Method of superposition applied to patch near-field acoustic holography

The method of superposition may be applied to reconstruct the field on a partial surface on a radiating structure from measurements made on a nearby limited surface. Unlike conformal near-field holography, where the measurement surface surrounds the entire structure, in patch holography the measurement surface need only be approximately as large as the patch on the structure surface where the reconstruction is required. Using the method of superposition, the field on and near the measurement surface may be approximated by the field produced by a source distribution placed on a surface inside the structure. The source strengths are evaluated by applying boundary conditions on the measurement surface. The algorithm requires the inversion of the Green’s function matrix which may be ill-conditioned. Truncated singular value decomposition is used to invert it. The field on the structure surface is then approximated by the field produced by the source distribution. The algorithm is easier to implement than the boundary elements method because it does not require integrations over singular integrands and may be applied to flat or curved surfaces.