Eikonal aberrations in planar double-reflector antennas

A formula describing the eikonal distribution on the main reflector of a 2D double-reflector system is derived for an arbitrary direction of the offset of the source from the focus, the second focus being at infinity. The formula takes into account four terms of the expansion of the eikonal in the powers of the offset of the source. The accuracy of the formula is analyzed by comparing the results of calculation of the eikonal in a 2D Schwarzschild system with the exact geometric-optics calculation. Formulas for the focal curve, the phase front inclination angle, and aberrations in an arbitrary double-reflector telescopic system are obtained. The formula obtained is used for the analysis and minimization of aberrations in a 2D Schwarzschild system.