Abstract

A generalization of a recently developed algebraic scene-based nonuniformity correction algorithm for focal plane array (FPA) sensors is presented. The new technique uses pairs of image frames exhibiting arbitrary one- or two-dimensional translational motion to compute compensator quantities that are then used to remove nonuniformity in the bias of the FPA response. Unlike its predecessor, the generalization does not require the use of either a blackbody calibration target or a shutter. The algorithm has a low computational overhead, lending itself to real-time hardware implementation. The high-quality correction ability of this technique is demonstrated through application to real IR data from both cooled and uncooled infrared FPAs. A theoretical and experimental error analysis is performed to study the accuracy of the bias compensator estimates in the presence of two main sources of error.

© 2005 Optical Society of America

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References

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  1. G. C. Holst, CCD Arrays, Cameras, and Displays (SPIE Optical Engineering Press, Bellingham, Wash., 1996).
  2. A. F. Milton, F. R. Barone, M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. (Bellingham) 24, 855–862 (1985).
    [CrossRef]
  3. D. L. Perry, E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. (Bellingham) 32, 1853–1859 (1993).
    [CrossRef]
  4. P. M. Narendra, “Reference-free nonuniformity compensation for IR imaging arrays,” in Smart Sensors II, D. F. Barbe, ed., Proc. SPIE252, 10–17 (1980).
    [CrossRef]
  5. P. M. Narendra, N. A. Foss, “Shutterless fixed pattern noise correction for infrared imaging arrays,” in Technical Issues in Focal Plane Development, W. S. Chan, E. Krikorian, eds., Proc. SPIE282, 44–51 (1981).
    [CrossRef]
  6. J. G. Harris, “Continuous-time calibration of VLSI sensors for gain and offset variations,” in Smart Focal Plane Arrays and Focal Plane Array Testing, M. Wigdor, M. A. Massie, eds., Proc. SPIE2474, 23–33 (1995).
    [CrossRef]
  7. J. G. Harris, Y. M. Chiang, “Nonuniformity correction using constant average statistics constraint: analog and digital implementations,” in Infrared Technology and Applications XXIII, B. F. Andersen, M. Strojnik, eds., Proc. SPIE3061, 895–905 (1997).
    [CrossRef]
  8. M. M. Hayat, S. N. Torres, E. E. Armstrong, B. Yasuda, “Statistical algorithm for non-uniformity correction in focal-plane arrays,” Appl. Opt. 38, 772–780 (1999).
    [CrossRef]
  9. S. N. Torres, M. M. Hayat, “Kalman filtering for adaptive nonuniformity correction in infrared focal plane arrays,” J. Opt. Soc. Am. A 20, 470–480 (2003).
    [CrossRef]
  10. W. F. O’Neil, “Dithered scan detector compensation,” in Proceedings of the 1993 International Meeting of the Infrared Information Symposium Specialty Group on Passive Sensors (Infrared Information Analysis Center, Ann Arbor, Mich., 1993).
  11. W. F. O’Neil, “Experimental verification of dithered scan nonuniformity correction,” in Proceedings of the 1996 International Meeting of the Infrared Information Symposium Specialty Group on Passive Sensors (Infrared Information Analysis Center, Ann Arbor, Mich., 1997), Vol. 1, pp. 329–339.
  12. W. F. O’Neil, “Dither image scanner with compensation for individual detector response and gain,” U.S. Patent No.5,514,865.
  13. R. C. Hardie, M. M. Hayat, E. E. Armstrong, B. Yasuda, “Scene-based nonuniformity correction using video sequences and registration,” Appl. Opt. 39, 1241–1250 (2000).
    [CrossRef]
  14. B. M. Ratliff, M. M. Hayat, R. C. Hardie, “An algebraic algorithm for nonuniformity correction in focal-plane arrays,” J. Opt. Soc. Am. A 19, 1737–1747 (2002).
    [CrossRef]
  15. B. M. Ratliff, M. M. Hayat, J. S. Tyo, “Radiometrically accurate scene-based nonuniformity correction for array sensors,” J. Opt. Soc. Am. A 20, 1890–1899 (2003).
    [CrossRef]
  16. R. C. Hardie, K. J. Barnard, J. G. Bognar, E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. (Bellingham) 37, 247–260 (1998).
    [CrossRef]

