We develop an original method for calculation of radiation from a charge moving in the presence of a dielectric object. The method can be applied to objects which are larger than the wavelengths under consideration. First, the field of a charge in an infinite medium (without external boundaries) is calculated. Further the field at the external boundary of the object ("the aperture") is found using the Snell's and Fresnel's laws. At final step of this technique, we calculate the field outside the target using Stratton-Chu formulae ("aperture integrals"). Contrary to the ray-optic technique, this method is valid for the observation point with arbitrary wave parameter (including Fraunhofer area) as well as in neighborhoods of focuses and caustics. We apply the method developed to the cone with vacuum channel where the charge moves (axially symmetrical problem). As well, this problem is simulated using COMSOL Multiphysics. Comparing results of both techniques one can conclude that the aperture method can be applied even for relatively small objects which have the size of several wavelengths. It is important as well that the accuracy of calculations increases with an increase in the distance from the aperture.