The Helmholtz equation least-squares method and Rayleigh hypothesis in near-field acoustical holography

2004 ◽  
Vol 115 (4) ◽  
pp. 1632-1640 ◽  
Author(s):  
Tatiana Semenova ◽  
Sean F. Wu
Keyword(s):  
Helmholtz Equation ◽  
Least Squares ◽  
Least Squares Method ◽  
Near Field ◽  
Helmholtz Equation Least Squares ◽  
Acoustical Holography ◽  
Rayleigh Hypothesis

A new data extrapolation method based on the modified Helmholtz equation least-squares method

2012 ◽  
Vol 227 (6) ◽  
pp. 1252-1265
Author(s):  
R Wang ◽  
J Chen ◽  
GM Dong
Keyword(s):  
Helmholtz Equation ◽  
Least Squares ◽  
Acoustic Field ◽  
Least Squares Method ◽  
Acoustic Radiation ◽  
Near Field ◽  
Extrapolation Method ◽  
Modified Helmholtz Equation ◽  
Helmholtz Equation Least Squares ◽  
Data Extrapolation

Fast Fourier transform-based near-field acoustic holography requires that the measurement aperture should completely enclose the source, which is impractical for large-scale sound sources. Helmholtz equation least-squares method can reconstruct the acoustic field with fewer measurements than fast Fourier transform-based near-field acoustic holography. However, it is not suitable for reconstructing acoustic radiation from multiple sources or a complicated source which consists of several separated parts. To circumvent this difficulty and enhance the reconstruction accuracy, a new data extrapolation method based on the modified Helmholtz equation least-squares method is proposed. The base of this data extrapolation method is a modified Helmholtz equation least-squares method which expresses the acoustic field of a complicated source as the superposition of the acoustic radiation from all of its separated parts. Using the acoustic pressures reconstructed with the modified Helmholtz equation least-squares method, the measurement surface is extended through an iterative procedure. Meanwhile, Tikhonov regularization method together with generalized cross-validation parameter choice method is utilized to treat the ill-posed problem in reconstructions. In the end, taking the extrapolated pressures as input data, the acoustic field can be reconstructed more precisely. Numerical simulation and experimental results demonstrate that this method can significantly enhance the reconstruction accuracy and efficiency.

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