Abstract

The principal component analysis is used to identify and quantify spatial distributions of relative photoresponse as a function of the exposure time for a visible CCD array. The analysis shows a simple way to define an invariant photoresponse nonuniformity and compare it with the definition of this invariant pattern as the one obtained for long exposure times. Experimental data of radiant exposure from levels of irradiance obtained in a stable and well-controlled environment are used.

© 2007 Optical Society of America

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References

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  1. G. C. Holst, CCD Arrays, Cameras and Displays (SPIE Press, 1998), pp. 102-145.
  2. A. F. Milton, F. R. Barone, and M. R. Kruer, "Influence of nonuniformity on infrared focal plane array," Opt. Eng. 24, 855-862 (1985).
  3. M. Schulz and L. Caldwell, "Nonuniformity correction and correctability of infrared focal plane arrays," Infrared Phys. Technol. 36, 763-777 (1995).
    [CrossRef]
  4. D. L. Perry and E. L. Dereniak, "Linear theory of nonuniformity correction infrared staring sensors," Opt. Eng. 32, 1854-1859 (1993).
    [CrossRef]
  5. H. Zhou, R. Lai, S. Liu, and G. Jiang, "New improved correction for infrared focal plane arrays," Opt. Commun. 245, 49-53 (2004).
    [CrossRef]
  6. A. Ferrero, J. Campos, and A. Pons, "Nonuniformity correction procedure for matrix detectors based on the prior compensation of its nonlinear behavior," Appl. Opt. 45, 2422-2427, (2006).
    [CrossRef] [PubMed]
  7. J. M. López-Alonso, J. Alda, and E. Bernabéu, Principal-component characterization of noise for infrared images," Appl. Opt. 41, 320-331, (2002).
    [CrossRef] [PubMed]
  8. J. M. López-Alonso and J. Alda, "Characterization of artifacts in fully-digital image-acquisition systems: Application to web cameras," Opt. Eng. 43, 257-265 (2004).
    [CrossRef]
  9. A. Ferrero, J. Campos, and A. Pons, "Apparent violation of the radiant exposure reciprocity law in interline CCDs," Appl. Opt. 45, 3991-3997 (2006).
    [CrossRef] [PubMed]
  10. Commission Internationale de l'Eclairage, International Lighting Vocabulary, CIE Publication 17.4 (1987).
  11. D. F. Morrison, Multivariate Statistical Methods, 3rd ed. (McGraw-Hill, 1990), Chap. 8.
  12. B. R. Frieden, Probability, Statistical Optics, and Data Testing, 3rd ed. (Springer Verlag, 2001), Chap. 3.
    [CrossRef]

2006 (2)

2004 (2)

J. M. López-Alonso and J. Alda, "Characterization of artifacts in fully-digital image-acquisition systems: Application to web cameras," Opt. Eng. 43, 257-265 (2004).
[CrossRef]

H. Zhou, R. Lai, S. Liu, and G. Jiang, "New improved correction for infrared focal plane arrays," Opt. Commun. 245, 49-53 (2004).
[CrossRef]

2002 (1)

1995 (1)

M. Schulz and L. Caldwell, "Nonuniformity correction and correctability of infrared focal plane arrays," Infrared Phys. Technol. 36, 763-777 (1995).
[CrossRef]

1993 (1)

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

1985 (1)

A. F. Milton, F. R. Barone, and M. R. Kruer, "Influence of nonuniformity on infrared focal plane array," Opt. Eng. 24, 855-862 (1985).

Alda, J.

J. M. López-Alonso and J. Alda, "Characterization of artifacts in fully-digital image-acquisition systems: Application to web cameras," Opt. Eng. 43, 257-265 (2004).
[CrossRef]

J. M. López-Alonso, J. Alda, and E. Bernabéu, Principal-component characterization of noise for infrared images," Appl. Opt. 41, 320-331, (2002).
[CrossRef] [PubMed]

Barone, F. R.

A. F. Milton, F. R. Barone, and M. R. Kruer, "Influence of nonuniformity on infrared focal plane array," Opt. Eng. 24, 855-862 (1985).

Bernabéu, E.

Caldwell, L.

M. Schulz and L. Caldwell, "Nonuniformity correction and correctability of infrared focal plane arrays," Infrared Phys. Technol. 36, 763-777 (1995).
[CrossRef]

Campos, J.

Dereniak, E. L.

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

Ferrero, A.

Frieden, B. R.

B. R. Frieden, Probability, Statistical Optics, and Data Testing, 3rd ed. (Springer Verlag, 2001), Chap. 3.
[CrossRef]

Holst, G. C.

G. C. Holst, CCD Arrays, Cameras and Displays (SPIE Press, 1998), pp. 102-145.

Jiang, G.

H. Zhou, R. Lai, S. Liu, and G. Jiang, "New improved correction for infrared focal plane arrays," Opt. Commun. 245, 49-53 (2004).
[CrossRef]

Kruer, M. R.

A. F. Milton, F. R. Barone, and M. R. Kruer, "Influence of nonuniformity on infrared focal plane array," Opt. Eng. 24, 855-862 (1985).

Lai, R.

H. Zhou, R. Lai, S. Liu, and G. Jiang, "New improved correction for infrared focal plane arrays," Opt. Commun. 245, 49-53 (2004).
[CrossRef]

Liu, S.

H. Zhou, R. Lai, S. Liu, and G. Jiang, "New improved correction for infrared focal plane arrays," Opt. Commun. 245, 49-53 (2004).
[CrossRef]

López-Alonso, J. M.

