Computational Methods in Nearfield Acoustic Holography (NAH). Appendix

摘要

The continuous integrals and integral equations which form the theory of Nearfield Acoustic Holography for planar and odd-shaped source boundary surfaces are reviewed, and the approximations and assumptions necessary to reduce these equations to a set of finite and discrete operations suitable for computation are developed. These equations represent the solution of the Helmholtz equation with specified boundary conditions by Green's function methods. Two computational methods for reconstructing planar source boundary fields from planar holograms are developed. The first method is an approximation of the continuous solution method which the convolution theorem of Fourier Transforms provides. As an alternative to this reconstruction method, a conjugate gradient descent method is developed based on the finite and discrete propagation method discussed. The reduction to finite and discrete form, by a Finite Element technique, of the relationship between the Dirichlet and Neumann boundary conditions for an odd shaped surface is reviewed. A technique for reconstructing the odd-shaped surface boundary conditions from a hologram of general two-dimensional shape is proposed. (Theses)