Reconstructed Photon Distribution Analysis

 I have been doing some analysis on the distribution of reconstructed photons in cells of the detector. 

In principle, if the gain correction of a given cell is too high and the gain corrections for adjacent cells are correct, then photons that hit in adjacent cells will be reconstructed closer to the cell with the high gain correction. Likewise, if the gain correction of a given cell is too low, photon hits in adjacent cells will be reconstruced farther from the cell with the low gain correction.

I looked at the x-distributions and y-distributions for all the cells in the small detectors and plotted their skewnesses:

NSTB3 x-distribution skewness:

NSTB3 y-distribution skewness:

NSTB4 x-distribution skewness:

NSTB4 y-distribution skewness:

Note that for skewnesses, there are essentially three possibilities:

skewness ~ 0: symmetric distribution

skewness < 0: mass of distribution lies toward higher numbers (asymmetric distribution)

skewness > 0: mass of distribution lies toward lower numbers (asymmetric distribution)

Thus the skewness of the reconstructed photon hits can be used to locate asymmetric distributions.


I looked at two specific cases for suspected cells that have too high or too low of gain corrections:

The "0" represents the central cell with the suspected gain correction problem; the "+" and "-" signs represent skewness signs

 - Gain correction too high:

- 0 +


 - Gain correction too low:

+ 0 -


Locating cells that have these skewness patterns combined with some additional cuts to filter out odd cases, I created histograms showing cells that probably have gains that are either too high (represented by +4) or too low (represented by -4). The 1s in the histogram represent cells that did not satisfy the above patterns and additional cuts. 

NSTB3 probable gain corrections:

NSTB4 probable gain corrections:


Next I chose a cell and adjusted the gain correction by increments of 0.2 from 0.2 to 2.0. Here are the results from that cell (nstb3,r3,c3)

Here are the results for a cell that I suspected to have too high of a gain correction (nstb4,r14,c7)

The x-axis is cell number; a range of two adjacent cells is plotted.