Investigation of the convergence of the iterative design algorithm for phase shifter pairs for simple beam transformations

The use of a pair of reflectors to convert a microwave beam from one amplitude/phase distribution to another is important in microwave technology. A simpler version of this problem is the use of a pair of hypothetical ideal thin phase correctors to transform the beam. This problem has many of the same features of the reflector design problem and small phase shift variations can usually be converted to equivalent mirror surface variations. The phase shift profiles and some convergence properties are presented for transformations between some simple Gaussian beam profiles.