Abstract

We present and evaluate two corrections applicable in determining the modulation transfer function (MTF) of a charge-coupled device (CCD) by the speckle method that minimize its uncertainty: one for the low frequency region and another for the high frequency region. The correction at the low-spatial-frequency region enables attenuation of the high power-spectral-density values that arise from the field and CCD response non-uniformities. In the high-spatial-frequency region the results show that the distance between the CCD and the aperture is critical and significantly influences the MTF; a variation of 1 mm in the distance can cause a root-mean-square error in the MTF higher than 10%. We propose a simple correction that minimizes the experimental error committed in positioning the CCD and that diminishes the error to 0.43%.

© 2006 Optical Society of America

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References

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  1. J. C. Feltz and M. A. Karim, "Modulation transfer function of charge-coupled devices," Appl. Opt. 29,717-722 (1990).
    [CrossRef] [PubMed]
  2. S. K. Park, R. Schowengerdt, and M. A. Kaczynski, "Modulation-transfer-function analysis for sampled image system," Appl. Opt. 23,2572-2582 (1984).
    [CrossRef] [PubMed]
  3. A. Daniels, G. D. Boreman, A. D. Ducharme, and E. Sapir, "Random transparency targets for modulation transfer function measurement in the visible and infrared regions," Opt. Eng. 34,860-868 (1995).
    [CrossRef]
  4. S. M. Backman, A. J. Makynen, T. T. Kolehmainen, and K. M. Ojala, "Random target method for fast MTF inspection," Opt. Express 12,2610-2615 (2004).
    [CrossRef] [PubMed]
  5. E. Levy, D. Peles, M. Opher-Lipson, and S. G. Lipson, "Modulation transfer function of a lens measured with a random target method," Appl. Opt. 38,679-683 (1999).
    [CrossRef]
  6. G. D. Boreman and E. L. Dereniak, "Method for measuring modulation transfer function of charge-coupled devices using laser speckle," Opt. Eng. 25,148-150 (1986).
  7. G. D. Boreman, Y. Sun, and A. B. James, "Generation of laser speckle with an integrating sphere," Opt. Eng. 29,339-342 (1990).
    [CrossRef]
  8. A. M. Pozo and M. Rubiño, "Optical characterization of ophthalmic lenses by means of modulation transfer function determination from a laser speckle pattern," Appl. Opt. 44,7744-7748 (2005).
    [CrossRef] [PubMed]
  9. M. Sensiper, G. D. Boreman, A. D. Ducharme, and D. R. Snyder, "Modulation transfer function testing of detector arrays using narrow-band laser speckle," Opt. Eng. 32,395-400 (1993).
    [CrossRef]
  10. A. M. Pozo and M. Rubiño, "Comparative analysis of techniques for measuring the modulation transfer functions of charge-coupled devices based on the generation of laser speckle," Appl. Opt. 44,1543-1547 (2005).
    [CrossRef] [PubMed]
  11. J. R. Janesick, Scientific Charge-Coupled Devices (SPIE Press, Bellingham,Washington, 2001), Chap. 4.
    [CrossRef]
  12. A. Ferrero, J. Campos, and A. Pons, "Correction of photoresponse nonuniformity for matrix detectors based on prior compensation for their nonlinear behavior," Appl. Opt. 45,2422-2427 (2006).
    [CrossRef] [PubMed]
  13. A. F. Milton, F. R. Barone, and M. R. Kruer, "Influence of nonuniformity on infrared focal plane array performance," Opt. Eng. 24,855-862 (1985).
  14. M. Schulz and L. Caldwell, "Nonuniformity correction and correctability of infrared focal plane arrays," Infrared Phys. Technol. 36,763-777 (1995).
    [CrossRef]
  15. D. L. Perry and E. L. Dereniak, "Linear theory of nonuniformity correction in infrared staring sensors," Opt. Eng. 32,1854-1859 (1993).
    [CrossRef]
  16. T. S. McKechnie, "Speckle reduction," in Laser speckle and related phenomena, Vol. 9 of Topics in Applied Physics, J. C. Dainty, ed. (Springer-Verlag, New York, 1984).
  17. E. Schröder, "Elimination of granulation in laser beam projections by means of moving diffusers," Opt. Commun. 3,68-72 (1971).
    [CrossRef]
  18. G. D. Boreman, "Fourier spectrum techniques for characterization of spatial noise in imaging arrays," Opt. Eng. 26,985-991 (1987).

