Abstract

Designs of N optical filters for color and polarization imaging are found by minimizing detector noise, photon shot noise, and interpolation error for the image acquisition in a division of focal plane configuration. To minimize interpolation error, a general tiling procedure and an optimized tiling pattern for N filters are presented. For multispectral imaging, a general technique to find the transmission band is presented. For full Stokes polarization imaging, the general design with optimized retardances and fast angles of the polarizers is compared with the solution of the Thomson problem. These results are applied to the design of a three-color full Stokes imaging camera.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Division of amplitude RGB full-Stokes camera using micro-polarizer arrays

Xingzhou Tu, Oliver J. Spires, Xiaobo Tian, Neal Brock, Rongguang Liang, and Stanley Pau
Opt. Express 25(26) 33160-33175 (2017)

Fundamental precision limits of full Stokes polarimeters based on DoFP polarization cameras for an arbitrary number of acquisitions

Xiaobo Li, Haofeng Hu, François Goudail, and Tiegen Liu
Opt. Express 27(22) 31261-31272 (2019)

Image interpolation for division of focal plane polarimeters with intensity correlation

Junchao Zhang, Haibo Luo, Bin Hui, and Zheng Chang
Opt. Express 24(18) 20799-20807 (2016)

References

  • View by:
  • |
  • |
  • |

  1. X. Li, B. Gunturk, and L. Zhang, “Image demosaicing: a systematic survey,” Proc. SPIE 6822, 68221J (2008).
    [Crossref]
  2. V. Gruev, R. Perkins, and T. York, “CCD polarization imaging sensor with aluminum nanowire optical filters,” Opt. Express 18(18), 19087–19094 (2010).
    [Crossref] [PubMed]
  3. X. Zhao, A. Bermak, F. Boussaid, and V. G. Chigrinov, “Liquid-crystal micropolarimeter array for full Stokes polarization imaging in visible spectrum,” Opt. Express 18(17), 17776–17787 (2010).
    [Crossref] [PubMed]
  4. W. L. Hsu, G. Myhre, K. Balakrishnan, N. Brock, M. Ibn-Elhaj, and S. Pau, “Full-Stokes imaging polarimeter using an array of elliptical polarizer,” Opt. Express 22(3), 3063–3074 (2014).
    [Crossref] [PubMed]
  5. G. Myhre, W. L. Hsu, A. Peinado, C. LaCasse, N. Brock, R. A. Chipman, and S. Pau, “Liquid crystal polymer full-stokes division of focal plane polarimeter,” Opt. Express 20(25), 27393–27409 (2012).
    [Crossref] [PubMed]
  6. N. Hagen and M. W. Kudenov, “Review of snapshot spectral imaging technologies,” Opt. Eng. 52(9), 090901 (2013).
    [Crossref]
  7. 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(22), 5453–5469 (2006).
    [Crossref] [PubMed]
  8. R. E. Carlson and C. A. Hall, “Error bounds for bicubic spline interpolation,” J. Approx. Theory 7(1), 41–47 (1973).
    [Crossref]
  9. H. Kuniba and R. S. Berns, “Spectral sensitivity optimization of color image sensors considering photon shot noise,” J. Electron. Imaging 18(2), 023002 (2009).
    [Crossref]
  10. S. Pau and A. Ashok, “Multispectral imaging based on computational imaging and a narrow-band absorptive filter array,” United States patent application US2014/060826.
  11. S. Gao and V. Gruev, “Bilinear and bicubic interpolation methods for division of focal plane polarimeters,” Opt. Express 19(27), 26161–26173 (2011).
    [Crossref] [PubMed]
  12. S. Gao and V. Gruev, “Gradient-based interpolation method for division-of-focal-plane polarimeters,” Opt. Express 21(1), 1137–1151 (2013).
    [Crossref] [PubMed]
  13. D. A. LeMaster and S. C. Cain, “Multichannel blind deconvolution of polarimetric imagery,” J. Opt. Soc. Am. A 25(9), 2170–2176 (2008).
    [Crossref] [PubMed]
  14. C. F. LaCasse, R. A. Chipman, and J. S. Tyo, “Band limited data reconstruction in modulated polarimeters,” Opt. Express 19(16), 14976–14989 (2011).
    [Crossref] [PubMed]
  15. A. Peinado, A. Lizana, J. Vidal, C. Iemmi, and J. Campos, “Optimization and performance criteria of a Stokes polarimeter based on two variable retarders,” Opt. Express 18(10), 9815–9830 (2010).
    [Crossref] [PubMed]
  16. D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
    [Crossref]
  17. D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25(11), 802–804 (2000).
    [Crossref] [PubMed]
  18. M. Atiyah and P. Sutcliffe, “Polyhedra in Physics, Chemistry and Geometry,” Milan J. Math. 71(1), 33–58 (2003).
    [Crossref]
  19. 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(7), 8024–8034 (2014).
    [Crossref] [PubMed]

