1
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I have to fit this peak (which seems to be a double gaussian from other experiments) to find the peak position of the one at around 2.43 eV.

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Initially I thought was pretty straightforward. Here is the code I am using

NonlinearModelFit[
  data[[100 ;; 330]], {amp1*Exp[-(x - mu1)^2/2 s1^2] + d2 + 
    amp2*Exp[-(x - mu2)^2/2 s2^2] - m*x + d, 
   mu1 < mu2}, {{s1, 20}, {amp1, 0.23}, {mu1, 2.43}, {m, 0.1}, {d, 
    0.3}, {amp2, 0.2}, {mu2, 2.44}, {s2, 40}, {d2, 0.2}}, x, 
  MaxIterations -> 15000]

But something goes wrong everytime I change slightly the fitting range (it finds a negative peak on the left side). Also the fit is not amazing. Can you suggest something to improve it? I also have to apply the same fit to similar dataset (where only the peak shifts) but again even if they are similar I get very different result. I would like to know how to make the fit more consistent and robust

enter image description here ;

enter image description here

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1 Answer 1

1
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Here's one approach that involves post-collection background correction.

(* Create background, arbitrary removal of peak *)
bg = Interpolation[Select[data, Not[2.3 < #[[1]] < 2.6] &], 
   InterpolationOrder -> 2];
(* Create background correction function *)
bgcorr[pt_] := {First@pt, Last@pt - bg[First@pt]}
(* Create background corrected dataset *)
corr = bgcorr /@ data;
(* Fit your corrected data with a model *)
nlm = NonlinearModelFit[corr, 
   a PDF[SkewNormalDistribution[b, c, d], x], {{a, 0.35}, {b, 
     2.5}, {c, 0.2}, {d, 0.5}}, x];
(* Show off the results *)
Plot[nlm[x] + bg[x], {x, 2.2, 3.4}, Epilog -> Point /@ data, 
 PlotLabel -> nlm["BestFitParameters"]]

enter image description here

This method is not completely automated, you'll need to

  • Manually select the limits of the peak - a large range to account for shifts in the data may be appropriate
  • Appropriate selection of model - I used a SkewNormalDistribution just for example.
  • Appropriate starting values for your model. These may be constant over the multiple datasets you have.

If you are looking for a trend and not a physical significance of the peak, then an arbitrary model as I've chosen here may be suitable for your analysis.

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3
  • $\begingroup$ There have been several similar questions and while all of the associated answers have been ingenious, the recommended solutions seem very, very ad hoc. I am totally ignorant about what I assume are "remove instrument drift" techniques but given that this issue must happen frequently, is there not some standard technique for removing instrument drift? (Fitting the results after removing the drift is a different issue.) $\endgroup$
    – JimB
    Jan 10, 2021 at 2:38
  • 1
    $\begingroup$ @JimB these solutions are likely ad hoc because there is no interest (at least explicitly stated in the question[s]) in the physical significance of the fit. Here, the author wants to monitor the peak as a function of some undefined variable (and MaxDetect or FindPeaks may be better solutions). As for accurate models of instrument drift (which is different from background, which is discussed in this Q&A) they exist for small subsets of instruments, but for the most part, it is easier to control the environmental conditions that introduce instrument drift than to model their effects. $\endgroup$ Jan 10, 2021 at 19:54
  • $\begingroup$ Thanks. As a retired statistician I still have plenty to do but some of these questions certainly grab my interest. I just don't have the subject matter knowledge to suggest more physically-based models. My desire to deal with physically-based models is to provide some measure of precision for the estimate of the height or location of the peak. (There are some fields - or at least some practitioners in those fields - that rarely seem to consider estimating precision.) $\endgroup$
    – JimB
    Jan 10, 2021 at 20:21

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