Abstract

The Air Force Research Laboratory has developed a new microgrid polarization imaging system capable of simultaneously reconstructing linear Stokes parameter images in two colors on a single focal plane array. In this paper, an effective method for extracting Stokes images is presented for this type of camera system. It is also shown that correlations between the color bands can be exploited to significantly increase overall spatial resolution. Test data is used to show the advantages of this approach over bilinear interpolation. The bounds (in terms of available reconstruction bandwidth) on image resolution are also provided.

© 2011 OSA

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References

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  1. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
    [CrossRef] [PubMed]
  2. J. Schott, Fundamentals of polarimetric remote sensing (SPIE Press, 2009).
    [CrossRef]
  3. D. LeMaster, R. Mack, D. Forrai, J. Harris, B. Ratliff, and J. Middendorf, “A snapshot two-color MWIR polarimetric imaging system,” in “Proceedings of the Military Sensing Symposium (MSS) Specialty Group on Passive Sensors,” (2011).
  4. J. S. Tyo, C. F. LaCasse, and B. M. Ratliff, “Total elimination of sampling errors in polarization imagery obtained with integrated microgrid polarimeters,” Opt. Lett. 34, 3187–3189 (2009).
    [CrossRef] [PubMed]
  5. B. M. Ratliff, C. F. LaCasse, and J. S. Tyo, “Interpolation strategies for reducing IFOV artifacts in microgrid polarimeter imagery,” Opt. Express 17, 9112–9125 (2009).
    [CrossRef] [PubMed]
  6. A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems (Prentice Hall, 1997).
  7. D. LeMaster, “Image reconstruction for two-color microgrid polarimetric imagers,” in “Aerospace conference, 2011 IEEE,” (2011), pp. 1 –7.
  8. J. Tyo, E. Pugh Jr, and N. Engheta, “Colorimetric representations for use with polarization-difference imaging of objects in scattering media,” JOSA A 15, 367–374 (1998).
    [CrossRef]
  9. D. Alleysson, S. Susstrunk, and J. Herault, “Linear demosaicing inspired by the human visual system,” IEEE Trans. Image Processing 14, 439 –449 (2005).
    [CrossRef]
  10. S. T. Thurman and J. R. Fienup, “Wiener reconstruction of undersampled imagery,” J. Opt. Soc. Am. A 26, 283–288 (2009).
    [CrossRef]
  11. E. Dubois, “Frequency-domain methods for demosaicking of bayer-sampled color images,” IEEE Signal Processing Lett. 12, 847 – 850 (2005).
    [CrossRef]

2009 (4)

2006 (1)

2005 (2)

E. Dubois, “Frequency-domain methods for demosaicking of bayer-sampled color images,” IEEE Signal Processing Lett. 12, 847 – 850 (2005).
[CrossRef]

D. Alleysson, S. Susstrunk, and J. Herault, “Linear demosaicing inspired by the human visual system,” IEEE Trans. Image Processing 14, 439 –449 (2005).
[CrossRef]

1998 (1)

J. Tyo, E. Pugh Jr, and N. Engheta, “Colorimetric representations for use with polarization-difference imaging of objects in scattering media,” JOSA A 15, 367–374 (1998).
[CrossRef]

1997 (1)

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems (Prentice Hall, 1997).

Alleysson, D.

D. Alleysson, S. Susstrunk, and J. Herault, “Linear demosaicing inspired by the human visual system,” IEEE Trans. Image Processing 14, 439 –449 (2005).
[CrossRef]

Chenault, D. B.

Dubois, E.

E. Dubois, “Frequency-domain methods for demosaicking of bayer-sampled color images,” IEEE Signal Processing Lett. 12, 847 – 850 (2005).
[CrossRef]

Engheta, N.

J. Tyo, E. Pugh Jr, and N. Engheta, “Colorimetric representations for use with polarization-difference imaging of objects in scattering media,” JOSA A 15, 367–374 (1998).
[CrossRef]

Fienup, J. R.

Goldstein, D. L.

Herault, J.

D. Alleysson, S. Susstrunk, and J. Herault, “Linear demosaicing inspired by the human visual system,” IEEE Trans. Image Processing 14, 439 –449 (2005).
[CrossRef]

LaCasse, C. F.

Nawab, S. H.

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems (Prentice Hall, 1997).

Oppenheim, A. V.

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems (Prentice Hall, 1997).

Pugh Jr, E.

J. Tyo, E. Pugh Jr, and N. Engheta, “Colorimetric representations for use with polarization-difference imaging of objects in scattering media,” JOSA A 15, 367–374 (1998).
[CrossRef]

Ratliff, B. M.

Schott, J.

