Abstract

A method for scene matching at low-light levels is analyzed. In this method photon-limited images are cross correlated with a classical intensity reference scene to provide an estimate of the high-light-level cross-correlation function. Expressions for the probability density function and characteristic function of the correlation signal are given for general input scenes and reference images. The theory of hypothesis testing is used to calculate the probabilities of detection and false alarm. The recognition capabilities of the method are illustrated with a simple example.

© 1984 Optical Society of America

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References

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  1. R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, London, 1977).
  2. E. L. Hall, Computer Image Processing and Recognition (Academic, New York, 1979).
  3. S. H. Lee, ed., Optical Information Processing. Fundamentals (Springer-Verlag, Berlin, 1981).
    [CrossRef]
  4. H. Stark, ed., Applications of Optical Fosurier Transforms (Academic, New York, 1982).
  5. A. Rose, VISION Human and Electronic (Plenum, New York, 1977), Chap. 1.
  6. J. J. Burke, “Estimating objects from their blurred and grainy images,” in Proceedings of the 1975 International Optical Computing Conference (Institute of Electrical and Electronics Engineers, New York, 1975), p. 48.
  7. J. W. Goodman, J. F. Belsher, “Fundamental limitations in linear invariant restoration of atmospherically degraded images,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141–154 (1976).
  8. H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), Vol. II, Chap. 10.
  9. “Digital correlation of photon counting tv images for stellar interferometry,” in Image Processing Techniques in Astronomy, C. deJager, H. Nieuwenhuijzen, eds. (D. Reidel, Dordrecht, The Netherlands, 1975), p. 79.
  10. J. C. Dainty, “Stellar speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., 2nd ed. (Springer-Verlag, Berlin, 1984).
  11. M. Lampton, “The microchannel image intensifier,” Sci. Am. 245, 62–71 (1981).
    [CrossRef]
  12. P. B. Boyce, “Low light detectors for astronomy,” Science 198, 145–148 (1977).
    [CrossRef] [PubMed]
  13. “Digital Image Tubes and Intensified Self-Scanned Array Detectors,” Application Note #E22, Electro-Optical Products Div., ITT (1980).
  14. C. B. Johnson, R. E. Blank, “Image tube intensified linear and area self-scanned array detectors for astronomy,” Proc. Soc. Photo-Opt. Instrum. Eng. 290, 102–108 (1981).
  15. E. M. Kellogg, S. S. Murray, D. Bardas, “The high speed photicon,”IEEE Trans. Nucl. Sci. NS-26, 403–410 (1979).
    [CrossRef]
  16. J. G. Timothy, G. H. Mount, R. L. Bybee, “Detector arrays for photometric measurements at soft x-ray, ultraviolet and visible wavelengths,” Proc. Soc. Photo-Opt. Instrum. Eng. 183, 169–181 (1979).
  17. M. Lampton, C. W. Carlson, “Low-distortion resistive anodes for two-dimensional position-sensitive MCP systems,” Rev. Sci. Instrum. 50, 1093–1097 (1979).
    [CrossRef] [PubMed]
  18. C. Firmani, E. Ruiz, C. W. Carlson, M. Lampton, F. Paresce, “High-resolution imaging with a two-dimensional resistive anode photon counter,” Rev. Sci. Instrum. 53, 570–574 (1982).
    [CrossRef]
  19. D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Miniature imaging photon detectors,”J. Phys. E 13, 763–770 (1980).
    [CrossRef]
  20. D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, “Miniature imaging photon detectors II. Devices with transparent photo-cathodes,”J. Phys. E 14, 229–233 (1981).
    [CrossRef]
  21. I. McWhirter, D. Rees, A. H. Greenaway, “Miniature imaging photon detectors III. An assessment of the performance of the resistive anode IPD,”J. Phys. E 15, 145–150 (1982).
    [CrossRef]
  22. A. H. Greenaway, A. Lyons, I. McWhirter, D. Rees, A. Cochran, “Miniature imaging photon detector,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 365–367 (1982).
  23. L. Mertz, T. D. Tarbell, A. Title, “Low noise imaging photon counter for astronomy,” Appl. Opt. 21, 628–634 (1982).
    [CrossRef] [PubMed]
  24. C. Papaliolios, L. Mertz, “New two-dimensional photon camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 360–364 (1982).
  25. L. Mandel, “Fluctuations of light beams,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. 2, p. 181.
    [CrossRef]
  26. L. Mandel, E. C. G. Sudarshan, E. Wolf, “Theory of photoelectric detection of light fluctuations,” Proc. Phys. Soc. 84, 435–444 (1964).
    [CrossRef]
  27. M. Bertolotti, “Photon Statistics,” in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins, E. R. Pike, eds. (Plenum, New York, 1974), p. 41.
  28. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965), p. 567.
  29. C. W. Helstrom, Statistical Theory of Signal Detection, 2nd ed. (Pergamon, Oxford, 1968), Chap. 3.
  30. W. J. Richter, T. I. Smits, “Numerical evaluation of Rice’s integral representation of the probability density function for Poisson impulsive noise,”J. Acoust. Soc. Am. 56, 481 (1974).
    [CrossRef]
  31. C. W. Helstrom, “Approximate evaluation of detection probabilities in radar and optical communications,” IEEE Trans. Aerosp. Electron. Syst. AES-14, 630 (1978).
    [CrossRef]
  32. C. W. Helstrom, “Performance analysis of optical receivers by the saddlepoint approximation,”IEEE Trans. Commun. COM-27, 186 (1979).
    [CrossRef]

