Abstract

We have utilized the extended Huygens-Fresnel principle to make an analysis of the first- and second-order statistics of the received intensity for speckle propagation through the turbulent atmosphere. The treatment includes the effects of the turbulent atmosphere on the laser beam as it propagates to the target and on the speckle as it propagates back to the receiver. Formulations have been developed for both the focused and collimated cases. It is assumed in the analysis that phase perturbation of the waves is the dominant effect due to the atmosphere. Utilizing this assumption it can be shown that the fields at the receiver are marginally Gaussian and that the space-averaged, spatial power spectral density at the receiver is “white“. Because of these results, we have assumed that the field statistics at the receiver are jointly Gaussian. This appears to be a reasonable assumption and allows a closed form solution for the variance and covariance to be derived. For a point detector it is found that the normalized variance is unity and independent of the turbulence strength, and that the transverse correlation length becomes proportional to ρ<sub>0</sub> as the turbulence strength increases.

© 1976 Optical Society of America

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  1. H. E. Bennett, "Specular Reflectance of Aluminized Ground Glass and the Height Distribution of Surface Irregularities," J. Opt. Soc. Am. 53, 1389 (1963).
  2. J. Porfens, "Relation Between the Height Distribution of a Rough Surface and the Reflection at Normal Incidence," J. Opt. Soc. Am. 53, 1394 (1963).
  3. D. P. Greenwood, "The Scattering from Curved Rough Surfaces of an EM Wave Transmitted Through a Turbulent Medium," IEEE Trans. Antennas Prop. AP-20, 19 (1972).
  4. C. N. Kurtz, "Transmitted Characteristics of Surface and the Design of Nearly Band-Limited Binary Diffusers," J. Opt. Soc. Am. 62, 982 (1972).
  5. R. A. Sprague, "Surface Roughness Measurement Using White Light Speckle," Appl. Opt. 11, 2811 (1972).
  6. K. Nagata, T. Unehara, and J. Nishiwaki, "The Determination of rms Roughness and Correlation Length of Rough Surface by Measuring Spatial Coherence Function," Jpn. J. Appl. Phys. 12, 694 (1973).
  7. G. O. Reynolds and T. J. Skinner, "Mutual Coherence Function Applied to Imaging through a Random Medium," J. Opt. Soc. Am. 54, 1302 (1964).
  8. G. Gould et al., "Coherent Detection of Light Scattered From a Diffusing Reflecting Surface," Appl. Opt. 3, 648 (1964).
  9. L. I. Goldfischer, "Autocorrelation Function and Power Density of Laser-Produced Speckle Patterns," J. Opt. Soc. Am. 55, 247 (1965).
  10. J. W. Goodman, "Some Effects of Target-Induced Scintillation on Optical Radar Performance," Proc. IEEE 53, 1688 (1965).
  11. S. Lowenthal and H. Arsenault, "Image Formation for Coherent Diffuse Objects: Statistical Properties," J. Opt. Soc. Am. 60, 1478 (1970).
  12. R. B. Crane, "Use of a Laser-Produced Speckle Pattern to Determine Surface Roughness," J. Opt. Soc. Am. 60, 1658 (1970).
  13. M. G. Miller, A. M. Schneiderman, and P. F. Kellen, "Second-Order Statistics of Laser-Speckle Patterns," J. Opt. Soc. Am. 65, 779 (1975).
  14. H. Fujii and T. Asakura, "Effect of Surface Roughness on the Statistical Distribution of Image Speckle Intensity," Opt. Commun. 11, 35 (1974).
  15. H. M. Pederson, "The Roughness Dependence of Partially Developed Monochromatic Speckle Patterns," Opt. Commun. 12, 156 (1974).
  16. G. S. Agarwal, "Scattering from Rough Surfaces," Opt. Commun. 14, 161 (1975).
  17. K. Nagata and T. Unebara, "Spatial Correlation of Gaussian Beam in Moving Ground Glass," Jpn. J. Appl. Phys. 12, 694 (1973).
  18. N. Takai, "Statistics of Dynamic Speckles Produced by a Moving Diffuser Under the Gaussian Beam Laser Illumination," Jpn. J. Appl. Phys. 13, 2025 (1974).
