Abstract

The atmospheric structure constant, CN2, has been measured by use of three instruments, one optical and two thermal. The data show very good correlation (ρxy = 0.88), but are related by a consistent scale factor: CN (optical) = 0.34 × 10−8 cm−2/3 + 1.45CN (thermal). Several effects are discussed-that may explain these results.

© 1975 Optical Society of America

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References

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  1. J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, OSA Topical Meeting on Optical Progagation through Turbulence, Boulder, Colo., July 1974, paper ThB5.
  2. J. E. Pearson, Coherent Optical Adaptive Techniques (COAT), , DARPA/RADC Contract No. F30602-73-C-0248, December1974 (available from RADC).
  3. We are grateful to G. R. Ochs of NOAA for suggesting this technique.
  4. G. R. Ochs, (U.S. Government Printing Office, Washington, D.C., 1967).
  5. P. M. Livingston, Appl. Opt. 11, 684 (1972).
    [Crossref] [PubMed]
  6. G. R. Ochs, R. R. Bergman, and J. R. Snyder, J. Opt. Soc. Am. 59, 231 (1969).
    [Crossref]
  7. D. L. Fried, J. Opt. Soc. Am. 57, 175 (1967).
    [Crossref]
  8. D. L. Fried and J. B. Seidman, J. Opt. Soc. Am. 57, 181 (1967).
    [Crossref]
  9. J. A. Dowling and P. M. Livingston, J. Opt. Soc. Am. 63, 846 (1973).
    [Crossref]
  10. Suggested independently by W. P. Brown and a reviewer.
  11. C. A. Friehe, C. H. Gibson, and G. Dreyer, J. Opt. Soc. Am. 62, 1340 (1972).
  12. G. E. Mevers, M. P. Keister, and D. L. Fried, J. Opt. Soc. Am. 59, 491 (1969).
  13. J. R. Kerr, J. Opt. Soc. Am. 62, 1040 (1972).
    [Crossref]
  14. J. R. Dunphy and J. R. Kerr, J. Opt. Soc. Am. 63, 981 (1973).
    [Crossref]

1973 (2)

1972 (3)

1969 (2)

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

G. E. Mevers, M. P. Keister, and D. L. Fried, J. Opt. Soc. Am. 59, 491 (1969).

1967 (2)

Bergman, R. R.

Bridges, W. B.

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, OSA Topical Meeting on Optical Progagation through Turbulence, Boulder, Colo., July 1974, paper ThB5.

Brown, W. P.

Suggested independently by W. P. Brown and a reviewer.

Dowling, J. A.

Dreyer, G.

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

Dunphy, J. R.

Fried, D. L.

Friehe, C. A.

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

Gibson, C. H.

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

Horwitz, L. S.

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, OSA Topical Meeting on Optical Progagation through Turbulence, Boulder, Colo., July 1974, paper ThB5.

Keister, M. P.

G. E. Mevers, M. P. Keister, and D. L. Fried, J. Opt. Soc. Am. 59, 491 (1969).

Kerr, J. R.

Livingston, P. M.

Mevers, G. E.

G. E. Mevers, M. P. Keister, and D. L. Fried, J. Opt. Soc. Am. 59, 491 (1969).

Ochs, G. R.

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

G. R. Ochs, (U.S. Government Printing Office, Washington, D.C., 1967).

Ogrodnik, R. F.

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, OSA Topical Meeting on Optical Progagation through Turbulence, Boulder, Colo., July 1974, paper ThB5.

Pearson, J. E.

J. E. Pearson, Coherent Optical Adaptive Techniques (COAT), , DARPA/RADC Contract No. F30602-73-C-0248, December1974 (available from RADC).

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, OSA Topical Meeting on Optical Progagation through Turbulence, Boulder, Colo., July 1974, paper ThB5.

Seidman, J. B.

Snyder, J. R.

Walsh, T. J.

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, OSA Topical Meeting on Optical Progagation through Turbulence, Boulder, Colo., July 1974, paper ThB5.

Appl. Opt. (1)

J. Opt. Soc. Am. (8)

Other (5)

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, OSA Topical Meeting on Optical Progagation through Turbulence, Boulder, Colo., July 1974, paper ThB5.

J. E. Pearson, Coherent Optical Adaptive Techniques (COAT), , DARPA/RADC Contract No. F30602-73-C-0248, December1974 (available from RADC).

We are grateful to G. R. Ochs of NOAA for suggesting this technique.

G. R. Ochs, (U.S. Government Printing Office, Washington, D.C., 1967).

Suggested independently by W. P. Brown and a reviewer.

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Figures (5)

FIG. 1
FIG. 1

Instruments used to measure C N 2. (a) Differential two-probe microthermometer. P1, P2: dual probes; A: amplifier; B: probe balance; F: high-pass filter; RMS: true rms module; I: integrator; R: recorder. (b) Optical scintillometer. L: He–Ne laser; O. F.: 6328 Å filter; P: pinholes; f: lens; D: photodiode; LA: logarithmic amplifier, 2V/decade. Other items as in (a).

FIG. 2
FIG. 2

Typical 24-h data record of air temperature, T, and of C N 2 as measured by three different instruments. SC: scintillometer; (ΔT)M: microthermometer at midrange, (ΔT)T: microthermometer at target; R: time of sunrise; N: sun overhead; S: sunset.

FIG. 3
FIG. 3

Correlation between CN measured by two separate (ΔT) instruments. (a) Two ΔT units placed at same midrange location. Straight-line fit to data is Y = 0.27 × 10−8 + 0.93X with a linear correlation coefficient, ρxy = 0.92. (b) One ΔT unit near the target at the end of the 99 m propagation range compared to a ΔT unit near midrange. Straight-line fit is Y = −1.22 × 10−8 + 1.08X with ρxy = 0.91.

FIG. 4
FIG. 4

Correlation between optical and thermal values of CN. Data from two ΔT units is shown: ● = midrange ΔT unit, ▲ = target ΔT unit. Straight line fit is Y = 0.34 × 10−8 + 1.45X with a linear correlation coefficient, ρxy = 0.88.

FIG. 5
FIG. 5

Turbulence frequency spectra as seen by microthermometer (ΔT) and scintillometer (SC). An amplitude change of 20 dB corresponds to a factor of 10 change of signal voltage.

Equations (7)

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C N = 7.76 × 10 - 5 r 1 / 3 ( P T 2 ) ( 1 + 0.00752 λ 2 ) ( Δ T ) rms ,
C N = 1.703 × 10 - 4 ( P T 2 ) ( Δ T ) rms cm - 1 / 3 .
C N 2 = C l ( 0 ) [ C l s ( 0 ) / C l ( 0 ) ] 0.124 k 7 / 6 R 11 / 6 ,
C l ( 0 ) = ln ( E ) - ln ( E 2 ,
V rms = 2 2.303 ln I - ln I 2 1 / 2 .
C N 2 = 1.97 × 10 - 13 V rms 2 cm - 2 / 3 .
σ 2 = C N 2 k 7 / 6 R 11 / 6 ,