1982 (5)

C. Firmani, E. Ruiz, C. W. Carlson, M. Lampton, F. Paresce, “High-resolution imaging with a two-dimensional resistive anode photon counter,” Rev. Sci. Instrum. 53, 570–574 (1982).
[CrossRef]

I. McWhirter, D. Rees, A. H. Greenaway, “Miniature imaging photon detectors III. An assessment of the performance of the resistive anode IPD,”J. Phys. E 15, 145–150 (1982).
[CrossRef]

A. H. Greenaway, A. Lyons, I. McWhirter, D. Rees, A. Cochran, “Miniature imaging photon detector,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 365–367 (1982).

L. Mertz, T. D. Tarbell, A. Title, “Low noise imaging photon counter for astronomy,” Appl. Opt. 21, 628–634 (1982).
[CrossRef] [PubMed]

C. Papaliolios, L. Mertz, “New two-dimensional photon camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 360–364 (1982).

1981 (3)

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, “Miniature imaging photon detectors II. Devices with transparent photo-cathodes,”J. Phys. E 14, 229–233 (1981).
[CrossRef]

M. Lampton, “The microchannel image intensifier,” Sci. Am. 245, 62–71 (1981).
[CrossRef]

C. B. Johnson, R. E. Blank, “Image tube intensified linear and area self-scanned array detectors for astronomy,” Proc. Soc. Photo-Opt. Instrum. Eng. 290, 102–108 (1981).

1980 (1)

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Miniature imaging photon detectors,”J. Phys. E 13, 763–770 (1980).
[CrossRef]

1979 (4)

E. M. Kellogg, S. S. Murray, D. Bardas, “The high speed photicon,”IEEE Trans. Nucl. Sci. NS-26, 403–410 (1979).
[CrossRef]

J. G. Timothy, G. H. Mount, R. L. Bybee, “Detector arrays for photometric measurements at soft x-ray, ultraviolet and visible wavelengths,” Proc. Soc. Photo-Opt. Instrum. Eng. 183, 169–181 (1979).

M. Lampton, C. W. Carlson, “Low-distortion resistive anodes for two-dimensional position-sensitive MCP systems,” Rev. Sci. Instrum. 50, 1093–1097 (1979).
[CrossRef] [PubMed]

C. W. Helstrom, “Performance analysis of optical receivers by the saddlepoint approximation,”IEEE Trans. Commun. COM-27, 186 (1979).
[CrossRef]

1978 (1)

C. W. Helstrom, “Approximate evaluation of detection probabilities in radar and optical communications,” IEEE Trans. Aerosp. Electron. Syst. AES-14, 630 (1978).
[CrossRef]

1977 (1)

P. B. Boyce, “Low light detectors for astronomy,” Science 198, 145–148 (1977).
[CrossRef] [PubMed]

1976 (1)

J. W. Goodman, J. F. Belsher, “Fundamental limitations in linear invariant restoration of atmospherically degraded images,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141–154 (1976).

