Stepped cylindrical antennas for radio astronomy

In this paper a stepped cylindrical mirror is described which satisfies the following requirements: 1) it is free from spherical aberration for a point source at infinity on the axis, 2) both off-axis spherical aberration and coma vanish for fixed values of the field angle, \bar{\Omega} , and of the aperture, \bar{\alpha} . The analysis has been carried out, in the approximation of para-geometrical optics, by considering a diffraction grating of the generalized type, equivalent to the stepped mirror. Three interesting results are obtained, and precisely: 1) independently of the values of \bar{\omega} and \bar{\alpha} , the equivalent diffraction grating has a quasi-parabolic cross section, 2) the off-axis spherical aberration turns out to be negligible over the whole aperture 0-\bar{\alpha} , for fields angles up to at least 20 degrees, 3) the residual coma turns out to be well corrected, too.