Experimental Resolution Function for Pixels Part II

1
Experimental Resolution Function for PixelsPart
II

• Sommary
• Introduction
• Two sets of F
• Support from the data
• Agreement with data
• Conclusions

2
IntroductionResolution Function

• Resolution function F density probability of
  residuals
• It is a function of track angle and clusters
  size FF(b,cw)
• More generally F is also a function of
• Detector technology
• Readout chip
• Finding Position Algorithm
• Detector bias and threshold
• Position
• Radiation damage
• It is justified from the data and from the toy
  model to write F has a sum of two part
  F (b) Fun-th (b) Ffull-cs (b)

Neighbor pixel under threshold
Full charge sharing d ray
3
Two sets of F

• If the Threshold is very small you have almost
  always charge sharing due to the diffusion of the
  charge collected
• No dependence of F to the cluster size but only
  respect to the angle
• For a fixed angle F is well described by a
  GaussianPower law fit with the exponent about 2
  
• But in real life the threshold is not negligible
  (this is also more true considering radiation
  damage effects) and often a pixel in the cluster
  is under threshold
• Two ranges of clusters size with a dependence on
  the angle
• In the first range F is well described by a
  Conv(box,Gaussian)Power law
• The second fit is a generalization of the first
  one and than make sense to use just this for the
  two part
• The data and the toy model suggest to write
  F (b) Fun-th (b) Ffull-cs (b)
• with both fitted by Conv(box,Gaussian)Power
  law

4
Support from the data
Pspray-fpix0 angle0
Cluster size2
Cluster size1
Cluster size4
Cluster size3
Cluster size6
Cluster size5
The distribution of xtrack-xmes for different
cluster size confirm that F is a sum of two
contribution one due to cluster size one and the
other due to cluster size bigger than one
5
Agreement with dataConv(Box,Gaussian) power
law fit
Fpix0-pstop angle0 cw 2
c21.46
Fpix0-pstop angle0 cw gt1
c21.03
To put cw2,3,4 Give better results
6
Agreement with dataFpix1-Pstop
Fpix1-pstop angle30 all cw
c20.8 For others angle the c2 is near to 1
In this case the contribution from clusters with
hits under threshold is negligible
7
Agreement with data Fpix1-Pstop
0 degrees considers only cluster with more
than one pixels
8
Conclusions

• F is experimentally well parameterized by two
  sets of 7 constants for each angle
• The two set shrink to one for angle gt 10
• The 7 constants have a physical interpretation
• The model is easy to implement in a simulation
  without loose in speed
• The tail satisfies a power law with universal
  exponent 2
• We have a quantitative way to study the tail for
• Comparison
• Improve Finding Position Algorithms
• There is a concrete possibility to do an accurate
  deconvolution of the non-Gaussian tails from the
  physical signals