ n [ w n ( q n + r n ) w n ( q n − r n ) cos ⁡ 2 θ n w n ( q n − r n ) sin ⁡ 2 θ n ] T s ,
g = 1 2 [ k 1 k 2 cos ⁡ 2 ( θ ′ + ψ ) k 2 sin ⁡ 2 ( θ ′ + ψ ) ] T s ,
k 1 = ∑ n w n ( q n + r n ) ,
k 2 = ( ∑ n w n ( q n − r n ) cos ⁡ 2 ψ n ) 2 + ( ∑ n w n ( q n − r n ) sin ⁡ 2 ψ n ) 2 ,
ψ = arctan ⁡ ( ∑ n w n ( q n − r n ) sin ⁡ 2 ψ n ∑ n w n ( q n − r n ) cos ⁡ 2 ψ n ) .
g ϕ = 1 2 ( k 1 + k 2 cos ⁡ 2 ( ϕ − ( θ ′ + ψ ) ) ) .
g ϕ q = 1 2 ( k 1 + k 2 ) ,
g ϕ r = 1 2 ( k 1 − k 2 ) .
g = 1 2 [ g ϕ q + g ϕ r ( g ϕ q − g ϕ r ) cos ⁡ ( 2 ϕ q ) ( g ϕ q − g ϕ r ) sin ⁡ ( 2 ϕ q ) ] T s .
g x , y = 1 2 ∑ λ T λ [ q x , y , λ + r x , y , λ ( q x , y , λ − r x , y , λ ) cos ⁡ 2 θ x , y ( q x , y , λ − r x , y , λ ) sin ⁡ 2 θ x , y ] T s x , y , λ .
g = H I ,
H = T M P ,
T = 1 2 E X Y ⊗ [ T λ 0   T λ 1   …   T λ L − 1 ] ,
M = [ M 0 , 0 , λ 0 0 … 0 0 … 0 0 M 0 , 0 , λ 1 … 0 0 … 0 ⋮ ⋮ ⋱ ⋮ ⋮ ⋱ ⋮ 0 0 … M 0 , 0 , λ L − 1 0 … 0 0 0 … 0 M 0 , 1 , λ 0 … 0 ⋮ ⋮ ⋱ ⋮ ⋮ ⋱ ⋮ 0 0 … 0 0 … M X − 1 , Y − 1 , λ L − 1 ] ,
M x , y , λ = [ q x , y , λ + r x , y , λ ( q x , y , λ − r x , y , λ ) cos ⁡ 2 θ x , y ( q x , y , λ − r x , y , λ ) sin ⁡ 2 θ x , y ] T ,
P = E X Y L ⊗ P ′ ,
I ^ = W g ,
W = R I H T ( H R I H T ) − 1 .

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