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We present a microlocal analysis of two novel Radon transforms of interest inCompton Scattering Tomography (CST), which map compactly supported $L^2$functions to their integrals over seven-dimensional sets of apple and lemonsurfaces. Specifically, we show that the apple and lemon transforms areelliptic Fourier Integral Operators (FIO), which satisfy the Bolker condition.After an analysis of the full seven-dimensional case, we focus our attention on$n$-D subsets of apple and lemon surfaces with fixed central axis, where $n<7$.Such subsets of surface integrals have applications in airport baggage andsecurity screening. When the data dimensionality is restricted, the appletransform is shown to violate the Bolker condition, and there are artifactswhich occur on apple-cylinder intersections. The lemon transform is shown tosatisfy the Bolker condition, when the support of the function is restricted tothe strip $\{0<z<1\}$.

Microlocal properties of seven-dimensional lemon and apple Radon transforms with applications in Compton scattering tomography