MATHEMATICAL DESCRIPTION OF THE PROCEDURES FOR COHERENT IMAGING OF NATURAL ENVIRONMENTS IN THE FRAUNHOFER REGION BY MULTICHANNEL RADIO-ENGINEERING SYSTEMS - Валерий Константинович Волосюк (Авіаційно-космічна техніка та технологія, 2018)
The structure of the electromagnetic field in the domain of its registration is considered in the case of the solution of problems of remote sensing of the underlying surfaces on the basis of the phenomenological approach. This approach is mainly based on the theory of ray optics and the Huygens-Fresnel principle. It allows to determine the radiated and scattered fields for complex types of surfaces. Analysis of the structure of the electromagnetic field shows that it can be regarded as a mathematical transformation over the true image of the surface. In this case, the basic procedures for the coherent imaging in the far-field Fraunhofer region by multichannel radio-engineering systems should be based on the inverse transformation. For incomplete restoration of the desired image, without the phase and attenuation due to propagation, the basic operation is the inverse Fourier transform on the angular coordinates. The quality of the imaging in the Fraunhofer zone is determined by the ambiguity function. In a simple case of a rectangular receiving domain, ambiguity function has the form of two sinc functions which width is proportional to wavelength, to height of sounding and the linear sizes of receiving domain. If the distance to each point of the surface is known, then it is possible to completely reconstruct the coherent image. In this case, it is necessary to apply sliding short-scale Fourier transform to the received electromagnetic field. Obtained results correspond to the classical theory of resonance scattering. While ambiguity function is constant in the infinite limits of integration for a specific fixed value of the direction, only one spectral component (spatial harmonic) can be extracted from the desired image.  it Is possible to allocate an ever wider range of spatial frequencies with the narrowing of the ambiguity function. In the limit, when the ambiguity function is a delta function, the full spectrum of frequencies of the desired image can be extracted, i.e. this function can be completely restored. If it is not possible to create a system with narrow ambiguity function then the higher-quality coherent image can be obtained by the same receiving domain by scanning or movement in space