Abstract
The previously obtained integral field representation in the form of double weighted Fourier transform (DWFT) describes effects of inhomogeneities with different scales. The first DWFT approximation describing the first-order effects does not account for incident wave distortions. However, in inhomogeneous media the multiscale second-order effects can also take place when large-scale inhomogeneities distort the field structure of the wave incident on small-scale inhomogeneities. The paper presents the results of the use of DWFT to derive formulas for wave statistical moments with respect to the first- and second-order effects. It is shown that, for narrow-band signals, the second-order effects do not have a significant influence on the frequency correlation. We can neglect the contribution of the second-order effects to the spatial intensity correlation when thickness of the inhomogeneous layer is small, but these effects become noticeable as the layer thickness increases. Accounting for the second-order effects enabled us to get a spatial intensity correlation function, which at large distances goes to the results obtained earlier by the path integral method. This proves that the incident wave distortion effects act on the intensity fluctuations of a wave propagating in a multiscale randomly inhomogeneous medium.
Highlights
The presence of random inhomogeneities in a radio signal path can have a profound effect on functioning of radiotechnical systems
We can neglect the contribution of the second-order effects to the spatial intensity correlation when thickness of the inhomogeneous layer is small, but these effects become noticeable as the layer thickness increases
Within the double weighted Fourier transform (DWFT), we were able to find a solution for the frequency coherence function and to show that, for narrow-band signals, the second-order effects do not significantly affect the frequency correlation
Summary
The presence of random inhomogeneities in a radio signal path can have a profound effect on functioning of radiotechnical systems. We will use here the DWFT method [26,27,28,29,30], which in the small-angle approximation describes both strong fluctuations associated with the random caustics that form in a large-scale inhomogeneous medium, and the Fresnel type diffraction effects typical for wave propagation in a medium with smallscale inhomogeneities. In the first DWFT approximation [26,27,28,29,30], the contribution of lowamplitude inhomogeneities to the partial wave phase takes the integral from permittivity perturbation along the unperturbed (direct) ray For such an effect that inhomogeneities of different scales impose on the wave field we shall call the firstorder effect.
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