Measurement of the absolute efficiency, with a precision better than 2%,

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

How to calibrate ? Comparison to a reference Calibrated source Calibrated detector (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 photocathodes RELATIVE • Comparison to a NIST photodiode @ 1 position ABSOLUTE

Mapping of the photocathodes

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

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 thatP2 = 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 be1 / 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.

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

SINGLE PHOTO-ELECTRON http://www.labsphere.com/data/userFiles/A%20Guide%20to%20Integrating%20Sphere%20Theory&Apps.pdf

Calibration of the system 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 PMT 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

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

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

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)

Measurement of the absolute efficiency, with a precision better than 2%,