Experimental study of the probability density function of
the intensity of a turbulence induced fluctuating laser beam
Reza Malek-MadaniSvetlana Avramov-Zamurovic
Joe WatkinsWill Peabody
Andrew BrowningUnited States Naval Academy
Olga KorotkovaUniversity of Miami
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Atmospheric signature from collected data at the receiverThe 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 Gamma-Laguerre (Barakat), in hoping of discovering if either one is capable of quantifying the turbulence in the medium.
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Outline
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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
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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
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Weather conditions at Hospital Point on November 14, 2010
Time Temp Humidity Sea Level Pressure Wind Dir Wind Speed Gust Speed Conditions:
1:54 PM 55.9 °F 62% 30.04 in ESE 8.1 mph none Clear2:54 PM 55.9 °F 62% 30.03 in SE 6.9 mph none Clear
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.
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Lab setup
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SourceTable
Tunnel TargetTable
Isolators
Target
Target Table
36 in
X axis
Z axisSource Table
Laser
Phase ScreenL1 L2 L3
Lab setup - schematic
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Lab setup - source
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Target
Source Laser2 mW HeNe
Phase Screen
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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
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5/623
2 2 7/6 11/6 11/62 3
2 5/6 23
ˆ1 1.93
ˆ ˆ2.25
ˆ1.83(Andrews and Phillips)
LT R
R n
n n
W W d
c k L d d
C d c
2 12 2/3 2 14 2/3
2 11 2/3 2 13 2/3
ˆNo Heat: 2 x 10 m 6 x 10 m
ˆAdded Heat: 2 x 10 m 6 x 10 mn n
n n
c C
c C
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Temperature and Centroid Fluctuations – Lab Setup
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0 20 40 60 80 100 120 140 160 180 200-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
sec
deg
C
Temp Fluctuations
temp1temp2
0 20 40 60 80 100 120 140 160 180 2000
50
100
150
200
250
300
350
400
450
time
m
Centroid Fluctuations
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Histogram of data from labno heat vs phase screen, hot pixel
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* No heat* Phase Screen
Intensity, cts
# o
f occ
urre
nces
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Probability Distribution Function Reconstruction Methods
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Gamma distribution modulated by series of generalized Laguerre polynomials proposed by BarakatMedium and source independent Uses first n moments of detected intensityValid in the presence of scatterers
Gamma- Gamma distribution based on the work of Nakagami et al. and presented by Andrews and PhillipsMedium and source dependent Uses 2 first momentsValid 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
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* Histogram* Gamma-Gamma* Gamma-Laguerre
Intensity, normalized
occu
rren
ces
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Gamma-Gamma and Gamma- Laguerre PDF of Field Data – above land
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* Histogram* Gamma-Gamma* Gamma-Laguerre
Intensity, normalized
occu
rren
ces
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Gamma-Gamma and Gamma- Laguerre PDF of Field Data – at boundary
* Histogram* Gamma-Gamma* Gamma-Laguerre
Intensity, normalized
occu
rren
ces
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Gamma-Gamma and Gamma-Laguerre PDFs of irradiance – lab, no heat
occu
rren
ces
Intensity, normalized
* Histogram* Gamma-Gamma* Gamma-Laguerre
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Gamma-Gamma and Gamma-Laguerre PDFs of irradiance – Lab, phase screen
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occu
rren
ces
Intensity, normalized
* Histogram* Gamma-Gamma* Gamma-Laguerre
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SummaryGamma-Gamma and Gamma-Laguerre pdfs
were developed using statistical moments from field and lab dataPDFs obtained from the field and the lab are
very similar in appearanceGamma-Laguerre fit the data better than
Gamma-Gamma in the presence of scatterers in the field
Gamma-Laguerre was unstable at high values of due to numerical instabilities
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2nC
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Future WorkBetter instrumentation for field dataApplication of different mathematical models
Multi-resolution wavelet analysisCoherence analysis independent of PDFs
AcknowledgementsOffice of Naval Research
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