Time walk correction (TOF and position) in HAND

Following discussion on June 23, I continued working on the time walk correction.

I combined number of production runs (runs # 3299, 3300, 3319, 3320, 3321, 3322, 3323, 3325) and plotted the TDC versus ADC for each PMT.

The reference point was scintillator bar that located in front of the examined bar. For example: when checking the bar 5 from layer 5, I use bar 5 from layer 4 as a reference.

I plotted the following:

Left TDC - 0.5*(TDC_left_ref.bar + TDC_right_ref.bar) vs Left ADC

and similar for the right sideThe cuts that I used:

TDC > 0 cut on TDC to be inside the integration window of ADC ( the correction is relevant only when

we have valid ADC data).

Fig 1: Red lines mark the ADC integration limits

cut on a small region of the reference bar ADC, to eliminate the contribution of time walk in the reference ADC.

The ADC vs TDC distribution for events with the cuts listed above are shown in Fig 2 and 3.

Fig 2: Top two graph show the TDC dependence on the ADC channel due to the time walk.The bottom two are time walk corrected. (left side graph are for left PMT and right are for right)

In order to make the script automatic for all planes and bars (and more efficient), I performed the relative calibration of TDCs. I arbitrary put all TDC in the same channel ( the data base structure allows me to do that, without affecting other constants).

Than, I performed the above procedure for all bars, in fig example for left side bars of plane 5.

fig 3: Example for all left side bars of layer 5

The function that I used to fit the data:

(1) TDC = a* X b +c *X + d

where a,b,c,d are fitted parameters and X is the ADC. The curve in Fig 2 (and 3) are the result of the fit to the data of the function above.

Example for the time walk correction that was done with laser (in Hall B) can be found in the:“Nuclear Instruments and Methods in Physics Research A 432 (1999) 265 – 298”The difference between fig 2 and fig 4 is TDC common stop and TDC common start respectively. The dependence that they measured:

fig 4: Typical example of the dependence of the TDC vs pulse height ADC

Fig 5 Left histogram show the TOF before the time walk correction and the right one after.

TOF resolution in this example ~ 1.209 / (2*sqrt(2)) = 0.42 [ns] (conversion between channel to ns is factor 2).

In fig 6 I summarized all the resolutions for all bars. Blue columns are the resolutions (S.D.) before the time walk corrections and the red ones are after the corrections. As it can be seen immediately there is a significant improvement in the resolution, about a factor of 2.

fig 6

13

57

911

1315

1719

2123

2527

2931

3335

3739

4143

4547

4951

5355

5759

6163

6567

6971

7375

7779

8183

8587

8991

9395

9799

101103

105107

109111

113115

117119

121123

125127

129131

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Non Corrected Corrected

Bar number

TO

F r

eso

luti

on

[n

s]

After I finished fitting all the data, I put all parameters together to see how they are distributed. The result is presented in fig 7:

fig 7: the parameters of equation (1) are: top left – a, top right – b ,bottom left – c, bottom right d.

I tried to use the mean value for each of the variables. The results were worser than the using bar specific parameters.

The next step was to implement this correction and check if we can get an improvement in position determination.First time I used rectangular shape to fit the data, however this algorithm didn't gave good results (the position resolution that I got, wasn't consistent with the resolution from TOF).

Instead we used following approach.I simulated position distribution in the following way:

I took uniform distribution between -50 and 50. each point from the uniform distribution I distorted with a Gaussian distribution with

sigma = 10 cm ( this is the average resolution that I got based on TOF)in fig 8 the expected distribution is presented:

fig 8: Position in cm

The experimental distribution for one of the bar (for example plane 2 bar 6):

fig 9

Than, I fitted these two distribution (when I generated the theoretical distribution, I left the same number of events in both graphs). I found the best scale parameter to stretch the data to fit the theoretical distribution, fig 10:

fig 10: Red Line is the theoretical distribution and black line is the data

I made same procedure for all layers and bars, fig 11:

fig 11: example for plane number 4

In the next step I wanted to make sure that I get position resolution consistent with the time of flight. Similar to the determination of TOF, I subtracted the position distribution of one bar from the position distribution of bar behind, fig 12:

fig 12.

So, the actual position resolution for the example above is 8.2 cm (sigma in Fig 12 should be divided by sqrt(2) because I used 2 bars, of course I assume same resolution...).

This value is consistent with the TOF data and with the resolution of these bars as was found by Ran in his M.Sc. Thesis.

Fig 13

If I do the same procedure for the non corrected data (with same number of events and same binning ), fig 14:

fig 14

13

57

911

1315

1719

2123

2527

2931

3335

3739

4143

4547

4951

5355

5759

6163

6567

6971

7375

7779

8183

8587

8991

9395

9799

101103

105107

109111

0

2

4

6

8

10

12

14

16

18

Position resolution

Based on TOFBased on POS

Ban number

Po

sitio

n r

eso

lutio

n in

[cm

]

and the difference if fig 15:

fig 15

in this case I get position resolution of 5 cm... This value is not consistent with TOF data and with previous measurements.

I think that the reason is that scale parameter calculated in the non corrected case if wrong. As it can be seen from fig 13, the theory doesn't match the data.

To summarize:

TOF resolutions are between 350 – 500 ps. Position resolution is ~ 8 cm (and consistent with TOF resolution assuming a velocity of ~20

cm/ns, Ran M.Sc. Thesis).