# Paper: Comparing Approaches to the Spherical and Planar Single Layer Potentials for Interior Sound Field Synthesis

Feel free to download the presentation slides of our recent contribution Schultz, F.; Spors, S. (2014): “Comparing Approaches to the Spherical and Planar Single Layer Potentials for Interior Sound Field Synthesis.” In: Proc. of the EAA Joint Symposium on Auralization and Ambisonics 2014, Berlin. The article was published as Schultz, F; Spors, S. (2014):  “Comparing Approaches to the Spherical and Planar Single Layer Potentials for Interior Sound Field Synthesis.” In: Acta Acust united Ac, 100(5):900-911.

The authors created a tutorial on 3D analytic methods for sound field synthesis based on this manuscript, which can be accessed as a public BitBucket git repository under https://bitbucket.org/fs446/analytical_3d_sfs

The paper gives a compact recollection of analytic and explicit solutions for sound field synthesis using the single layer potential. It is shown that for planar and spherical secondary source distributions the same basic principles in solving the Fredholm integral equation within the spectral representation hold. The solutions are well introduced in literature known as Nearfield Compensated Higher Order Ambisonics (NFC-HOA) for spherical geometry and Spectral Division Method (SDM) for planar geometry. Taking the Helmholtz integral equation as starting point for solving the sound field synthesis problem, the equivalent sound-soft scattering approach leads to the same results. In the special case of a planar secondary source distribution the Neumann Green’s function incidentally leads to a single layer potential representation of the Helmholtz integral, which as the Rayleigh integral is an implicit and exact solution and was used for modern formulation of wave field synthesis.

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