1974 (1)

W. J. Richter, T. I. Smits, “Numerical evaluation of Rice’s integral representation of the probability density function for Poisson impulsive noise,”J. Acoust. Soc. Am. 56, 481 (1974).
[CrossRef]

1964 (1)

L. Mandel, E. C. G. Sudarshan, E. Wolf, “Theory of photoelectric detection of light fluctuations,” Proc. Phys. Soc. 84, 435–444 (1964).
[CrossRef]

Bardas, D.

E. M. Kellogg, S. S. Murray, D. Bardas, “The high speed photicon,”IEEE Trans. Nucl. Sci. NS-26, 403–410 (1979).
[CrossRef]

Barlow, F. E.

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, “Miniature imaging photon detectors II. Devices with transparent photo-cathodes,”J. Phys. E 14, 229–233 (1981).
[CrossRef]

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Miniature imaging photon detectors,”J. Phys. E 13, 763–770 (1980).
[CrossRef]

Barrett, H. H.

H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), Vol. II, Chap. 10.

Belsher, J. F.

J. W. Goodman, J. F. Belsher, “Fundamental limitations in linear invariant restoration of atmospherically degraded images,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141–154 (1976).

Bertolotti, M.

M. Bertolotti, “Photon Statistics,” in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins, E. R. Pike, eds. (Plenum, New York, 1974), p. 41.

Blank, R. E.

C. B. Johnson, R. E. Blank, “Image tube intensified linear and area self-scanned array detectors for astronomy,” Proc. Soc. Photo-Opt. Instrum. Eng. 290, 102–108 (1981).

Boyce, P. B.

P. B. Boyce, “Low light detectors for astronomy,” Science 198, 145–148 (1977).
[CrossRef] [PubMed]

Burke, J. J.

J. J. Burke, “Estimating objects from their blurred and grainy images,” in Proceedings of the 1975 International Optical Computing Conference (Institute of Electrical and Electronics Engineers, New York, 1975), p. 48.

Bybee, R. L.

J. G. Timothy, G. H. Mount, R. L. Bybee, “Detector arrays for photometric measurements at soft x-ray, ultraviolet and visible wavelengths,” Proc. Soc. Photo-Opt. Instrum. Eng. 183, 169–181 (1979).

Carlson, C. W.

C. Firmani, E. Ruiz, C. W. Carlson, M. Lampton, F. Paresce, “High-resolution imaging with a two-dimensional resistive anode photon counter,” Rev. Sci. Instrum. 53, 570–574 (1982).
[CrossRef]

M. Lampton, C. W. Carlson, “Low-distortion resistive anodes for two-dimensional position-sensitive MCP systems,” Rev. Sci. Instrum. 50, 1093–1097 (1979).
[CrossRef] [PubMed]

Cochran, A.

A. H. Greenaway, A. Lyons, I. McWhirter, D. Rees, A. Cochran, “Miniature imaging photon detector,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 365–367 (1982).

Dainty, J. C.

J. C. Dainty, “Stellar speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., 2nd ed. (Springer-Verlag, Berlin, 1984).

Firmani, C.

C. Firmani, E. Ruiz, C. W. Carlson, M. Lampton, F. Paresce, “High-resolution imaging with a two-dimensional resistive anode photon counter,” Rev. Sci. Instrum. 53, 570–574 (1982).
[CrossRef]

Gonzalez, R. C.

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, London, 1977).

Goodman, J. W.

J. W. Goodman, J. F. Belsher, “Fundamental limitations in linear invariant restoration of atmospherically degraded images,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141–154 (1976).

Greenaway, A. H.

I. McWhirter, D. Rees, A. H. Greenaway, “Miniature imaging photon detectors III. An assessment of the performance of the resistive anode IPD,”J. Phys. E 15, 145–150 (1982).
[CrossRef]

A. H. Greenaway, A. Lyons, I. McWhirter, D. Rees, A. Cochran, “Miniature imaging photon detector,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 365–367 (1982).

Hall, E. L.

E. L. Hall, Computer Image Processing and Recognition (Academic, New York, 1979).

Helstrom, C. W.

C. W. Helstrom, “Performance analysis of optical receivers by the saddlepoint approximation,”IEEE Trans. Commun. COM-27, 186 (1979).
[CrossRef]

C. W. Helstrom, “Approximate evaluation of detection probabilities in radar and optical communications,” IEEE Trans. Aerosp. Electron. Syst. AES-14, 630 (1978).
[CrossRef]

C. W. Helstrom, Statistical Theory of Signal Detection, 2nd ed. (Pergamon, Oxford, 1968), Chap. 3.

Johnson, C. B.

