Reza Malek-Madani
Svetlana Avramov-Zamurovic
Joe Watkins
Will Peabody
Andrew Browning
United States Naval Academy
Olga Korotkova
University of Miami
Atmospheric signature from
collected data at the receiver
 The main goal of this effort is to characterize the signature of the
atmospheric turbulence inherent in a medium from the beam
data collected at a target.
 The analysis presented here involves two sets of data, one
collected in a laboratory setting, and the other from field
experiments, both carried out at the Naval Academy.
 Our first attempt in characterizing the signature is based on
computing the probability density functions (pdfs) associated
with data.
 Our computational methodology is based on constructing pdfs
using the Gamma-Gamma (Andrews and Phillips) and GammaLaguerre (Barakat), in hoping of discovering if either one is
capable of quantifying the turbulence in the medium.
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Outline
 Experiment:
• Instrumentation set up in the field at the United States Naval Academy
• Measure intensity statistics of the beam in its transverse cross-section
during daylight.
• Using precision instrumentation in the DE Beam Control Lab, compare to
field measurements
 Theory:
• Calculations of statistical moments of intensity
• Apply two PDF reconstruction models
 Data comparison
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Field setup one
Target is a white board. Light intensities amplitude range of 255 was
measured. Sequencing 30 frames per second - three minutes of data
collected. Pixel size was effectively measuring 0.3 mm2 .
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Field setup two
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Field setup three
Target is ccd sensor with 633 nm
notch filter. The sensing area is 7.6
mm (horizontal) × 6.2 mm (vertical)
with pixel size of 4.65 μm.
Time
Temp
1:54 PM
2:54 PM
55.9 °F
55.9 °F
Weather conditions at Hospital Point on November 14, 2010
Sea Level
Humidity
Wind Dir
Wind Speed
Pressure
62%
30.04 in
ESE
8.1 mph
62%
30.03 in
SE
6.9 mph
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Gust Speed
Conditions:
none
none
Clear
Clear
6
Lab setup
Tunnel
Target
Table
Source
Isolators
Table
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Lab setup - schematic
Target
Laser
Phase Screen
36 in
Source Table
L1
L2
X axis
L3
Z axis
Target Table
Lab setup - source
Phase
Screen
Target
Source Laser
2 mW HeNe
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Lab setup – phase screen
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Lab setup - target
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Quantifying the turbulence in the
lab setup
5/6
2
WLT  W 1  1.93ˆ R  d 3 
ˆ  2.25cˆ k L d 2 d
2
R
2
n
7/6 11/6
11/6
3
C  1.83d cˆ
2
n
5/6 2
3
n
(Andrews and Phillips)
No Heat: cˆn2  2 x 1012 m2/3
Cn2  6 x 1014 m2/3
Added Heat: cˆn2  2 x 1011m2/3
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Cn2  6 x 1013m2/3
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Temperature and Centroid
Fluctuations – Lab Setup
Centroid Fluctuations
450
400
350
Temp Fluctuations
0.8
temp1
temp2
300
0.6
m
250
0.4
200
0.2
deg C
150
100
50
0
0
-0.2
0
20
40
60
80
100
time
120
140
160
180
200
-0.4
-0.6
-0.8
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0
20
40
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60
80
100
sec
120
140
160
180
14
200
Histogram of data from lab
no heat vs phase screen, hot pixel
# of occurrences
* No heat
* Phase Screen
Intensity, cts
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Probability Distribution Function
Reconstruction Methods
 Gamma distribution modulated by series of generalized Laguerre
polynomials proposed by Barakat
 Medium and source independent
 Uses first n moments of detected intensity
 Valid in the presence of scatterers
 Gamma- Gamma distribution based on the work of Nakagami et al.
and presented by Andrews and Phillips
 Medium and source dependent
 Uses 2 first moments
 Valid only in clear air atmosphere
 Both require normalization of the moments
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Gamma-Gamma and Gamma- Laguerre
PDF of Field Data – above water
occurrences
* Histogram
* Gamma-Gamma
* Gamma-Laguerre
Intensity, normalized
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Gamma-Gamma and Gamma- Laguerre
PDF of Field Data – above land
occurrences
* Histogram
* Gamma-Gamma
* Gamma-Laguerre
Intensity, normalized
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Gamma-Gamma and Gamma- Laguerre
PDF of Field Data – at boundary
occurrences
* Histogram
* Gamma-Gamma
* Gamma-Laguerre
Intensity, normalized
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Gamma-Gamma and Gamma-Laguerre
PDFs of irradiance – lab, no heat
occurrences
* Histogram
* Gamma-Gamma
* Gamma-Laguerre
Intensity, normalized
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Gamma-Gamma and Gamma-Laguerre
PDFs of irradiance – Lab, phase screen
occurrences
* Histogram
* Gamma-Gamma
* Gamma-Laguerre
Intensity, normalized
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Summary
 Gamma-Gamma and Gamma-Laguerre pdfs were
developed using statistical moments from field and
lab data
 PDFs obtained from the field and the lab are very similar
in appearance
 Gamma-Laguerre fit the data better than Gamma-
Gamma in the presence of scatterers in the field
 Gamma-Laguerre was unstable at high values of Cn2
due to numerical instabilities
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Future Work
 Better instrumentation for field data
 Application of different mathematical models
 Multi-resolution wavelet analysis
 Coherence analysis independent of PDFs
 Acknowledgements
 Office of Naval Research
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