Abstract

Measurements of the vertical-path atmospheric modulation transfer function (MTF) have been completed at both desert and mountain locations for daytime and nighttime conditions. The average atmospheric MTF characterized by the parameter r0 is found to be virtually identical, 34 mm, for both the desert and the mountain locations during the day, whereas a ratio of 1.7 is observed at night, 47 mm versus 82 mm, respectively. Relative peaks in r0 for both the mountain and the desert sites corresponding to the daily air-surface temperature crossover periods are observed. By collecting data at both 2 and 8 m above the desert surface, the effects of tower height are investigated.

© 1981 Optical Society of America

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References

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  1. D. L. Walters, D. L. Favier, and J. R. Hines, “Vertical path atmospheric MTF measurements,” J. Opt. Soc. Am. 69, 828–837 (1979).
    [Crossref]
  2. D. L. Fried, “Optical resolution looking down through a randomly homogeneous medium for very long and very short exposures,” J. Opt. Soc. Am. 56, 1372–1379 (1966).
    [Crossref]
  3. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), pp. 164–172.
  4. R. E. Hufnagel and N. R. Stanley, “Modulation transfer function associated with image transmission through turbulent media,” J. Opt. Soc. Am. 54, 52–61 (1964).
    [Crossref]
  5. R. F. Lutamirski and H. T. Yura, “Wave structure function and mutual coherence function of an optical wave in a turbulent atmosphere,” J. Opt. Soc. Am. 61, 482–487 (1971).
    [Crossref]
  6. D. L. Walters and K. E. Kunkel, “Atmospheric modulation transfer function for desert and mountain locations—the atmospheric effects on r0,” J. Opt. Soc. Am. 71, 397–405 (1981).
    [Crossref]

1981 (1)

1979 (1)

1971 (1)

1966 (1)

1964 (1)

Favier, D. L.

Fried, D. L.

Hines, J. R.

Hufnagel, R. E.

Kunkel, K. E.

Lutamirski, R. F.

Stanley, N. R.

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), pp. 164–172.

Walters, D. L.

Yura, H. T.

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Figures (8)

Fig. 1
Fig. 1

Average diurnal variation of the 500-nm transverse coherence length r0 for a desert location at 2 and 8 m above the surface. The 2-m data include 646 measurements collected during April–June 1978, and the 8-m data include 1264 measurements collected during July–December 1978, all averaged in 1-h intervals.

Fig. 2
Fig. 2

Transverse coherence data for the 2-m desert site of Fig. 1 compared with the previous data for mountain site A of Ref. 1. The mountain data were also collected at 2 m above the mountain surface. The data are averaged in 1-h intervals.

Fig. 3
Fig. 3

Transverse coherence length data of Fig. 1 replotted with a normalized time scale such that sunrise (0600 h) and sunset (1800 h) are fixed throughout the year (see the Appendix). The data are averaged in 20-min intervals.

Fig. 4
Fig. 4

Transverse coherence length data of Fig. 2, replotted with a normalized time scale such that sunrise (0600 h) and sunset (1800 h) are fixed throughout the year (see the Appendix). The data are averaged in 20-min intervals.

Fig. 5
Fig. 5

Transverse coherence length data for the three mountain sites of Ref. 1 replotted with a normalized time scale such that sunrise (0600 h) and sunset (1800 h) are fixed throughout the year (see the Appendix). The data are averaged in 20-min intervals.

Fig. 6
Fig. 6

Log-normal cumulative probability curves for the 2-m desert site. The daytime median and standard deviation are 34.1 ÷ × 1.23 mm, and the nighttime median and standard deviation are 47.5 ÷ × 1.33 mm.

Fig. 7
Fig. 7

Log-normal cumulative probability curves for the 8-m desert site. The daytime median and standard deviation are 51.9 ÷ × 36 mm, and the nighttime median and standard deviation are 46.0 ÷ × 1.32 mm.

Fig. 8
Fig. 8

Log-normal cumulative probability curves for the three mountain sites of Ref. 1 based on normalized time. The daytime medians and standard deviations are 33.1 ÷ × 1.22 , 44.3 ÷ × 1.31, and 34.1 ÷ × 1.26 mm for sites A, B, and C, respectively. The nighttime medians and standard deviations are 86.5 ÷ × 1.32 , 81.5 ÷ × 1.36, and 79.8 ÷ × 1.49 mm for sites A, B, and C, respectively.

Equations (6)

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MTF a ( f ) = exp [ - 3.44 ( λ R f / r 0 ) 5 / 3 ] ,
MCF ( ρ ) = exp [ - ( ρ / ρ 0 ) 5 / 3 ] ,
ρ 0 = ( 1.46 k 2 0 L C n 2 d z ) - 3 / 5 ,
r 0 = 2.1 ρ 0 .
ρ 0 = R λ f e .
t n + 1 = t m s + ( 6 - t r ) sin 2 ( 2 π t n / 24 ) , t m s 12 , t n + 1 = t m s + ( 18 - t s ) sin 2 ( 2 π t n / 24 ) , 12 < t m s 24.