Conformal generalized near‐field acoustic holography: Theory and algorithm

Abstract

The normal velocity field on the boundary σ of a radiating source is reconstructed with high resolution by using pressure data, measured in the very near field to include evanescent components. The measurement points belong to a surface conformal to σ. The reconstruction is performed by identifying the boundary normal velocity distribution generating the pressure field best mean square fitting the measurement data. The ensuing normal equations are solved by resorting to the singular value decomposition (SVD) of the discretized transformation from the boundary normal velocity to the pressure at the measurement points. The reconstruction boundary normal velocity is represented as a linear combination of basis functions, each associated with a singular value (SV). The errors in the estimation of the coefficients of the linear combination are proportional to the inverses of the corresponding SVs. To achieve robustness, the SVD is truncated to retain the terms corresponding to a limited dynamic range of the SVs. From the normal velocity on σ, the boundary pressure and the intensity field are identified, so that the energy flow from the structure can be studied.