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Reza Malek-Madani Svetlana Avramov-Zamurovic Joe Watkins Will Peabody Andrew Browning

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Reza Malek-Madani Svetlana Avramov-Zamurovic Joe Watkins Will Peabody Andrew Browning - PowerPoint PPT Presentation


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Experimental study of the probability density function of the intensity of a turbulence induced fluctuating laser beam. Reza Malek-Madani Svetlana Avramov-Zamurovic Joe Watkins Will Peabody Andrew Browning United States Naval Academy Olga Korotkova University of Miami.

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Presentation Transcript
slide1

Experimental study of the probability density function of the intensity of a turbulence induced fluctuating laser beam

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
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 Gamma-Laguerre (Barakat), in hoping of discovering if either one is capable of quantifying the turbulence in the medium.

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outline
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
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
Field setup two

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field setup three
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.

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lab setup
Lab setup

Tunnel

Target

Table

Source

Table

Isolators

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slide8

Laser

Lab setup - schematic

Target

Phase Screen

36 in

L1

L2

L3

X axis

Source Table

Z axis

Target Table

lab setup source
Lab setup - source

Target

Phase

Screen

Source Laser

2 mWHeNe

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lab setup phase screen
Lab setup – phase screen

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lab setup target
Lab setup - target

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quantifying the turbulence in the lab setup
Quantifying the turbulence in the lab setup

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temperature and centroid fluctuations lab setup
Temperature and Centroid Fluctuations – Lab Setup

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histogram of data from lab no heat vs phase screen hot pixel
Histogram of data from labno heat vs phase screen, hot pixel

* No heat

* Phase Screen

# of occurrences

Intensity, cts

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probability distribution function reconstruction methods
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
Gamma-Gamma and Gamma- Laguerre PDF of Field Data – above water

* Histogram

*Gamma-Gamma

* Gamma-Laguerre

occurrences

Intensity, normalized

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gamma gamma and gamma laguerre pdf of field data above land
Gamma-Gamma and Gamma- Laguerre PDF of Field Data – above land

* Histogram

*Gamma-Gamma

* Gamma-Laguerre

occurrences

Intensity, normalized

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gamma gamma and gamma laguerre pdf of field data at boundary
Gamma-Gamma and Gamma- Laguerre PDF of Field Data – at boundary

* Histogram

*Gamma-Gamma

* Gamma-Laguerre

occurrences

Intensity, normalized

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Gamma-Gamma and Gamma-Laguerre PDFs of irradiance – lab, no heat

* Histogram

*Gamma-Gamma

* Gamma-Laguerre

occurrences

Intensity, normalized

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gamma gamma and gamma laguerre pdfs of irradiance lab phase screen
Gamma-Gamma and Gamma-Laguerre PDFs of irradiance – Lab, phase screen

* Histogram

*Gamma-Gamma

* Gamma-Laguerre

occurrences

Intensity, normalized

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summary
Summary
  • Gamma-Gamma and Gamma-Laguerrepdfs 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 due to numerical instabilities

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future work
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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