 Kuzmin reflection method

Reflect a vacuum gravitational potential in the upper half-space evenly across $z=0$. For the convention in which gravitational acceleration is $\nabla \psi$, the derivative jump is $2{\partial }_z\psi (R,0^{+})=-4\pi G\Sigma (R)$. Thus a point mass $m$ below the plane produces a Kuzmin disk, and superposing point masses with weight $\mu (b)db$ produces $\Sigma (R)=(2\pi {)}^{-1}{\int }_0^{\infty }b\mu (b)(R^2+b^2{)}^{-3/2}db$. Positive weights give a nonnegative surface density wherever the integral converges.