Difference between revisions of "ADC data"

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(ADC data)
(ADC data)
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*# <math>E_{R} = \epsilon_{R}E_{0}e^{\frac{-(L+x)}{d}} </math>
 
*# <math>E_{R} = \epsilon_{R}E_{0}e^{\frac{-(L+x)}{d}} </math>
 
*# <math>x = ln( \frac{E_{L}}{E_{R}} \frac{\epsilon_{R}}{\epsilon_{L}})\frac{d}{2} </math>
 
*# <math>x = ln( \frac{E_{L}}{E_{R}} \frac{\epsilon_{R}}{\epsilon_{L}})\frac{d}{2} </math>
 +
 +
Now we can plot the x information from the TDC against the x information from the ADC:
 +
*# [[File:paddle33_xTvsxE.gif|400px|tumb||walk correction fit]]

Revision as of 17:40, 18 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}}

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

    1. walk correction fit