View source for First look at TOF calibration

=== First Look ===
* first select data sample with the following conditions:
*# only consider hits within 50ns of the timing peak both for ADC data and TDC data
*# only consider paddles that have hits on both ends
*# take care of the 6fold trigger timing shift in the TDC (24ns window)

* Do a rough determination of the walk correction by using the time in the ADC as reference.
*# calculate Time difference: <math>\Delta t = t^{i}_{TDC}-t^{i}_{ADC}</math> 
*# calculate Integral: I = pulse_integral - pulse_pedestal*nsamples
*# [[File:w.gif|400px|tumb||walk correction fit]] 
*# Note: the minimum ionizing peak is between 6000 and 10000
*# After using the correct timing conversion of 23.4375 ps/bin the following much narrower distribution is achieved
*# [[File:Screenshot-walk_correction_example.pdf.png|400px|tumb||walk correction and fit]] 

* Do mean time comparison between different planes
*# calculate MeanTime of Paddle i in plane j: <math> MT^{i}_{plane j} = (t_{right} + t_{left})/2. </math>
*# calculate MeanTime for all Paddles n in plane k: <math> MT^{n}_{plane k} = (t_{right} + t_{left})/2. </math>
*# For each Reference paddle in plane j: <math> MT^{paddle_{n}}_{plane_{k}} - MT^{REF}_{plane_{j}} </math>
*# [[File:example_mtdiff.gif|400px]]
*# and after using the correct timing conversion of 23.4375ps/bin:
*# [[File:mantimediff_goodtiming.png|400px]]
*# Fit the meant time peak of each projection. This is the relative mean-time difference.
*# [[File:Fit_projection_example1.gif|400px]] example 1
*# [[File:Fit_projection_example2.gif|400px]] example 2
*# and now a good example after using the correct timing conversion
*# [[File:Screenshot-mtdiff_vs_padnum_proj_example42.pdf.png|400px]]
*# and an example where the automatic fit failed because the meantime peak is smaller than the background
*# [[File:Screenshot-mtdiff_vs_padnum_proj_example44.pdf.png|400px]]
*# Do this for each paddle in the first plane as reference paddle.
*# Choose one paddle in the first plane as THE REFERENCE PADDLE
*# Calculate the difference between the fit results of each paddle in the first plane w.r.t. THE REFERENCE PADDLE and fit the distribution
*# [[File:Meantime_average_to_refpaddle_example.gif|400px]] average difference of mean time to REFERENCE PADDLE
*# Now we have offsets for the Mean-Time for all Paddles w.r.t. THE REFERENCE PADDLE

* Do time difference comparison of one paddle with the paddle number in the other plane
*# calculate time difference: <math> \Delta t^{i}_{plane j} = (t_{right} - t_{left})/2. </math>
*# plot this time difference vs. paddle number of paddles that got hit in the other plane
*# [[File:PaddleNumber_vs_deltat_example.gif|400px]] 
*# again look at each projection and fit the <math>\Delta t</math> peak
*# [[File:deltat_fitposition_example.gif|400px]]  [[File:deltat_fitposition_p18_example.gif|400px]]  example fits
*# now one can also plot the fit results as a function of paddle number. The inverse slope is the speed module paddle pitch
*# [[File:velocity_example.gif|400px]]
*# one can also plot the difference between symmetric paddles around the beam hole <math>\Delta t_{left} - \Delta t_{right}</math>
*# [[File:timediff_planesymmetry_example.gif|400px]] choose the intersection at zero for the time difference offset

* Now we have offsets for time difference (TD) and mean time (MT)
*# offset for the left pmt: <math> c_{left} = (MT-TD)/2.  </math>
*# offset for the right pmt: <math> c_{right} = (MT+TD)/2.  </math>
*# as a bonus we get the effective speed of light for each paddle.