Fourier Transform of sampled reflectance measurements
This elaborates on my comment and my linked FTIR example. Once the FTIR spectrum is obtained, the phase spectrum can be obtained via the Hilbert Transform of the spectrum and that can be performed as a convolution. The Hilbert Transform can be performed by various software packages. In Igor Pro (v. 6.3), the Help text on Hilbert Transforms (page 723 of the Manual), is simply:



In the linked example, the IR spectrum of ethyl acrylate was obtained via a Mueller optical calculus simulation. For present illustrative purposes, the spectrum was adjusted in two ways. First, everything below 800 wavenumbers was set to zero. This is typically where the noise is worst because IR detectors are relatively insensitive and noisy compared with detectors in higher energy ranges. Second, the spectrum was zero filled from 4001 to 4095 wavenumbers, in order to achieve a total of 4096 wavenumber values. This spectrum is shown below:



Performing the Hilbert Transform, as per the Igor Pro command in the first figure, then yields the phase spectrum:



Maybe this helps and maybe it doesn't. But it points to a way forward: find a reflectance spectrum in the refereed literature and the dispersion and absorption spectra that were computed from it. This has to be something about which there is no doubt, i.e., it will be the standard. Then try using software to compute the Hilbert transform and see if the result agrees with the standard. Lastly, if you still want to do so, then pursue the pathway you have outlined in your question text. Hope this helps a bit!