Appendix: How to Do the Bootstrap

Students in Physics 3730 may skip this analysis.

The bootstrap method generates a series of artificial data sets based
on the assumed probability distribution of measurement. These data
sets are called bootstrap samples. We will make a dozen or so
samples. We do a Fourier analysis of each sample and collect the
spectrum for each one. For each frequency in the spectrum we then
calculate the mean and the standard deviation. To get the error in
the spectrum we use the population standard deviation and *not*
the standard deviation of the mean.

To generate the bootstrap samples you should assume the signal at each mirror displacement is distributed according to a Gaussian normal distribution with mean value equal to the measured mean value and standard deviation given by the standard deviation of the mean value. Those numbers are the ones in the interferogram file. So to make one bootstrap sample, for each point in the interferogram you need to generate a new random value.

For an Numpy example of generating random numbers according to a Gaussian distribution, see on-line notes.