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.