Abstract

This paper presents bilinear and bicubic interpolation methods tailored for the division of focal plane polarization imaging sensor. The interpolation methods are targeted for a 1-Mega pixel polarization imaging sensor operating in the visible spectrum. The five interpolation methods considered in this paper are: bilinear, weighted bilinear, bicubic spline, an approximated bicubic spline and a bicubic interpolation method. The modulation transfer function analysis is applied to the different interpolation methods, and test images as well as numerical error analyses are also presented. Based on the comparison results, the full frame bicubic spline interpolation achieves the best performance for polarization images.

© 2011 OSA

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2011

M. Sarkar, D. San Segundo Bello, C. van Hoof, and A. Theuwissen, “Integrated polarization analyzing CMOS image sensor for material classification,” IEEE Sens. J. 11(8), 1692–1703 (2011).
[CrossRef]

T. York, S. Powell, and V. Gruev, “A comparison of polarization image processing across different platforms,” Proc. SPIE 8160, 816004, 816004-7 (2011).
[CrossRef]

J. G. Ok, H. J. Park, M. K. Kwak, C. A. Pina-Hernandez, S. H. Ahn, and L. J. Guo, “Continuous patterning of nanogratings by nanochannel-guided lithography on liquid resists,” Adv. Mater. (Deerfield Beach Fla.) 23(38), 4444–4448 (2011).
[CrossRef] [PubMed]

T. Weber, T. Käsebier, E. B. Kley, and A. Tünnermann, “Broadband iridium wire grid polarizer for UV applications,” Opt. Lett. 36(4), 445–447 (2011).
[CrossRef] [PubMed]

2010

2009

M. W. Kudenov, L. J. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[CrossRef]

B. M. Ratliff, C. F. LaCasse, and J. S. Tyo, “Interpolation strategies for reducing IFOV artifacts in microgrid polarimeter imagery,” Opt. Express 17(11), 9112–9125 (2009).
[CrossRef] [PubMed]

2007

J. Wang, F. Walters, X. Liu, P. Sciortino, and X. Deng, “High-performance, large area, deep ultraviolet to infrared polarizers based on 40 nm line/78 nm space nanowire grids,” Appl. Phys. Lett. 90, 611041 (2007).

2006

B. M. Ratliff, J. K. Boger, M. P. Fetrow, J. S. Tyo, and W. T. Black, “Image processing methods to compensate for IFOV errors in microgrid imaging polarimeters,” Proc. SPIE 6240, 6240OE (2006).

M. Momeni and A. H. Titus, “An analog VLSI chip emulating polarization vision of Octopus retina,” IEEE Trans. Neural Netw. 17(1), 222–232 (2006).
[CrossRef] [PubMed]

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]

J. S. Tyo, “Hybrid division of aperture/division of a focal-plane polarimeter for real-time polarization imagery without an instantaneous field-of-view error,” Opt. Lett. 31(20), 2984–2986 (2006).
[CrossRef] [PubMed]

2005

J. L. Pezzaniti and D. B. Chenault, “A division of aperture MWIR imaging polarimeter,” Proc. SPIE 5888, 58880V, 58880V-12 (2005).
[CrossRef]

B. K. Gunturk, J. Glotzbach, Y. Altunbasak, R. W. Schafer, and R. M. Mersereau, “Demosaicking: color filter array interpolation,” IEEE Signal Process. Mag. 22(1), 44–54 (2005).
[CrossRef]

2002

B. K. Gunturk, Y. Altunbasak, and R. M. Mersereau, “Color plane interpolation using alternating projections,” IEEE Trans. Image Process. 11(9), 997–1013 (2002).
[CrossRef] [PubMed]

C. K. Harnett and H. G. Craighead, “Liquid-crystal micropolarizer array for polarization-difference imaging,” Appl. Opt. 41(7), 1291–1296 (2002).
[CrossRef] [PubMed]

2001

C. A. Farlow, D. B. Chenault, K. D. Spradley, M. G. Gulley, M. W. Jones, and C. M. Persons, “Imaging polarimeter development and application,” Proc. SPIE 4819, 118–125 (2001).

