1. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 Analytic and Experimental Results of Spatial Correlations of Vector Intensity Sensors Nathan K. Naluai Graduate Program in Acoustics Pennsylvania State University University Park, PA 16802 nathan.naluai@navy.mil

2. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 “Diffuse Field” Model of Isotropic Noise Generally assumes sound coming from all directions One model definition (Jacobsen) –Sound field in unbounded medium –Generated by distant, uncorrelated sources –Sources uniformly distributed over all directions –Field would be homogeneous and isotropic –Time-averaged intensity is zero at all positions

3. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 k ij θiθi φjφj u x (r b,t ) u z (r a,t ) x y z p(0,t) Coordinate System Orientation Notation conventions:

4. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 Analytic Solutions for Spatial Correlations of Separated Sensors in Isotropic Noise

5. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 Instantaneous Intensity: The correlation between spatially separated intensity sensors is: Intensity Correlation Derivations

6. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 For four Gaussian random variables [Bendat & Piersol]: Can re-write the intensity correlation expression as Intensity Correlation Derivations

7. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 Analytic Expressions for Spatial Correlations of Intensity Sensors in Isotropic Noise

8. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 Correlations for Separated Sensors in Isotropic Noise 00.511.5 -0.5 0 0.5 1 Correlation Coefficient Spacing (in wavelengths, λ) 00.511.5 -0.5 0 0.5 1 Spacing (in wavelengths, λ) Correlation Coefficient

9. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 N4N4 N7N7 N 10 Computational Experiment Design/Layout Computational Simulation in MATLAB environment Source distribution determined by variable M, (no. of sources about “equator”) Each source generating noise (0-6.4kHz band) Signals oversampled to allow for 1mm separation resolution Assumptions –Plane wave superposition –Sensor separation: 7cm –Air-like medium ( c, ρ) r1r1 r2r2

10. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 012345678 0 0.2 0.4 0.6 0.8 1 Pressure-Pressure Spatial Correlations ρ p p 2 kd Simulation Theory Input Parameters for Computational Experiment Where S can be considered the number of sample “locations” in field. Resulting curve is the average over those locations

11. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 Equal Amplitude Distribution (Ideal Case) 012345678 0 0.2 0.4 0.6 0.8 1  xy 2 kd Simulation Theory

12. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 Equal Amplitude Distribution (Ideal Case) 00.511.522.533.54 0 0.2 0.4 0.6 0.8 1 kd Simulation Theory  xy 2

13. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 Random Amplitude Source Weighting 012345678 0 0.5 1 kd Random Amplit. Theory COS Weighting 012345678 0 0.5 1 kd Random Amplit. Theory COS Weighting

14. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 Effect of Inter-channel Phase Offsets on Correlation 00.511.522.533.54 0 0.1 0.2 0.3 0.4 0.5 0.6 kd Theory Mismatched 00.511.522.533.54 0 0.1 0.2 0.3 0.4 0.5 0.6 kd Theory Mismatched Random Phase held fixed over averaging period Phase shift applied on every 3 rd average

15. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 Physical Correlation Measurements Reverberant Acoustic Test Tank (ASB-PSU) Two Lubell LL-9162 sources (uncorrelated noise) –Low freq. rolloff at 1-kHz pa-probe (McConnell) –Sensitivity axes aligned Outputs recorded at four separate locations in tank. –64 avgs at each location 5.5m 8.5m 6.1 m 0.197 m to Amp (R-Ch) to Amp (L-Ch)

16. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 Physical Correlation Measurements

17. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 Physical Correlation Measurements

18. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 Physical Correlation Measurements

19. Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada 03-05 Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 20670 Summary Analytical solutions for spatially separated Intensity measurements have been derived and verified experimentally Constant phase offsets have no effect on the agreement between the coherence and the theoretical predictions Intensity measurements demonstrate shorter correlation lengths than the component measures Suggest that intensity processing of vector sensor arrays may be less susceptible to ambient noise contamination than traditional pressure hydrophone array. Examine performance of intensity vector sensor arrays –Possible gains in directivity