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.