The localization of ionospheric irregularities by the holographic method

The holographic method has been recently introduced to study satellite scintillations. Only one ground station is needed to receive the radio hologram. The object wave scattered or diffracted by irregularities is measured in relation to a harmonic reference wave. The resulting amplitude and phase information can be interpreted, by using the reciprocity theorem, as the one-dimensional radio hologram at the height of the satellite orbit. In this paper the mathematical theory is developed to reconstruct the image. The theory is analogous to that used in acoustical holography to form the image digitally. Since the hologram is only one dimensional, the image can be reconstructed two-dimensionally in the plane which is defined by the vector from the ground station to the satellite and the satellite velocity vector. The Fresnel-Fourier transform is used to form the image in the reconstruction plane at various distances from satellite to ground. The calculations with the computer are carried out by using the fast Fourier transform. The coefficients of the Fresnel-Fourier transform represent the spatial spectrum of the object wave at the desired distance giving the reconstructed image of the irregularities from the radio hologram. The amplitude of the spectrum corresponds to the intensity of the scattered object wave. The coordinates of the irregularities are those given at that distance where the intensity reaches its maximum value, i.e., when the image is ‘focused.’ The irregularities analyzed so far have been localized at heights between 100 and 300 km. The observed irregularity region consists of several small-scale irregularities with cross sections from 50 to 300 m. The strength of these irregularities has not been discussed in the present theory.