Abstract

Laser-beam propagation through atmospheric turbulence is analyzed theoretically and compared with measurements at λ=0.63 and 10.6 µm. Calculations based either on irradiance statistics or mutual coherence function (MCF) are analyzed; a general expression for long-term-average beam spread based on the turbulence MCF is obtained. The spread of a laser beam focused over moderate distances can be separated into short- and long-term averages that differ by beam wander, which has been found to be essentially independent of wavelength and adequately described by geometric optics. However, a significant wavelength dependence of short-term-average beam spread is found experimentally. Measurements at 10.6 µm are nearly diffraction limited, whereas corresponding data for 0.63 µm are strongly influenced by variations of the refractive-index structure constant <i>C<sub>n</sub></i>. An empirical formula for long-term-average beam spread is at variance with the wave-number-dependent functional form predicted by MCF calculations. Both the irradiance and MCF approaches go over into the same asymptotic functional dependence for visible wavelengths and long ranges. Angular-beam-spread measurements at 0.63 µm support this conclusion.

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  2. R. A. Schmeltzer, Q. Appl. Math. 24, 339 (1966).
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  11. D. A. de Wolf, Radio Sci. 2, 1379 (1967); Radio Sci. 3, 308 (1968).
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  13. A. D. Varvatsis and M. I. Sancer, Can. J. Phys. 49, 1233 (1971).
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  28. P. M. Livingston, Appl. Opt. 11, 684 (1972).
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Alcaraz, E. C.

E. C. Alcaraz and P. M. Livingston, in Proceedings Electro-Optical Design Conference, 1972-West (Indus, and Scientific Management Inc., Chicago, Ill., 1971), p. 76.

Beran, M.

M. Beran, J. Opt. Soc. Am. 56, 1475 (1966).

Bergman, R. R.

G. R. Ochs, R. R. Bergman, and J. R. Snyder, J. Opt. Soc. Am. 59, 231 (1969).

Born, M.

M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, Oxford, 1964).

Brown, W. P.

W. P. Brown, IEEE Trans. Antennas Propag. 15, 81 (1967).

W. P. Brown, J. Opt. Soc. Am. 61, 1051 (1971).

Buck, A. L.

A. L. Buck, Proc. IEEE 55, 448 (1967).

Carlson, F. P.

F. P. Carlson and A. Ishimaru, J. Opt. Soc. Am. 59, 319 (1969).

Chiba, T.

T. Chiba, Appl. Opt. 10, 2456 (1971).

Collins, S. A.

F. G. Gebhardt and S. A. Collins, J. Opt. Soc. Am. 59, 1139 (1969).

de Wolf, D. A.

D. A. de Wolf (private communication).

D. A. de Wolf, Radio Sci. 2, 1379 (1967); Radio Sci. 3, 308 (1968).

Dreyer, G.

C. A. Friehe, C. H. Gibson, and G. Dreyer, J. Opt. Soc. Am. 62, 1340 (1972).

Efroymson, M. A.

M. A. Efroymson, in Multiple Regression Analysis in Mathematical Methods for Digital Computers, Volume 1, edited by Anthony Ralston and Herbert S. Wilf (Wiley, New York, 1960).

Fried, D. L.

D. L. Fried and J. B. Seidman, J. Opt. Soc. Am. 57, 181 (1967).

D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966); J. Opt. Soc. Am. 56, 1380 (1966).

D. L. Fried, J. Opt. Soc. Am. 57, 175 (1967).

Friehe, C. A.

C. A. Friehe, C. H. Gibson, and G. Dreyer, J. Opt. Soc. Am. 62, 1340 (1972).

Gebhardt, F. G.

F. G. Gebhardt and S. A. Collins, J. Opt. Soc. Am. 59, 1139 (1969).

Gibson, C. H.

C. A. Friehe, C. H. Gibson, and G. Dreyer, J. Opt. Soc. Am. 62, 1340 (1972).

Greenebaum, M.

M. Greenebaum (private communication).

Harris, R. W.

R. W. Harris, J. Opt. Soc. Am. 62, 722A (1972).

Ishimaru, A.

A. Ishimaru, Proc. IEEE 57, 407 (1969).

F. P. Carlson and A. Ishimaru, J. Opt. Soc. Am. 59, 319 (1969).

Livingston, P. M.

E. C. Alcaraz and P. M. Livingston, in Proceedings Electro-Optical Design Conference, 1972-West (Indus, and Scientific Management Inc., Chicago, Ill., 1971), p. 76.

P. M. Livingston, Appl. Opt. 11, 684 (1972).

Ochs, G. R.

