I am having trouble with one of my simulation of normal reflectance experiment. so I simulated my reflectivity as a lorentzian peak and I want to find the dielectric function ultimately. so of course the reflectivity and phase is related through kramers kronig which can then be used to compute the dielectric but this is the part I'm stuck at for almost 2 weeks. so firstly I used IGOR wavemetrics to do a Hilbert transform relating the real reflectivity and imaginary phase parts but I ended up getting a negative complex dielectric which is not possible. so thinking that maybe the built in code in igor for the hilbert transform was inaccurate, I tried doing the kramers kronig relation numerically in mathematica. you can refer to my post in their forum for more info about the code http://mathematica.stackexchange.com/questions/39148/kramers-kronig-relation-for-phase-and-complex-reflectivity the results were different but sadly still negative. I decided to try my luck here hoping I get faster replies with anyone with past experience in such calculations. thank you!