measurement of the absolute efficiency, with a precision better than 2%, of a pmt working in single...
TRANSCRIPT
Measurement of the absolute efficiency, with a precision better than 2%,
of a PMT working in single photoelectron mode
Philippe GorodetzkyAPC lab, Paris, France
VLVT09, Athens, October14, 2009
How to calibrate ?
Comparison to a reference
Calibratedsource
Calibrateddetector
(photodiode)
1) Calibrated Source
• GOOD : Only 1 measurement– Time variations of no importance
• BAD : Control of the spatial variations of the source. ==> IMPOSSIBLE– Angle & surface of emission (Liouville)
2) Calibrated Detector
• GOOD : Spatial variations of no importance if comparison made in same conditions
• BAD : Need 2 measurements=> time variations important, but can
be controlled through a third detector ==> POSSIBLE
Needs
• NIST photodiodes have a gain of about 0.5. So the light flux has to be reduced ~106 times
• Avoid geometry problems in illumination=> exactly same geometry for PMT and
calibrated detector
How (is the calibration done)2 steps
• Mapping of the photocathodesRELATIVE
• Comparison to a NIST photodiode @ 1 position
ABSOLUTE
Mapping of the photocathodes
Very few photons
We illuminate with an LED of the good wavelength, and pulse at one kHz in order for the ADC to follow. To make a single photoelectron spectrum, while we acquire on the ADC, we lower the quantity of photons sent per pulse until the obtained peak has a stable position*. Then the number of events in that peak lowers while the number of events in the pedestal increases. When do we stop lowering the light?
The spectrum is mainly a one pe (the bump), but there is still a « peak » at 2 pe, very weak, which will be troublesome when a discriminator is set between the pedestal and the 1 pe, and we count with a scaler: each 2 pe counts double, and the result will be wrong.
scaler
scaler
•One can also use an oscilloscope and watch when the base-line under the pulse begins to fill
SINGLE PHOTO-ELECTRON
We use Poisson: and P0, P1, P2 are the respective populations of the
pedestal, of the 1 pe and of the 2 pe
P0 = (m0 / 0!)e-m = e-m
P1 = (m1 / 1!) e-m = m e-m = m P0
P2 = (m2 / 2!) e-m = (m2 / 2) e-m = (m / 2)P1 = (m2 / 2)P0
If one wants that P2 = 1% x P1, (m / 2)P1 = 0.01P1, then m / 2 = 0.01, and m = 0.02
Now, the ratio between P0 and P1: P0 / P1 = P0 / (mP0) = 1 / m will be 1 / 0.02 = 50
In our case, as soon as the pedestal is 50 times more important than the 1 pe, the 2 pe will be less than 1% of the 1 pe
Usually, one takes: pedestal = 100 times 1 pe. Then we are sure not to pollute the measurement. Now we can set the discriminator threshold to be in the bottom between the pedestal and the 1 pe (at 0.25 of the 1 pe), and we just have to count in two scalers the pulses sent to the LED and the discriminator output. Exit the ADC: one can pulse until 100 kHz, which allows comfortable statistics in a few minutes.
Also, the threshold being in a valley, the measurement will not be very sensitive to a small variation of the threshold, or of the gain due to HV small changes.
€
Px =mx
x!e−m
SINGLE PHOTO-ELECTRON
Mapping of the photocathodes
Reduce the light per pulse & adjust the gain
Optical fiber
•One can also use an oscilloscope and watch when the base-line under the pulse begins to fill
Mapping of the photocathodes
In red: Coïncidences between generator & PMT discriminator
Mapping : « PMT-JY »
The photocathode is naked ( = 51 mm)
Mapping of the photocathodes.Here, absolute
Better efficiency if we use only the central part=> diaphragm of 20 mm
Full pmt (40 mm diameter)
Absolute measurement
• PMT and 1 photodiode at the same time
• BUT : very different gains : 1 vs 107
=> how to divide a light flux by 107 ?
Absolute measurement
• Use of integrating spheres to reduce light
• Measurement of the light flux reduction
• Measure the PMT efficiency
http://www.labsphere.com/data/userFiles/A%20Guide%20to%20Integrating%20Sphere%20Theory&Apps.pdf
SINGLE PHOTO-ELECTRON
If one measures 1 nW in the second diode (noise = 1 pW) and 0.775 mW in the first :
Ratio = 7.75 105
Calibration of the system
ANALYSIS
100 kHz: 14.425 nW in NIST
As the ratio = 7.75 105
One sends on the PMT: 14.425 nW / 7.75 105 = 1.861 10-5 nW
Energy of a photon @ 378 nm: E = h = hc/
E = 6.026 10-34 x 3 108 / 378 10-9 = 4.783 10-19 J
One knows that 1 J = 2.090 1018 photons
So 1.861 10-5 nW ==> 1.861 10-14 x 2.090 1018
= 38912 photons / sec.
In one measurement of 100 sec, we have sent on the PMT: 3891200 ph
We have measured 686797 pe ==> efficiency (discri) = 686797 / 3891200 = 17.65%
We have to add 8.8% (discri) so efficiency = 19.2 % at 377 nm (PMT center), and 15.8% for full pmt, instead of 22% given by Photonis
Discri
Calibration of the PMT
Absolute measurement
Uncertainties :
• Flux reduction (ratio) : 3 % (2 NIST diodes)
ΔR/R = (ΔI/I + Δα/α)udt + (ΔI/I + Δα/α)o1
• Efficiency measurement : 1.7 % (1st NIST cancels out)
Δε/ε = ΔR/R - (ΔI/I + Δα/α)udt
3 Leds
NIST Photodiode
trans-impedance amp.
Integrating sphere
4 cmAmplification of TTL pulses in 40 V pulses with a risetime of 2 ns collimator
If one wants a more collimated photon beaminstead of Lambertian distribution
Another way to look at the set-up: the first sphere is a "perfect" splitter (to the NIST and the first diaphragm)followed by a very stable light reducer.
One application: AntaresAnd why not NESTOR, or km3 ?
They calibrate their system with atmospheric muons,but do not know very well (!!!) the efficiency in the back of the tube
X,Y,Z, , movement in a black box
The light source:
- integrating sphere
- collimator
Another application: JEM-EUSO 36 pixel Hamamatsu PMT
Efficiency of pixel 22, at 378 nm, and looking only at anode 22 = (17.9 ± 0.32)%
Then, the sum of all 9 pixels gives the full pixel 22 absolute efficiency at 378 nm when looking at all 9 anodes: (29.8 ± 0.54)% where the relative uncertainty has the same causes than above, and is 1.8%.
Assuming a collection efficiency of 70% (Hamamatsu), one gets a quantumefficiency of 40%Less than 1% of the counts are in coincidence in any combination of 2 pixels
So, it is not a cross-talk, but a point spread function of 5.8 mm diameter, twice thediameter of the PSF of the lenses, that is 4 times its surface.
Hence, Hamamatsu is designing a new PMT, with a better focus (a 64 pixels)
We illuminate the center of pixel 22 with a spot of 1 mm size.