2014 (2)

2013 (2)

N. Hagen and M. W. Kudenov, “Review of snapshot spectral imaging technologies,” Opt. Eng. 52(9), 090901 (2013).
[Crossref]

S. Gao and V. Gruev, “Gradient-based interpolation method for division-of-focal-plane polarimeters,” Opt. Express 21(1), 1137–1151 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (2)

2010 (3)

2009 (1)

H. Kuniba and R. S. Berns, “Spectral sensitivity optimization of color image sensors considering photon shot noise,” J. Electron. Imaging 18(2), 023002 (2009).
[Crossref]

2008 (2)

2006 (1)

2003 (1)

M. Atiyah and P. Sutcliffe, “Polyhedra in Physics, Chemistry and Geometry,” Milan J. Math. 71(1), 33–58 (2003).
[Crossref]

2000 (2)

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25(11), 802–804 (2000).
[Crossref] [PubMed]

1973 (1)

R. E. Carlson and C. A. Hall, “Error bounds for bicubic spline interpolation,” J. Approx. Theory 7(1), 41–47 (1973).
[Crossref]

Atiyah, M.

M. Atiyah and P. Sutcliffe, “Polyhedra in Physics, Chemistry and Geometry,” Milan J. Math. 71(1), 33–58 (2003).
[Crossref]

Balakrishnan, K.

Bermak, A.

Berns, R. S.

H. Kuniba and R. S. Berns, “Spectral sensitivity optimization of color image sensors considering photon shot noise,” J. Electron. Imaging 18(2), 023002 (2009).
[Crossref]

Boussaid, F.

Brock, N.

Cain, S. C.

Campos, J.

Carlson, R. E.

R. E. Carlson and C. A. Hall, “Error bounds for bicubic spline interpolation,” J. Approx. Theory 7(1), 41–47 (1973).
[Crossref]

Chenault, D. B.

Chigrinov, V. G.

Chipman, R. A.

Dereniak, E. L.

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25(11), 802–804 (2000).
[Crossref] [PubMed]

Descour, M. R.

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25(11), 802–804 (2000).
[Crossref] [PubMed]

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

Fan, X.

Gao, S.

Garcia, J. P.

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

Goldstein, D. L.

Gruev, V.

Gunturk, B.

X. Li, B. Gunturk, and L. Zhang, “Image demosaicing: a systematic survey,” Proc. SPIE 6822, 68221J (2008).
[Crossref]

Hagen, N.

N. Hagen and M. W. Kudenov, “Review of snapshot spectral imaging technologies,” Opt. Eng. 52(9), 090901 (2013).
[Crossref]

Hall, C. A.

R. E. Carlson and C. A. Hall, “Error bounds for bicubic spline interpolation,” J. Approx. Theory 7(1), 41–47 (1973).
[Crossref]

Hsu, W. L.

Ibn-Elhaj, M.

Iemmi, C.

Kemme, S. A.

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25(11), 802–804 (2000).
[Crossref] [PubMed]

Kudenov, M. W.

N. Hagen and M. W. Kudenov, “Review of snapshot spectral imaging technologies,” Opt. Eng. 52(9), 090901 (2013).
[Crossref]

Kuniba, H.

H. Kuniba and R. S. Berns, “Spectral sensitivity optimization of color image sensors considering photon shot noise,” J. Electron. Imaging 18(2), 023002 (2009).
[Crossref]

LaCasse, C.

LaCasse, C. F.

LeMaster, D. A.

Li, X.

X. Li, B. Gunturk, and L. Zhang, “Image demosaicing: a systematic survey,” Proc. SPIE 6822, 68221J (2008).
[Crossref]

Lizana, A.

Locke, A. M.

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

Myhre, G.

Pan, X.

Pau, S.

Peinado, A.

Perkins, R.

Phipps, G. S.

