Geometrical optics phase matching of radio occultation signals

Remote measurements of the atmospheric state can be performed by radio occultation between satellites, a GPS satellite transmitting a radio signal to a receiving low Earth orbit (LEO) satellite, or between LEO satellites. The bending angle of the traversing optical ray can be measured by detecting the Doppler shift of radio signals. The bending angle is an integrated measure of the refractive index in the atmosphere traversed by the optical ray. With a time series (profile) of the bending angle, it is possible to perform an inversion to obtain the refractive index. Various techniques for the retrieval of the bending profile already exist. The most recent methods have solved the problem of multipath, i.e., when the atmosphere allows several rays to exist simultaneously. The paper presents a new method for the reconstruction of bending angle as a single-valued function of impact parameter from complex radio occultation signal under multipath propagation conditions. The method utilizes the assumption of spherical symmetry of refractivity, i.e., n(inline equation) = n(r), and the principle of synthetic aperture, thus allowing sub-Fresnel resolution. A distinctive feature of the method, as compared to previously known methods, is direct applicability for arbitrary orbits of transmitting and receiving satellites, without intermediate propagation of complex electromagnetic field to circle or straight line. This comes at the expense of impossibility to reduce the method to a FFT. The method can be useful for inverting radio occultation signals and for validation of other radio holographic methods.