1. Pre-calibration of PM gain by photo-statistics
A = k * G * N(p.e.) * e / s(adc)
N(p.e.) = is the number of photoelectrons; N(p.e.) = f *[A(LED)-A(PED)]²/[σ(LED)²-σ(PED)²];
e is electron charge;
s(adc) is ADC sensitivity; s(adc) = pC per ADC count;
f is Fano factor; f ~ 1.2;
k is clipping coefficient; k = 1/3;
A(LED) is LED peak position;
σ(LED) is LED peak r.m.s;
A(PED) is pedestal peak position;
σ(PED) is pedestal peak r.m.s.;
G = * (σ(LED)² - σ(PED)²) / (A(LED) – A(PED))
Irina Machikhiliyan,

2. Gain by photostatistics-II
Contribution from the photostatistics should dominate other possible sources. Natural strategy is to decrease the intensity of the LED light as much as possible increasing simultaneously the gain of phototubes;
To exclude dependence on time-alignment quality: 5TAE events are collected in the form of timing scan of many steps:
For each step #i (i=1,100):
for each cell: find maximal value of LED response over 5 TAE A(i);
Over all steps:
for each cell find points with optimal timing over A(i). Calculate gain in this point;
Several maxima give additional benefit allowing to estimate the stability of the PM response in time.
A(i), ADC cnt
Step i
Irina Machikhiliyan,

3. STEP #1 Settings: PM gain: 250K (Hamamatsu reg. curves are used);
LED intensity: 0V;
DAQ: timing scan, 5TAE events, 100 points / 2400 events per step (300 entries in LED peak per step);
Many ECAL LEDs produce residual light at zero intensity setting.
This light is seen by phototubes if their gain is high enough.
Signals from some LEDs are so large that PM responses saturate ADC.
Response on LED
Irina Machikhiliyan,

4. STEP #1(cont)
Measured value of the gain with respect to the prediction (HAMAMATSU reg curves):
R.M.S. is 18%
HV is in kV
Bend at HV > 1.45kV
The same effect is seen if compare with test-benches prediction
The assumption: MV setting 90V is not enough to reach desired HV values
Irina Machikhiliyan,

5. STEP #2 Settings: Medium voltage is set to 97V;
PM gain: tuned, for most of the cells: 250K;
LED intensity: tuned, from 0V up to 1.3V;
DAQ: timing scan, 5TAE events, 100 points / 5000 events per step (625 entries in LED peak per step);
Gain settings: from 80K up to 250K
Response on LED
Much better, but further tuning is needed, sometimes on the level of individual cells
Irina Machikhiliyan,

6. STEP #2(cont) LAL reg. curves Hamamatsu reg. curves
Ratio G(meas)/G(LAL) depends on HV in the similar way we saw during lab-studies (see talk from 24 Nov 2008)
With MV=97V:
no bend!
Irina Machikhiliyan,

7. LAL: systematics 1.23; r.m.s.: 14.4% fit: 12.1%
STEP #2(cont)
Measured value of the gain with respect to predictions
LAL: systematics 1.23;
r.m.s.: 14.4%
fit: 12.1%
IHEP: systematics 1.24;
r.m.s.: 14.4%
fit: 12.5%
Irina Machikhiliyan,

8. Measured value of the gain with respect to the prediction
STEP #2(cont)
Measured value of the gain with respect to the prediction
ITEP: for some PMs measurements seems to be not correct.
Further (in this presentation): ITEP data will be excluded from consideration
HAM: systematics 1.44;
r.m.s.: 14.0%
fit: 11.1%
Irina Machikhiliyan,

9. Relative width of LED peak
STEP #2(cont)
Relative width of LED peak
G(HAM) ≤ 100K
100K< G(HAM) ≤ 200K
G(HAM) > 200K
Irina Machikhiliyan,

10. Absolute width of LED peak
STEP #2(cont)
Absolute width of LED peak
G(HAM) ≤ 100K
100K< G(HAM) ≤ 200K
G(HAM) > 200K
Absolute width of LED peak is higher than 9 ADC counts: pedestal r.m.s. (1.2÷1.3) can be neglected
Irina Machikhiliyan,

11. Many thanks to Jacques and Pavel for very fruitful discussions
STEP #2(cont)
Results seems to be promising. Another iteration has been done during last weekend, data processing is now in progress. Next request on LED data will be issued in one-two weeks;
During access periods: the cells with measured gains which differ significantly from expected values were checked. As a result, several PMs were found which position was mixed with respect to DB. Also several signal connectors of bad quality were repaired;
Our summer student Viveca is here to participate in the data analysis;
Many thanks to Jacques and Pavel for very fruitful discussions
Irina Machikhiliyan,

12. Lab measurements: factor f
By I. Machikhiliyan & P. Shatalov
Test setup:
PM Vctrl 3.2÷3.5V (1.35÷1.48kV)
R/O crate with FEB and CROC_v2 was borrowed from Jacques and Frederic (many thx!)
CAT DAQ. Timing scan to find the optimal point.
Few photoelectrons mode:
Additional amplifier: gain g(amp)=18.18
Very low LED
Normal mode:
No additional amplifier
higher LED (position Qn, width sn)
Fit function to obtain one photoelectron response (position Q1, width s1):
E.H. Bellamy et al “Absolute calibration and monitoring of spectrometric channel using a photomultiplier” NIM A339 (1994)
PM gain:
G(1 p.e.) = Q1 * s / (g(amp)*k*q) = *Q1, where
s – ADC sensitivity, k=1/3 – clipping factor, q – charge of the electron
G(normal mode) = * sn^2 / (Qn-256) ( here f=1.2 is excluded )
New value of f:
f = G(normal mode) / G(1 p.e.)
Irina Machikhiliyan,

13. HV=3.3V; 49K of events (1st 1K is rejected)
Example: PM LA4612 (1)
HV=3.3V; 49K of events (1st 1K is rejected)
g(1 p.e.) =
G(normal mode)=
f=1.4
Irina Machikhiliyan,

14. HV=3.3V; 9K of events (1st 1K is rejected), different LED intensity-I
Example: PM LA4612 (2)
HV=3.3V; 9K of events (1st 1K is rejected), different LED intensity-I
HV=3.3V; 9K of events (1st 1K is rejected), different LED intensity-II
Irina Machikhiliyan,

15. Lab measurements (cont)
In general we checked 4 phototubes at different HV/LED LV settings. Calculated value of f varies between 1.4 and 1.6
Ratios from step #2 when f=1.2 is excluded from the formula for G(meas):
New value of f gives better agreement of G(meas) with test-benches data;
Can be pure coincidence…
The goal is to achieve acceptable level of inter-calibration. Absolute normalization can be extracted confidently from physical signals only…
Which value of f should be used?
Irina Machikhiliyan,

16. Spare slides
Irina Machikhiliyan,

17. PM LA4612 (3) TADC=23 TADC=0 TADC=2 TADC=4 TADC=5 TADC=6
Irina Machikhiliyan,

18. PM LA4612 (4)
TADC=8
TADC=10
TADC=12
Irina Machikhiliyan,