Fourier transform, vibrational line shapes

We shall now briefly review the Kubo-Oxtoby theory of vibrational line-shape. The starting point for most theories of vibrational dephasing is the stochastic theory of lineshape first developed by Kubo [131]. This theory gives a simple expression for the broadened isotropic Raman line shape (/(< )) in terms of the Fourier transform of the normal coordinate time correlation function by... 

The majority of studies of vibrational dephasing have looked at the width or shape of the isotropic Raman line. The Raman line shape is the Fourier transform of the coherence decay function that characterizes dephasing (20,21). The coherence decay can also be measured directly in... 

Correction of scattering effects in cellular pixel spectra indicated by the binary mask. Resonant-Mie-induced scattering effects, discussed earlier, that can mix the real (dispersive) and imaginary (absorptive) line shapes of a vibrational transition, and thereby creating shifts in band position and intensity distortions in the observed spectra, are corrected by a phase-correction algorithm [28] between the real and imaginary components obtained by finite Hilbert transform (truncated reverse fast Fourier transform, FFT) [29]. 

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