Kramers kronig in mathematica

[clanx]

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!

 

[_coyote_]

It sounds like you have done a lot of work already and I'm sorry to hear you are still stuck. One possibility is that your data may not be accurate enough for the Kramers-Kronig relation to yield a valid result. The Kramers-Kronig relation essentially assumes that you have perfect knowledge of the reflectivity and phase data, which is often not the case in practice. You might try smoothing or interpolating the data to see if that helps. Another possibility is that you have the wrong Lorentzian peak parameters. Make sure the parameters you are using are appropriate for your system. Finally, you can try using an alternative method for computing the dielectric function, such as the maximum entropy method (MEM).