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.