Continuation of my track correction studies ...

Here I investigate how well I can correct the FF (bad) spectra back to the RFF (good) spectra given the model described in previous blog posts.

The first step was to see if I could transform the good RFF spectrum into the bad FF specturm by changing the track's sagitta by some amount. The size of the shift is a random value following a gaussian distribution. A previous study determined that the parameters of the gaussian which reproduce the bad spectra were: Mean = 0.66, Sigma = 0.35. Once I could reproduce the bad spectra using a good spectra, the next step was to create a correlation matrix which related the modified RFF values (which should correspond to the unmodified FF values) to the unmodified RFF values.

Figure 1: This figure shows the relationship between the modified RFF values on the Y-Axis Vs the unmodified RFF values on the X-Axis. The idea is that the modified RFF values correspond to the bad FF spectra so we can see what the FF values "should" be if there was no distortion. The top figure is for positive tracks and the bottom figure is for negative tracks.

When doing the actual correction, I create 12 matrices for each charge sign like the ones shown in figure 1. Each matrix is for a unique range of track lengths. So the correction I apply is a function of pt as well as track length. Here are the correlation matrice for the positive and negative tracks.

As can be seen in Figure 1, the modified to unmodified relationship has some width, so there is not a one-to-one mapping from the bad FF spectra to the corrected spectra. I will need to charactarize the distributions in figure 1 in some way in order to carry out the correction. There are many ways you could think of doing this, but as a first try, for each modified RFF bin (corresponding to a FF bin) I will take the average value of the RFF unmodified bins.

Figure 2: This figure shows the correction matrices I use to transform the FF spectra. The top 4 pannels are for positive tracks and the bottom 4 pannels are for negative tracks. The left column shows the full correlation matrices as seen in figure 1. The right column shows the correction matrices created from the left column, for each bin in Y, the average value along X is plotted. This is an aggregate of the twelve correlation matrices with different track lengths which is why the figures on the right have a width. The first and third rows show the full range and the second and fourth rows are zoom-ins.

Now, using the correction matrices seen in figure 2, I can correct the FF spectra back into what I believe they should look like based on the shape of the RFF spectra.

Figure 3: This figure compares the original FF spectra, the original RFF spectra, and the corrected FF spectra for the positive tracks (top) and negative tracks (bottom).