operator, then the special case of the projection-slice theorem for circularly symmetric functions states that In other words, applying the Abel transform to a 1-dimensional function and then applying the Fourier transform to that result is the same as applying the Hankel transform to that function. This concept can be extended to higher dimensions. Relationship to the Radon transform Abel transform can be viewed as the Radon transform of an isotropic 2D function f(r). As f(r) is isotropic, its Radon transform is the same at different angles of the viewing axis. Thus, the Abel transform is a function of the distance along the viewing axis only. See also GPS radio occultation References Integral transforms Image processing Niels Henrik Abel