C. B. Johnson, R. E. Blank, “Image tube intensified linear and area self-scanned array detectors for astronomy,” Proc. Soc. Photo-Opt. Instrum. Eng. 290, 102–108 (1981).

Kellock, S. J.

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Miniature imaging photon detectors,”J. Phys. E 13, 763–770 (1980).
[CrossRef]

Kellogg, E. M.

E. M. Kellogg, S. S. Murray, D. Bardas, “The high speed photicon,”IEEE Trans. Nucl. Sci. NS-26, 403–410 (1979).
[CrossRef]

Lampton, M.

C. Firmani, E. Ruiz, C. W. Carlson, M. Lampton, F. Paresce, “High-resolution imaging with a two-dimensional resistive anode photon counter,” Rev. Sci. Instrum. 53, 570–574 (1982).
[CrossRef]

M. Lampton, “The microchannel image intensifier,” Sci. Am. 245, 62–71 (1981).
[CrossRef]

M. Lampton, C. W. Carlson, “Low-distortion resistive anodes for two-dimensional position-sensitive MCP systems,” Rev. Sci. Instrum. 50, 1093–1097 (1979).
[CrossRef] [PubMed]

Lyons, A.

A. H. Greenaway, A. Lyons, I. McWhirter, D. Rees, A. Cochran, “Miniature imaging photon detector,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 365–367 (1982).

Mandel, L.

L. Mandel, E. C. G. Sudarshan, E. Wolf, “Theory of photoelectric detection of light fluctuations,” Proc. Phys. Soc. 84, 435–444 (1964).
[CrossRef]

L. Mandel, “Fluctuations of light beams,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. 2, p. 181.
[CrossRef]

McWhirter, I.

A. H. Greenaway, A. Lyons, I. McWhirter, D. Rees, A. Cochran, “Miniature imaging photon detector,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 365–367 (1982).

I. McWhirter, D. Rees, A. H. Greenaway, “Miniature imaging photon detectors III. An assessment of the performance of the resistive anode IPD,”J. Phys. E 15, 145–150 (1982).
[CrossRef]

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, “Miniature imaging photon detectors II. Devices with transparent photo-cathodes,”J. Phys. E 14, 229–233 (1981).
[CrossRef]

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Miniature imaging photon detectors,”J. Phys. E 13, 763–770 (1980).
[CrossRef]

Mertz, L.

C. Papaliolios, L. Mertz, “New two-dimensional photon camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 360–364 (1982).

L. Mertz, T. D. Tarbell, A. Title, “Low noise imaging photon counter for astronomy,” Appl. Opt. 21, 628–634 (1982).
[CrossRef] [PubMed]

Mount, G. H.

J. G. Timothy, G. H. Mount, R. L. Bybee, “Detector arrays for photometric measurements at soft x-ray, ultraviolet and visible wavelengths,” Proc. Soc. Photo-Opt. Instrum. Eng. 183, 169–181 (1979).

Murray, S. S.

E. M. Kellogg, S. S. Murray, D. Bardas, “The high speed photicon,”IEEE Trans. Nucl. Sci. NS-26, 403–410 (1979).
[CrossRef]

Papaliolios, C.

C. Papaliolios, L. Mertz, “New two-dimensional photon camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 360–364 (1982).

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965), p. 567.

Paresce, F.

C. Firmani, E. Ruiz, C. W. Carlson, M. Lampton, F. Paresce, “High-resolution imaging with a two-dimensional resistive anode photon counter,” Rev. Sci. Instrum. 53, 570–574 (1982).
[CrossRef]

Rees, D.

I. McWhirter, D. Rees, A. H. Greenaway, “Miniature imaging photon detectors III. An assessment of the performance of the resistive anode IPD,”J. Phys. E 15, 145–150 (1982).
[CrossRef]

A. H. Greenaway, A. Lyons, I. McWhirter, D. Rees, A. Cochran, “Miniature imaging photon detector,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 365–367 (1982).

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, “Miniature imaging photon detectors II. Devices with transparent photo-cathodes,”J. Phys. E 14, 229–233 (1981).
[CrossRef]

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Miniature imaging photon detectors,”J. Phys. E 13, 763–770 (1980).
[CrossRef]

Richter, W. J.

