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Linear Approximation in Frequency Domain

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Evanescent Field Based Photoacoustics: Optical Property Evaluation at Surfaces

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Patch near-field acoustic holography: regularized extension and statistically optimized methods.

Jean-Claude Pascal¹, Sébastien Paillasseur, Jean-Hugh Thomas

¹Laboratoire d'Acoustique de l'Universite du Maine, rue Aristote, Le Mans, France. jean-claude.pascal@univ-lemans.fr

The Journal of the Acoustical Society of America

|September 11, 2009

Summary

This summary is machine-generated.

Patch holography uses a small microphone array for extended structure measurements. Two methods, pressure extrapolation and statistically optimized processing, are shown to be similar and yield close results for wavenumber spectrum estimation.

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Area of Science:

Acoustics
Signal Processing
Structural Analysis

Background:

Patch holography enables acoustic measurements on large structures with limited microphone arrays.
Two distinct techniques, pressure field extrapolation and statistically optimized processing, are commonly used.

Purpose of the Study:

To propose a singular value decomposition formulation for statistically optimized processing in patch holography.
To demonstrate the inherent similarity between pressure extrapolation and statistically optimized processing methods.
To compare the effectiveness of these techniques in wavenumber spectrum estimation.

Main Methods:

Development of a singular value decomposition (SVD) formulation for statistically optimized processing.
Application of convolution with measured pressure patches for wavenumber spectrum estimation.
Utilizing the Morozov discrepancy principle for regularization parameter computation.

Main Results:

The study reveals a fundamental similarity between pressure extrapolation and statistically optimized processing.
Both methods effectively use convolution of measured pressure data for backward propagation.
Employing the Morozov discrepancy principle leads to highly comparable results from both techniques.

Conclusions:

Patch holography techniques, despite apparent differences, share a common mathematical foundation for acoustic analysis.
Statistically optimized processing, when formulated with SVD, offers a robust approach comparable to pressure extrapolation.
Accurate wavenumber spectrum estimation is achievable using either method with appropriate regularization.