2000

A. Goldberg, T. Fischer, S. Kennerly, S. Wang, M. Sundaram, P. Uppal, M. Winn, G. Milne, and M. Stevens, “Dual band QWIP MWIR/LWIR focal plane array test results,” Proc. SPIE 4028, 276–287 (2000).
[CrossRef]

1999

R. Kimmel, “Demosaicing: image reconstruction from color CCD samples,” IEEE Trans. Image Process. 8(9), 1221–1228 (1999).
[CrossRef] [PubMed]

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, “Diffractive optical element for Stokes vector measurement with a focal plane array,” Proc. SPIE 3754, 169–177 (1999).
[CrossRef]

1997

J. D. Barter, P. H. Y. Lee, and H. R. Thompson, “Stokes parameter imaging of scattering surfaces,” Proc. SPIE 3121, 314–320 (1997).
[CrossRef]

1995

W. S. Russell, “Polynomial interpolation schemes for internal derivative distributions on structured grids,” Appl. Numer. Math. 17(2), 129–171 (1995).
[CrossRef]

1985

1981

J. E. Solomon, “Polarization imaging,” Appl. Opt. 20(9), 1537–1544 (1981).
[CrossRef] [PubMed]

R. Walraven, “Polarization imagery,” Opt. Eng. 20, 14–18 (1981).

1978

H. Hou and H. Andrews, “Cubic splines for image interpolation and digital filtering,” IEEE Trans. Acoust. Speech Signal Process. 26(6), 508–517 (1978).
[CrossRef]

Ahn, S. H.

J. G. Ok, H. J. Park, M. K. Kwak, C. A. Pina-Hernandez, S. H. Ahn, and L. J. Guo, “Continuous patterning of nanogratings by nanochannel-guided lithography on liquid resists,” Adv. Mater. (Deerfield Beach Fla.) 23(38), 4444–4448 (2011).
[CrossRef] [PubMed]

Altunbasak, Y.

B. K. Gunturk, J. Glotzbach, Y. Altunbasak, R. W. Schafer, and R. M. Mersereau, “Demosaicking: color filter array interpolation,” IEEE Signal Process. Mag. 22(1), 44–54 (2005).
[CrossRef]

B. K. Gunturk, Y. Altunbasak, and R. M. Mersereau, “Color plane interpolation using alternating projections,” IEEE Trans. Image Process. 11(9), 997–1013 (2002).
[CrossRef] [PubMed]

Andrews, H.

H. Hou and H. Andrews, “Cubic splines for image interpolation and digital filtering,” IEEE Trans. Acoust. Speech Signal Process. 26(6), 508–517 (1978).
[CrossRef]

Azzam, R. M. A.

Barter, J. D.

J. D. Barter, P. H. Y. Lee, and H. R. Thompson, “Stokes parameter imaging of scattering surfaces,” Proc. SPIE 3121, 314–320 (1997).
[CrossRef]

Black, W. T.

B. M. Ratliff, J. K. Boger, M. P. Fetrow, J. S. Tyo, and W. T. Black, “Image processing methods to compensate for IFOV errors in microgrid imaging polarimeters,” Proc. SPIE 6240, 6240OE (2006).

Boger, J. K.

B. M. Ratliff, J. K. Boger, M. P. Fetrow, J. S. Tyo, and W. T. Black, “Image processing methods to compensate for IFOV errors in microgrid imaging polarimeters,” Proc. SPIE 6240, 6240OE (2006).

Chenault, D. B.

M. E. Roche, D. B. Chenault, J. P. Vaden, A. Lompado, D. Voelz, T. J. Schulz, R. N. Givens, and V. L. Gamiz, “Synthetic aperture imaging polarimeter,” Proc. SPIE 7672, 767206, 767206-12 (2010).
[CrossRef]

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]

J. L. Pezzaniti and D. B. Chenault, “A division of aperture MWIR imaging polarimeter,” Proc. SPIE 5888, 58880V, 58880V-12 (2005).
[CrossRef]

C. A. Farlow, D. B. Chenault, K. D. Spradley, M. G. Gulley, M. W. Jones, and C. M. Persons, “Imaging polarimeter development and application,” Proc. SPIE 4819, 118–125 (2001).

Craighead, H. G.

Deguzman, P. C.

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, “Diffractive optical element for Stokes vector measurement with a focal plane array,” Proc. SPIE 3754, 169–177 (1999).
[CrossRef]

Deng, X.

J. Wang, F. Walters, X. Liu, P. Sciortino, and X. Deng, “High-performance, large area, deep ultraviolet to infrared polarizers based on 40 nm line/78 nm space nanowire grids,” Appl. Phys. Lett. 90, 611041 (2007).

Engheta, N.

Farlow, C. A.

C. A. Farlow, D. B. Chenault, K. D. Spradley, M. G. Gulley, M. W. Jones, and C. M. Persons, “Imaging polarimeter development and application,” Proc. SPIE 4819, 118–125 (2001).

Fetrow, M. P.