G. R. Ochs, A Resistance Thermometer for Measurement of Rapid Air Temperature Fluctuations, ESSA Tech. Report No. IER 47-ITSA 46 (U.S. Government Printing Office, Washington, D.C., 1967).

G. R. Ochs, R. R. Bergman, and J. R. Snyder, J. Opt. Soc. Am. 59, 231 (1969).

G. R. Ochs, A Circuit for the Measurement of Normalized Crosscorrelations, ESSA Tech. Report No. ERL 63-WPL 2 (U.S. Government Printing Office, Washington, D.C., 1968).

Sancer, M. I.

A. D. Varvatsis and M. I. Sancer, Can. J. Phys. 49, 1233 (1971).

Schmeltzer, R. A.

R. A. Schmeltzer, Q. Appl. Math. 24, 339 (1966).

Seidman, J. B.

D. L. Fried and J. B. Seidman, J. Opt. Soc. Am. 57, 181 (1967).

Snyder, J. R.

G. R. Ochs, R. R. Bergman, and J. R. Snyder, J. Opt. Soc. Am. 59, 231 (1969).

Strohbehn, J. W.

J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

Varvatsis, A. D.

A. D. Varvatsis and M. I. Sancer, Can. J. Phys. 49, 1233 (1971).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, Oxford, 1964).

Yura, H. T.

H. T. Yura, J. Opt. Soc. Am. 62, 889 (1972).

H. T. Yura, Appl. Opt. 11, 1399 (1972).

Zwang, L. R.

L. R. Zwang, Izv. Akad. Nauk SSSR Ser. Geofiz. 8, 1252 (1960).

Other

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

R. A. Schmeltzer, Q. Appl. Math. 24, 339 (1966).

A. Ishimaru, Proc. IEEE 57, 407 (1969).

F. P. Carlson and A. Ishimaru, J. Opt. Soc. Am. 59, 319 (1969).

F. G. Gebhardt and S. A. Collins, J. Opt. Soc. Am. 59, 1139 (1969).

M. Greenebaum (private communication).

A. L. Buck, Proc. IEEE 55, 448 (1967).

M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, Oxford, 1964).

M. Beran, J. Opt. Soc. Am. 56, 1475 (1966).

J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).

D. A. de Wolf, Radio Sci. 2, 1379 (1967); Radio Sci. 3, 308 (1968).

W. P. Brown, IEEE Trans. Antennas Propag. 15, 81 (1967).

A. D. Varvatsis and M. I. Sancer, Can. J. Phys. 49, 1233 (1971).

H. T. Yura, Appl. Opt. 11, 1399 (1972).

W. P. Brown, J. Opt. Soc. Am. 61, 1051 (1971).

H. T. Yura, J. Opt. Soc. Am. 62, 889 (1972).

D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966); J. Opt. Soc. Am. 56, 1380 (1966).

D. A. de Wolf (private communication).

R. W. Harris, J. Opt. Soc. Am. 62, 722A (1972).

G. R. Ochs, A Circuit for the Measurement of Normalized Crosscorrelations, ESSA Tech. Report No. ERL 63-WPL 2 (U.S. Government Printing Office, Washington, D.C., 1968).

L. R. Zwang, Izv. Akad. Nauk SSSR Ser. Geofiz. 8, 1252 (1960).

G. R. Ochs, A Resistance Thermometer for Measurement of Rapid Air Temperature Fluctuations, ESSA Tech. Report No. IER 47-ITSA 46 (U.S. Government Printing Office, Washington, D.C., 1967).

G. R. Ochs, R. R. Bergman, and J. R. Snyder, J. Opt. Soc. Am. 59, 231 (1969).

D. L. Fried and J. B. Seidman, J. Opt. Soc. Am. 57, 181 (1967).

D. L. Fried, J. Opt. Soc. Am. 57, 175 (1967).

M. A. Efroymson, in Multiple Regression Analysis in Mathematical Methods for Digital Computers, Volume 1, edited by Anthony Ralston and Herbert S. Wilf (Wiley, New York, 1960).

C. A. Friehe, C. H. Gibson, and G. Dreyer, J. Opt. Soc. Am. 62, 1340 (1972).

P. M. Livingston, Appl. Opt. 11, 684 (1972).

E. C. Alcaraz and P. M. Livingston, in Proceedings Electro-Optical Design Conference, 1972-West (Indus, and Scientific Management Inc., Chicago, Ill., 1971), p. 76.

T. Chiba, Appl. Opt. 10, 2456 (1971).

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