Shape of voigt profile

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Tue, 11/10/2015 - 03:26 am

Hi all,

I have a question regarding the value for the shape of voigt profile.....How is it determined actually? I know that if the value is close to 0 it becomes gaussian and as it approaches 1 is Lorentzian. As a result, i guess its the width ratio : WL/WG, where WL is the width of the Lorentzian part and WG is the width of the Gaussian part. However, if i take the ratio of the values as given from the fitting outcome (gaussian and lorentzian width given after fitting) and compare with the value given for the shape, there is no match. There is always a systematic deviation of factor 1.2. Does anybody know where this deviation comes from? Thanks a lot.
Hi Konstantinos,

I think the shape tends to Lorentzian as the shape parameter tends to infinity (DisplayHelpTopic("MPFXVoigtPeak")).

Have you looked at the technical note TN026 mentioned here (http://www.igorexchange.com/node/6814), and the references therein?

Hope this helps,
Kurt

November 10, 2015 at 04:12 am - Permalink

Hi Curt,

Yes i have checked the Technote 20 regarding voigt profile and i also read the paper of Humnicek that is the pattern used to calculate the voigt function in igor pro....However, i am still not understanding what is the mathematical relation between the widths of gaussian and Lorentzian parts that give the final value of the shape. Maybe i am missing something here and i apologise for that but i have a gap in this.

November 10, 2015 at 04:33 am - Permalink

I also suggest you look at the Wikipedia reference for a quick summary, https://en.wikipedia.org/wiki/Voigt_profile .
You have to keep in mind that the function is a convolution, and convolutions can get messy and need not have easily formulated analytic parameters except in special cases.

Another useful tidbit to remember is that if you think of the Voigt function as a power spectrum with argument in the frequency domain, its Fourier transform (in the time, or delay, domain) is an autocorrelation function. This happens to be the product of the Gaussian autocorrelation (also a Gaussian) and the Lorentzian autocorrelation (a simple double-sided exponential decay).

November 10, 2015 at 04:48 am - Permalink

The shape parameter is the ratio of Gaussian to Lorenzian, so shape=0 is pure Gaussian, shape=inf is pure Lorenzian. The curve fit doesn't like extreme values of the shape parameter- if it is far outside the range of maybe (0.1,10) you should consider fitting with a Gaussian or Lorenzian peak shape. (That range may be too conservative).

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com

November 10, 2015 at 05:27 pm - Permalink

John,

I am attaching some Voigt equations from the recent "NIST Handbook of Mathematical Functions", which give some normalized forms of the Voigt convolution integrals. Since you have said that shape = 0 corresponds to pure Gaussian, it seems that equation 7.19.4 is appropriate (the Lorentzian component becomes a delta-function as a->0). Then

a = ( FWHM(Lor)/FWHM(Gauss) ) * (2*sqrt(ln(2))).

Does 'a' have a simple relation to Igor's Voigt profile shape parameter?
Voigt.PNG

November 12, 2015 at 09:07 am - Permalink

I seem to have missed this posting...

I think the NIST equations are basically consistent with Igor's Voigt (or in Igor 7 lately, VoigtFunc) but with a slightly different coefficient at the front. I would have to study all this carefully to figure it all out.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com

March 3, 2016 at 09:42 am - Permalink