reza malek-madani svetlana avramov-zamurovic joe watkins will peabody andrew browning

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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