The spectrum ratio is treated as a waveform, and that waveform is analyzed with a Wiener filter in the "time" domain.  It is actually a matched filter where the noise is characterized by taking the ratio of non-exposed spectra from different images - should be flat but the instability of the reference optical spectrum causes it to have correlated movements.  So, the procedure for producing those matched filter weights goes like this:

1. Collect several non-xray exposed spectra ("dropped shots" or "event code 162")
2. Define an ROI (e.g. 50 pixels) around the signal region. use this ROI for all calculations below, although it has to move to follow the location when the average signal is computed (step 5).
3. for each background shot divide by the background averaged over many shots ("normalize")
4. Matt says it's not so scientific how one obtains this "averaged signal": one could find several events, center the edge in a window, and then take an average of as many events as it takes for it to "look good". Or just take one event and smooth out the background somehow. He did the latter when he computed the weights.
5. for each background shot divide by the background averaged over many shots ("normalize")
6. calculate the auto-correlation function ("calculate the auto-correlation function ("acf") of those normalized waveforms. One correlates each sample with each sample n-away in the same waveform creating an array of the same size as the input waveform. The acf is the average of all those products.
7. Collect your best averaged ratio (signal divided by averaged background) with signal; this averaging smooths out any non-physics features (etalon effect won't average out)

There's a script (https://github.com/lcls-psana/TimeTool/blob/master/data/timetool_setup.py) which shows the last steps of the calibration process that produces the matched filter weights from the autocorrelation function and the signal waveform.  That script has the auto-correlation function and averaged-signal hard-coded into it, but it shows the procedure.  It requires some manual intervention to get a sensible answer, since there are often undesirable features in the signal that the algorithm picks up and tries to optimize towards. The fundamental formula in that script is weights=scipy.linalg.inv(scipy.linalg.toeplitz(acf))*(averaged_signal).

The above procedure optimizes the filter to reject the background. Matt doesn't currently remember a physical picture of why the "toeplitz" formula optimizes the weights to reject background. If one wants to simplify by ignoring the background suppression optimization, the "average signal" (ignoring the background) can also be used as a set of weights for np.convolve.