Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD Analytic and Experimental Results of Spatial Correlations of Vector Intensity Sensors Nathan K. Naluai Graduate Program in Acoustics Pennsylvania State University University Park, PA

Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD “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

Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 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:

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

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

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

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

Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD Correlations for Separated Sensors in Isotropic Noise Correlation Coefficient Spacing (in wavelengths, λ) Spacing (in wavelengths, λ) Correlation Coefficient

Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 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

Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 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

Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD Equal Amplitude Distribution (Ideal Case)  xy 2 kd Simulation Theory

Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD Equal Amplitude Distribution (Ideal Case) kd Simulation Theory  xy 2

Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD Random Amplitude Source Weighting kd Random Amplit. Theory COS Weighting kd Random Amplit. Theory COS Weighting

Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD Effect of Inter-channel Phase Offsets on Correlation kd Theory Mismatched kd Theory Mismatched Random Phase held fixed over averaging period Phase shift applied on every 3 rd average

Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 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 m to Amp (R-Ch) to Amp (L-Ch)

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

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

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

Pacific Rim Underwater Acoustics Conf. Vancouver, BC, Canada Oct 2007 Naluai – NAVAIR Acoustics Systems Patuxent River, MD 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