1. Measurement of the absolute efficiency,
with a precision better than 2%,
of a PMT working in single photoelectron mode
Philippe Gorodetzky
APC lab, Paris, France
VLVT09, Athens, October14, 2009

2. Comparison to a reference
How to calibrate ?
Comparison to a reference
Calibrated
source
Calibrated
detector
(photodiode)

3. 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)

4. 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

5. 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

6. How (is the calibration done)
2 steps
Mapping of the photocathodes
RELATIVE
Comparison to a NIST 1 position
ABSOLUTE

7. Mapping of the photocathodes

8. SINGLE PHOTO-ELECTRON
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

9. 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.

10. 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

11. Mapping of the photocathodes
In red: Coïncidences between generator & PMT discriminator

12. The photocathode is naked ( = 51 mm)
Mapping : « PMT-JY »
The photocathode is naked ( = 51 mm)

13. Mapping of the photocathodes. Here, absolute
Better efficiency if we use only the central part
=> diaphragm of 20 mm
Full pmt (40 mm diameter)

14. 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 ?

15. Absolute measurement Use of integrating spheres to reduce light
Measurement of the light flux reduction
Measure the PMT efficiency

16. SINGLE PHOTO-ELECTRON

17. Calibration of the system
If one measures 1 nW in the second diode (noise = 1 pW) and mW in the first :
Ratio =

18. Calibration of the PMT ANALYSIS 100 kHz: 14.425 nW in NIST
As the ratio =
One sends on the PMT: nW / = nW
Energy of a 378 nm: E = h = hc/
E = x / = J
One knows that 1 J = photons
So nW ==> x
= photons / sec.
In one measurement of 100 sec, we have sent on the PMT: ph
We have measured pe ==> efficiency (discri) = / = 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

19. 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

20. If one wants a more collimated photon beam
instead of Lambertian distribution
3 Leds
NIST Photodiode
trans-impedance amp.
Integrating
sphere
  4 cm
Amplification of TTL pulses in 40 V pulses with a risetime of 2 ns
collimator
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.

21. One application: Antares
And 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
The light source:
- integrating sphere
- collimator
X,Y,Z, ,  movement in a black box

22. Another application: JEM-EUSO 36 pixel Hamamatsu PMT
We illuminate the center of pixel 22 with a spot of 1 mm size.
Assuming a collection efficiency of 70% (Hamamatsu), one gets a quantum
efficiency 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 the
diameter 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)