Canonical Transform Methods for Radio Occultation Data

Abstract

In the present work, we study a canonical transform that directly maps the measured field to the impact parameter representation without first carrying out a back-propagation. This canonical transform is determined to first order in a small parameter that measures the deviation of the satellite orbit from a circle. When the parameter is equal to zero, i.e., for circular orbits, our canonical transform reduces to a Fourier transform. In the general case, the form of the generating function is such that it does not directly allow an implementation as an FFT-like algorithm. However, using approximations the direct canonical transform mapping yields fast, efficient numerical implementations.