ALGORITHM FOR CALCULATING SURFACES OF BIFOCAL LENS ANTENNAS

An algorithm is proposed that makes it possible to calculate the coefficients of power polynomials approximating the illuminated and shadow surfaces of bifocal lens antennas. The algorithm is based on providing equality of electrical lengths of rays passing from the focus points through lens body and its edge and on the assumption that the phase front is flat and is inclined at a determined angle relative to the main optical axis of the lens on the aperture of the lens antenna. For each of the rays an expression was written that determines its electrical length. The electrical length of the rays depends on the points coordinates of the illuminated and shadow surface of the lens, in which they are refracted. The analytical solution of the obtained equation is difficult. Therefore, it is proposed to determine the exact coordinate values by numerical methods. The proposed algorithm determines in series the three points lying on the illuminated and shadow surfaces. The coordinates of the points are used to form systems of equations whose solutions are the coefficients of power polynomials approximating the illuminated and shadow surfaces of the lens antenna. The algorithm does not impose restrictions on the relative dielectric constant of the material from which the lens antenna is made.