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25(11), 802–804 (2000).
[Crossref] [PubMed]

Sabatke, D. S.

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25(11), 802–804 (2000).
[Crossref] [PubMed]

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

Shaw, J. A.

Sutcliffe, P.

M. Atiyah and P. Sutcliffe, “Polyhedra in Physics, Chemistry and Geometry,” Milan J. Math. 71(1), 33–58 (2003).
[Crossref]

Sweatt, W. C.

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25(11), 802–804 (2000).
[Crossref] [PubMed]

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

Tyo, J. S.

Vidal, J.

Xu, P.

York, T.

Zhang, L.

X. Li, B. Gunturk, and L. Zhang, “Image demosaicing: a systematic survey,” Proc. SPIE 6822, 68221J (2008).
[Crossref]

Zhao, X.

Appl. Opt. (1)

J. Approx. Theory (1)

R. E. Carlson and C. A. Hall, “Error bounds for bicubic spline interpolation,” J. Approx. Theory 7(1), 41–47 (1973).
[Crossref]

J. Electron. Imaging (1)

H. Kuniba and R. S. Berns, “Spectral sensitivity optimization of color image sensors considering photon shot noise,” J. Electron. Imaging 18(2), 023002 (2009).
[Crossref]

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

Milan J. Math. (1)

M. Atiyah and P. Sutcliffe, “Polyhedra in Physics, Chemistry and Geometry,” Milan J. Math. 71(1), 33–58 (2003).
[Crossref]

Opt. Eng. (1)

N. Hagen and M. W. Kudenov, “Review of snapshot spectral imaging technologies,” Opt. Eng. 52(9), 090901 (2013).
[Crossref]

Opt. Express (9)

S. Gao and V. Gruev, “Bilinear and bicubic interpolation methods for division of focal plane polarimeters,” Opt. Express 19(27), 26161–26173 (2011).
[Crossref] [PubMed]

S. Gao and V. Gruev, “Gradient-based interpolation method for division-of-focal-plane polarimeters,” Opt. Express 21(1), 1137–1151 (2013).
[Crossref] [PubMed]

C. F. LaCasse, R. A. Chipman, and J. S. Tyo, “Band limited data reconstruction in modulated polarimeters,” Opt. Express 19(16), 14976–14989 (2011).
[Crossref] [PubMed]

A. Peinado, A. Lizana, J. Vidal, C. Iemmi, and J. Campos, “Optimization and performance criteria of a Stokes polarimeter based on two variable retarders,” Opt. Express 18(10), 9815–9830 (2010).
[Crossref] [PubMed]

V. Gruev, R. Perkins, and T. York, “CCD polarization imaging sensor with aluminum nanowire optical filters,” Opt. Express 18(18), 19087–19094 (2010).
[Crossref] [PubMed]

X. Zhao, A. Bermak, F. Boussaid, and V. G. Chigrinov, “Liquid-crystal micropolarimeter array for full Stokes polarization imaging in visible spectrum,” Opt. Express 18(17), 17776–17787 (2010).
[Crossref] [PubMed]

W. L. Hsu, G. Myhre, K. Balakrishnan, N. Brock, M. Ibn-Elhaj, and S. Pau, “Full-Stokes imaging polarimeter using an array of elliptical polarizer,” Opt. Express 22(3), 3063–3074 (2014).
[Crossref] [PubMed]

G. Myhre, W. L. Hsu, A. Peinado, C. LaCasse, N. Brock, R. A. Chipman, and S. Pau, “Liquid crystal polymer full-stokes division of focal plane polarimeter,” Opt. Express 20(25), 27393–27409 (2012).
[Crossref] [PubMed]

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(7), 8024–8034 (2014).
[Crossref] [PubMed]

Opt. Lett. (1)

Proc. SPIE (2)

D. S. Sabatke, A. M. Locke, M. R. Descour, W. C. Sweatt, J. P. Garcia, E. L. Dereniak, S. A. Kemme, and G. S. Phipps, “Figures of merit for complete Stokes polarimeter optimization,” Proc. SPIE 4133, 75–81 (2000).
[Crossref]

X. Li, B. Gunturk, and L. Zhang, “Image demosaicing: a systematic survey,” Proc. SPIE 6822, 68221J (2008).
[Crossref]

Other (1)

