Abstract

A theory is presented which relates the minimum detectable contrast level for an object in the presence of noise to the statistics of the speckle. Consideration is given to smoothing of the noise by multiple looks and by area. Measurements of the minimum detectable contrast are made for two types of speckle noise. First, a coherent, plane wave is added to an ideal diffuse wave and the threshold of detection is established as a function of the beam ratio. Secondly, these results are compared to the technique of speckle smoothing using an N-fold intensity superposition of fully developed speckle pattens. Good agreement of experiments with theory is observed.

© 1976 Optical Society of America

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  1. T. S. McKechnie, "Speckle Reduction," in Laser Speckle, edited by J. C. Dainty (Springer-Verlag, Berlin, 1975), p. 123.
  2. J. C. Dainty, "Detection of images immersed in speckle noise," Opt. Acta 18, 327–339 (1971).
  3. A. Kozma and C. R. Christensen, "The effects of speckle on resolution," J. Opt. Soc. Am. 66, 1257–1260 (1976) (this issue).
  4. Albert Rose, Vision, Human and Electronic (Plenum. New York, 1974).
  5. N. George and A. Jain, "Space and Wavelength Dependence of Speckle Intensity," Appl. Phys. 4, 201–212 (1974).
  6. J. W. Goodman, "Statistical Properties of Laser Speckle Patterns," in Ref. 1, p. 9.
  7. J. M. Burch, "Interferometry with Scattered Light," in Optical Instruments and Techniques, edited by J. Home Dickson (Oriel, Newcastle upon Tyne, England, 1970).
  8. J. D. Briers, "A note on the statistics of laser speckle patterns," Opt. Quantum Electron. 7, 422–424 (1975).
  9. A. Papoulis, "Probability, Random Variables, and Stochastic Processes," (McGraw-Hill, New York, 1965).
  10. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, (Academic, New York, 1965).
  11. N. George, A. Jain, and R. D. S. Melville, "Experiments on the Space and Wavelength Dependence of Speckle," Appl. Phys. 7, 157–169 (1975).
  12. POTA is composed of 1-phenyl-3-pyrazolidone, 1.5 g; sodium sulfite, 30 g; and cold water (25 °C) to make 1000 cm3.
  13. S. Lowenthal and D. Joyeux, "Speckle removal by a slowly moving diffuser associated with a motionless diffuser," J. Opt. Soc. Am. 61, 847–851 (1971).
  14. E. G. Rawson, A. B. Nafarrate, R. E. Norton, and J. W. Goodman, "Speckle-free rear-projection screen using two close screens with slow relative motion," J. Opt. Soc. Am. 66, 1290–1294 (1976) (following article).
  15. C. R. Christensen, Nicholas George, B. D. Guenther, and J. S. Bennett, "Noise in Coherent Optical Systems: Minimum Detectable Object Contrast and Speckle Smoothing," U. S. Army Missile Command Technical Report No. TR-RR-7T-2, Redstone Arsenal, 1976.

1976 (2)

1975 (2)

J. D. Briers, "A note on the statistics of laser speckle patterns," Opt. Quantum Electron. 7, 422–424 (1975).

N. George, A. Jain, and R. D. S. Melville, "Experiments on the Space and Wavelength Dependence of Speckle," Appl. Phys. 7, 157–169 (1975).

1974 (1)

N. George and A. Jain, "Space and Wavelength Dependence of Speckle Intensity," Appl. Phys. 4, 201–212 (1974).

1971 (2)

Bennett, J. S.

C. R. Christensen, Nicholas George, B. D. Guenther, and J. S. Bennett, "Noise in Coherent Optical Systems: Minimum Detectable Object Contrast and Speckle Smoothing," U. S. Army Missile Command Technical Report No. TR-RR-7T-2, Redstone Arsenal, 1976.

Briers, J. D.

J. D. Briers, "A note on the statistics of laser speckle patterns," Opt. Quantum Electron. 7, 422–424 (1975).

Burch, J. M.

J. M. Burch, "Interferometry with Scattered Light," in Optical Instruments and Techniques, edited by J. Home Dickson (Oriel, Newcastle upon Tyne, England, 1970).

Christensen, C. R.

A. Kozma and C. R. Christensen, "The effects of speckle on resolution," J. Opt. Soc. Am. 66, 1257–1260 (1976) (this issue).