W. J. Richter, T. I. Smits, “Numerical evaluation of Rice’s integral representation of the probability density function for Poisson impulsive noise,”J. Acoust. Soc. Am. 56, 481 (1974).
[CrossRef]

Rose, A.

A. Rose, VISION Human and Electronic (Plenum, New York, 1977), Chap. 1.

Rounce, P. A.

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, “Miniature imaging photon detectors II. Devices with transparent photo-cathodes,”J. Phys. E 14, 229–233 (1981).
[CrossRef]

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Miniature imaging photon detectors,”J. Phys. E 13, 763–770 (1980).
[CrossRef]

Ruiz, E.

C. Firmani, E. Ruiz, C. W. Carlson, M. Lampton, F. Paresce, “High-resolution imaging with a two-dimensional resistive anode photon counter,” Rev. Sci. Instrum. 53, 570–574 (1982).
[CrossRef]

Smits, T. I.

W. J. Richter, T. I. Smits, “Numerical evaluation of Rice’s integral representation of the probability density function for Poisson impulsive noise,”J. Acoust. Soc. Am. 56, 481 (1974).
[CrossRef]

Sudarshan, E. C. G.

L. Mandel, E. C. G. Sudarshan, E. Wolf, “Theory of photoelectric detection of light fluctuations,” Proc. Phys. Soc. 84, 435–444 (1964).
[CrossRef]

Swindell, W.

H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), Vol. II, Chap. 10.

Tarbell, T. D.

Timothy, J. G.

J. G. Timothy, G. H. Mount, R. L. Bybee, “Detector arrays for photometric measurements at soft x-ray, ultraviolet and visible wavelengths,” Proc. Soc. Photo-Opt. Instrum. Eng. 183, 169–181 (1979).

Title, A.

Wintz, P.

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, London, 1977).

Wolf, E.

L. Mandel, E. C. G. Sudarshan, E. Wolf, “Theory of photoelectric detection of light fluctuations,” Proc. Phys. Soc. 84, 435–444 (1964).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Aerosp. Electron. Syst. (1)

C. W. Helstrom, “Approximate evaluation of detection probabilities in radar and optical communications,” IEEE Trans. Aerosp. Electron. Syst. AES-14, 630 (1978).
[CrossRef]

IEEE Trans. Commun. (1)

C. W. Helstrom, “Performance analysis of optical receivers by the saddlepoint approximation,”IEEE Trans. Commun. COM-27, 186 (1979).
[CrossRef]

IEEE Trans. Nucl. Sci. (1)

E. M. Kellogg, S. S. Murray, D. Bardas, “The high speed photicon,”IEEE Trans. Nucl. Sci. NS-26, 403–410 (1979).
[CrossRef]

J. Acoust. Soc. Am. (1)

W. J. Richter, T. I. Smits, “Numerical evaluation of Rice’s integral representation of the probability density function for Poisson impulsive noise,”J. Acoust. Soc. Am. 56, 481 (1974).
[CrossRef]

J. Phys. E (3)

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, S. J. Kellock, “Miniature imaging photon detectors,”J. Phys. E 13, 763–770 (1980).
[CrossRef]

D. Rees, I. McWhirter, P. A. Rounce, F. E. Barlow, “Miniature imaging photon detectors II. Devices with transparent photo-cathodes,”J. Phys. E 14, 229–233 (1981).
[CrossRef]

I. McWhirter, D. Rees, A. H. Greenaway, “Miniature imaging photon detectors III. An assessment of the performance of the resistive anode IPD,”J. Phys. E 15, 145–150 (1982).
[CrossRef]

Proc. Phys. Soc. (1)

L. Mandel, E. C. G. Sudarshan, E. Wolf, “Theory of photoelectric detection of light fluctuations,” Proc. Phys. Soc. 84, 435–444 (1964).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (5)

C. Papaliolios, L. Mertz, “New two-dimensional photon camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 360–364 (1982).

C. B. Johnson, R. E. Blank, “Image tube intensified linear and area self-scanned array detectors for astronomy,” Proc. Soc. Photo-Opt. Instrum. Eng. 290, 102–108 (1981).

A. H. Greenaway, A. Lyons, I. McWhirter, D. Rees, A. Cochran, “Miniature imaging photon detector,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 365–367 (1982).