J. Schott, Fundamentals of polarimetric remote sensing (SPIE Press, 2009).
[CrossRef]

Shaw, J. A.

Susstrunk, S.

D. Alleysson, S. Susstrunk, and J. Herault, “Linear demosaicing inspired by the human visual system,” IEEE Trans. Image Processing 14, 439 –449 (2005).
[CrossRef]

Thurman, S. T.

Tyo, J.

J. Tyo, E. Pugh Jr, and N. Engheta, “Colorimetric representations for use with polarization-difference imaging of objects in scattering media,” JOSA A 15, 367–374 (1998).
[CrossRef]

Tyo, J. S.

Willsky, A. S.

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems (Prentice Hall, 1997).

Appl. Opt. (1)

IEEE Signal Processing Lett. (1)

E. Dubois, “Frequency-domain methods for demosaicking of bayer-sampled color images,” IEEE Signal Processing Lett. 12, 847 – 850 (2005).
[CrossRef]

IEEE Trans. Image Processing (1)

D. Alleysson, S. Susstrunk, and J. Herault, “Linear demosaicing inspired by the human visual system,” IEEE Trans. Image Processing 14, 439 –449 (2005).
[CrossRef]

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

JOSA A (1)

J. Tyo, E. Pugh Jr, and N. Engheta, “Colorimetric representations for use with polarization-difference imaging of objects in scattering media,” JOSA A 15, 367–374 (1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (4)

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems (Prentice Hall, 1997).

D. LeMaster, “Image reconstruction for two-color microgrid polarimetric imagers,” in “Aerospace conference, 2011 IEEE,” (2011), pp. 1 –7.

J. Schott, Fundamentals of polarimetric remote sensing (SPIE Press, 2009).
[CrossRef]

D. LeMaster, R. Mack, D. Forrai, J. Harris, B. Ratliff, and J. Middendorf, “A snapshot two-color MWIR polarimetric imaging system,” in “Proceedings of the Military Sensing Symposium (MSS) Specialty Group on Passive Sensors,” (2011).

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Figures (8)

Fig. 1:
Fig. 1:

The 2-color microgrid array pattern.

Fig. 2:
Fig. 2:

Representation of the DSFT spectrum for one and two-color microgrid imagers

Fig. 3:
Fig. 3:

Discrete space Fourier spectra of the target scene.

Fig. 4:
Fig. 4:

Cross-sections of the filters used throughout this example.

Fig. 5:
Fig. 5:

Reconstruction results for S 0.

Fig. 6:
Fig. 6:

Reconstruction results for S 1.

Fig. 7:
Fig. 7:

Reconstruction results for S 2.

Fig. 8:
Fig. 8:

Color mapped examples using the technique in [8].

Tables (2)

Tables Icon

Table 1: Reconstruction filter matrix

Tables Icon

Table 2: Normalized RMSE for the various reconstruction techniques

Equations (11)

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S 0 = i H + i V = i 45 + i 45 S 1 = i H i V S 2 = i 45 i 45 .
I ( m , n ) = 1 2 S 0 ( m , n ) + 1 4 cos ( π m ) [ S 1 ( m , n ) + S 2 ( m , n ) ] + 1 4 cos ( π n ) [ S 1 ( m , n ) S 2 ( m , n ) ] ,
Ĩ ( ξ , η ) = 1 2 S ˜ 0 ( ξ , η ) + π 4 [ S ˜ 1 ( ξ π , η ) + S ˜ 2 ( ξ π , η ) ] + π 4 [ S ˜ 1 ( ξ , η π ) S ˜ 2 ( ξ , η π ) ] ,
M x ( m , n ) = I x ( m , n ) C x ( m , n ) ,
C x ( m , n ) = 1 2 + ( 1 ) ( 1 + x ) 2 [ cos ( π 2 ( m n ) ) + sin ( π 2 ( m + n ) ) ] ,
M ˜ x ( ξ , η ) = 1 2 Ĩ x ( ξ , η ) + R ˜ x ( ξ , η ) ,
R ˜ x ( ξ , η ) = ( - 1 ) ( 1 + x ) 4 [ Ĩ x ( ξ - π 2 , η + π 2 ) + Ĩ x ( ξ + π 2 , η - π 2 ) - j Ĩ x ( ξ - π 2 , η - π 2 ) + - j Ĩ x ( ξ + π 2 , η + π 2 ) ] .
r S 0 + r S 1 ± S 2 < π 2 ,
r S 0 + r max < π 2 2
r S 1 ± S 2 + r max < π 2 2 .
M ˜ ( ξ , η ) = 1 2 [ Ĩ 1 ( ξ , η ) + Ĩ 2 ( ξ , η ) ] + R ˜ 1 ( ξ , η ) + R ˜ 2 ( ξ , η ) ,

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