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 number, without any relevance for the physical reality of the experiment):
counts | 100 | 100 | 100 | 121 | 121 |
wavelength | 10 +/- 1 | 20 +/- 1 | 30 +/- 1 | 50 +/- 1 | 60 +/- 1 |
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. without not too much data dependent. Thank you!