  In this paper I present three new results of astronomical interest concerning
the theory of Abel inversion. 1) I show that in the case of a spatial
emissivity that is constant on toroidal surfaces and projected along the
symmetry axis perpendicular to the torus' equatorial plane, it is possible to
invert the projection integral. From the surface (i.e. projected) brightness
profile one then formally recovers the original spatial distribution as a
function of the toroidal radius. 2) By applying the above-described inversion
formula, I show that if the projected profile is described by a truncated
off-center gaussian, the functional form of the related spatial emissivity is
very simple and - most important - nowhere negative for any value of the
gaussian parameters, a property which is not guaranteed - in general - by Abel
inversion. 3) Finally, I show how a generic multimodal centrally symmetric
brightness distribution can be deprojected using a sum of truncated off-center
gaussians, recovering the spatial emissivity as a sum of nowhere negative
toroidal distributions.