B. M. Ratliff, J. K. Boger, M. P. Fetrow, J. S. Tyo, and W. T. Black, “Image processing methods to compensate for IFOV errors in microgrid imaging polarimeters,” Proc. SPIE 6240, 6240OE (2006).

Fischer, T.

A. Goldberg, T. Fischer, S. Kennerly, S. Wang, M. Sundaram, P. Uppal, M. Winn, G. Milne, and M. Stevens, “Dual band QWIP MWIR/LWIR focal plane array test results,” Proc. SPIE 4028, 276–287 (2000).
[CrossRef]

Gamiz, V. L.

M. E. Roche, D. B. Chenault, J. P. Vaden, A. Lompado, D. Voelz, T. J. Schulz, R. N. Givens, and V. L. Gamiz, “Synthetic aperture imaging polarimeter,” Proc. SPIE 7672, 767206, 767206-12 (2010).
[CrossRef]

Gerhart, G. R.

M. W. Kudenov, L. J. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[CrossRef]

Givens, R. N.

M. E. Roche, D. B. Chenault, J. P. Vaden, A. Lompado, D. Voelz, T. J. Schulz, R. N. Givens, and V. L. Gamiz, “Synthetic aperture imaging polarimeter,” Proc. SPIE 7672, 767206, 767206-12 (2010).
[CrossRef]

Glotzbach, J.

B. K. Gunturk, J. Glotzbach, Y. Altunbasak, R. W. Schafer, and R. M. Mersereau, “Demosaicking: color filter array interpolation,” IEEE Signal Process. Mag. 22(1), 44–54 (2005).
[CrossRef]

Goldberg, A.

A. Goldberg, T. Fischer, S. Kennerly, S. Wang, M. Sundaram, P. Uppal, M. Winn, G. Milne, and M. Stevens, “Dual band QWIP MWIR/LWIR focal plane array test results,” Proc. SPIE 4028, 276–287 (2000).
[CrossRef]

Goldstein, D. L.

Gruev, V.

Gulley, M. G.

C. A. Farlow, D. B. Chenault, K. D. Spradley, M. G. Gulley, M. W. Jones, and C. M. Persons, “Imaging polarimeter development and application,” Proc. SPIE 4819, 118–125 (2001).

Gunturk, B. K.

B. K. Gunturk, J. Glotzbach, Y. Altunbasak, R. W. Schafer, and R. M. Mersereau, “Demosaicking: color filter array interpolation,” IEEE Signal Process. Mag. 22(1), 44–54 (2005).
[CrossRef]

B. K. Gunturk, Y. Altunbasak, and R. M. Mersereau, “Color plane interpolation using alternating projections,” IEEE Trans. Image Process. 11(9), 997–1013 (2002).
[CrossRef] [PubMed]

Guo, L. J.

J. G. Ok, H. J. Park, M. K. Kwak, C. A. Pina-Hernandez, S. H. Ahn, and L. J. Guo, “Continuous patterning of nanogratings by nanochannel-guided lithography on liquid resists,” Adv. Mater. (Deerfield Beach Fla.) 23(38), 4444–4448 (2011).
[CrossRef] [PubMed]

Harnett, C. K.

Hou, H.

H. Hou and H. Andrews, “Cubic splines for image interpolation and digital filtering,” IEEE Trans. Acoust. Speech Signal Process. 26(6), 508–517 (1978).
[CrossRef]

Jones, M.

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, “Diffractive optical element for Stokes vector measurement with a focal plane array,” Proc. SPIE 3754, 169–177 (1999).
[CrossRef]

Jones, M. W.

C. A. Farlow, D. B. Chenault, K. D. Spradley, M. G. Gulley, M. W. Jones, and C. M. Persons, “Imaging polarimeter development and application,” Proc. SPIE 4819, 118–125 (2001).

Käsebier, T.

Kennerly, S.

A. Goldberg, T. Fischer, S. Kennerly, S. Wang, M. Sundaram, P. Uppal, M. Winn, G. Milne, and M. Stevens, “Dual band QWIP MWIR/LWIR focal plane array test results,” Proc. SPIE 4028, 276–287 (2000).
[CrossRef]

Kimmel, R.

R. Kimmel, “Demosaicing: image reconstruction from color CCD samples,” IEEE Trans. Image Process. 8(9), 1221–1228 (1999).
[CrossRef] [PubMed]

Kley, E. B.

Kudenov, M. W.

M. W. Kudenov, L. J. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[CrossRef]

Kwak, M. K.

