Abstract

LWIR imaging arrays are often affected by nonresponsive pixels, or “dead pixels.” These dead pixels can severely degrade the quality of imagery and often have to be replaced before subsequent image processing and display of the imagery data. For LWIR arrays that are integrated with arrays of micropolarizers, the problem of dead pixels is amplified. Conventional dead pixel replacement (DPR) strategies cannot be employed since neighboring pixels are of different polarizations. In this paper we present two DPR schemes. The first is a modified nearest-neighbor replacement method. The second is a method based on redundancy in the polarization measurements. We find that the redundancy-based DPR scheme provides an order-of-magnitude better performance for typical LWIR polarimetric data.

© 2007 Optical Society of America

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References

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  1. J. A. Shaw, "Degree of linear polarization in spectral radiances from water-viewing infrared polarimeters," Appl. Opt. 38, 3157-3165 (1999).
    [CrossRef]
  2. R. A. Millikan, "A study of the polarization of the light emitted by incandescnet solid and liquid surfaces. I," Phys. Rev. 3, 81-99 (1895).
  3. R. A. Millikan, "A study of the polarization of the light emitted by incandescnet solid and liquid surfaces. II," Phys. Rev. 3, 177-192 (1895).
  4. O. Sandus, "A review of emission polarization," Appl. Opt. 4, 1634-1642 (1965).
    [CrossRef]
  5. T. J. Rogne, "Passive detection using polarized components of infrared signatures," Proc. SPIE 1317, 242 - 251 (1990).
  6. J. S. Tyo, D. H. Goldstein, D. B. Chenault, and J. A. Shaw, "Review of passive imaging polarimetry for remote sensing applications," Appl. Opt. 45, 5453 - 5469 (2006). and references therein.
    [CrossRef] [PubMed]
  7. A. G. Andreou and Z. K. Kalayjian, "Polarization imaging: principles and integrated polarimeters," IEEE Sens. J. 2, 566 - 576 (2002).
    [CrossRef]
  8. D. L. Perry and E. L. Dereniak, "Linear theory of nonuniformity correction in infrared staring sensors," Opt. Eng. 32, 1854-1859 (1993).
    [CrossRef]
  9. R. Walraven, "Polarization Imagery," Opt. Eng. 20, 14 - 18 (1981).
  10. J. S. Tyo, "Optimum linear combination strategy for an N-channel polarization sensitive vision or imaging system," J. Opt. Soc. Am. A 15, 359-366 (1998).
    [CrossRef]
  11. J. S. Tyo, "Design of optimal polarimers: maximization of SNR and minimization of systematic errors," Appl. Opt. 41, 619-630 (2002).
    [CrossRef] [PubMed]
  12. D. S. Sabatke, M. R. Descour, E. Dereniak, W. C. Sweatt, S. A. Kemme, and G. S. Phipps, "Optimization of retardance for a complete Stokes Polarimeter," Opt. Lett. 25, 802-804 (2000).
    [CrossRef]
  13. 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).
  14. J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," Proc. SPIE 5888, 227-238 (2005).
  15. D. Bowers, J. K. Boger, L. D. Wellens, W. T. Black, S. E. Ortega, B. M. Ratliff, M. P. Fetrow, J. E. Hubbs, and J. S. Tyo, "Evaluation and display of polarimetric image data using long-wave cooled microgrid focal plane arrays," Proc. SPIE 6240, 6240OF (2006).
  16. L. B. Wolff, "Polarization camera for computer vision with a beam splitter," J. Opt. Soc. Am. A 11, 2935-2945 (1994).
    [CrossRef]
  17. 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).

2006 (1)

2005 (1)

J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," Proc. SPIE 5888, 227-238 (2005).

2002 (2)

J. S. Tyo, "Design of optimal polarimers: maximization of SNR and minimization of systematic errors," Appl. Opt. 41, 619-630 (2002).
[CrossRef] [PubMed]

A. G. Andreou and Z. K. Kalayjian, "Polarization imaging: principles and integrated polarimeters," IEEE Sens. J. 2, 566 - 576 (2002).
[CrossRef]

2000 (1)

1999 (2)

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).

