Phase recovery and reconstruction of the Raman amplitude from the Raman excitation profile

The phase recovery from the Raman excitation profile and the reconstruction of the Raman amplitude is solved for the general situation where the Raman amplitude, when extended in the complex plane, may have zeros in the right-half plane. New results for phase recovery are derived for the dispersion method by contour integration, which extends the usual minimum phase problem to the non-minimum phase case. An iterative procedure, with rapid convergence, is presented to overcome the problem of the experimental Raman excitation profile being given in a limited energy range. Calculations are presented for azulene and iodobenzene to illustrate the theory.