2006

2005

2004

1999

1995

A. Daniels, G. D. Boreman, A. D. Ducharme, and E. Sapir, "Random transparency targets for modulation transfer function measurement in the visible and infrared regions," Opt. Eng. 34,860-868 (1995).
[CrossRef]

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

1993

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

M. Sensiper, G. D. Boreman, A. D. Ducharme, and D. R. Snyder, "Modulation transfer function testing of detector arrays using narrow-band laser speckle," Opt. Eng. 32,395-400 (1993).
[CrossRef]

1990

G. D. Boreman, Y. Sun, and A. B. James, "Generation of laser speckle with an integrating sphere," Opt. Eng. 29,339-342 (1990).
[CrossRef]

J. C. Feltz and M. A. Karim, "Modulation transfer function of charge-coupled devices," Appl. Opt. 29,717-722 (1990).
[CrossRef] [PubMed]

1987

G. D. Boreman, "Fourier spectrum techniques for characterization of spatial noise in imaging arrays," Opt. Eng. 26,985-991 (1987).

1986

G. D. Boreman and E. L. Dereniak, "Method for measuring modulation transfer function of charge-coupled devices using laser speckle," Opt. Eng. 25,148-150 (1986).

1985

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

1984

1971

E. Schröder, "Elimination of granulation in laser beam projections by means of moving diffusers," Opt. Commun. 3,68-72 (1971).
[CrossRef]

Backman, S. M.

Barone, F. R.

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

Boreman, G. D.

A. Daniels, G. D. Boreman, A. D. Ducharme, and E. Sapir, "Random transparency targets for modulation transfer function measurement in the visible and infrared regions," Opt. Eng. 34,860-868 (1995).
[CrossRef]

M. Sensiper, G. D. Boreman, A. D. Ducharme, and D. R. Snyder, "Modulation transfer function testing of detector arrays using narrow-band laser speckle," Opt. Eng. 32,395-400 (1993).
[CrossRef]

G. D. Boreman, Y. Sun, and A. B. James, "Generation of laser speckle with an integrating sphere," Opt. Eng. 29,339-342 (1990).
[CrossRef]

G. D. Boreman, "Fourier spectrum techniques for characterization of spatial noise in imaging arrays," Opt. Eng. 26,985-991 (1987).

G. D. Boreman and E. L. Dereniak, "Method for measuring modulation transfer function of charge-coupled devices using laser speckle," Opt. Eng. 25,148-150 (1986).

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.

Daniels, A.

A. Daniels, G. D. Boreman, A. D. Ducharme, and E. Sapir, "Random transparency targets for modulation transfer function measurement in the visible and infrared regions," Opt. Eng. 34,860-868 (1995).
[CrossRef]

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]

G. D. Boreman and E. L. Dereniak, "Method for measuring modulation transfer function of charge-coupled devices using laser speckle," Opt. Eng. 25,148-150 (1986).

Ducharme, A. D.

A. Daniels, G. D. Boreman, A. D. Ducharme, and E. Sapir, "Random transparency targets for modulation transfer function measurement in the visible and infrared regions," Opt. Eng. 34,860-868 (1995).
[CrossRef]

M. Sensiper, G. D. Boreman, A. D. Ducharme, and D. R. Snyder, "Modulation transfer function testing of detector arrays using narrow-band laser speckle," Opt. Eng. 32,395-400 (1993).
[CrossRef]

Feltz, J. C.

Ferrero, A.

James, A. B.

G. D. Boreman, Y. Sun, and A. B. James, "Generation of laser speckle with an integrating sphere," Opt. Eng. 29,339-342 (1990).
[CrossRef]

Kaczynski, M. A.

Karim, M. A.

Kolehmainen, T. T.

Kruer, M. R.

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

Levy, E.

Lipson, S. G.

Makynen, A. J.

Milton, A. F.

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

Ojala, K. M.

Opher-Lipson, M.

Park, S. K.

Peles, D.

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]

Pons, A.

Pozo, A. M.

Rubiño, M.

Sapir, E.

A. Daniels, G. D. Boreman, A. D. Ducharme, and E. Sapir, "Random transparency targets for modulation transfer function measurement in the visible and infrared regions," Opt. Eng. 34,860-868 (1995).
[CrossRef]

Schowengerdt, R.

Schröder, E.

E. Schröder, "Elimination of granulation in laser beam projections by means of moving diffusers," Opt. Commun. 3,68-72 (1971).
[CrossRef]

Schulz, M.

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

Sensiper, M.

