A Double Green Function Method for an Inverse Source Problem Related to a Hemisphere

In this study, a novel estimation method to determine the electromagnetic or acoustic sources located in a hemisphere using two different Green functions is developed. The inverse source problem is formulated for a scalar function which can be considered as an electromagnetic scalar potential or an acoustic pressure field. Using the explicit expressions of the Green functions obtained for two different boundary conditions satisfied by the corresponding scalar function on the surface of the hemisphere, the inverse source problem is first reduced into an integral equation and then its solution is obtained by discretizing the resulting integral equation.