In the solution of the wave equation $$[\nabla^2-\frac{1}{v^2} \frac{\partial^2}{\partial t^2}]U=0$$
and consequently the Helmholtz equation $$[\nabla^2+k^2]G(R,\tau)=\delta(R)=\delta(\vec{x}-\vec{x}')$$ with sources located at $\vec{x}'$
for diffraction scalar problems is usually used the method of images to construct a proper Green function with the Neumann's and the Dirichlet's conditions.
$$G_D=\frac{e^{ikR}}{R}-\frac{e^{ikR'}}{R'}$$ $$G_N=\frac{e^{ikR}}{R}+\frac{e^{ikR'}}{R'}$$
This is page 480 Electrodynamics by Jackson.
I am having troubles figuring out what is the geometry where are the vectors $\vec{x}$, $\vec{x}'$, $\vec{x}''$, $R=|\vec{x}-\vec{x}'|$ and $R'=|\vec{x}-\vec{x}''|$ what is image of what and where is the observation point.