J. G. Ok, H. J. Park, M. K. Kwak, C. A. Pina-Hernandez, S. H. Ahn, and L. J. Guo, “Continuous patterning of nanogratings by nanochannel-guided lithography on liquid resists,” Adv. Mater. (Deerfield Beach Fla.) 23(38), 4444–4448 (2011).
[CrossRef] [PubMed]

LaCasse, C. F.

Lee, P. H. Y.

J. D. Barter, P. H. Y. Lee, and H. R. Thompson, “Stokes parameter imaging of scattering surfaces,” Proc. SPIE 3121, 314–320 (1997).
[CrossRef]

Liu, X.

J. Wang, F. Walters, X. Liu, P. Sciortino, and X. Deng, “High-performance, large area, deep ultraviolet to infrared polarizers based on 40 nm line/78 nm space nanowire grids,” Appl. Phys. Lett. 90, 611041 (2007).

Lompado, A.

M. E. Roche, D. B. Chenault, J. P. Vaden, A. Lompado, D. Voelz, T. J. Schulz, R. N. Givens, and V. L. Gamiz, “Synthetic aperture imaging polarimeter,” Proc. SPIE 7672, 767206, 767206-12 (2010).
[CrossRef]

Meier, J. T.

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, “Diffractive optical element for Stokes vector measurement with a focal plane array,” Proc. SPIE 3754, 169–177 (1999).
[CrossRef]

Mersereau, R. M.

B. K. Gunturk, J. Glotzbach, Y. Altunbasak, R. W. Schafer, and R. M. Mersereau, “Demosaicking: color filter array interpolation,” IEEE Signal Process. Mag. 22(1), 44–54 (2005).
[CrossRef]

B. K. Gunturk, Y. Altunbasak, and R. M. Mersereau, “Color plane interpolation using alternating projections,” IEEE Trans. Image Process. 11(9), 997–1013 (2002).
[CrossRef] [PubMed]

Milne, G.

A. Goldberg, T. Fischer, S. Kennerly, S. Wang, M. Sundaram, P. Uppal, M. Winn, G. Milne, and M. Stevens, “Dual band QWIP MWIR/LWIR focal plane array test results,” Proc. SPIE 4028, 276–287 (2000).
[CrossRef]

Momeni, M.

M. Momeni and A. H. Titus, “An analog VLSI chip emulating polarization vision of Octopus retina,” IEEE Trans. Neural Netw. 17(1), 222–232 (2006).
[CrossRef] [PubMed]

Nordin, G. P.

G. P. Nordin, J. T. Meier, P. C. Deguzman, and M. Jones, “Diffractive optical element for Stokes vector measurement with a focal plane array,” Proc. SPIE 3754, 169–177 (1999).
[CrossRef]

Ok, J. G.

J. G. Ok, H. J. Park, M. K. Kwak, C. A. Pina-Hernandez, S. H. Ahn, and L. J. Guo, “Continuous patterning of nanogratings by nanochannel-guided lithography on liquid resists,” Adv. Mater. (Deerfield Beach Fla.) 23(38), 4444–4448 (2011).
[CrossRef] [PubMed]

Park, H. J.

J. G. Ok, H. J. Park, M. K. Kwak, C. A. Pina-Hernandez, S. H. Ahn, and L. J. Guo, “Continuous patterning of nanogratings by nanochannel-guided lithography on liquid resists,” Adv. Mater. (Deerfield Beach Fla.) 23(38), 4444–4448 (2011).
[CrossRef] [PubMed]

Perkins, R.

Persons, C. M.

C. A. Farlow, D. B. Chenault, K. D. Spradley, M. G. Gulley, M. W. Jones, and C. M. Persons, “Imaging polarimeter development and application,” Proc. SPIE 4819, 118–125 (2001).

Pezzaniti, J. L.

J. L. Pezzaniti and D. B. Chenault, “A division of aperture MWIR imaging polarimeter,” Proc. SPIE 5888, 58880V, 58880V-12 (2005).
[CrossRef]

Pezzaniti, L. J.

M. W. Kudenov, L. J. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[CrossRef]

Pina-Hernandez, C. A.

J. G. Ok, H. J. Park, M. K. Kwak, C. A. Pina-Hernandez, S. H. Ahn, and L. J. Guo, “Continuous patterning of nanogratings by nanochannel-guided lithography on liquid resists,” Adv. Mater. (Deerfield Beach Fla.) 23(38), 4444–4448 (2011).
[CrossRef] [PubMed]

Powell, S.

T. York, S. Powell, and V. Gruev, “A comparison of polarization image processing across different platforms,” Proc. SPIE 8160, 816004, 816004-7 (2011).
[CrossRef]

Ratliff, B. M.

