Study of Target Edge Response Viewed Through Atmospheric Turbulence over Water

P. M. Livingston

doi:10.1364/AO.11.002352

Applied Optics
Vol. 11,
Issue 10,
pp. 2352-2357
(1972)
•https://doi.org/10.1364/AO.11.002352

Study of Target Edge Response Viewed Through Atmospheric Turbulence over Water

P. M. Livingston

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P. M. Livingston, "Study of Target Edge Response Viewed Through Atmospheric Turbulence over Water," Appl. Opt. 11, 2352-2357 (1972)

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Abstract

Photographed edge response of a quadrant target made through atmospheric turbulence at a range of 1.6 km 10.7 m above water was found to fit an error function form quite accurately. A theoretical estimate of the intensity point spread function based upon a parabolic approximation to the wave structure function for a point source is consistent with the data. Assuming the validity of the approximation, thermal values of C_n give turbulence inner scales in the millimeter range.

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Date/time		Code	No. of values averaged	β × 10⁷	Variation coefficient, %	Exp. time (sec)
12-6-71	1513	227H	4	6.981	1.7	$\frac{1}{2}$
12-6-71	1513	228H	7	6.617	2.6	$\frac{1}{4}$
12-6-71	1513	229H	6	6.314	2.7	1
12-6-71	1513	230H	4	5.499	3.6	$\frac{1}{8}$
12-6-71	1513	231H	5	6.117	3.2	$\frac{1}{15}$
12-6-71	1513	227V	3	5.442	8.4	$\frac{1}{2}$
12-6-71	1513	228V	4	6.824	1.8	$\frac{1}{4}$
12-6-71	1513	229V	3	5.642	3.1	1
12-6-71	1513	230V	5	5.343	7.3	$\frac{1}{8}$
12-6-71	1513	231V	3	5.883	3.7	$\frac{1}{15}$
12-8-71	1234	310H	8	2.397	4.3	$\frac{1}{4}$
12-8-71	1234	311H	9	2.536	3.3	$\frac{1}{8}$
12-8-71	1234	322H	7	1.720	4.1	$\frac{1}{4}$
12-8-71	1234	323H	13	2.692	11.0	$\frac{1}{2}$
12-8-71	1234	310V	3	2.748	5.5	$\frac{1}{4}$
12-8-71	1234	311V	5	1.651	0.98	$\frac{1}{8}$
12-8-71	1234	322V	3	2.144	4.0	$\frac{1}{4}$
12-8-71	1234	323V	6	2.063	2.0	$\frac{1}{2}$

Date/Time		Thermal $C_{N} (m^{\frac{1}{3}})$	Normal wind speed (m/sec)	Air temp.(°C)	Water temp (°C)	Relative humidity (%)	General weather condition
12-6-71	1513	(1.32 ± 0.1) × 10⁻⁷	4.1	13.0	12.0	76	Partly cloudy visibility ~6mi
12-8-71	1234	(7.8 ± 0.7) × 10⁻⁸	1.2	10.0	10.5	94	Haze/light, fog/light rain

Date/time	12-6-71 1513	12-8-71 1234
Avg. horiz. β × 10⁷	6.31	2.542
Coef. of var. (%)	7.9	2.0
Avg. vert. β × 10⁷	5.83	2.10
Coef. of var. (%)	9.1	4.74
Probability, W(β,β)	0.94	0.15
Date is isotropic
Inferred inner scale (m)	1.0 × 10⁻³ (averaged)	9.0 × 10⁻³ horizontal
		3.0 × 10⁻³ vertical

Date/time		Code	No. of values averaged	β × 10⁷	Variation coefficient, %	Exp. time (sec)
12-6-71	1513	227H	4	6.981	1.7	$\frac{1}{2}$
12-6-71	1513	228H	7	6.617	2.6	$\frac{1}{4}$
12-6-71	1513	229H	6	6.314	2.7	1
12-6-71	1513	230H	4	5.499	3.6	$\frac{1}{8}$
12-6-71	1513	231H	5	6.117	3.2	$\frac{1}{15}$
12-6-71	1513	227V	3	5.442	8.4	$\frac{1}{2}$
12-6-71	1513	228V	4	6.824	1.8	$\frac{1}{4}$
12-6-71	1513	229V	3	5.642	3.1	1
12-6-71	1513	230V	5	5.343	7.3	$\frac{1}{8}$
12-6-71	1513	231V	3	5.883	3.7	$\frac{1}{15}$
12-8-71	1234	310H	8	2.397	4.3	$\frac{1}{4}$
12-8-71	1234	311H	9	2.536	3.3	$\frac{1}{8}$
12-8-71	1234	322H	7	1.720	4.1	$\frac{1}{4}$
12-8-71	1234	323H	13	2.692	11.0	$\frac{1}{2}$
12-8-71	1234	310V	3	2.748	5.5	$\frac{1}{4}$
12-8-71	1234	311V	5	1.651	0.98	$\frac{1}{8}$
12-8-71	1234	322V	3	2.144	4.0	$\frac{1}{4}$
12-8-71	1234	323V	6	2.063	2.0	$\frac{1}{2}$

Date/Time		Thermal $C_{N} (m^{\frac{1}{3}})$	Normal wind speed (m/sec)	Air temp.(°C)	Water temp (°C)	Relative humidity (%)	General weather condition
12-6-71	1513	(1.32 ± 0.1) × 10⁻⁷	4.1	13.0	12.0	76	Partly cloudy visibility ~6mi
12-8-71	1234	(7.8 ± 0.7) × 10⁻⁸	1.2	10.0	10.5	94	Haze/light, fog/light rain

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Applied Optics