J. A. Shaw, "Degree of linear polarization in spectral radiances from water-viewing infrared polarimeters," Appl. Opt. 38, 3157-3165 (1999).
[CrossRef]

1998 (1)

1994 (1)

1993 (1)

D. L. Perry and E. L. Dereniak, "Linear theory of nonuniformity correction in infrared staring sensors," Opt. Eng. 32, 1854-1859 (1993).
[CrossRef]

1990 (1)

T. J. Rogne, "Passive detection using polarized components of infrared signatures," Proc. SPIE 1317, 242 - 251 (1990).

1981 (1)

R. Walraven, "Polarization Imagery," Opt. Eng. 20, 14 - 18 (1981).

1965 (1)

1895 (2)

R. A. Millikan, "A study of the polarization of the light emitted by incandescnet solid and liquid surfaces. I," Phys. Rev. 3, 81-99 (1895).

R. A. Millikan, "A study of the polarization of the light emitted by incandescnet solid and liquid surfaces. II," Phys. Rev. 3, 177-192 (1895).

Andreou, A. G.

A. G. Andreou and Z. K. Kalayjian, "Polarization imaging: principles and integrated polarimeters," IEEE Sens. J. 2, 566 - 576 (2002).
[CrossRef]

Black, W.

J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," Proc. SPIE 5888, 227-238 (2005).

Boger, J. K.

J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," Proc. SPIE 5888, 227-238 (2005).

Chenault, D. B.

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).

Dereniak, E.

Dereniak, E. L.

D. L. Perry and E. L. Dereniak, "Linear theory of nonuniformity correction in infrared staring sensors," Opt. Eng. 32, 1854-1859 (1993).
[CrossRef]

Descour, M. R.

Fetrow, M. P.

J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," Proc. SPIE 5888, 227-238 (2005).

Goldstein, D. H.

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).

Kalayjian, Z. K.

A. G. Andreou and Z. K. Kalayjian, "Polarization imaging: principles and integrated polarimeters," IEEE Sens. J. 2, 566 - 576 (2002).
[CrossRef]

Kemme, S. A.

Kumar, R.

J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," Proc. SPIE 5888, 227-238 (2005).

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).

Millikan, R. A.

R. A. Millikan, "A study of the polarization of the light emitted by incandescnet solid and liquid surfaces. I," Phys. Rev. 3, 81-99 (1895).

R. A. Millikan, "A study of the polarization of the light emitted by incandescnet solid and liquid surfaces. II," Phys. Rev. 3, 177-192 (1895).

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).

Perry, D. L.

D. L. Perry and E. L. Dereniak, "Linear theory of nonuniformity correction in infrared staring sensors," Opt. Eng. 32, 1854-1859 (1993).
[CrossRef]

Phipps, G. S.

Ratliff, B. M.

J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," Proc. SPIE 5888, 227-238 (2005).

Rogne, T. J.

T. J. Rogne, "Passive detection using polarized components of infrared signatures," Proc. SPIE 1317, 242 - 251 (1990).

Sabatke, D. S.

Sandus, O.

Shaw, J. A.

Sweatt, W. C.

Tyo, J. S.

Walraven, R.

R. Walraven, "Polarization Imagery," Opt. Eng. 20, 14 - 18 (1981).

Wolff, L. B.

Appl. Opt. (4)

IEEE Sens. J. (1)

A. G. Andreou and Z. K. Kalayjian, "Polarization imaging: principles and integrated polarimeters," IEEE Sens. J. 2, 566 - 576 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (2)

D. L. Perry and E. L. Dereniak, "Linear theory of nonuniformity correction in infrared staring sensors," Opt. Eng. 32, 1854-1859 (1993).
[CrossRef]

R. Walraven, "Polarization Imagery," Opt. Eng. 20, 14 - 18 (1981).

Opt. Lett. (1)

Phys. Rev. (2)

R. A. Millikan, "A study of the polarization of the light emitted by incandescnet solid and liquid surfaces. I," Phys. Rev. 3, 81-99 (1895).

R. A. Millikan, "A study of the polarization of the light emitted by incandescnet solid and liquid surfaces. II," Phys. Rev. 3, 177-192 (1895).

Proc. SPIE (3)

T. J. Rogne, "Passive detection using polarized components of infrared signatures," Proc. SPIE 1317, 242 - 251 (1990).

J. K. Boger, J. S. Tyo, B. M. Ratliff, M. P. Fetrow, W. Black, and R. Kumar, "Modeling precision and acuracy of a LWIR microgrid array imaging polarimeter," Proc. SPIE 5888, 227-238 (2005).

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).