J. G. Timothy, G. H. Mount, R. L. Bybee, “Detector arrays for photometric measurements at soft x-ray, ultraviolet and visible wavelengths,” Proc. Soc. Photo-Opt. Instrum. Eng. 183, 169–181 (1979).

J. W. Goodman, J. F. Belsher, “Fundamental limitations in linear invariant restoration of atmospherically degraded images,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141–154 (1976).

Rev. Sci. Instrum. (2)

M. Lampton, C. W. Carlson, “Low-distortion resistive anodes for two-dimensional position-sensitive MCP systems,” Rev. Sci. Instrum. 50, 1093–1097 (1979).
[CrossRef] [PubMed]

C. Firmani, E. Ruiz, C. W. Carlson, M. Lampton, F. Paresce, “High-resolution imaging with a two-dimensional resistive anode photon counter,” Rev. Sci. Instrum. 53, 570–574 (1982).
[CrossRef]

Sci. Am. (1)

M. Lampton, “The microchannel image intensifier,” Sci. Am. 245, 62–71 (1981).
[CrossRef]

Science (1)

P. B. Boyce, “Low light detectors for astronomy,” Science 198, 145–148 (1977).
[CrossRef] [PubMed]

Other (14)

“Digital Image Tubes and Intensified Self-Scanned Array Detectors,” Application Note #E22, Electro-Optical Products Div., ITT (1980).

L. Mandel, “Fluctuations of light beams,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. 2, p. 181.
[CrossRef]

M. Bertolotti, “Photon Statistics,” in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins, E. R. Pike, eds. (Plenum, New York, 1974), p. 41.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965), p. 567.

C. W. Helstrom, Statistical Theory of Signal Detection, 2nd ed. (Pergamon, Oxford, 1968), Chap. 3.

H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), Vol. II, Chap. 10.

“Digital correlation of photon counting tv images for stellar interferometry,” in Image Processing Techniques in Astronomy, C. deJager, H. Nieuwenhuijzen, eds. (D. Reidel, Dordrecht, The Netherlands, 1975), p. 79.

J. C. Dainty, “Stellar speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., 2nd ed. (Springer-Verlag, Berlin, 1984).

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, London, 1977).

E. L. Hall, Computer Image Processing and Recognition (Academic, New York, 1979).

S. H. Lee, ed., Optical Information Processing. Fundamentals (Springer-Verlag, Berlin, 1981).
[CrossRef]

H. Stark, ed., Applications of Optical Fosurier Transforms (Academic, New York, 1982).

A. Rose, VISION Human and Electronic (Plenum, New York, 1977), Chap. 1.

J. J. Burke, “Estimating objects from their blurred and grainy images,” in Proceedings of the 1975 International Optical Computing Conference (Institute of Electrical and Electronics Engineers, New York, 1975), p. 48.

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Figures (6)

Fig. 1
Fig. 1

System diagram for scene matching at low-light levels.

Fig. 2
Fig. 2

Probability density functions under hypotheses 0 and 1.

Fig. 3
Fig. 3

(a) Real part and (b) imaginary part of the characteristic function under hypothesis 1. The reference image is given in Eq. (24).

Fig. 4
Fig. 4

Probability density function P1(C) with (a) N ¯ r= 2, (b) N ¯ r= 5, and (c) N ¯ r= 10.

Fig. 5
Fig. 5

Probability density functions for null and positive hypotheses with (a) N ¯= 50, (b) N ¯= 150, and (c) N ¯= 250.

Fig. 6
Fig. 6

(a) Probability of false alarm as a function of the correlation threshold CT and the average number of background photons N ¯ n, (b) probability of detection as a function of CT and the average number of reference image photons N ¯ r.

Equations (32)