2003

2002

2000

1999

1998

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. (Bellingham) 37, 247–260 (1998).
[CrossRef]

1993

D. L. Perry, E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. (Bellingham) 32, 1853–1859 (1993).
[CrossRef]

1985

A. F. Milton, F. R. Barone, M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. (Bellingham) 24, 855–862 (1985).
[CrossRef]

Armstrong, E. E.

Barnard, K. J.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. (Bellingham) 37, 247–260 (1998).
[CrossRef]

Barone, F. R.

A. F. Milton, F. R. Barone, M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. (Bellingham) 24, 855–862 (1985).
[CrossRef]

Bognar, J. G.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. (Bellingham) 37, 247–260 (1998).
[CrossRef]

Chiang, Y. M.

J. G. Harris, Y. M. Chiang, “Nonuniformity correction using constant average statistics constraint: analog and digital implementations,” in Infrared Technology and Applications XXIII, B. F. Andersen, M. Strojnik, eds., Proc. SPIE3061, 895–905 (1997).
[CrossRef]

Dereniak, E. L.

D. L. Perry, E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. (Bellingham) 32, 1853–1859 (1993).
[CrossRef]

Foss, N. A.

P. M. Narendra, N. A. Foss, “Shutterless fixed pattern noise correction for infrared imaging arrays,” in Technical Issues in Focal Plane Development, W. S. Chan, E. Krikorian, eds., Proc. SPIE282, 44–51 (1981).
[CrossRef]

Hardie, R. C.

B. M. Ratliff, M. M. Hayat, R. C. Hardie, “An algebraic algorithm for nonuniformity correction in focal-plane arrays,” J. Opt. Soc. Am. A 19, 1737–1747 (2002).
[CrossRef]

R. C. Hardie, M. M. Hayat, E. E. Armstrong, B. Yasuda, “Scene-based nonuniformity correction using video sequences and registration,” Appl. Opt. 39, 1241–1250 (2000).
[CrossRef]

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. (Bellingham) 37, 247–260 (1998).
[CrossRef]

Harris, J. G.

J. G. Harris, Y. M. Chiang, “Nonuniformity correction using constant average statistics constraint: analog and digital implementations,” in Infrared Technology and Applications XXIII, B. F. Andersen, M. Strojnik, eds., Proc. SPIE3061, 895–905 (1997).
[CrossRef]

J. G. Harris, “Continuous-time calibration of VLSI sensors for gain and offset variations,” in Smart Focal Plane Arrays and Focal Plane Array Testing, M. Wigdor, M. A. Massie, eds., Proc. SPIE2474, 23–33 (1995).
[CrossRef]

Hayat, M. M.

Holst, G. C.

G. C. Holst, CCD Arrays, Cameras, and Displays (SPIE Optical Engineering Press, Bellingham, Wash., 1996).

Kruer, M. R.

A. F. Milton, F. R. Barone, M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. (Bellingham) 24, 855–862 (1985).
[CrossRef]

Milton, A. F.

A. F. Milton, F. R. Barone, M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. (Bellingham) 24, 855–862 (1985).
[CrossRef]

Narendra, P. M.

P. M. Narendra, “Reference-free nonuniformity compensation for IR imaging arrays,” in Smart Sensors II, D. F. Barbe, ed., Proc. SPIE252, 10–17 (1980).
[CrossRef]

P. M. Narendra, N. A. Foss, “Shutterless fixed pattern noise correction for infrared imaging arrays,” in Technical Issues in Focal Plane Development, W. S. Chan, E. Krikorian, eds., Proc. SPIE282, 44–51 (1981).
[CrossRef]

O’Neil, W. F.

W. F. O’Neil, “Dither image scanner with compensation for individual detector response and gain,” U.S. Patent No.5,514,865.

