- #1
Malamala
- 299
- 26
Hello! I have some measurements of a given transition in an atom, where each event consist of the measurement of this transition and the associated uncertainty (as details, the way it is done, is for each event recorded we measure the laser frequency and Doppler shift it to the frame of the atom), so my data is ##(f_i,df_i)##. For the purpose of this question we can assume that the uncertainty is the same for all measurements. From these measurements, I want to extract the central value of the transition and associated uncertainty. I am not sure how to do it properly. One way is to just take the mean of these values as the central value and the uncertainty would be ##\frac{df}{\sqrt{N}}##, where ##N## is the number of events. However, this doesn’t seem to account for the linewidth of the transition (I expect that the uncertainty on the central value to be smaller for a smaller linewidth). Another way to do it is to make a histogram of the measured frequencies, fit it with a Voigt (or Lorentz) profile and from there extract the central value, associated uncertainty and even the linewidth. However, in this case (when building a histogram), I am not sure how to include the uncertainty in the frequency when building the histogram. Basically, I am not sure how to account both for the uncertainty in individual measurements and the linewidth of the transition. Can someone help me with this? Thank you!