B. M. Ratliff, C. F. LaCasse, and J. S. Tyo, “Interpolation strategies for reducing IFOV artifacts in microgrid polarimeter imagery,” Opt. Express 17(11), 9112–9125 (2009).
[CrossRef] [PubMed]

B. M. Ratliff, J. K. Boger, M. P. Fetrow, J. S. Tyo, and W. T. Black, “Image processing methods to compensate for IFOV errors in microgrid imaging polarimeters,” Proc. SPIE 6240, 6240OE (2006).

Roche, M. E.

M. E. Roche, D. B. Chenault, J. P. Vaden, A. Lompado, D. Voelz, T. J. Schulz, R. N. Givens, and V. L. Gamiz, “Synthetic aperture imaging polarimeter,” Proc. SPIE 7672, 767206, 767206-12 (2010).
[CrossRef]

Russell, W. S.

W. S. Russell, “Polynomial interpolation schemes for internal derivative distributions on structured grids,” Appl. Numer. Math. 17(2), 129–171 (1995).
[CrossRef]

San Segundo Bello, D.

M. Sarkar, D. San Segundo Bello, C. van Hoof, and A. Theuwissen, “Integrated polarization analyzing CMOS image sensor for material classification,” IEEE Sens. J. 11(8), 1692–1703 (2011).
[CrossRef]

Sarkar, M.

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http://www.kodak.com .

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Figures (8)

Fig. 1
Fig. 1

Block diagram of division of focal plane (a) polarization sensor and (b) color sensor with Bayer pattern filters.

Fig. 2
Fig. 2

A 4 by 4 interpolated block in DoFP polarimeter.

Fig. 3
Fig. 3

Interpolation kernels for weighted bilinear interpolation for: (a) 0° pixel, (b) 45° pixel, (c) 90° pixel, (d) 135° pixel. (e) a 12 pixels neighborhood used for weighted bilinear interpolation.

Fig. 4
Fig. 4

A system of n linear equations is constructed for solving the values of Mi. The value of the newly interpolated curve is computed using Eq. (8).

Fig. 5
Fig. 5

(a) Known 0° intensity value pixels, (b) three directional derivatives.

Fig. 6
Fig. 6

The MTF of S0 for interpolation methods (a) Bilinear, (b) Weighted bilinear, (c) Bicubic, (d) Bicubic spline, (e) The MTF results of S0 along fx = fy.

Fig. 7
Fig. 7

High resolution image representation of the true (a) Intensity, (b) DoLP, (c) AoP and an imaged scene.

Fig. 8
Fig. 8

Comparison of the images of different interpolation methods on the intensity, DoLP and AoP. (a) true polarization, (b) bilinear interpolation, (c) weighted bilinear interpolation, (d) bicubic interpolation, (e) bicubic-spline interpolation with 10 x 10 window, (f) bicubic-spline interpolation.

Tables (1)

Tables Icon

Table 1 The MSE Performance Comparison for the Toy Horse

Equations (19)

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

I 0 p (2,2)= 1 4 [ I 0 (1,1)+ I 0 (1,3)+ I 0 (3,1)+ I 0 (3,3) ]
I 45 p (2,2)= 1 2 [ I 45 (1,2)+ I 45 (3,2) ]
I 135 p (2,2)= 1 2 [ I 135 (2,1)+ I 135 (2,3) ]
I 0 p (1,1)=A* I 0 (3,3)+B* I 0 (1,3)+B* I 0 (3,1)
I 45 p (1,1)=A* I 45 (3,2)+B* I 45 (1,2)+B* I 45 (3,4)
I 90 p (1,1)=A* I 90 (2,2)+B* I 90 (2,4)+B* I 90 (4,2)
I 135 p (1,1)=A* I 135 (2,3)+B* I 135 (2,1)+B* I 135 (4,3)
f i (x)= a i + b i (x x i )+ c i (x x i ) 2 + d i (x x i ) 3
a i =I(i,j)
b i =I(i+1,j)I(i,j) M i+1 M i 6
c i = Mi 2
d i = M i+1 M i 6
M i 4* M i+1 + M i+2 =6( I(i,j)2(i+1,j)+I(i+2,j) )
f i (x,y)= i=0 3 j=0 3 a i j x i y j
I 0 (x,y)=cos(2π f x x+2π f y y)+1
I 45 (x,y)=2*cos(2π f x x+2π f y y)+2
I 90 (x,y)=cos(2π f x x+2π f y y)+1
I 135 (x,y)=0
MSE= 1 MN 1iM 1jN ( I true (i,j) I interpolated (i,j) ) 2

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