Phase characterization of gyrotron beams from intensity measurements using the moment method

We present the formulation of the moment method applied to the determination of phase profiles of microwave beams from known amplitudes. While traditional approaches to this problem employ an iterative error-reduction algorithm, the moment method calculates a two-dimensional polynomial phasefront based on weighted moments of intensity measurements. Since this novel formulation calculates the moments of quasioptical Gaussian-like beams, the moment method has the very important advantage of quantifying and compensating for measurement error. The validity of the moment method is tested and confirmed by examining a simple case of an ideal Gaussian beam. The effectiveness of this approach is further demonstrated by applying intensity measurements from cold-test gyrotron data to produce a phasefront solution calculated via the moment method. The accuracy of these results is shown to be comparable with that obtained from the previously developed iteration method.