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Analytic and Experimental Results of Spatial Correlations of Vector Intensity Sensors

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. “Diffuse Field” Model of Isotropic Noise.

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Analytic and Experimental Results of Spatial Correlations of Vector Intensity Sensors

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  1. Analytic and Experimental Results of Spatial Correlations ofVector Intensity Sensors Nathan K. Naluai Graduate Program in Acoustics Pennsylvania State University University Park, PA 16802 nathan.naluai@navy.mil

  2. “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. z θi kij uz(ra ,t) ux(rb ,t) p(0,t) y φj x Coordinate System Orientation Notation conventions:

  4. Analytic Solutions for Spatial Correlationsof Separated Sensors in Isotropic Noise

  5. Intensity Correlation Derivations Instantaneous Intensity: The correlation between spatially separated intensity sensors is:

  6. Intensity Correlation Derivations For four Gaussian random variables [Bendat & Piersol]: Can re-write the intensity correlation expression as

  7. Analytic Expressions for Spatial Correlationsof Intensity Sensors in Isotropic Noise

  8. 1 1 0.5 0.5 Correlation Coefficient 0 0 -0.5 -0.5 -1 -1 0 0.5 1 1.5 0 0.5 1 1.5 Spacing (in wavelengths, λ) Correlations for Separated Sensors in Isotropic Noise Correlation Coefficient Spacing (in wavelengths, λ)

  9. N4 N7 N10 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) r1 r2

  10. Where S can be considered the number of sample “locations” in field. Resulting curve is the average over those locations Pressure-Pressure Spatial Correlations 1 Simulation 0.8 Theory 0.6 p 2 p ρ 0.4 0.2 0 0 1 2 3 4 5 6 7 8 kd Input Parameters for Computational Experiment

  11. 1 Simulation Theory 0.8 0.6 xy 2 r 0.4 0.2 0 0 1 2 3 4 5 6 7 8 kd Equal Amplitude Distribution (Ideal Case)

  12. 1 Simulation Theory 0.8 0.6 xy 2 r 0.4 0.2 0 0 0.5 1 1.5 2 2.5 3 3.5 4 kd Equal Amplitude Distribution (Ideal Case)

  13. 1 Random Amplit. Theory COS Weighting 0.5 0 0 1 2 3 4 5 6 7 8 kd 1 Random Amplit. Theory COS Weighting 0.5 0 0 1 2 3 4 5 6 7 8 kd Random Amplitude Source Weighting

  14. Effect of Inter-channel Phase Offsets on Correlation Random Phase held fixed over averaging period Theory 0.6 Mismatched 0.5 0.4 0.3 0.2 0.1 0 0 0.5 1 1.5 2 2.5 3 3.5 4 kd Phase shift applied on every 3rd average Theory 0.6 Mismatched 0.5 0.4 0.3 0.2 0.1 0 0 0.5 1 1.5 2 2.5 3 3.5 4 kd

  15. 8.5m to Amp (R-Ch) to Amp (L-Ch) 5.5m 0.197 m 6.1 m 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

  16. 1 1 Theory Theory Simulation Simulation Experimental Experimental 0.5 0.5 0 0 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 kd kd Physical Correlation Measurements

  17. 1 1 Theory Theory Simulation Simulation Experimental Experimental 0.5 0.5 0 0 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 kd kd Physical Correlation Measurements

  18. 1 1 Theory Theory Simulation Simulation Experimental Experimental 0.5 0.5 0 0 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 kd kd Physical Correlation Measurements

  19. 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

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