When analyzing antennas, and especially when developing new ones, including mirrors, there is a problem of calculating their basic parameters. For this purpose it is necessary to study the electromagnetic field excited in the focus region of the paraboloid of rotation, which is irradiated by the horn irradiator. At present, such calculations are made using modern computer simulation software. They are based on common numerical methods for solving Maxwell's equations and are presented as a finished product without disclosing internal content. So, estimating the error of calculations with the help of such programs is almost impossible. Due to the mathematical complexity of even the simplest scattering and diffraction problems, it is rarely possible to obtain closed-form solutions that are convenient for the direct calculation of virtually useful physical characteristics. Thus it is necessary to allow a certain degree of approximation when forming boundary conditions, solving equations, or at all stages. The previously obtained calculation algorithms have the disadvantage that they can be implemented only by numerical methods, since the integrals obtained are not tabular and cannot be reduced to such. There is a need to simplify the expressions for the field scattered by the horn by approximating and obtaining simple formulas. The paper proposes to determine the electromagnetic field in the focus area of the paraboloid of the rotation of the mirror antenna and on the axis of the mirror by solving the integral equations by a numerical method with the normal polarization of the incident wave. The novelty is the use of a new numerical method for determining the scattered electromagnetic field, irradiated by a horn irradiator, which is located in the focus of the antenna system's rotational paraboloid in order to improve the tactical and technical characteristics of the radio stations at which they are installed. Finite expressions, albeit approximate ones, are obtained, from which the physics of the phenomenon of re-reflection is understood.
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