Microphone Array on a Spherical Cap for 3-dimensional Recording of the Wave Field

Diploma thesis (pdf 5.042 KB)

The objective of this diploma thesis is to develop a microphone array for 3-dimensional recording of the surrounding wave field. The used array is basically spherical but differs from known arrays by one feature: the sphere is mounted on top of a cone which masks a subpatch of the surface from the south pole up to a defined elevation angle. In this masked region the wave field is zero, so there is no need to sample it with microphones. Therefore the remaining spherical cap can be sampled with better accuracy using the same number of microphones. But there are a lot of problems coming up with that approach. First of all the wave field equation has to be solved with respect to the new boundary condition added by the cone. Accordingly, the part of the solution with respect to the angle is represented by spherical cap harmonics which differ from the well known spherical harmonics in requiring non-integer orders. Furthermore an opening angle for the cone and a meaningful distribution of the microphone positions should be determined to decompose the wave field in a set of weighted spherical cap harmonics with a minimum error.