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V ^ ( x , y ) = k = 1 N δ ( x - x k , y - y k ) ,
P ( N ) = [ t t + τ d t A d 2 r λ ( r , t ) ] N N ! × exp [ - t t + τ d t A d 2 r λ ( r , t ) ] ,
λ ( r , t ) = η V ( r , t ) / h ν ¯ ,
P ( N ) = N ¯ N N ! e - N ¯ ,
N ¯ = [ η τ / ( h ν ¯ ) ] A V ( x , y ) d x d y
C ( x , y ) = d x d y V ( x , y ) R ( x + x , y + y ) ,
C ( x , y ) = k = 1 N R ( x + x k , y + y k ) ,
Φ ( ω ) = e i ω C = - d C P ( C ) e i ω C .
Φ ( ω ) = exp ( η τ h ν ¯ A d x d y V ( x , y ) × { exp [ i ω R ( x + x , y + y ) ] - 1 } ) .
C k ( x , y ) = ( - i ) k d k Φ ( 0 ) d ω k .
C ( x , y ) = N ¯ A d x d y p [ x , y V ( x , y ) ] × R ( x + x , y + y )
σ 2 = C 2 ( x , y ) - C ( x , y ) 2 = N ¯ d x d y p [ x , y V ( x , y ) ] × R 2 ( x + x , y + y ) ,
p [ x , y V ( x , y ) ] = V ( x , y ) A d x d y V ( x , y ) .
SNR = N × A d x d y p [ x , y V ( x y ) ] R ( x + x , y + y ) [ A d x d y p [ x , y V ( x , y ) ] R 2 ( x + x , y + y ) ] 1 / 2 .
P [ C ( x , y ) V ( x , y ) ] = 1 2 π - d ω Φ ( ω ) exp [ - i ω C ( x , y ) ] .
Φ ( ω ) = e - N ¯ k = 0 N ¯ k Λ k ( ω ) k ! ,
Λ ( ω ) = A d x d y p [ x , y V ( x , y ) ] × exp [ i ω R ( x + x , y + y ) ] .
g [ C ( x , y ) ] 1 2 π - d ω Λ ( ω ) exp [ - i ω C ( x , y ) ] ,
P [ C ( x , y ) V ( x , y ) ] = e - N ¯ { δ [ C ( x , y ) ] + N ¯ g ( C ) + N ¯ 2 2 ! g ( C ) * g ( C ) + + N ¯ k k ! g ( C ) * g ( C ) * * g ( ) C k times + } ,
E ( x , y ) = C ( x , y ) - C ( x , y ) σ
Φ E ( ω ) = exp [ - i ( ω / σ ) C ( x , y ) ] × exp ( N ¯ A d x d y p [ x , y V ( x , y ) ] × { exp [ i ( ω / σ ) R ( x + x , y + y ) ] - 1 } ) .
N ¯ A d x d y p [ x , y V ( x , y ) ] × { exp [ i ( ω / σ ) R ( x + x , y + y ) ] - 1 } = [ i ω N ¯ / σ ] × A d x d y p [ x , y V ( x , y ) ] R ( x + x , y + y ) - [ ω 2 N ¯ / ( 2 σ 2 ) ] A d x d y p [ x , y V ( x , y ) ] × R 2 ( x + x , y + y ) - [ i ω 3 N ¯ / ( 6 σ 3 ) ] × A d x d y p [ x , y V ( x , y ) ] R 3 ( x + x , y + y ) + + [ ( i ω ) k N ¯ / k ! σ k ) ] × A d x d y p [ x , y V ( x , y ) R k ( x + x , y + y ) + .
lim N ¯ Φ E ( ω ) = e - ω 2 / 2 .
P f a = C T P 0 ( C ) d C .
P d = C T P 1 ( C ) d C .
R ( x , y ) = { 1 - x , L - L x L - L y L 0 otherwise
Φ 0 ( ω ) = exp { [ N ¯ n / ( 4 L 2 ) ] × - L L d x d y [ exp [ i ω R ( x , y ) ] - 1 ] } ,
Φ 0 ( ω ) = exp { N ¯ n [ exp ( i ω / 2 ) sin ( ω / 2 ) ( ω / 2 ) - 1 ] } .
Φ 1 ( ω ) = exp { [ N ¯ r / ( 2 L 2 ) ] - L L d x d y R ( x y ) × [ exp [ i ω R ( x , y ) - 1 ] } ,
Λ ( ω ) = - L L d x d y { exp [ i ω R ( x y ) ] - 1 } .
- i Λ ( ω ) = - L L d x d y R ( x , y ) exp [ i ω R ( x , y ) ] .
Φ 1 ( ω ) = exp ( - N ¯ r ) exp { - i [ N ¯ r / ( 2 L 2 ) ] Λ ( ω ) } = exp ( N ¯ r { exp ( i ω / 2 ) sin ( ω / 2 ) ( ω / 2 ) - [ i exp ( i ω / 2 ) ( ω / 2 ) ] × [ cos ( ω / 2 ) - sin ( ω / 2 ) ( ω / 2 ) ] - 1 } ) .

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