Undergrad Rebinning Strategies for Unequally Spaced Data in Spectroscopy Experiments

[kelly0303]

Hello! I am working on a spectroscopy experiment and for each wavelength of a laser I have some counts. For the purpose of my question I will make up some data to illustrate my problem, in the table below (these are just numbers, without any relevance for the physical reality of the experiment):
$$
\begin{array}{|c|c|c|c|}
\hline counts & 100 & 100 & 100 & 121 & 121 \\
\hline wavelength & 10\pm 1 & 20 \pm 1 & 30 \pm 1 & 50 \pm 1 & 60 \pm 1 \\
\hline
\end{array}$$

I have some errors on the "wavelength" due to the error on the knowledge of the laser frequency and the error on the counts is just Poisson error. I want to re-bin this data, but I am not sure what is the best way to do it. As you can see, the data is not equally spaced (the wavelength = 40 is missing), so I can't bin in terms of bin width. If I would bin, let's say, in 2 bins between 0 and 30 and between 30 and 60, the first bin would have 300 counts while the second one 242, but this is just because the data is missing, not because the physics process has a lower probability at that wavelength. Should I do the rebinning in terms of number of points per bin? Or how should I proceed? Also, if I do it in terms of points per bin, what would be the value of the wavelength? The average of the points in a bin? And what would be the error? I just do error propagation for the average of N numbers? For my experiment I have few tens of thousands of data points, and the missing data is not regularly spaced, so I would need a general approach for this i.e. not too much data dependent. Thank you!

 

[mfb]

Why do you want to rebin it? The best way to do that will depend on what you want to achieve.

 

[kelly0303]

Why do you want to rebin it? The best way to do that will depend on what you want to achieve.

I want to make a fit to some peaks in the data. However the way it is now, is very noisy. I know where the peaks should be, I just want to make the fit actually work. But it doesn't work so far, so I am trying to do a rebinning to make the data a bit more smooth (I know I would lose some information, but hopefully I can make the fit work). Thank you!

 

[mfb]

If rebinning would help the fit then something else went wrong.

 

[sophiecentaur]

Data analysis doesn't require equal bin sizes. I can't remember the details but, as with sampling of waveforms, the initial sampling need not be regular. One way round the 'bin' problem could be to over-sample and spread the contents of bins over more bins to fill the gap. That would be a form of filtering / interpolation, I guess, and that's a valid thing to do.