Gaussian beam transformation with cylindrical lenses

We develop formulas for Gaussian beam transformation with fixed total distance between beamwaists, and consider the use of cylindrical lenses or mirrors to produce beams which are not symmetric about the axis of propagation. For antenna feeds, it is necessary that the beam waists for both planes perpendicular to the axis of propagation be coincident. This requirement is analyzed, and appropriate transformation formulas obtained. The far-field patterns of a scalar feed born cylindrical lens combination operating at a frequency of 94 GHz have been measured and found to be in quite good agreement with the elliptical patterns predicted by the transformation formulas.