Phase Recovery from the Raman Excitation Profile,Time Domain Information and Transform Theory

The phase recovery from the vibrational Raman excitation profile (REP), which contains only the modulus of the Raman amplitude, is discussed for the general situation where the Raman amplitude, with excitation energy extended in the complex plane, may have zeros in the right-half plane. The focus is on the dispersion method, with all results derived by contour integration. The new results for phase recovery, however, apply to both the dispersion and maximum entropy methods. An iterative procedure, with rapid convergence, is presented to overcome the experimental REP data being given in a limited energy range. The forward transform from the electronic absorption spectrum (ABS) to the REP and the inverse transform from the REP to the ABS are presented in a unified manner. The ubiquitous Hilbert transform is shown to be readily evaluated by the fast Fourier transform algorithm. Calculations are presented for β-carotene, a two-mode harmonic model with diffuse vibrational structure, azulene and iodobenzene to illustrate the theory. © 1997 John Wiley & Sons, Ltd.