  19. P. Kirkpatrick and H. M. A. El-Sum, "Image Formation by Reconstruction Wavefront. I. Physical Principles and Methods of Refinement," J. Opt. Soc. Am. 46, 825 (1956).
  20. E. N. Leith and J. Upatnieks, "Reconstructed Wavefronts and Communication Theory," J. Opt. Soc. Am. 52, 1123 (1962).
  21. E. N. Leith and J. Upatnieks, "Wavefront Reconstruction with Diffused Illumination and Three-Dimensional Objects," J. Opt. Soc. Am. 54, 1295 (1964).
  22. J. Upatnieks, "Improvement of Two-Dimensional Image Quality in Coherent Optical Systems," Appl. Opt. 11, 1905 (1967).
  23. L. H. Enloe, "Noise-Like Structure in the Image of Diffusely Reflecting Objects in Coherent Illumination," Bell. Syst. Tech. J. 46, 1479 (1967).
  24. P. H. Deitz, "Image Information by Means of Speckle-Pattern Processing," J. Opt. Soc. Am. 65, 279 (1975).
  25. L. E. Estes And R. Boucher, "Temporal And Spatial-intensity-Interferometer Imaging Through A Random Medium," J. Opt. Soc. Am. 65, 760 (1975).
  26. M. J. Lahart and A. S. Marathay, "Image Speckle Patterns of Weak Diffusers," J. Opt. Soc. Am. 65, 769 (1975).
  27. H. Fujii and T. Asakura, "A Contrast Variation of Image Speckle Intensity Under Illumination of Partially Coherent Light," Opt. Commun. 12, 32 (1974).
  28. J. W. Goodman, "Dependence of Image Speckle Contrast on Surface Roughness," Opt. Commun. 14, 324 (1975).
  29. M. Elbaum, M. King, and M. Greenebaum, "Laser Correlography: Transmission of High-Resolution Object Signatures through the Turbulent Atmosphere," Riverside Research Institute, Technical Report No. T-1/306-3-11, 80 West End Ave., New York, N.Y. 10023, 31 October 1974. (unpublshed).
  30. S. F. Clifford, G. R. Ochs, and T. Wang, "Theoretical Analysis and Experimental Evaluation of a Prototype Passive Sensor to Measure Crosswinds," U. S. Department of Commerce, National Oceanic and Atmospheric Administration, Technical Report No. ERL 312-WPL 35, Boulder, Colo. 80302, September 1974 (unpublished).
  31. M. C. Teich, "Homodyne Detection of Infrared Radiation from a Moving Diffuse Target," Proc. IEEE 57, 786 (1969).
  32. N. George and A. Jain, "Space and Wavelength Dependence of Speckle Intensity," Appl. Phys. 4, 201 (1974).
  33. R. F. Lutomirski, and H. T. Yura, "Propagation of a Finite Optical Beam in an Inhomogeneous Medium," Appl. Opt. 10, 1652 (1971).
  34. H. T. Yura, "Mutual Coherence Function of a Finite Cross Section Optical Beam Propagating in a Turbulent Medium," Appl. Opt. 11, 1399 (1972).
  35. M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N. J., 1964).
  36. R. S. Lawrence and J. W. Strohbehn, "A Survey of Clean-Air Propagation Effects Relevant to Optical Communications," Proc. IEEE 58, 1523 (1970).
  37. R. F. Lutomirski and H. T. Yura, "Propagation of a Finite Optical Beam in an Inhomogeneous Medium," Appl. Opt. 10, 1652 (1971).
  38. V. A. Banakh et al., "Focused-Laser-Beam Scintillations in the Turbulent Atmosphere," J. Opt. Soc. Am. 64, 516 (1974).
  39. R. F. Lutomirski and R. E. Warren, "Atmospheric Distortions in a Retroreflected Laser Signal," Appl. Opt. 14, 840 (1975).
  40. D. L. Fried, "Differential Angle of Arrival: Theory, Evaluation, and Measurement Feasibility," Radio Sci. 10, 71 (1975).
  41. D. L. Fried, "Effects of Atmospheric Turbulence on Static and Tracking Optical Heterodyne Receivers," Optical Sciences Consultants, Technical Report No. TR-027, P. O. Box 388, Yorba Linda, Calif. 92686, August 1971 (unpublished).
  42. D. L. Fried, "Atmospheric Modulation Noise in an Optical Heterodyne Receiver," IEEE Trans. Quantum Electron. QE-3, 213 (1967).
  43. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  44. T. Wang, S. F. Clifford, and G. R. Ochs, "Wind and Refractive-Turbulence Sensing Using Crossed Laser Beams," Appl. Opt. 13, 2602 (1974).

