# Time-walk corrections in 2D

A possibility to do time-walk corrections per Elton Smith's
prescription (see GlueX-doc-1719) was studied. A sort trigger
paddle was rotated 90deg in relation to long TOD paddle to
simulate 2 TOF planes. In this method, hit's time in one plane
is used to eliminate t0 from hit's time in another plane:

t'_{x1} = t_{x1} - (t_{y1} + t_{y2})/2, etc...

Next plot is Fig.3 from Elton which shows dependence of t' times on pulse
height in the generated Monte Carlo:

The same distribution measured with cosmic rays in our test setup is
shown below:

All 4 distributions look like an overlap of 2 different time-walk dependencies.
This dependences roughly correspond to 2 parts of the ADC spectrum - main
Landau peak plus background of the unknown origin which, however, seems
also to have a proper time-walk dependece. MeasuredADC spectrum is shown
below on the left, and Elton's MC distribution on the right:

After fitting time-walks accroding to:

t^{cor} = t - b0/(1+b1*sqrt(ADC))

and using corrected times, the distribution of
TOF time of the hit (t'^{cor}_{L} + t'^{cor}_{R})/2
is shown below:
Fitted gaussian width is 5.3 TDC counts (or 132 ps). However, the distribution
is highly non-gaussian, with RMS almost 3 times worse.