Abstract

The dependence of the complex optical transfer function of an image-forming system on range through the atmosphere has been investigated experimentally. The simple case of a horizontal line of sight over flat terrain has been studied and empirical equations have been obtained which relate the transfer function to range and to the atmospheric temperature structure function. These equations agree with a general theory of wave propagation in a turbulent medium and are therefore applicable to a wide range of situations, provided that the distribution of the temperature structure function along the line of sight can be obtained. The experimental results also furnish evidence that the Kolmogorov expression for the temperature structure function (“the two-thirds law”) is applicable to scale sizes of about a centimeter or so.

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  1. L. A. Chernov, Wave Propagation in a Random Medium, translated by R. A. Silverman (McGraw-Hill Book Co., Inc., New York, 1960).
  2. V. I. Tatarski, Wave Propagation in a Turbulent Medium, translated by R. A. Silverman (McGraw-Hill Book Co., Inc., Inc., New York, 1961).
  3. J. R. Meyer-Arendt and C. B. Emmanuel, Optical Scintillation: a Survey of the Literature (National Bureau of Standards Technical Note 225, April 1965).
  4. E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Co. Inc., Reading, Massachusetts, 1963).
  5. R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).
  6. C. E. Coulman, J. Opt. Soc. Am. 55, 806 (1965).
  7. J. L. Lumley and H. A. Panofsky, The Structure of Atmospheric Turbulence (Interscience Publishers, New York, 1964).
  8. L. R. Tswang, Izv. Akad. Nauk SSSR, Ser. Geofiz. No. 8, 1252 (1960).
  9. V. I. Tatarski, Izv. Akad. Nauk SSSR, Ser. Geofiz. No. 6, 689 (1956).
  10. E. K. Webb, Appi. Opt. 3, 1329 (1964).
  11. R. T. Leslie, D. Shaw, and C. E. Coulman, J. Opt. Soc. Am. 56, 1261 (1966).
  12. O. G. Sutton, Atmospheric Turbulence (Methuen and Co., London, 1955).
  13. W. C. Swinbank, Quart. J. Roy. Meteorol. Soc. 90, 119 (1964).
  14. V. I. Tatarski, Ref. 2, Chap. 8.
  15. S. M. Rytov, Izv. Akad. Nauk, SSSR, Ser. Fiz. No. 2, 223 (1937).
  16. J. L. Lumley and H. A. Panofsky, Ref. 7, Chap. 5.
  17. V. I. Tatarski, Ref. 2, Chap. 9 and Note 9(e), p. 273.
  18. E. Djurle and A. Bäck, J. Opt. Soc. Am. 51, 1029 (1961).
  19. C. B. Rogers, J. Opt. Soc. Am. 55, 1151 (1965).

1966

R. T. Leslie, D. Shaw, and C. E. Coulman, J. Opt. Soc. Am. 56, 1261 (1966).

1965

C. E. Coulman, J. Opt. Soc. Am. 55, 806 (1965).

C. B. Rogers, J. Opt. Soc. Am. 55, 1151 (1965).

1964

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

E. K. Webb, Appi. Opt. 3, 1329 (1964).

W. C. Swinbank, Quart. J. Roy. Meteorol. Soc. 90, 119 (1964).

1961

E. Djurle and A. Bäck, J. Opt. Soc. Am. 51, 1029 (1961).

1960

L. R. Tswang, Izv. Akad. Nauk SSSR, Ser. Geofiz. No. 8, 1252 (1960).

1956

V. I. Tatarski, Izv. Akad. Nauk SSSR, Ser. Geofiz. No. 6, 689 (1956).

1955

O. G. Sutton, Atmospheric Turbulence (Methuen and Co., London, 1955).

1937

S. M. Rytov, Izv. Akad. Nauk, SSSR, Ser. Fiz. No. 2, 223 (1937).

Bäck, A.

E. Djurle and A. Bäck, J. Opt. Soc. Am. 51, 1029 (1961).

Chernov, L. A.

L. A. Chernov, Wave Propagation in a Random Medium, translated by R. A. Silverman (McGraw-Hill Book Co., Inc., New York, 1960).

Coulman, C. E.

R. T. Leslie, D. Shaw, and C. E. Coulman, J. Opt. Soc. Am. 56, 1261 (1966).

C. E. Coulman, J. Opt. Soc. Am. 55, 806 (1965).

Djurle, E.

E. Djurle and A. Bäck, J. Opt. Soc. Am. 51, 1029 (1961).

Emmanuel, C. B.