M. Sensiper, G. D. Boreman, A. D. Ducharme, and D. R. Snyder, "Modulation transfer function testing of detector arrays using narrow-band laser speckle," Opt. Eng. 32,395-400 (1993).
[CrossRef]

Snyder, D. R.

M. Sensiper, G. D. Boreman, A. D. Ducharme, and D. R. Snyder, "Modulation transfer function testing of detector arrays using narrow-band laser speckle," Opt. Eng. 32,395-400 (1993).
[CrossRef]

Sun, Y.

G. D. Boreman, Y. Sun, and A. B. James, "Generation of laser speckle with an integrating sphere," Opt. Eng. 29,339-342 (1990).
[CrossRef]

Appl. Opt.

Infrared Phys. Technol.

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

Opt. Commun.

E. Schröder, "Elimination of granulation in laser beam projections by means of moving diffusers," Opt. Commun. 3,68-72 (1971).
[CrossRef]

Opt. Eng.

G. D. Boreman, "Fourier spectrum techniques for characterization of spatial noise in imaging arrays," Opt. Eng. 26,985-991 (1987).

D. L. Perry and E. L. Dereniak, "Linear theory of nonuniformity correction in 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 performance," Opt. Eng. 24,855-862 (1985).

M. Sensiper, G. D. Boreman, A. D. Ducharme, and D. R. Snyder, "Modulation transfer function testing of detector arrays using narrow-band laser speckle," Opt. Eng. 32,395-400 (1993).
[CrossRef]

G. D. Boreman and E. L. Dereniak, "Method for measuring modulation transfer function of charge-coupled devices using laser speckle," Opt. Eng. 25,148-150 (1986).

G. D. Boreman, Y. Sun, and A. B. James, "Generation of laser speckle with an integrating sphere," Opt. Eng. 29,339-342 (1990).
[CrossRef]

A. Daniels, G. D. Boreman, A. D. Ducharme, and E. Sapir, "Random transparency targets for modulation transfer function measurement in the visible and infrared regions," Opt. Eng. 34,860-868 (1995).
[CrossRef]

Opt. Express

Other

J. R. Janesick, Scientific Charge-Coupled Devices (SPIE Press, Bellingham,Washington, 2001), Chap. 4.
[CrossRef]

T. S. McKechnie, "Speckle reduction," in Laser speckle and related phenomena, Vol. 9 of Topics in Applied Physics, J. C. Dainty, ed. (Springer-Verlag, New York, 1984).

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Figures (5)

Fig. 1.
Fig. 1.

Experimental set-up for the measurement of the MTF of the CCD. R is a rotating transmissive diffuser, D is a fixed transmissive diffuser, A is a single-slit aperture, P is a polarizer.

Fig. 2.
Fig. 2.

PSDs determined for a distance of 30.8 mm between the window of the CCD and the single-slit aperture (a) without correction of response non-uniformity and (b) with correction. On the abscissa axis, the spatial frequency is normalized to the Nyquist frequency of the CCD (50.5 cycles/mm).

Fig. 3.
Fig. 3.

Detail of PSDs found at three different distances between the window of the CCD and the single-slit aperture. Represented on the abscissa axis is the spatial frequency normalized to the Nyquist frequency of the CCD.

Fig. 4.
Fig. 4.

MTFs of the CCD determined from the PSDs shown in Fig. 3. On the abscissa axis, the spatial frequency is normalized to the Nyquist frequency of the CCD.

Fig. 5.
Fig. 5.

MTFs for distances of 29.8 mm and 30.8 mm between the window of the CCD and the aperture determined after applying the correction of the baseline value. Also represented is the MTF (without correction) for a distance of 31.8 mm between the window of the CCD and the aperture. Integration MTF sets the theoretical limit for MTF performance. On the abscissa axis the spatial frequency normalized to the Nyquist frequency of the CCD is represented.

Equations (6)

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PSD output ( ξ , η ) = [ MTF ( ξ , η ) ] 2 PSD input ( ξ , η ) ,
PSD input ( ξ , η ) = I 2 [ δ ( ξ , η ) + ( λ z ) 2 l 1 l 2 tri ( λ z l 1 ξ ) tri ( λ z l 2 η ) ] ,
MTF TOTAL = MTF I MTF D MTF CTE .
MTF l = sin ( π ξ Δ x 2 ξ N y x ) π ξ Δ x 2 ξ N y x ,
( Speckle corrected ) i , j = ( Speckle raw ) i , j ( Dark ) i , j ( Flat ) i , j ( Dark ) i , j ( Flat ) i , j ( Dark ) i , j
z = l 1 λ ξ N y ,

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