  Here we present a novel microlocal analysis of generalized Radon transforms
which describe the integrals of $L^2$ functions of compact support over
surfaces of revolution of $C^{\infty}$ curves $q$. We show that the Radon
transforms are elliptic Fourier Integral Operators (FIO) and provide an
analysis of the left projections $\Pi_L$. Our main theorem shows that $\Pi_L$
satisfies the semi-global Bolker assumption if and only if $g=q'/q$ is an
immersion. An analysis of the visible singularities is presented, after which
we derive novel Sobolev smoothness estimates for the Radon FIO. Our theory has
specific applications of interest in Compton Scattering Tomography (CST) and
Bragg Scattering Tomography (BST). We show that the CST and BST integration
curves satisfy the Bolker assumption and provide simulated reconstructions from
CST and BST data. Additionally we give example "sinusoidal" integration curves
which do not satisfy Bolker and provide simulations of the image artefacts. The
observed artefacts in reconstruction are shown to align exactly with our
predictions.
