 Spherical density projection

A spherical mass density $\rho$ gives projected surface density $\Sigma (R)={\int }_{-\infty }^{\infty }\rho (\sqrt{R^2+z^2})dz$. On the positive half of the line of sight, substitute $r=\sqrt{R^2+z^2}$ to obtain the displayed Abel transform. Spherical symmetry is essential: a general three-dimensional density cannot be reconstructed uniquely from one projection.