S. Pau and A. Ashok, “Multispectral imaging based on computational imaging and a narrow-band absorptive filter array,” United States patent application US2014/060826.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1 Schematics of two different ways for interpolation with the same sampling method. The connection lines are represented by dashed lines.
Fig. 2
Fig. 2 The optimized tiling configuration for N = 2 to N = 9. The direction of first interpolation is represented by a black arrow, while the second is represented by the white one. The unit cell is encircled by bold line. Note that the unit cell is not unique. There can be more than one unit cell for each N.
Fig. 3
Fig. 3 Images used for interpolation: (A) vegetables. (B) fruits and (C) chess pieces. The MSE of different tiling methods for the images: (D) vegetables, (E) fruits, and (F) chess pieces.
Fig. 4
Fig. 4 The transmission spectrum of N = 3 color filters and the corresponding transmission matrix.
Fig. 5
Fig. 5 Detector and shot noise factors are plotted as a function of N, the number of spectral band, for the case of minimum detector noise, minimum shot noise, and maximum transmission.
Fig. 6
Fig. 6 Two common designs of imaging polarimeter: (A) division of time. (B) division of focal plane.
Fig. 7
Fig. 7 Constant retardance curves on the Poincaré sphere.
Fig. 8
Fig. 8 Optimized micro-polarizer designs (one-layer configuration) for N = 4 to N = 30. The polarizer is represented by blue spots on the Poincaré Sphere. The red curve represents constant retardance.
Fig. 9
Fig. 9 The schematic of two-layer configuration.
Fig. 10
Fig. 10 Thomson solution for N = 4 to N = 30.
Fig. 11
Fig. 11 Comparison of two solutions for three figures of merit. (A) CN, (B) EWV, (C) RAD, (D) CN difference between optimized design and Thomson solution, (E) EWV difference between optimized design and Thomson solution, (F) RAD difference between optimized design and Thomson solution.
Fig. 12
Fig. 12 Design of an optimized three color full Stokes camera. Left side is the optimized tiling pattern of the filter array for N = 12.The direction of first interpolation is represented by a black arrow, while the second is represented by the white one. The unit cell is encircled by bold line. Right side is the structure of the camera made of RGB color filters and achromatic elliptical polarizers.

Tables (3)

Tables Icon

Table 1 Transmission Matrices for N = 2 to N = 7 Optimized for Detector Noise Factor

Tables Icon

Table 2 Retardance and Fast Axis Angles of the Optimized N Measurement Designs

Tables Icon

Table 3 CN/EWV/RAD of the Optimized Designs of One-layer and Two-layer Configuration

Equations (14)

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

( f - s f ) ( k , 1 ) ε 4 1 , k f ( k - 1 , 1 ) h x ( 4 k ) + ε 2 k ε 21 f ( 2 , 2 ) h x 2 - k h y 2 - 1 + ε 4 1 , k f ( k , 4 - k ) h y 4 - 1 .
I true -I interpolated ε 4,0 ( I true (4,0) a 4 + I true (0,4) b 4 ) + ε 2,0 2 I true (2,2) N 2
MSE = 1 MN 1 i M 1 j N (I true (i,j) I interpolated (i,j)) 2 ,
[ i 1 .. .. i N ] T = T [ b 1 .. .. b N ] T I = T B
[ b 1 .. .. b N ] T = T 1 [ i 1 .. .. i N ] T b n = m = 1 N (T 1 ) nm i m
v n = σ × m = 1 N (T 1 ) nm 2
v = σ × m = 1 N n = 1 N (T 1 ) mn 2
N F detector = v / = m = 1 N n = 1 N (T 1 ) mn 2 / N
v n m = 1 N [ (T 1 ) nm 2 k = 1 N T mk ]
NF sn = m = 1 N n = 1 N k = 1 N (T 1 ) nm 2 T mk / N
T o p t i m i z e d = | 1 1 1 1 . . 1 1 0 1 1 . . 1 1 1 0 1 . . 1 1 1 1 0 . . 1 . . . . . . . . . . . . 1 1 1 1 . . 0 |
S = W + I
R A D = Π j = 0 R 1 1 / μ j C N = μ m a x / μ m i n E W V = j = 0 R 1 1 / μ j 2
[ 1 , cos 2 ( 2 θ k ) + cos ( δ ) sin 2 ( 2 θ k ) , sin 2 ( δ / 2 ) sin ( 4 θ k ) , sin ( δ ) sin ( 2 θ k ) ]

Metrics