Difference between revisions of "ADC data"

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(ADC data)
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*[[File:paddle33_xTvsxE.gif|400px|tumb|| X-pos from TDC vs X-pos from ADC]]  [[File:paddle21_xevsxt.gif|400px|tumb|| X-pos from TDC vs X-pos from ADC]]
 
*[[File:paddle33_xTvsxE.gif|400px|tumb|| X-pos from TDC vs X-pos from ADC]]  [[File:paddle21_xevsxt.gif|400px|tumb|| X-pos from TDC vs X-pos from ADC]]
  
Fitting the slope will result in the attenuation length d and the horizontal shift is the ration of the two epsilons. You also notice the dip close to
+
Fitting the slope will result in the attenuation length d with this simple assumption and the horizontal shift is the ration of the two epsilons. You also notice the dip close to x=0. This is due to the fact that ln(1) is zero. We know that the attenuation length is x-dependent and for a better description we need two attenuation lengths.
x=0. This is due to the fact that ln(1) is zero.
+
For a central paddle like paddle 21 the distribution is distorted rather strongly. The slopes are quite different in the center and in the tails. Note this is a log plot in z because the center has so much more events. Also in this particular case the TDC x position also seems to be a little off, indicating that the timing calibration for this paddle in this RUN is not yet perfect.
Note that for the central paddle 21 this distribution is distorted rather strongly. The slopes are quite different in the center and in the tails. This is a log plot in z because the center has so much more events. Also
+
in this particular case the TDC x position also seem to be a little off, indicating that the timing calibration for this paddle is not yet perfect.
+
  
 
   
 
   
And also the Energy vs. the X-Pos of the ADC:
+
One can also plot the Energy vs. the X-Pos from the ADC data:
 
*[[File:paddle33_EvsxE.gif|400px|tumb|| E0 vs X-pos from ADC]]
 
*[[File:paddle33_EvsxE.gif|400px|tumb|| E0 vs X-pos from ADC]]
  
the position of the minimum ionizing peak can be determined by a projection to the vertical axis. The location of the peak varies from paddle to paddle.
+
Projecting to the vertical axis or just plot E0 give the histogram below. The location of the peak varies from paddle to paddle.
 
*[[File:adc_E33.gif|400px|tumb|| E0]]
 
*[[File:adc_E33.gif|400px|tumb|| E0]]
  
Alternatively the energies <math>E_{R}, E_{L}</math> can be plotted separately but requiring that <math>\Delta T </math> is close to zero meaning that the particle passed though the paddle at or close to the center so both sides see the same amount of light modulo light coupling, detection efficiency and gain. This approach lead to the following two plots:
+
Alternatively the energies <math>E_{R}, E_{L}</math> can be plotted separately but requiring that <math>\Delta T </math> is close to zero meaning that the particle passed though the paddle at or close to the center. In this case both sides see the same amount of light modulo light coupling, detection efficiency and gain. This approach leads to the following two plots:
 
* [[File:e_paddle33_pmtleft.gif|400px|tumb|| E left]]  [[File:e_paddle33_pmtright.gif|400px|tumb|| E right]]
 
* [[File:e_paddle33_pmtleft.gif|400px|tumb|| E left]]  [[File:e_paddle33_pmtright.gif|400px|tumb|| E right]]
 +
 +
'''What do we want?'''
 +
# Procedure (probably iterative) to align all PMT minimum ionizing peaks to the same value. This requires HV changes based on the knowledge of the PMT gains.
 +
# Having all MPVs a the same value will allow a better adjustment of the common threshold settings in the ADCs and discriminators.

Revision as of 08:51, 19 May 2015

ADC data

Given that the center of the paddle is x=0 and +x is to the left and -x is to the right we have the following quantities.

  • From TDC: with L the length of the paddle, t_{{o}} the time of flight of the particle, v_{{o}} the effective speed of light in the paddle t_{{L}} is the internal delay including all cables, PMT transit times ect. and same for t_{{R}}
    1. T_{{L}}=t_{{o}}+{\frac  {L-x}{v_{{o}}}}+t_{{L}}
    2. T_{{R}}=t_{{o}}+{\frac  {L+x}{v_{{o}}}}+t_{{R}}
    3. \Delta T=T_{{R}}-T_{{L}}
    4. \delta =t_{{R}}-t_{{L}}
    5. x={\frac  {1}{2}}(\Delta T-\delta )v_{{o}}
  • From ADC: with E_{{0}} the original energy deposition, d the attenuation length and \epsilon _{{L}} the light transmission through all couplings including the gain of the PMT and attenuation in the cables. L and R refer to left and right.
    1. E_{{L}}=\epsilon _{{L}}E_{{0}}e^{{{\frac  {-(L-x)}{d}}}}
    2. E_{{R}}=\epsilon _{{R}}E_{{0}}e^{{{\frac  {-(L+x)}{d}}}}
    3. x=ln({\frac  {E_{{L}}}{E_{{R}}}}{\frac  {\epsilon _{{R}}}{\epsilon _{{L}}}}){\frac  {d}{2}}
    4. E_{{0}}={\sqrt  {{\frac  {E_{{L}}E_{{R}}}{\epsilon _{{L}}\epsilon _{{R}}}}}}e^{{{\frac  {L}{d}}}}


  • Note: The values T_{{R}},T_{{L}},E_{{R}},E_{{L}} are the measured quantities. And in the following the time measurements are corrected by the relative offsets derived from the calibration procedure. But they have not been corrected for walk.

Now we can plot the x information from the TDC against the x information from the ADC:

  • X-pos from TDC vs X-pos from ADC X-pos from TDC vs X-pos from ADC

Fitting the slope will result in the attenuation length d with this simple assumption and the horizontal shift is the ration of the two epsilons. You also notice the dip close to x=0. This is due to the fact that ln(1) is zero. We know that the attenuation length is x-dependent and for a better description we need two attenuation lengths. For a central paddle like paddle 21 the distribution is distorted rather strongly. The slopes are quite different in the center and in the tails. Note this is a log plot in z because the center has so much more events. Also in this particular case the TDC x position also seems to be a little off, indicating that the timing calibration for this paddle in this RUN is not yet perfect.


One can also plot the Energy vs. the X-Pos from the ADC data:

  • E0 vs X-pos from ADC

Projecting to the vertical axis or just plot E0 give the histogram below. The location of the peak varies from paddle to paddle.

  • E0

Alternatively the energies E_{{R}},E_{{L}} can be plotted separately but requiring that \Delta T is close to zero meaning that the particle passed though the paddle at or close to the center. In this case both sides see the same amount of light modulo light coupling, detection efficiency and gain. This approach leads to the following two plots:

  • E left E right

What do we want?

  1. Procedure (probably iterative) to align all PMT minimum ionizing peaks to the same value. This requires HV changes based on the knowledge of the PMT gains.
  2. Having all MPVs a the same value will allow a better adjustment of the common threshold settings in the ADCs and discriminators.