[Research] Investigating the theoretical optimal MCPTimepx3 configuration for super-pixeling

[suannchong]

Motivation

The native resolution of the timepix3 chip is 512x512, and the current Sohpiread is using peak fitting to achieve 4K resolution, the process of which is also know as super-pixelling (or super resolution).
The theory behind the decision of 4K has yet to be established.
Therefore, the objective of this study is to provide theoretical foundations on the usage of super pixelling in Sophiread.

Hypothesis

Theoretically speaking, the accuracy and precision of peak fitting increases with the number of data points.
In other words, larger clusters should provide more accurate peak position due to better statistics.
However, large clusters also means higher chance for overlapping, making it challenging to properly label each clusters.
So there should be a sweet spot (i.e. cluster size) where it provides sufficient statistics for peak fitting while small enough to ensure correct clustering results.

Expected Outcome

• A believable reason behind the selected scaling factor used in super pixeling.
• A physical/mathematical/numerical reasoning behind how the cluster size distribution can affect the optimal spatial resolution of the MCPTPX3 detector.
• The best model for fitting the clusters. Possible candidates are:
  • Gaussian
    • skew Gaussian (if there is a good reason to believe that clusters are not isotropic)
  • Lorentzian
  • Voigt
  • Sinc peak/function

Plans

Numerical study

Case study 0: ideal situation (zero noise and error)

Here are the tentative steps to model the super resolution:

• In a 512x512 grid, place a supposed peak type in a off center position.
• Bin the grid into a lower resolution:
  • 2x: mimic super-pixeling MCPTPX3 into 1K detector
  • 4x: mimic super-pixeling MCPTPX3 into 2k detector
  • 8x: mimic super-pixeling MCPTPX3 into 4k detector
• Calculate the peak center via with different number of neighbors (self[1 pt], 1st order neighbor [9 pt], 2nd order neighbor [25 pt], 3rd order neighbor [49 pt]).
  • peak fitting
    • correct model
    • incorrect model
  • centroiding
  • fast Gaussian
• Rescale the calculated peak center to the original resolution (i.e. 512x512), and check the accuracy
• repeat the test with random peak parameters to get better statistics

Case study 1: non-ideal situation (added noise to amplitude)

Since the position reading from TPX3 is supposed to be accurate (pixel position cannot be off), the only source of errors would be the TOT value, which corresponds to the amplitude of the peak.
Here we will repeat the study done in Case 0, but with added known level (relative) errors to the amplitude, and check the positional (x, y) errors induced by the amplitude errors.

Experiments

Here are some candidate tasks for the experiment side:

• Identify characteristics of clusters (hits) from real data, possible features should include
  • clustering method used (currently only ABS available)
  • number of data points
  • spatial span (x, y) and shape (circular, ellipse, or other type of polygons)
  • temporal span (toa)
  • tot distribution
• Identify a good model for the general shape of these clusters
  • check the peak types above
• Can we use the cluster characteristics to
  • identify clusters from neutrons and gamma rays
    • there should be some data where MCP detector is radiated with gamma rays, and we could check if the corresponding clusters have different characteristics than the neutron one.

Support Materials

This section contains supporting materials for this study.

• lmfit: https://lmfit.github.io/lmfit-py/