Abstract

An analytic formulation for the speckle-intensity autocovariance function generated by a laser beam with random pointing error is developed. The analysis utilizes the extended Huygens–Fresnel principle and includes the effects of atmospheric turbulence on propagation of the misaligned laser beam to a diffuse target and on propagation of the speckle field back to the receiver. The main object of the development is to estimate the effects of deterministic and random pointing errors of the illuminating source on the statistics of the received intensity. In addition, methods for numerical evaluation of the autocovariance function are discussed, and some numerical results are shown. It is found that the autocovariance can be substantially increased above its vacuum value by the atmospheric turbulence.

© 1981 Optical Society of America

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  1. J. F. Holmes et al., Experimental Pulsed Laser, Remote Crosswind Measurement System—Feasibility Study and Design (Part V), U. S. Army Armament Command, Research and Development Contractor Report ARSCD-CR-79-007 (Fire Control and Small Caliber Weapon Systems Laboratory, Dover, N.J., 1978).
  2. H. Lee, J. F. Holmes, and J. R. Kerr, "Statistics of speckle propagation through the turbulent atmosphere," J. Opt. Soc. Am. 66, 1164–1172 (1976).
  3. J. F. Holmes, M. H. Lee, and J. R. Kerr, "The effect of the logamplitude covariance function on the statistics of speckle propagation through the turbulent atmosphere," J. Opt. Soc. Am. 70, 355–360 (1980).
  4. R. F. Lutomirski and H. T. Yura, "Propagation of a finite optical beam in an inhomogeneous medium," Appl. Opt. 10, 1652–1658 (1971).
  5. H. T. Yura, "Mutual coherence function of a finite cross section optical beam propagation in a turbulent medium," Appl. Opt. 11, 1399–1406 (1972).
  6. D. L. Fried, "Statistics of laser beam fade induced by pointing jitter," Appl. Opt. 12, 422–423 (1973).
  7. S. O. Rice, in Selected Papers on Noise and Stochastic Processes, N. Wax ed. (Dover, New York, 1954), p. 133.
  8. I. S. Gradshteyn and I. W. Ryzhik, Table of Integrals Series and Products (Academic, New York, 1965), p. 718, Eq. 6.633.4.
  9. J. F. Holmes et al., Experimental Pulsed Laser, Remote Crosswind Measurement System—Feasibility Study and Design (Part IV), U.S. Army Armament Command, Research and Development Technical Report FA-TA-76065 (Frankford Arsenal, Philadelphia, Pa., 1976).
  10. M. H. Lee, J. F. Holmes, and J. R. Kerr, "Generalized spherical wave mutual coherence function," J. Opt. Soc. Am. 67, 1279–1281 (1977).

1980 (1)

1977 (1)

1976 (1)

1973 (1)

1972 (1)

1971 (1)

Fried, D. L.

Gradshteyn, I. S.

I. S. Gradshteyn and I. W. Ryzhik, Table of Integrals Series and Products (Academic, New York, 1965), p. 718, Eq. 6.633.4.

Holmes, J. F.

J. F. Holmes, M. H. Lee, and J. R. Kerr, "The effect of the logamplitude covariance function on the statistics of speckle propagation through the turbulent atmosphere," J. Opt. Soc. Am. 70, 355–360 (1980).

M. H. Lee, J. F. Holmes, and J. R. Kerr, "Generalized spherical wave mutual coherence function," J. Opt. Soc. Am. 67, 1279–1281 (1977).

H. Lee, J. F. Holmes, and J. R. Kerr, "Statistics of speckle propagation through the turbulent atmosphere," J. Opt. Soc. Am. 66, 1164–1172 (1976).

J. F. Holmes et al., Experimental Pulsed Laser, Remote Crosswind Measurement System—Feasibility Study and Design (Part IV), U.S. Army Armament Command, Research and Development Technical Report FA-TA-76065 (Frankford Arsenal, Philadelphia, Pa., 1976).

J. F. Holmes et al., Experimental Pulsed Laser, Remote Crosswind Measurement System—Feasibility Study and Design (Part V), U. S. Army Armament Command, Research and Development Contractor Report ARSCD-CR-79-007 (Fire Control and Small Caliber Weapon Systems Laboratory, Dover, N.J., 1978).

Kerr, J. R.

Lee, H.

Lee, M. H.

Lutomirski, R. F.

Rice, S. O.

S. O. Rice, in Selected Papers on Noise and Stochastic Processes, N. Wax ed. (Dover, New York, 1954), p. 133.

Ryzhik, I. W.

I. S. Gradshteyn and I. W. Ryzhik, Table of Integrals Series and Products (Academic, New York, 1965), p. 718, Eq. 6.633.4.

Yura, H. T.

Appl. Opt. (3)

J. Opt. Soc. Am. (3)

Other (4)

J. F. Holmes et al., Experimental Pulsed Laser, Remote Crosswind Measurement System—Feasibility Study and Design (Part V), U. S. Army Armament Command, Research and Development Contractor Report ARSCD-CR-79-007 (Fire Control and Small Caliber Weapon Systems Laboratory, Dover, N.J., 1978).

S. O. Rice, in Selected Papers on Noise and Stochastic Processes, N. Wax ed. (Dover, New York, 1954), p. 133.

I. S. Gradshteyn and I. W. Ryzhik, Table of Integrals Series and Products (Academic, New York, 1965), p. 718, Eq. 6.633.4.

J. F. Holmes et al., Experimental Pulsed Laser, Remote Crosswind Measurement System—Feasibility Study and Design (Part IV), U.S. Army Armament Command, Research and Development Technical Report FA-TA-76065 (Frankford Arsenal, Philadelphia, Pa., 1976).

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