1975 (8)

1974 (7)

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

T. Wang, S. F. Clifford, and G. R. Ochs, "Wind and Refractive-Turbulence Sensing Using Crossed Laser Beams," Appl. Opt. 13, 2602 (1974).

H. Fujii and T. Asakura, "Effect of Surface Roughness on the Statistical Distribution of Image Speckle Intensity," Opt. Commun. 11, 35 (1974).

H. M. Pederson, "The Roughness Dependence of Partially Developed Monochromatic Speckle Patterns," Opt. Commun. 12, 156 (1974).

N. Takai, "Statistics of Dynamic Speckles Produced by a Moving Diffuser Under the Gaussian Beam Laser Illumination," Jpn. J. Appl. Phys. 13, 2025 (1974).

H. Fujii and T. Asakura, "A Contrast Variation of Image Speckle Intensity Under Illumination of Partially Coherent Light," Opt. Commun. 12, 32 (1974).

V. A. Banakh et al., "Focused-Laser-Beam Scintillations in the Turbulent Atmosphere," J. Opt. Soc. Am. 64, 516 (1974).

1973 (2)

K. Nagata, T. Unehara, and J. Nishiwaki, "The Determination of rms Roughness and Correlation Length of Rough Surface by Measuring Spatial Coherence Function," Jpn. J. Appl. Phys. 12, 694 (1973).

K. Nagata and T. Unebara, "Spatial Correlation of Gaussian Beam in Moving Ground Glass," Jpn. J. Appl. Phys. 12, 694 (1973).

1972 (4)

1971 (2)

1970 (2)

1967 (3)

J. Upatnieks, "Improvement of Two-Dimensional Image Quality in Coherent Optical Systems," Appl. Opt. 11, 1905 (1967).

D. L. Fried, "Atmospheric Modulation Noise in an Optical Heterodyne Receiver," IEEE Trans. Quantum Electron. QE-3, 213 (1967).

L. H. Enloe, "Noise-Like Structure in the Image of Diffusely Reflecting Objects in Coherent Illumination," Bell. Syst. Tech. J. 46, 1479 (1967).

1965 (1)

1964 (3)

1963 (2)

1962 (1)

1956 (1)

Agarwal, G. S.

G. S. Agarwal, "Scattering from Rough Surfaces," Opt. Commun. 14, 161 (1975).

Arsenault, H.

Asakura, T.

H. Fujii and T. Asakura, "Effect of Surface Roughness on the Statistical Distribution of Image Speckle Intensity," Opt. Commun. 11, 35 (1974).

H. Fujii and T. Asakura, "A Contrast Variation of Image Speckle Intensity Under Illumination of Partially Coherent Light," Opt. Commun. 12, 32 (1974).

Banakh, V. A.

Bennett, H. E.

Beran, M. J.

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N. J., 1964).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Boucher, R.

Clifford, S. F.

T. Wang, S. F. Clifford, and G. R. Ochs, "Wind and Refractive-Turbulence Sensing Using Crossed Laser Beams," Appl. Opt. 13, 2602 (1974).

S. F. Clifford, G. R. Ochs, and T. Wang, "Theoretical Analysis and Experimental Evaluation of a Prototype Passive Sensor to Measure Crosswinds," U. S. Department of Commerce, National Oceanic and Atmospheric Administration, Technical Report No. ERL 312-WPL 35, Boulder, Colo. 80302, September 1974 (unpublished).

Crane, R. B.

Deitz, P. H.

Elbaum, M.

M. Elbaum, M. King, and M. Greenebaum, "Laser Correlography: Transmission of High-Resolution Object Signatures through the Turbulent Atmosphere," Riverside Research Institute, Technical Report No. T-1/306-3-11, 80 West End Ave., New York, N.Y. 10023, 31 October 1974. (unpublshed).

El-Sum, H. M. A.

Enloe, L. H.