J. M. López-Alonso and J. Alda, "Characterization of artifacts in fully-digital image-acquisition systems: Application to web cameras," Opt. Eng. 43, 257-265 (2004).
[CrossRef]

J. M. López-Alonso, J. Alda, and E. Bernabéu, Principal-component characterization of noise for infrared images," Appl. Opt. 41, 320-331, (2002).
[CrossRef] [PubMed]

Milton, A. F.

A. F. Milton, F. R. Barone, and M. R. Kruer, "Influence of nonuniformity on infrared focal plane array," Opt. Eng. 24, 855-862 (1985).

Morrison, D. F.

D. F. Morrison, Multivariate Statistical Methods, 3rd ed. (McGraw-Hill, 1990), Chap. 8.

Perry, D. L.

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

Pons, A.

Schulz, M.

M. Schulz and L. Caldwell, "Nonuniformity correction and correctability of infrared focal plane arrays," Infrared Phys. Technol. 36, 763-777 (1995).
[CrossRef]

Zhou, H.

H. Zhou, R. Lai, S. Liu, and G. Jiang, "New improved correction for infrared focal plane arrays," Opt. Commun. 245, 49-53 (2004).
[CrossRef]

Appl. Opt. (3)

Infrared Phys. Technol. (1)

M. Schulz and L. Caldwell, "Nonuniformity correction and correctability of infrared focal plane arrays," Infrared Phys. Technol. 36, 763-777 (1995).
[CrossRef]

Opt. Commun. (1)

H. Zhou, R. Lai, S. Liu, and G. Jiang, "New improved correction for infrared focal plane arrays," Opt. Commun. 245, 49-53 (2004).
[CrossRef]

Opt. Eng. (3)

J. M. López-Alonso and J. Alda, "Characterization of artifacts in fully-digital image-acquisition systems: Application to web cameras," Opt. Eng. 43, 257-265 (2004).
[CrossRef]

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

A. F. Milton, F. R. Barone, and M. R. Kruer, "Influence of nonuniformity on infrared focal plane array," Opt. Eng. 24, 855-862 (1985).

Other (4)

G. C. Holst, CCD Arrays, Cameras and Displays (SPIE Press, 1998), pp. 102-145.

Commission Internationale de l'Eclairage, International Lighting Vocabulary, CIE Publication 17.4 (1987).

D. F. Morrison, Multivariate Statistical Methods, 3rd ed. (McGraw-Hill, 1990), Chap. 8.

B. R. Frieden, Probability, Statistical Optics, and Data Testing, 3rd ed. (Springer Verlag, 2001), Chap. 3.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Experimental setup based on an integrating sphere that is illuminated by an argon laser. Power is stabilized before entering the integrating sphere. Also the speckle is canceled by the use of a rotating diffuser. The output port of the integrating sphere illuminates the detector that can be moved back and forth along a rail. The output of the CCD is sent to an A∕D card plugged into the computer.

Fig. 2
Fig. 2

(a) Four of the relative responsivity frames obtained at the HI level. The first three frames correspond to the shortest exposure times (10, 110, and 210   μs ). The last row in this column shows the 21st frame corresponding to the longest exposure time ( 2010   μs ) of this data series. (b) First three frames of the LI data. The exposure times are 500, 1000, and 1500   μs , respectively. The last frame, the 20th, corresponds to an exposure time of 10,000   μs , and it is shown at the bottom of the right column.

Fig. 3
Fig. 3

Relative mean responsivity of the frames for (a) the HI and (b) the LI cases. The responsivity is normalized with respect to the mean of the last frame for each series of data. Note the change in the axis range for each case.

Fig. 4
Fig. 4

First eigenframes obtained for (a) the HI data and (b) the modified set HI − lf. In (b) we have also included the last frame (at 2010   μs ) aligned with the second eigenframe (the one showing the highest resemblance). The numbers placed between these images are the correlation coefficients between each pair.

Fig. 5
Fig. 5

First eigenframes obtained for (a) the LI data and (b) the LI lf data set. In (b) we have included the last frame aligned with the first eigenframe. The numbers placed between these images are the correlation coefficients between each pair.

Fig. 6
Fig. 6

Relative contribution to each frame (as a percentage) of PRNUs associated with the first four eigenframes in the case of (a) HI and (b) HI lf , and the first three eigenframes in the case of (c) LI and (d) LI lf . In (b) and (d) the solid lines represent the PRNUs of the last frame. The plots contain two horizontal axes. The axis at the bottom is for the exposure time. The axis at the top of each plot is for the response level (in counts).

Tables (3)

Tables Icon

Table 1 Values of the Cosine of the Angle between the eiPRNU and the First Four Eigenvectors a

Tables Icon

Table 2 Values of the Relative Importance (%) of the First Four Eigenvalues a

Tables Icon

Table 3 Values of the Eigenvalues λ 1 to λ 4 and Total Variance ( j = 1 N λ j ) a

Equations (11)

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i = R i R o , i E i t exp ,
w j = 100 × λ j j = 1 N λ j .
F ¯ i = i = 1 N e i , j A j ,
σ 2 [ F i ] = σ 2 [ F ¯ i ] = 1 M 1 α = 1 M ( F ¯ i α ) 2 ,
( F ¯ i α ) 2 = ( j = 1 N e i , j A j α ) 2 = j = 1 N k = 1 N e i , j e i , k A j α A k α .
σ 2 [ F i ] = j = 1 N k = 1 N e i , j e i , k 1 M 1 α = 1 M A j α A k α = j = 1 N e i , j 2 λ j ,
Σ 2 = E 2 Λ ,
σ i , j = | e i , j | λ j .
i 2 i 2 = constant,
e iPRNU = ( ± 1 N , ± 1 N , … ,  ± 1 N ) ,
σ ( t exp , R ) = j = 1 M σ , j 2 ( t exp , R ) ,

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