About me
Project description
Data taking and results
Error estimation
Conclusions
Calibration of PM Gain Using
Photo Statistics
Viveca Lindahl
CERN Summer Student
LHCb calorimeter group
Supervisor: Irina Machikhiliyan
Summer 2009
Viveca Lindahl
Calibration of PM Gain Using Photo Statistics
About me
Project description
Data taking and results
Error estimation
Conclusions
A little about ECAL
Project contents
Background
Project contents
Pre-calibration of photomultiplier (PM) gain at the electromagnetic
calorimeter (ECAL) using photo statistics
This includes:
Calculate PM gains according to statistical theory
Compare this with the expected gains using parameters from
earlier measurements.
Survey the PM gain stability over time
Estimate the statistical and systematic errors
Viveca Lindahl
Calibration of PM Gain Using Photo Statistics
About me
Project description
Data taking and results
Error estimation
Conclusions
A little about ECAL
Project contents
Background
Project contents
Pre-calibration of photomultiplier (PM) gain at the electromagnetic
calorimeter (ECAL) using photo statistics
This includes:
Calculate PM gains according to statistical theory
Compare this with the expected gains using parameters from
earlier measurements.
Survey the PM gain stability over time
Estimate the statistical and systematic errors
Viveca Lindahl
Calibration of PM Gain Using Photo Statistics
About me
Project description
Data taking and results
Error estimation
Conclusions
A little about ECAL
Project contents
Background
Background
The average amplitude hAi of the digital output signal of the PM
(in ADC counts) is related to the gain Gs of the PM and to the average
number of photoelectrons before amplification hN i by:
hAi =
k Gs hN i e
SADC
where
hAi = average amplitude of PM output (ADC counts)
k = clipping factor
hN i = average no. of photoelectrons before amplification
e = electron charge
SADC = sensitivity of the ADC (pC/ADC counts)
Viveca Lindahl
Calibration of PM Gain Using Photo Statistics
(1)
About me
Project description
Data taking and results
Error estimation
Conclusions
A little about ECAL
Project contents
Background
Background
Photo statistics relates hN i to the average amplitude hAi and to the
standard deviation of hAi by
hN i = f
hAi2
σA2
(2)
where f is the Fano factor. We can then eliminate hN i from (1) and (2)
and get the gain Gs as
Gs =
Viveca Lindahl
SADC σA2
k f e hAi
Calibration of PM Gain Using Photo Statistics
(3)
About me
Project description
Data taking and results
Error estimation
Conclusions
A little about ECAL
Project contents
Background
Background
Photo statistics relates hN i to the average amplitude hAi and to the
standard deviation of hAi by
hN i = f
hAi2
σA2
(2)
where f is the Fano factor. We can then eliminate hN i from (1) and (2)
and get the gain Gs as
Gs =
Viveca Lindahl
SADC σA2
k f e hAi
Calibration of PM Gain Using Photo Statistics
(3)
About me
Project description
Data taking and results
Error estimation
Conclusions
A little about ECAL
Project contents
Background
Background
Numerically we have:
Sensitivity SADC = 0.020 ± 0.001 pC/ADC
Clipping factor k =
1
3
Fano factor f = 1.50 ± 0.03
Which gives for Gs
Gs = 244 · 103
Viveca Lindahl
σA2
hAi
Calibration of PM Gain Using Photo Statistics
(4)
About me
Project description
Data taking and results
Error estimation
Conclusions
A little about ECAL
Project contents
Background
Background
The gain during data taking was set to GHam using parameters
provided by Hamamatsu. The parametrization being
G = G0
HV
α
HV0
(5)
where
G0 and α = parametrization parameters
HV0 = 1 kV = a reference voltage
HV = the high voltage (in kV) supplied to the PM
For about half of the PMs there are measurements of G0 and α taken
by LAL making it possible to also compare Gs to GLAL .
Viveca Lindahl
Calibration of PM Gain Using Photo Statistics
About me
Project description
Data taking and results
Error estimation
Conclusions
Data taking
Results
Data taking
Conditions
Two separate runs of data taking about a month apart in time1
Low LED intensity and high gain (∼ 250 k) so that the signal width
is dominated by photo statistical contributions.
