Converging beams in unstable telescopic resonators

A theoretical analysis is made of the diffraction transformation of converging into diverging waves in unstable telescopic resonators. The diffraction theory of optical instruments is used in the analysis. An expression is obtained for the number of passes necessary for the contraction and subsequent diffraction expansion of a beam. The analysis is carried out for initial rectangular and Gaussian amplitude distributions in a plane wave. In both cases the transformation of converging into diverging beams obeys the same law.