Radon and Abel Transform equivalence in atmospheric radio occultation

The Radon Transform plays a central role in the image reconstruction technique known as computed tomography, used commonly in radio astronomy and medical imaging. Although usually formulated as a projection of a spatial density function along straight ray paths, the Radon Transform kernel also permits curved path projections, providing the path can be defined. Reformulation of the Radon Transform as a path integral for the case of a radio ray refracting in a spherically symmetric atmosphere leads directly to the Abel Transform formulation commonly used in atmospheric radio occultation.