C. R. Christensen, Nicholas George, B. D. Guenther, and J. S. Bennett, "Noise in Coherent Optical Systems: Minimum Detectable Object Contrast and Speckle Smoothing," U. S. Army Missile Command Technical Report No. TR-RR-7T-2, Redstone Arsenal, 1976.

Dainty, J. C.

J. C. Dainty, "Detection of images immersed in speckle noise," Opt. Acta 18, 327–339 (1971).

George, N.

N. George, A. Jain, and R. D. S. Melville, "Experiments on the Space and Wavelength Dependence of Speckle," Appl. Phys. 7, 157–169 (1975).

N. George and A. Jain, "Space and Wavelength Dependence of Speckle Intensity," Appl. Phys. 4, 201–212 (1974).

George, Nicholas

C. R. Christensen, Nicholas George, B. D. Guenther, and J. S. Bennett, "Noise in Coherent Optical Systems: Minimum Detectable Object Contrast and Speckle Smoothing," U. S. Army Missile Command Technical Report No. TR-RR-7T-2, Redstone Arsenal, 1976.

Goodman, J. W.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, (Academic, New York, 1965).

Guenther, B. D.

C. R. Christensen, Nicholas George, B. D. Guenther, and J. S. Bennett, "Noise in Coherent Optical Systems: Minimum Detectable Object Contrast and Speckle Smoothing," U. S. Army Missile Command Technical Report No. TR-RR-7T-2, Redstone Arsenal, 1976.

Jain, A.

N. George, A. Jain, and R. D. S. Melville, "Experiments on the Space and Wavelength Dependence of Speckle," Appl. Phys. 7, 157–169 (1975).

N. George and A. Jain, "Space and Wavelength Dependence of Speckle Intensity," Appl. Phys. 4, 201–212 (1974).

Joyeux, D.

Kozma, A.

Lowenthal, S.

McKechnie, T. S.

T. S. McKechnie, "Speckle Reduction," in Laser Speckle, edited by J. C. Dainty (Springer-Verlag, Berlin, 1975), p. 123.

Melville, R. D. S.

N. George, A. Jain, and R. D. S. Melville, "Experiments on the Space and Wavelength Dependence of Speckle," Appl. Phys. 7, 157–169 (1975).

Nafarrate, A. B.

Norton, R. E.

Papoulis, A.

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

Rawson, E. G.

Rose, Albert

Albert Rose, Vision, Human and Electronic (Plenum. New York, 1974).

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, (Academic, New York, 1965).

Appl. Phys. (2)

N. George and A. Jain, "Space and Wavelength Dependence of Speckle Intensity," Appl. Phys. 4, 201–212 (1974).

N. George, A. Jain, and R. D. S. Melville, "Experiments on the Space and Wavelength Dependence of Speckle," Appl. Phys. 7, 157–169 (1975).

J. Opt. Soc. Am. (3)

Opt. Acta (1)

J. C. Dainty, "Detection of images immersed in speckle noise," Opt. Acta 18, 327–339 (1971).

Opt. Quantum Electron. (1)

J. D. Briers, "A note on the statistics of laser speckle patterns," Opt. Quantum Electron. 7, 422–424 (1975).

Other (8)

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

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, (Academic, New York, 1965).

J. W. Goodman, "Statistical Properties of Laser Speckle Patterns," in Ref. 1, p. 9.

J. M. Burch, "Interferometry with Scattered Light," in Optical Instruments and Techniques, edited by J. Home Dickson (Oriel, Newcastle upon Tyne, England, 1970).

T. S. McKechnie, "Speckle Reduction," in Laser Speckle, edited by J. C. Dainty (Springer-Verlag, Berlin, 1975), p. 123.

Albert Rose, Vision, Human and Electronic (Plenum. New York, 1974).

C. R. Christensen, Nicholas George, B. D. Guenther, and J. S. Bennett, "Noise in Coherent Optical Systems: Minimum Detectable Object Contrast and Speckle Smoothing," U. S. Army Missile Command Technical Report No. TR-RR-7T-2, Redstone Arsenal, 1976.

POTA is composed of 1-phenyl-3-pyrazolidone, 1.5 g; sodium sulfite, 30 g; and cold water (25 °C) to make 1000 cm3.

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