L. H. Enloe, "Noise-Like Structure in the Image of Diffusely Reflecting Objects in Coherent Illumination," Bell. Syst. Tech. J. 46, 1479 (1967).

Estes, L. E.

Fried, D. L.

D. L. Fried, "Differential Angle of Arrival: Theory, Evaluation, and Measurement Feasibility," Radio Sci. 10, 71 (1975).

D. L. Fried, "Atmospheric Modulation Noise in an Optical Heterodyne Receiver," IEEE Trans. Quantum Electron. QE-3, 213 (1967).

D. L. Fried, "Effects of Atmospheric Turbulence on Static and Tracking Optical Heterodyne Receivers," Optical Sciences Consultants, Technical Report No. TR-027, P. O. Box 388, Yorba Linda, Calif. 92686, August 1971 (unpublished).

Fujii, H.

H. Fujii and T. Asakura, "A Contrast Variation of Image Speckle Intensity Under Illumination of Partially Coherent Light," Opt. Commun. 12, 32 (1974).

H. Fujii and T. Asakura, "Effect of Surface Roughness on the Statistical Distribution of Image Speckle Intensity," Opt. Commun. 11, 35 (1974).

George, N.

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

Goldfischer, L. I.

Goodman, J. W.

J. W. Goodman, "Dependence of Image Speckle Contrast on Surface Roughness," Opt. Commun. 14, 324 (1975).

J. W. Goodman, "Some Effects of Target-Induced Scintillation on Optical Radar Performance," Proc. IEEE 53, 1688 (1965).

Gould, G.

Greenebaum, M.

M. Elbaum, M. King, and M. Greenebaum, "Laser Correlography: Transmission of High-Resolution Object Signatures through the Turbulent Atmosphere," Riverside Research Institute, Technical Report No. T-1/306-3-11, 80 West End Ave., New York, N.Y. 10023, 31 October 1974. (unpublshed).

Greenwood, D. P.

D. P. Greenwood, "The Scattering from Curved Rough Surfaces of an EM Wave Transmitted Through a Turbulent Medium," IEEE Trans. Antennas Prop. AP-20, 19 (1972).

Jain, A.

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

Kellen, P. F.

King, M.

M. Elbaum, M. King, and M. Greenebaum, "Laser Correlography: Transmission of High-Resolution Object Signatures through the Turbulent Atmosphere," Riverside Research Institute, Technical Report No. T-1/306-3-11, 80 West End Ave., New York, N.Y. 10023, 31 October 1974. (unpublshed).

Kirkpatrick, P.

Kurtz, C. N.

Lahart, M. J.

Lawrence, R. S.

R. S. Lawrence and J. W. Strohbehn, "A Survey of Clean-Air Propagation Effects Relevant to Optical Communications," Proc. IEEE 58, 1523 (1970).

Leith, E. N.

Lowenthal, S.

Lutomirski, R. F.

Marathay, A. S.

Miller, M. G.

Nagata, K.

K. Nagata, T. Unehara, and J. Nishiwaki, "The Determination of rms Roughness and Correlation Length of Rough Surface by Measuring Spatial Coherence Function," Jpn. J. Appl. Phys. 12, 694 (1973).

K. Nagata and T. Unebara, "Spatial Correlation of Gaussian Beam in Moving Ground Glass," Jpn. J. Appl. Phys. 12, 694 (1973).

Nishiwaki, J.

K. Nagata, T. Unehara, and J. Nishiwaki, "The Determination of rms Roughness and Correlation Length of Rough Surface by Measuring Spatial Coherence Function," Jpn. J. Appl. Phys. 12, 694 (1973).

Ochs, G. R.

T. Wang, S. F. Clifford, and G. R. Ochs, "Wind and Refractive-Turbulence Sensing Using Crossed Laser Beams," Appl. Opt. 13, 2602 (1974).

S. F. Clifford, G. R. Ochs, and T. Wang, "Theoretical Analysis and Experimental Evaluation of a Prototype Passive Sensor to Measure Crosswinds," U. S. Department of Commerce, National Oceanic and Atmospheric Administration, Technical Report No. ERL 312-WPL 35, Boulder, Colo. 80302, September 1974 (unpublished).

Parrent, G. B.

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N. J., 1964).

