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
Numerical solution of the integral equations of the electromagnetic field in geosteering problems