Other (2)

D. Bowers, J. K. Boger, L. D. Wellens, W. T. Black, S. E. Ortega, B. M. Ratliff, M. P. Fetrow, J. E. Hubbs, and J. S. Tyo, "Evaluation and display of polarimetric image data using long-wave cooled microgrid focal plane arrays," Proc. SPIE 6240, 6240OF (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).

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Figures (11)

Fig. 1.
Fig. 1.

Layout of the microgrid FPA depicting the 2 × 2 superpixels that contain all four micro-polarizer orientations.

Fig. 2.
Fig. 2.

Candidate pixels used for replacement of a dead pixel in the nearest like-polarization neighbor (NLPN) replacement scheme. The darker blue pixels are chosen first because they have the closest Euclidean distance to the dead pixel. The algorithm will select pixels farther away only when the closest ones are themselves dead.

Fig. 3.
Fig. 3.

Example cases illustrating when RE can/cannot estimate the value of a given dead pixel (indicated with an “x”). The requirement is that there be at least one good neighboring pixel from each of the three polarizer orientations opposite the dead pixel’s.

Fig. 4.
Fig. 4.

Sample dead pixel patterns and the iteration that the dead pixel is replaced under the RE DPR scheme.

Fig. 5.
Fig. 5.

Test images: (a) raw uncalibrated microgrid image; (b) image after multi-point calibration but before dead pixel replacement. The red-outlined regions are sub-images that are investigated in greater detail below.

Fig. 6.
Fig. 6.

Dead pixel map for the sensor.

Fig. 7.
Fig. 7.

Regions of the multi-point calibrated image of Fig. 5.b: (a) Image region (1,200)×(230,430) and (b) image region (401,590)×(351,480).

Fig. 8.
Fig. 8.

The multi-point calibrated image of Fig. 5.b after application of the (a) NLPN and (b) RE replacement schemes.

Fig. 9.
Fig. 9.

Zoomed regions of the NLPN and RE corrected images of Fig. 8: (a) NLPN and (b) RE image region (1,200)×(230,430); (c) NLPN and (d) RE image region (401,590)×(351,480).

Fig. 10.
Fig. 10.

Histogram of the relative error of the replaced pixels using the two methods discussed in this paper. The relative error was computed by replacing good pixels with the values predicted using the NLPN and RE schemes, then comparing to the actual value at that pixel.

Fig. 11.
Fig. 11.

Zoomed regions of the DoLP images computed using the no-interpolation method from the NLPN and RE corrected images of Fig. 8: (a) NLPN and (b) RE DoLP image region (1,200)×(230,430); (c) NLPN and (d) RE DoLP image region (401,590)×(351,480).

Tables (1)

Tables Icon

Table 1. Statistics of the normalized error of the DPR schemes.

Equations (14)

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S ̂ = [ s ̂ 0 s ̂ 1 s ̂ 2 ] = [ 1 2 ( I 0 + I 90 + I 45 + I 135 ) I 0 I 90 I 45 I 135 ] ,
M LP = 1 2 [ A B cos D B sin D 0 B cos D A cos 2 D + C sin 2 D ( A C ) sin D cos D 0 B sin D ( A C ) sin D cos D A sin 2 D + C cos 2 D 0 0 0 0 2 C ]
M 0 = 1 2 [ 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ] M 45 = 1 2 [ 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 ]
M 90 = 1 2 [ 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ] M 135 = 1 2 [ 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 ] .
I 0 = 1 2 ( s ̂ 0 + s ̂ 1 ) ; I 45 = 1 2 ( s ̂ 0 + s ̂ 2 )
I 90 = 1 2 ( s ̂ 0 s ̂ 1 ) ; I 135 = 1 2 ( s ̂ 0 s ̂ 2 ) .
s ̂ 0 = I 0 + I 90 ; s ̂ 0 = I 45 + I 135
s ̂ 1 = I 0 I 90 ; s ̂ 0 = 2 I 0 I 45 I 135 ; s ̂ 1 = I 45 2 I 90 + I 135
s ̂ 2 = I 45 I 135 ; s ̂ 2 = 2 I 45 I 0 I 90 ; s ̂ 2 = I 0 2 I 45 + I 90 .
I ¯ 0 = I 45 I 90 + I 135 ; I ¯ 45 = I 0 + I 90 I 135
I ¯ 90 = I 0 + I 45 + I 135 ; I ¯ 135 = I 0 I 45 + I 90 .
s ̂ 1 = I ¯ 0 I 90
= I 45 + I 135 2 I 90
= s ̂ 0 2 I 90 ,

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