Pederson, H. M.

H. M. Pederson, "The Roughness Dependence of Partially Developed Monochromatic Speckle Patterns," Opt. Commun. 12, 156 (1974).

Porfens, J.

Reynolds, G. O.

Schneiderman, A. M.

Skinner, T. J.

Sprague, R. A.

Strohbehn, J. W.

R. S. Lawrence and J. W. Strohbehn, "A Survey of Clean-Air Propagation Effects Relevant to Optical Communications," Proc. IEEE 58, 1523 (1970).

Takai, N.

N. Takai, "Statistics of Dynamic Speckles Produced by a Moving Diffuser Under the Gaussian Beam Laser Illumination," Jpn. J. Appl. Phys. 13, 2025 (1974).

Teich, M. C.

M. C. Teich, "Homodyne Detection of Infrared Radiation from a Moving Diffuse Target," Proc. IEEE 57, 786 (1969).

Unebara, T.

K. Nagata and T. Unebara, "Spatial Correlation of Gaussian Beam in Moving Ground Glass," Jpn. J. Appl. Phys. 12, 694 (1973).

Unehara, T.

K. Nagata, T. Unehara, and J. Nishiwaki, "The Determination of rms Roughness and Correlation Length of Rough Surface by Measuring Spatial Coherence Function," Jpn. J. Appl. Phys. 12, 694 (1973).

Upatnieks, J.

Wang, T.

T. Wang, S. F. Clifford, and G. R. Ochs, "Wind and Refractive-Turbulence Sensing Using Crossed Laser Beams," Appl. Opt. 13, 2602 (1974).

S. F. Clifford, G. R. Ochs, and T. Wang, "Theoretical Analysis and Experimental Evaluation of a Prototype Passive Sensor to Measure Crosswinds," U. S. Department of Commerce, National Oceanic and Atmospheric Administration, Technical Report No. ERL 312-WPL 35, Boulder, Colo. 80302, September 1974 (unpublished).

Warren, R. E.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Yura, H. T.

Appl. Opt. (8)

Appl. Phys. (1)

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

Bell. Syst. Tech. J. (1)

L. H. Enloe, "Noise-Like Structure in the Image of Diffusely Reflecting Objects in Coherent Illumination," Bell. Syst. Tech. J. 46, 1479 (1967).

IEEE Trans. Antennas Prop. (1)

D. P. Greenwood, "The Scattering from Curved Rough Surfaces of an EM Wave Transmitted Through a Turbulent Medium," IEEE Trans. Antennas Prop. AP-20, 19 (1972).

IEEE Trans. Quantum Electron. (1)

D. L. Fried, "Atmospheric Modulation Noise in an Optical Heterodyne Receiver," IEEE Trans. Quantum Electron. QE-3, 213 (1967).

J. Opt. Soc. Am. (15)

P. Kirkpatrick and H. M. A. El-Sum, "Image Formation by Reconstruction Wavefront. I. Physical Principles and Methods of Refinement," J. Opt. Soc. Am. 46, 825 (1956).

E. N. Leith and J. Upatnieks, "Wavefront Reconstruction with Diffused Illumination and Three-Dimensional Objects," J. Opt. Soc. Am. 54, 1295 (1964).

G. O. Reynolds and T. J. Skinner, "Mutual Coherence Function Applied to Imaging through a Random Medium," J. Opt. Soc. Am. 54, 1302 (1964).

L. I. Goldfischer, "Autocorrelation Function and Power Density of Laser-Produced Speckle Patterns," J. Opt. Soc. Am. 55, 247 (1965).

S. Lowenthal and H. Arsenault, "Image Formation for Coherent Diffuse Objects: Statistical Properties," J. Opt. Soc. Am. 60, 1478 (1970).

R. B. Crane, "Use of a Laser-Produced Speckle Pattern to Determine Surface Roughness," J. Opt. Soc. Am. 60, 1658 (1970).

C. N. Kurtz, "Transmitted Characteristics of Surface and the Design of Nearly Band-Limited Binary Diffusers," J. Opt. Soc. Am. 62, 982 (1972).

P. H. Deitz, "Image Information by Means of Speckle-Pattern Processing," J. Opt. Soc. Am. 65, 279 (1975).

L. E. Estes And R. Boucher, "Temporal And Spatial-intensity-Interferometer Imaging Through A Random Medium," J. Opt. Soc. Am. 65, 760 (1975).