W. F. O’Neil, “Dithered scan detector compensation,” in Proceedings of the 1993 International Meeting of the Infrared Information Symposium Specialty Group on Passive Sensors (Infrared Information Analysis Center, Ann Arbor, Mich., 1993).

W. F. O’Neil, “Experimental verification of dithered scan nonuniformity correction,” in Proceedings of the 1996 International Meeting of the Infrared Information Symposium Specialty Group on Passive Sensors (Infrared Information Analysis Center, Ann Arbor, Mich., 1997), Vol. 1, pp. 329–339.

Perry, D. L.

D. L. Perry, E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. (Bellingham) 32, 1853–1859 (1993).
[CrossRef]

Ratliff, B. M.

Torres, S. N.

Tyo, J. S.

Watson, E. A.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. (Bellingham) 37, 247–260 (1998).
[CrossRef]

Yasuda, B.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng. (Bellingham)

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. (Bellingham) 37, 247–260 (1998).
[CrossRef]

A. F. Milton, F. R. Barone, M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. (Bellingham) 24, 855–862 (1985).
[CrossRef]

D. L. Perry, E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. (Bellingham) 32, 1853–1859 (1993).
[CrossRef]

Other

P. M. Narendra, “Reference-free nonuniformity compensation for IR imaging arrays,” in Smart Sensors II, D. F. Barbe, ed., Proc. SPIE252, 10–17 (1980).
[CrossRef]

P. M. Narendra, N. A. Foss, “Shutterless fixed pattern noise correction for infrared imaging arrays,” in Technical Issues in Focal Plane Development, W. S. Chan, E. Krikorian, eds., Proc. SPIE282, 44–51 (1981).
[CrossRef]

J. G. Harris, “Continuous-time calibration of VLSI sensors for gain and offset variations,” in Smart Focal Plane Arrays and Focal Plane Array Testing, M. Wigdor, M. A. Massie, eds., Proc. SPIE2474, 23–33 (1995).
[CrossRef]

J. G. Harris, Y. M. Chiang, “Nonuniformity correction using constant average statistics constraint: analog and digital implementations,” in Infrared Technology and Applications XXIII, B. F. Andersen, M. Strojnik, eds., Proc. SPIE3061, 895–905 (1997).
[CrossRef]

W. F. O’Neil, “Dithered scan detector compensation,” in Proceedings of the 1993 International Meeting of the Infrared Information Symposium Specialty Group on Passive Sensors (Infrared Information Analysis Center, Ann Arbor, Mich., 1993).

W. F. O’Neil, “Experimental verification of dithered scan nonuniformity correction,” in Proceedings of the 1996 International Meeting of the Infrared Information Symposium Specialty Group on Passive Sensors (Infrared Information Analysis Center, Ann Arbor, Mich., 1997), Vol. 1, pp. 329–339.

W. F. O’Neil, “Dither image scanner with compensation for individual detector response and gain,” U.S. Patent No.5,514,865.

G. C. Holst, CCD Arrays, Cameras, and Displays (SPIE Optical Engineering Press, Bellingham, Wash., 1996).

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Figures (6)

Fig. 1
Fig. 1

(a) Depiction of the bilinear signal interpolation model for the case of subpixel 2D motion. The shaded pixels represent the interpolated signal value at time k+1. (b) Representation of the recursive operation of the algorithm. The pixel partitions in bold outline correspond to each Gl, representing the group of detectors whose biases are estimated iteratively in l. The arrows indicate the direction of algorithm iteration within each Gl.

Fig. 2
Fig. 2

Image frame 325 from data set 1: (a) raw image, (b) after correction by the ASBA, (c) after correction by the RASBA, (d) after correction by the GASBA. All images are statistically scaled to the same dynamic range.

Fig. 3
Fig. 3

Imagery from data set 2: (a) raw image frame 320, (b) image frame 320 after correction by the GASBA. Imagery from data set 3: (c) raw image frame 585, (d) image frame 585 after correction by the GASBA. All images are statistically scaled to the same dynamic range.

