Determination of the density value specifically at the focal point of the mirror concentrating system

When designing mirror concentrating systems, it is necessary to determine in advance the optical-geometric and optical-energy characteristics of the installation. One is required to choose the mirrors with a reflection coefficient to satisfy the expected energy distribution in the focal area and to pay attention to the accuracy of the reflective surfaces of the mirrors, to the accuracy of the tracking system of the heliostats to the trajectory of the apparent motion of the Sun, to the partial shading to the reflective surfaces, etc. Based on these data, it is necessary to calculate the irradiance distribution in the focal zone of the installation. During installation and utilization of the equipment it is necessary to measure and monitor these parameters and, if necessary, to recalculate the energy distribution taking into account the new parameters.The methods for calculating the density distribution of the radiant flux in the focal zone of mirror-concentrating systems have been developed in parallel with the requirements of exploitation. They do not always correctly reflect the true picture formed in the focus of the heliostat. In this paper, the analysis presents the existing methods for calculating paraboloid concentrators based on the Gaussian distribution of energy in the focal plane. Developing the method of fallen and reflected elementary cone beam and on the basis of generated scattered optical images of the Sun and of the visible angular size (2$\gamma_0$ = 32 angle of minutes) of the Sun, which shows non-Gaussian nature of the resulting distribution in the focal plane due to the influence of aberration of the optical paraboloidal surface depending on the change of the aperture angle 2U, we obtained an analytical calculation formula to determine the value of the concentrated radiant flux specifically at the focal point of a paraboloid mirror concentrating system.