  The aim of this paper is to solve an important inverse source problem which
arises from the well-known inverse scattering problem. We propose to truncate
the Fourier series of the solution to the governing equation with respect to a
special basis of L2. By this, we obtain a system of linear elliptic equations.
Solutions to this system are the Fourier coefficients of the solution to the
governing equation. After computing these Fourier coefficients, we can directly
find the desired source function. Numerical examples are presented.