Fig. 4
Fig. 4

Propagation of error: (a) subpixel 1D motion case for a shift of (0, 0.5), (b) superpixel 1D motion case for a shift of (0, 1.5), (c) frame 1 of the test pattern image pair (the bright pixels indicate the nonzero values used to introduce residual nonuniformity and bilinear-interpolation error), (d) plot of column 64 for the images in (a) and (b).

Fig. 5
Fig. 5

Propagation of error: (a) subpixel 2D motion case for a shift of (0.5, 0.5), (b) superpixel 2D motion case for a shift of (1.5, 1.5), (c) frame 1 of the second test pattern image (the bright pixels indicate the nonzero values used to introduce residual nonuniformity and bilinear-interpolation error), (d) plot of the diagonal elements ck(i, i), i=1,2,,128, for the images in (a) and (b).

Fig. 6
Fig. 6

(a) Image frame 119 from data set 1 after correction by the GASBA, (b) bias compensator estimates produced from the correction of frames 119 and 120 (linearly scaled to the full dynamic range), (c) bias compensator estimates after averaging 112 estimate matrices, (d) plot showing the mean and the variance of the bias compensator estimates as a function of the number of estimates in the average.

Equations (17)

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yk(i, j)=zk(i, j)+b(i, j),
zˆk+1(i, j)=γ1,kzk(i-αk-1, j-βk-1)+γ2,kzk(i-αk, j-βk-1)+γ3,kzk(i-αk-1, j-βk)+γ4,kzk(i-αk, j-βk).
yk+1(i, j)=γ1,kzk(i-αk-1, j-βk-1)+γ2,kzk(i-αk, j-βk-1)+γ3,kzk(i-αk-1, j-βk)+γ4,kzk(i-αk, j-βk)+b(i, j).
Δk(i, j)=γ1,kyk(i-αk-1, j-βk-1)+γ2,kyk(i-αk, j-βk-1)+γ3,kyk(i-αk-1, j-βk)+γ4,kyk(i-αk, j-βk)-yk+1(i, j).
Δk(i, j)=γ1,kb(i-αk-1, j-βk-1)+γ2,kb(i-αk, j-βk-1)+γ3,kb(i-αk-1, j-βk)+γ4,kb(i-αk, j-βk)-b(i, j).
ck(i, j)=Δk(i, j)+γ1,kck(i-αk-1, j-βk-1)+γ2,kck(i-αk, j-βk-1)+γ3,kck(i-αk-1, j-βk)+γ4,kck(i-αk, j-βk).
Δk(2+αk, 2+βk)=γ1,kb+γ2,kb+γ3,kb+γ4,kb-b(2+αk, 2+βk).
Δk(2+αk, 2+βk)=b-b(2+αk, 2+βk).
BI,k(i, j)=zk+1(i, j)-zˆk+1(i, j),
cASBA(i, j)=b-b(i, j)+RN(i, j).
ck(i, j)=b-b(i, j)+ck(i, j)
Δk(i, j)=γ1,kRN(i-αk-1, j-βk-1)+γ2,kRN(i-αk, j-βk-1)+γ3,kRN(i-αk-1, j-βk)+γ4,kRN(i-αk, j-βk)+BI,k(i, j).
ck(i, j)=-1|Δαk| m=2i Δk(m, j).
ck(i, j)=-m=2+αki l=0i-m Δk(m, j)(-|Δαk|)l.
ck(i, j)=-m=2i n=2j l=0min(p,q) A(p, q, l)Δk(m, n)×γ1,klγ2,kp-lγ3,kq-l(1-γ4,k)p+q-l+1,
A(p, q, l)=(p+q-l)!l![p+q-l-max(p, q)]![max(p, q)-l]!.
ck(i, j)=-m=m0i n=n0nf l=l0lf r=r0lf (-1)-(l0+r0)×B(p, q, l, r)Δk(m, n)(-|Δβk|)l(-|Δαk|)r,

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