Kramers-Kronig / Hilbert Transforms
(June 10, 1999 - Igor Mailing List)
There is now a new addition to the User Contributions directory. After the number of requests I had to my procedures, I asked the kind folks at WM to upload them on the FTP site and they did.
The uploaded package includes:
1) Dielectric1.0.0b4.ipf: The procedure file
2) Dielectric1.0.0b4_Info.ifn: A notebook file that sort of explains it all
3) three xx.nff files: these are the real and imaginary portions of the atomic scattering factors, known as f1 and f2. You can use them to practice
Note that the xx.nff files already include both f1 and f2 as a function of photon energy. Kramers-Kronig transforms are used to get f1 from known f2 data. So, by running the routines, one can verify if the f1 included in the xx.nff files are same as those calculated.
The reason why I originally wrote the routines were two-fold: 1) I had experimental data for f2 at much much higher resolution and accuracy near an absorption edge. So, I would start with f2 data from the xx.nff tables, insert my own data in the appropriate section of that data and re-calculate the f1. The result is such that, f1 values far away from the absorption edge in question are same as the f1 values in the xx.nff files. However, f1 in the vicinity of the absorption edge is now much more accurate (which is what I needed).
2) Using this now 'improved' f1, f2 set, I calculated the dielectric tensor. The routines include both diagonal and off diagonal calculation. Unless you're interested in magneto-optic phenomena, you won't need the off-diagonal calculations. If you do, contact me and I'll give you the info you need. I suppose I'll document this in the next release.
The files can be found at:
Dr. Varoujan Chakarian
Etec Systems, Inc.
26460 Corporate Ave, M/S: 317
Hayward, CA 94545
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