1. Reza Malek-Madani Svetlana Avramov-Zamurovic Joe Watkins Will Peabody Andrew Browning United States Naval Academy Olga Korotkova University of Miami

2. 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. United States Naval Academy2

3. Outline United States Naval Academy Distribution A3 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

4. Field setup one United States Naval Academy Distribution A4 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 mm 2.

5. Field setup two United States Naval Academy Distribution A5

6. Field setup three United States Naval Academy Distribution A6 Weather conditions at Hospital Point on November 14, 2010 TimeTempHumidity Sea Level Pressure Wind DirWind SpeedGust SpeedConditions: 1:54 PM55.9 °F62%30.04 inESE8.1 mphnoneClear 2:54 PM55.9 °F62%30.03 inSE6.9 mphnoneClear 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.

7. Lab setup United States Naval Academy Distribution A7 Source Table Tunnel Target Table Isolators

8. Target Target Table 36 in X axis Z axis Source Table Laser Phase Screen L1 L2 L3 Lab setup - schematic

9. Lab setup - source United States Naval Academy Distribution A9 Target Source Laser 2 mW HeNe Phase Screen

10. Lab setup – phase screen United States Naval Academy Distribution A10

11. Lab setup - target United States Naval Academy Distribution A11

12. Quantifying the turbulence in the lab setup SLIDE HIDDEN United States Naval Academy Distribution A12

13. Quantifying the turbulence in the lab setup United States Naval Academy Distribution A13

14. Temperature and Centroid Fluctuations – Lab Setup United States Naval Academy Distribution A14

15. Histogram of data from lab no heat vs phase screen, hot pixel United States Naval Academy Distribution A15 * No heat * Phase Screen Intensity, cts # of occurrences

16. Probability Distribution Function Reconstruction Methods United States Naval Academy Distribution A16 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

17. Gamma-Gamma and Gamma- Laguerre PDF of Field Data – above water United States Naval Academy Distribution A17 * Histogram * Gamma-Gamma * Gamma-Laguerre Intensity, normalized occurrences

18. Gamma-Gamma and Gamma- Laguerre PDF of Field Data – above land United States Naval Academy Distribution A18 * Histogram * Gamma-Gamma * Gamma-Laguerre Intensity, normalized occurrences

19. United States Naval Academy Distribution A19 Gamma-Gamma and Gamma- Laguerre PDF of Field Data – at boundary * Histogram * Gamma-Gamma * Gamma-Laguerre Intensity, normalized occurrences

20. United States Naval Academy Distribution A20 Gamma-Gamma and Gamma-Laguerre PDFs of irradiance – lab, no heat occurrences Intensity, normalized * Histogram * Gamma-Gamma * Gamma-Laguerre

21. Gamma-Gamma and Gamma-Laguerre PDFs of irradiance – Lab, phase screen United States Naval Academy Distribution A21 occurrences Intensity, normalized * Histogram * Gamma-Gamma * Gamma-Laguerre

22. 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 due to numerical instabilities United States Naval Academy Distribution A22

23. 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 United States Naval Academy Distribution A23