OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 66, Iss. 11 — Nov. 1, 1976
  • pp: 1164–1172

Statistics of speckle propagation through the turbulent atmosphere

Myung Hun Lee, J. Fred Holmes, and J. Richard Kerr  »View Author Affiliations

JOSA, Vol. 66, Issue 11, pp. 1164-1172 (1976)

View Full Text Article

Acrobat PDF (862 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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 ρ0 as the turbulence strength increases.

© 1976 Optical Society of America

Myung Hun Lee, J. Fred Holmes, and J. Richard Kerr, "Statistics of speckle propagation through the turbulent atmosphere," J. Opt. Soc. Am. 66, 1164-1172 (1976)

Sort:  Author  |  Year  |  Journal  |  Reset


  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).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited