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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

The generalized structure of the electromagnetic field in the registration area is considered in the case of the solution of problems of remote sensing of the underlying surfaces. Examples of the existing radar and optical coherent devices are given. Analytical expressions for the electromagnetic field in the reception area when sounding is carried out in a near-field Fresnel region, in the assumption that the size of the field of registration and radiation is considerably less than a distance between them, are concretized. It is shown the main operations that are necessary for the recovery of coherent images in a near-field Fresnel region by the methods of multichannel signal processing. Research shows that as the amplitude-phase distribution of the registration field is necessary to choose the classical basic function of Fresnel transformation with the reversed sign in the exponent power. Formally, in an infinite range, the Fresnel transform is invertible, i.e. in the ideal case, the function can be completely restored. However physically to Fresnel's region satisfies area with finite sizes. From the analysis of the obtained operations over the received field, it follows that the radar or optical system forms an estimate of the coherent image in the form of a convolution of a true image of the underlying surface with an ambiguity function. Generally, this function contains two multipliers, one of which determines the resolution of recovery of the coherent image. In that specific case, when the linear sizes of the field of registration go to infinity, ambiguity function takes a form of delta function and the required image can be restored without distortions. It is offered to determine resolution by the width between first zeros of ambiguity function. For rectangular area ambiguity function has the form of two sinc functions which width is directly proportional to wavelength, to the height of sounding and is inversely proportional to the linear sizes of receiving area on the corresponding coordinates. Finally, it is mentioned that for the higher-quality coherent imaging with good resolution by the same receiving area it is necessary to perform scanning and movement in space

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A method for processing spatio-temporal radio signals, which allows the formation of high spatial resolution images from aerospace carriers, has been synthesized. In this case, a swath is ±15° from the nadir relative to the flight line is considered. Traditionally this swath is not visible from aerospace carriers. A block diagram of an active-passive type radar is proposed. Initially the image obtained at the output of such a radar has a low quality of visual perception. Such image is called primary, since it was obtained at the stage of primary signal processing. The physical sense of such image is investigated. It approximately represents the operation of convolution of the ambiguity function with a spatial function proportional to the ideal image. The physical sense of the ideal image depends on the characteristics of the imaging system. In the problem under consideration, this is the specific radar cross section. In order to improve the quality of the image it is proposed additional processing (filtering). The paper substantiates the method of filtering (secondary processing) of images based on the solution of the inverse integral equation. It is shown that the exact solution to this equation is difficult to obtain because the form of the ambiguity function is not known exactly and can be estimated only approximately and, in addition, not for each ambiguity function it is possible to obtain a non-singular solution of the inversion equation. Therefore, an approximate solution to the problem is given. It solution is sufficient to solve practical problems of improving image quality. Using numerical simulation methods, the influence of the error in determining the shape of the uncertainty function on the task of improving image quality is studied. Examples of primary and secondary images obtained at the output of wideband active aperture synthesis systems with various geometries of spatially distributed antenna systems are given.