M. J. Lahart and A. S. Marathay, "Image Speckle Patterns of Weak Diffusers," J. Opt. Soc. Am. 65, 769 (1975).

M. G. Miller, A. M. Schneiderman, and P. F. Kellen, "Second-Order Statistics of Laser-Speckle Patterns," J. Opt. Soc. Am. 65, 779 (1975).

V. A. Banakh et al., "Focused-Laser-Beam Scintillations in the Turbulent Atmosphere," J. Opt. Soc. Am. 64, 516 (1974).

H. E. Bennett, "Specular Reflectance of Aluminized Ground Glass and the Height Distribution of Surface Irregularities," J. Opt. Soc. Am. 53, 1389 (1963).

J. Porfens, "Relation Between the Height Distribution of a Rough Surface and the Reflection at Normal Incidence," J. Opt. Soc. Am. 53, 1394 (1963).

E. N. Leith and J. Upatnieks, "Reconstructed Wavefronts and Communication Theory," J. Opt. Soc. Am. 52, 1123 (1962).

Jpn. J. Appl. Phys. (3)

K. Nagata and T. Unebara, "Spatial Correlation of Gaussian Beam in Moving Ground Glass," Jpn. J. Appl. Phys. 12, 694 (1973).

N. Takai, "Statistics of Dynamic Speckles Produced by a Moving Diffuser Under the Gaussian Beam Laser Illumination," Jpn. J. Appl. Phys. 13, 2025 (1974).

K. Nagata, T. Unehara, and J. Nishiwaki, "The Determination of rms Roughness and Correlation Length of Rough Surface by Measuring Spatial Coherence Function," Jpn. J. Appl. Phys. 12, 694 (1973).

Opt. Commun. (5)

H. Fujii and T. Asakura, "Effect of Surface Roughness on the Statistical Distribution of Image Speckle Intensity," Opt. Commun. 11, 35 (1974).

H. M. Pederson, "The Roughness Dependence of Partially Developed Monochromatic Speckle Patterns," Opt. Commun. 12, 156 (1974).

G. S. Agarwal, "Scattering from Rough Surfaces," Opt. Commun. 14, 161 (1975).

H. Fujii and T. Asakura, "A Contrast Variation of Image Speckle Intensity Under Illumination of Partially Coherent Light," Opt. Commun. 12, 32 (1974).

J. W. Goodman, "Dependence of Image Speckle Contrast on Surface Roughness," Opt. Commun. 14, 324 (1975).

Radio Sci. (1)

D. L. Fried, "Differential Angle of Arrival: Theory, Evaluation, and Measurement Feasibility," Radio Sci. 10, 71 (1975).

Other (8)

D. L. Fried, "Effects of Atmospheric Turbulence on Static and Tracking Optical Heterodyne Receivers," Optical Sciences Consultants, Technical Report No. TR-027, P. O. Box 388, Yorba Linda, Calif. 92686, August 1971 (unpublished).

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N. J., 1964).

R. S. Lawrence and J. W. Strohbehn, "A Survey of Clean-Air Propagation Effects Relevant to Optical Communications," Proc. IEEE 58, 1523 (1970).

M. Elbaum, M. King, and M. Greenebaum, "Laser Correlography: Transmission of High-Resolution Object Signatures through the Turbulent Atmosphere," Riverside Research Institute, Technical Report No. T-1/306-3-11, 80 West End Ave., New York, N.Y. 10023, 31 October 1974. (unpublshed).

S. F. Clifford, G. R. Ochs, and T. Wang, "Theoretical Analysis and Experimental Evaluation of a Prototype Passive Sensor to Measure Crosswinds," U. S. Department of Commerce, National Oceanic and Atmospheric Administration, Technical Report No. ERL 312-WPL 35, Boulder, Colo. 80302, September 1974 (unpublished).

M. C. Teich, "Homodyne Detection of Infrared Radiation from a Moving Diffuse Target," Proc. IEEE 57, 786 (1969).

J. W. Goodman, "Some Effects of Target-Induced Scintillation on Optical Radar Performance," Proc. IEEE 53, 1688 (1965).

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