View source for TOF Calibration

= Overview =

One place to start learning about TOF calibration is with the location of the source code on github where one finds a README file explicitly listed at the bottom of the [https://github.com/JeffersonLab/hd_utilities/tree/master/TOF_calib '''''code listing''''']. Note that the tof calibration code itself is located in the git repository '''hd_utilities''' in the directory '''TOF_calib''' and consists mostly of root scripts controlled by regular shell scripts. These calibration procedure requires root input files that contain the TOF raw data. These root files are created using the plugin '''TOF_calib''' located in the github repository '''halld_recon''' in '''src/plugins/Calibration/'''.

A more details description of the calibration procedures and basic ideas behind the approach can be found in a GlueX document (DocID 2767)
[https://halldweb.jlab.org/doc-private/DocDB/ShowDocument?docid=2767 '''''tofcalib.pdf''''']. Since the original version of the calibration the procedure to apply a walk correction has changed several times. The current version is labeled "V4". In addition the TOF detector was upgraded in between 2019 and 2020 for GlueX II to cope with the hither rates. As a consequence this new TOF detector has a bigger beam hole and four "half length" paddles rather than two in each plane. Also the width of these paddles changed from 6cm to 4.5cm. These changes have no impact on the basic ideas and steps of the calibration. 

=== TOF Geometry ===
* 44 paddle positions per plane: paddle positions 21 and 22 are "half" paddles (two top/north, two bottom/south, all 6cm wide)
* the beam hole is 12cm by 12cm
* nominal paddle width is 6cm with 2 special 3cm width paddles right next to the beam hole. (for both horizontal and vertical plane)
* [https://halldweb.jlab.org/wiki/index.php/File:Tof.png TOF geometry schetch]

=== TOF2 Geometry ===
* 46 paddle positions per plane: paddle positions 22, 23, 24 and 25 are "half" paddles (four top/north, four bottom/south, all 4.5cm wide)
* the beam hole is 18cm by 18cm
* nominal paddle width is 6cm with 2 special 3cm width paddles right next to the beam hole followed by two special 4.5cm width paddles. (both for horizontal and vertical plane)

=Calibration Generals =
The TOF calibration is manly focused on timing, the most important observable the TOF detector is providing. The main correction to the measured time from any given PMT is the walk correction caused by the fact that leading edge discriminators are used to generate the logical signal from the analog PMT signal. Up to now this walk correction has been determined
by the shape of the two dimensional distribution of time vs. ADC integral where the time has been referenced to the time as reported by the flash ADC integral. This has the disadvantage that for high rate paddles close to the photon beam line the integral can be distorted due to pile up. A better approach is to use the ADC peak amplitude instead. However such a distribution requires a different functional form as a model. In addition it is also no longer possible to model the full ADC range with one functional form for all paddles at all locations and still have a stable procedure. Instead the ADC region is divided in two with the location of the separation being the dip before the rise of the minimum landau distribution in the ADC response function.

# The functional form has four parameters and is as follows: <br> a + b*pow(ADC,-0.5) + c*pow(ADC,-0.33) + d*pow(ADC,-0.2) <br> The two distinct fit regions are indicated by the two colors blue and red, the jump at ADC 4090 is due to overflow and binning effects.<br>The vertical axis is Ttdc-Tadc, the horizontal axis is ADC amplitude.<br> [[File:walk_fit_example.jpg]]
# Using this approach for the walk correction and leaving the rest of the calibration procedure <br>the same leads to much more stable results for the timing offsets over the whole running period.<br> Here we show paddle 9 with both PMTs on either end.<br> Note the variation of the offsets is very small (<10ps) for these two PMTs <br> [[File:tpar_paddle9.jpg]]
# The stability of the PMT response over the run period is shown here for PMT10.<br>In this particular instance the gain reduction is about 5%.<br>[[File:adc_vs_time_pmt10.jpg]]

= Calibration Particulars =
The most important correction to the TDC timing is the walk correction as outline above. Over the course of the years several different approaches have been made to describe the function form of the time difference vs. ADC peak histogram. The latest version of walk correction currently in use in V4. The run period of spring 2017 has been calibration using version V3 and that is what was used in the production of the REST files. In view of a future reproduction of the REST files with the latest code a new calibration effort has been executed using version V4 for the TOF walk correction. The result was tested and compared with verstion V3 for run 30610 and the result is shown below. It demonstrates a 5% improvement in the timing resolution in this particular case.<br>
[[File:tofcalib_test_v3v4_run30610.gif | 500px]]<br>

For completeness the funcational form of the fit function for the walk correction V4 looks like this:<br>
<math> f(x) = a + b/\sqrt x + c/x + d/x^2 + e/x^4</math><br>
with a total of 5 parameters (a,b,c,d,e) and where x is the pedestal subtracted ADC peak value of the signal.