Propagation of an Infinite Plane Wave in a Randomly Inhomogeneous Medium

D. L. Fried; J. D. Cloud

doi:10.1364/JOSA.56.001667

Journal of the Optical Society of America
Vol. 56,
Issue 12,
pp. 1667-1676
(1966)
•https://doi.org/10.1364/JOSA.56.001667

Propagation of an Infinite Plane Wave in a Randomly Inhomogeneous Medium

D. L. Fried and J. D. Cloud

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D. L. Fried and J. D. Cloud, "Propagation of an Infinite Plane Wave in a Randomly Inhomogeneous Medium," J. Opt. Soc. Am. 56, 1667-1676 (1966)

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Abstract

The results concerning the log-amplitude covariance for propagation of an infinite plane wave through a turbulent medium as derived by Tatarski, are developed further in analytic form. The numerical-integration data obtained by Tatarski for horizontal propagation are replaced by analytic results. Propagation of starlight down through the atmosphere is studied using a function fitted to Hufnagel’s data for the vertical distribution of turbulence. Here, also, analytic results are obtained, representing the first available data for the covariance of log-amplitude fluctuations of starlight. Results for the phase-structure functions for both types of propagation path are presented.

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Corrections

D. L. Fried and J. D. Cloud, "Erratum: Propagation of an Infinite Plane Wave in a Randomly Inhomogeneous Medium," J. Opt. Soc. Am. 57, 1166-1166 (1967)
https://opg.optica.org/josa/abstract.cfm?uri=josa-57-9-1166

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Equations (76)

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n	a_n	b_n
0	1.00000	6.84209
1	−7.63889 × 10⁻¹	5.27939 × 10⁻²
2	1.23778 × 10⁻²	−4.00354 × 10⁻³
3	−2.83086 × 10⁻³	8.98375 × 10⁻⁴
4	1.08825 × 10⁻³	−3.09202 × 10⁻⁴
5	−5.34385 × 10⁻⁴	1.34605 × 10⁻⁴
6	3.03065 × 10⁻⁴	−6.80418 × 10⁻⁵
7	−1.89046 × 10⁻⁴	3.81508 × 10⁻⁵
8	1.26184 × 10⁻⁴	−2.30845 × 10⁻⁵
9	−8.86012 × 10⁻⁵	1.48081 × 10⁻⁵

n	a_n	b_n	C_n	d_n
0	1.00000	6.22008	−7.85622 × 10⁻¹	1.45145 × 10⁻¹
1	−5.55556 × 10⁻¹	−1.79179 × 10⁻¹	2.28026 × 10⁻²	−1.73367 × 10⁻³
2	3.74486 × 10⁻¹	5.05797 × 10⁻²	−4.36773 × 10⁻³	1.67119 × 10⁻⁴
3	−3.13723 × 10⁻¹	−2.24463 × 10⁻²	1.45802 × 10⁻³	−3.32886 × 10⁻⁵
4	2.79596 × 10⁻¹	1.23097 × 10⁻²	−6.40001 × 10⁻⁴	9.68214 × 10⁻⁶
5	−2.56692 × 10⁻¹	−7.63945 × 10⁻³	3.30962 × 10⁻⁴	−3.55757 × 10⁻⁶
6	2.39822 × 10⁻¹	5.14252 × 10⁻³	−1.90915 × 10⁻⁴	1.53244 × 10⁻⁶
7	−2.26661 × 10⁻¹	−3.66677 × 10⁻³	1.19079 × 10⁻⁴	−7.40745 × 10⁻⁷
8	2.15982 × 10⁻¹	2.72914 × 10⁻³	−7.87611 × 10⁻⁵	3.907 76 × 10⁻⁷
9	−2.07068 × 10⁻¹	−2.09991 × 10⁻³	5.45286 × 10⁻⁵	−2.20795 × 10⁻⁷

n	a_n	b_n
0	1.00000	6.84209
1	−7.63889 × 10⁻¹	5.27939 × 10⁻²
2	1.23778 × 10⁻²	−4.00354 × 10⁻³
3	−2.83086 × 10⁻³	8.98375 × 10⁻⁴
4	1.08825 × 10⁻³	−3.09202 × 10⁻⁴
5	−5.34385 × 10⁻⁴	1.34605 × 10⁻⁴
6	3.03065 × 10⁻⁴	−6.80418 × 10⁻⁵
7	−1.89046 × 10⁻⁴	3.81508 × 10⁻⁵
8	1.26184 × 10⁻⁴	−2.30845 × 10⁻⁵
9	−8.86012 × 10⁻⁵	1.48081 × 10⁻⁵

n	a_n	b_n	C_n	d_n
0	1.00000	6.22008	−7.85622 × 10⁻¹	1.45145 × 10⁻¹
1	−5.55556 × 10⁻¹	−1.79179 × 10⁻¹	2.28026 × 10⁻²	−1.73367 × 10⁻³
2	3.74486 × 10⁻¹	5.05797 × 10⁻²	−4.36773 × 10⁻³	1.67119 × 10⁻⁴
3	−3.13723 × 10⁻¹	−2.24463 × 10⁻²	1.45802 × 10⁻³	−3.32886 × 10⁻⁵
4	2.79596 × 10⁻¹	1.23097 × 10⁻²	−6.40001 × 10⁻⁴	9.68214 × 10⁻⁶
5	−2.56692 × 10⁻¹	−7.63945 × 10⁻³	3.30962 × 10⁻⁴	−3.55757 × 10⁻⁶
6	2.39822 × 10⁻¹	5.14252 × 10⁻³	−1.90915 × 10⁻⁴	1.53244 × 10⁻⁶
7	−2.26661 × 10⁻¹	−3.66677 × 10⁻³	1.19079 × 10⁻⁴	−7.40745 × 10⁻⁷
8	2.15982 × 10⁻¹	2.72914 × 10⁻³	−7.87611 × 10⁻⁵	3.907 76 × 10⁻⁷
9	−2.07068 × 10⁻¹	−2.09991 × 10⁻³	5.45286 × 10⁻⁵	−2.20795 × 10⁻⁷

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Figures (4)

Tables (2)

Equations (76)

Journal of the Optical Society of America