J. R. Meyer-Arendt and C. B. Emmanuel, Optical Scintillation: a Survey of the Literature (National Bureau of Standards Technical Note 225, April 1965).

Hufnagel, R. E.

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

Leslie, R. T.

R. T. Leslie, D. Shaw, and C. E. Coulman, J. Opt. Soc. Am. 56, 1261 (1966).

Lumley, J. L.

J. L. Lumley and H. A. Panofsky, The Structure of Atmospheric Turbulence (Interscience Publishers, New York, 1964).

J. L. Lumley and H. A. Panofsky, Ref. 7, Chap. 5.

Meyer-Arendt, J. R.

J. R. Meyer-Arendt and C. B. Emmanuel, Optical Scintillation: a Survey of the Literature (National Bureau of Standards Technical Note 225, April 1965).

O&Neill, E. L.

E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Co. Inc., Reading, Massachusetts, 1963).

Panofsky, H. A.

J. L. Lumley and H. A. Panofsky, The Structure of Atmospheric Turbulence (Interscience Publishers, New York, 1964).

J. L. Lumley and H. A. Panofsky, Ref. 7, Chap. 5.

Rogers, C. B.

C. B. Rogers, J. Opt. Soc. Am. 55, 1151 (1965).

Rytov, S. M.

S. M. Rytov, Izv. Akad. Nauk, SSSR, Ser. Fiz. No. 2, 223 (1937).

Shaw, D.

R. T. Leslie, D. Shaw, and C. E. Coulman, J. Opt. Soc. Am. 56, 1261 (1966).

Stanley, N. R.

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

Sutton, O. G.

O. G. Sutton, Atmospheric Turbulence (Methuen and Co., London, 1955).

Swinbank, W. C.

W. C. Swinbank, Quart. J. Roy. Meteorol. Soc. 90, 119 (1964).

Tatarski, V. I.

V. I. Tatarski, Izv. Akad. Nauk SSSR, Ser. Geofiz. No. 6, 689 (1956).

V. I. Tatarski, Wave Propagation in a Turbulent Medium, translated by R. A. Silverman (McGraw-Hill Book Co., Inc., Inc., New York, 1961).

V. I. Tatarski, Ref. 2, Chap. 8.

V. I. Tatarski, Ref. 2, Chap. 9 and Note 9(e), p. 273.

Tswang, L. R.

L. R. Tswang, Izv. Akad. Nauk SSSR, Ser. Geofiz. No. 8, 1252 (1960).

Webb, E. K.

E. K. Webb, Appi. Opt. 3, 1329 (1964).

Other

L. A. Chernov, Wave Propagation in a Random Medium, translated by R. A. Silverman (McGraw-Hill Book Co., Inc., New York, 1960).

V. I. Tatarski, Wave Propagation in a Turbulent Medium, translated by R. A. Silverman (McGraw-Hill Book Co., Inc., Inc., New York, 1961).

J. R. Meyer-Arendt and C. B. Emmanuel, Optical Scintillation: a Survey of the Literature (National Bureau of Standards Technical Note 225, April 1965).

E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Co. Inc., Reading, Massachusetts, 1963).

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

C. E. Coulman, J. Opt. Soc. Am. 55, 806 (1965).

J. L. Lumley and H. A. Panofsky, The Structure of Atmospheric Turbulence (Interscience Publishers, New York, 1964).

L. R. Tswang, Izv. Akad. Nauk SSSR, Ser. Geofiz. No. 8, 1252 (1960).

V. I. Tatarski, Izv. Akad. Nauk SSSR, Ser. Geofiz. No. 6, 689 (1956).

E. K. Webb, Appi. Opt. 3, 1329 (1964).

R. T. Leslie, D. Shaw, and C. E. Coulman, J. Opt. Soc. Am. 56, 1261 (1966).

O. G. Sutton, Atmospheric Turbulence (Methuen and Co., London, 1955).

W. C. Swinbank, Quart. J. Roy. Meteorol. Soc. 90, 119 (1964).

V. I. Tatarski, Ref. 2, Chap. 8.

S. M. Rytov, Izv. Akad. Nauk, SSSR, Ser. Fiz. No. 2, 223 (1937).

J. L. Lumley and H. A. Panofsky, Ref. 7, Chap. 5.

V. I. Tatarski, Ref. 2, Chap. 9 and Note 9(e), p. 273.

E. Djurle and A. Bäck, J. Opt. Soc. Am. 51, 1029 (1961).

C. B. Rogers, J. Opt. Soc. Am. 55, 1151 (1965).

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