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crusty
3 Posts |
 Posted - 05/12/2014 : 12:14:42 PM
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9.0.0 G SR2 on WIN7
Hello,
I tried to make an nonlinear fit to this cosinus-equation:
y=A+B*cos((2*pi/(x))*(2-0,44*(p1+(p2^2/x^2)+(x^2/p3^2))))
The fit goes to too little periods. The equation is a non constant periodic cosinus function (white light interfermoetry).
Is there an option in Origin where I can select an area where the y value of the fit have to be positive/negative?
In my case the maxima and minima are critical and the amplitude is noncritical.
Can anybody help me or give me an hint/advice for this problem?
basti |
Edited by - crusty on 05/16/2014 05:09:05 AM |
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Drbobshepherd
USA
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Posted - 05/13/2014 : 11:43:11 AM
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Basti,
Have you tried FFT analysis? Your function looks like an interferogram from an FTIR spectrometer, with zero-path-defference (ZPD) at 1048. Split the data set at that apparent ZPD point and swap halves. Then perform an FFT and see what you get.
DrBob |
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crusty
3 Posts |
Posted - 05/15/2014 : 07:15:16 AM
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Dr.Bob,
the experimental setup is an Michelson-interferometer for measuring the chromatic dispersion of erbiumdoped fibers.
One interferometer-arm is a moveable airpath and the other arm an erbium doped fiber with mirror at the end.
The spectrum I posted here is taken with an Optical Spectrum Analyzer on one Position(airpath).
Now I try to Fit the spectrum to an interferometry-equation with a sellmeier equation (ng(lambda)) in the cos-term.
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I think an FFT wont help me evaluating these p- parameters.
Or how do you think an FFT will help me?
Thank you very much for your response!!!
Basti |
Edited by - crusty on 05/15/2014 07:26:20 AM |
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Drbobshepherd
USA
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Posted - 05/15/2014 : 11:44:43 AM
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Basti,
To fit a spectrum to a theoretical equation requires that you have a spectrum to begin with. Your data does not look like a spectrum to me; it looks like an interferogram from a Michelson interferometer. If this is the case, the x-axis is not wavelength (lambda), it is Otical Path Difference. You derive the spectrum by performing an FFT on the interferogram. Then phase-correct the spectrum to eliminate the sine coefficients and thus make A and B real.
The x-axis of the spectrum will be in units of spatial frequency, so you will have to convert to them to wavelength.
I admit I am not an interferometry expert, but I have processed more than a few FTIR interferograms so I am acquainted with the theory of the Michelson interferometer. I hope this gets you closer to a solution for your problem.
DrBob |
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crusty
3 Posts |
Posted - 05/16/2014 : 04:59:21 AM
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The noncorrected measured Spectrum is:
I am sure it is a spectrum because I recorded it with an OSA (Optical Spectrum Analyzer) in the wavelength area [950nm - 1100nm].
My recently posted graph are corrected (with Iair and Ifiber) that only the interference oscillation remains.
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Edited by - crusty on 05/16/2014 05:01:20 AM |
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Drbobshepherd
USA
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Posted - 05/16/2014 : 11:31:58 AM
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Basti,
You have convinced me, it is a spectrum. I wish I could help, but I have to admit I am not familiar enough with this technique to be of any assistance. Perhaps some other Origin user is. Good luck.
DrBob |
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cpyang
USA
1406 Posts |
Posted - 05/16/2014 : 6:58:05 PM
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If you can make a good guess of the parameters, which I assume the important ones are A, p1 and p2, then manually do 1-iteration to see if the fit is going in the right direction.
For a starter, you should be able to find A by using the first few points and last few points and to fix it to maybe around -0,15? If you start by fixing one of two parameters and relax them after the fits are closer, then you will have a better chance to arrive at a correct fit.
CP
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cos function nonlinear-fit - 5 parameters