5 consecutive readout time slots, 25 ns each, to control timing
between PM system, LED system and readout system.
Timing scan technique: time delays are introduced with steps of
1 ns.
A total of 100 time steps were taken with 10 k events/step for the
first run and 15 k events/step for the second run.
1
First and second run were labeled 52177 and 53889, respectively.
Viveca Lindahl
Calibration of PM Gain Using Photo Statistics
About me
Project description
Data taking and results
Error estimation
Conclusions
Data taking
Results
Results
Relative PM response
1
0.5
0
50
100
Time delay (ns)
Figure: Example of the PM response to the LED flash as a function of relative
delay of the LED flash for a normally functioning PM cell.
Viveca Lindahl
Calibration of PM Gain Using Photo Statistics
About me
Project description
Data taking and results
Error estimation
Conclusions
Data taking
Results
Results
Relative PM response
1
0.5
0
50
100
Time delay (ns)
Figure: Example of the PM response to the LED flash as a function of relative
delay of the LED flash for an abnormally functioning PM cell.
Viveca Lindahl
Calibration of PM Gain Using Photo Statistics
About me
Project description
Data taking and results
Error estimation
Conclusions
Short-term stability
Counts
Results
Data taking
Results
Entries
200
0
0
2187
Mean
0.2016
RMS
0.2128
Underflow
0
Overflow
9
1
2
max ∆h (%)
<h>
Figure: The maximum difference between PM response peaks relative to the
mean peak amplitude (first run data).
Viveca Lindahl
Calibration of PM Gain Using Photo Statistics
About me
Project description
Data taking and results
Error estimation
Conclusions
Long-term stability
Counts
Results
Data taking
Results
400
Entries
5957
Mean
3.073
RMS
2.415
Underflow
Overflow
200
0
0
10
0
59
20
σ (Gs) / <Gs> (%)
Figure: Distribution for the standard deviation of Gs relative to the mean using
data from both runs.
Viveca Lindahl
Calibration of PM Gain Using Photo Statistics
About me
Project description
Data taking and results
Error estimation
Conclusions
Results
Data taking
Results
Long-term stability
Figure: 2D distribution for the standard deviation of Gs relative to the mean
using data from both runs.
Viveca Lindahl
Calibration of PM Gain Using Photo Statistics
About me
Project description
Data taking and results
Error estimation
Conclusions
Results
Data taking
Results
Comparison with earlier measurements
Entries
Mean
RMS
Underflow
Overflow
χ2 / ndf
Constant
Mean
Sigma
400
5955
-12.48
12.83
0
15
207.1 / 79
514.1 ± 8.7
-12.89 ± 0.12
8.897 ± 0.094
Entries
Mean
RMS
Underflow
Overflow
χ2 / ndf
Constant
Mean
Sigma
200
100
2718
2.316
14.29
0
5
130.6 / 66
189.8 ± 4.7
2.05 ± 0.23
10.86 ± 0.16
200
0
-100
-50
0
50
100
GHam - Gs
(%)
Gs
0
-100
-50
0
50
100
GLAL - Gs
(%)
Gs
Figure: Difference between expected gain, according to Hamamatsu
parametrization (left) and LAL parametrization (right), and Gs (first run data).
Viveca Lindahl
Calibration of PM Gain Using Photo Statistics
About me
Project description
Data taking and results
Error estimation
Conclusions
Error estimation
The errors involved in determining Gs are:
q
Statistical error: decreasing as
where N = no. of signal events.
First run: ∼ 4%
Second run: ∼ 3%
2
N
Systematic errors:
SADC has a given uncertainty of ±5%
The Fano factor: ±2%
Viveca Lindahl
Calibration of PM Gain Using Photo Statistics
About me
Project description
Data taking and results
Error estimation
Conclusions
Conclusions
The ECAL PM gains have been measured.
Both systematic and statistical errors were estimated.
Measured gains show good consistency with LAL data.
Hamamatsu data show an average systematic shift of about
−13% relative to the measured gains.
Problematic PM cells and LEDs are to be or have already been
checked and dealt with.
Viveca Lindahl
Calibration of PM Gain Using Photo Statistics