Preprint typeset in JINST style - HYPER VERSION
Simulation, Reconstruction and Experimental
Prototype studies of the PANDA Barrel DIRC
G. Kalicya b , H. Kumawata c∗, J. Schwieninga
a GSI
Helmholtzzentrum fur Schwerionenforschung GmbH
Planckstrasse 1, 64291 Darmstadt, Germany
c Nuclear Physics Division, Bhabha Atomic Research Centre
Mumbai-400085, India
b Goethe University Frankfurt
Senckerberganlage 31, 60325 Frankfurt am Main, Germany
E-mail: G.Kalicy@gsi.de H.Kumawat@gsi.de
for the PANDA Cherenkov Group
A BSTRACT: The PANDA experiment at FAIR will perform high precision experiments in the
charm quark sector using cooled anti-proton beams of unprecedented intensities of L=2×1032 cm−2
s−1 in the momentum range of 1.5-15 GeV/c impinging on fixed targets. The charged particle identification in the target spectrometer region needs a thin detector operating in a strong magnetic field.
A ring imaging Cherenkov detector using the DIRC principle is an excellent match to those requirements. This article describes the status of the R&D of the PANDA barrel DIRC detector, with main
focus on different design options. Monte Carlo simulation studies for DIRC constructed with narrow bars or wide plates have been carried out. The performance in terms of photon yield, single
photon resolution, track Cherenkov angle resolution, π/K separation using likelihood approach are
investigated. Moreover, the photon yield and the single photon Cherenkov angle resolution are
measured in the prototype experiments with different setups. The results are consistent with the
expectations obtained from ray tracing software and GEANT simulations. Other aspects of the
prototyping are also briefly discussed.
K EYWORDS : Particle identification methods; Cherenkov detectors;.
∗ Corresponding
author.
Contents
1.
Introduction
1
2.
Barrel DIRC Design Options
2
3.
Simulation and Reconstruction
4
4.
Prototyping of the PANDA Barrel DIRC
4.1 Photon Detection
4.2 Radiators
4.3 PANDA Barrel DIRC Prototypes in Particle Beams
7
7
8
9
5.
Conclusions
11
1. Introduction
Excellent charged Particle Identification (PID) over a large range of solid angle and particle momenta is an essential requirement to meet the physics objectives of the PANDA detector [1] at the
future FAIR facility at GSI. The detailed Physics program and the PID requirements for PANDA, as
well as the PID systems covering particles in the forward region, are described in detail in Ref. [2].
The barrel section of the target spectrometer of the charged hadron PID covers an angular range of
22-140◦ , and needs to separate pions from kaons of momenta up to 3.5 GeV/c with a 3σ separation. It has to operate in the B≈2T solenoid magnetic field and should be capable of handling an
interaction rate of up to 50MHz. Since it is surrounded by an electromagnetic calorimeter, it should
be thin in both, radius and radiation length. All these requirements can be met by a Ring Imaging Cherenkov (RICH) detector, based on the DIRC (Detection of Internally Reflected Cherenkov
light) principle. A charged particle going through a solid radiator at a velocity faster than light in
that medium emits Cherenkov photons. They are emitted on a cone with the half opening angle
θC , defined as cosθC = 1/n(λ )β , where β = v/c, v is the particle velocity, n(λ ) is the index of
refraction of the material, which in a dispersive medium is a function of the wavelength (λ ) of the
Cherenkov photon. For β ≈ 1 some part of the photons undergo always total internal reflection.
Photons propagating forward are reflected by the mirror towards the readout end of the radiator
where they get focused and imaged on the photo-detector plane. Radiators are usually narrow bars
or wide plates from synthetic fused silica. The initial direction vectors are preserved inside the bars
due to its good optical qualities. The measured hit pixel coordinates and photon propagation time
along with particle momentum and bar hit position, are used to reconstruct Cherenkov angle and
determine the corresponding PID likelihoods.
In this article, the DIRC design options are presented in section 2, followed by simulation
and reconstruction studies for a selection of them in section 3. Prototyping of the barrel DIRC is
described in detail in section 4.
–1–
Figure 1. CATIA drawing of the PANDA Barrel DIRC baseline design.
2. Barrel DIRC Design Options
The PANDA barrel DIRC design is inspired by the BaBar DIRC detector [3]. Some key improvements have been investigated and are applied to optimize the needs for the PANDA. Focusing
optics and fast timing are used to improve resolution and a smaller size expansion volume will
help to decrease the sensitivity to accelerator induced background and simplify the overall detector
design. The baseline design components of the barrel DIRC detector are shown in Fig. 1 Synthetic
fused silica was selected as a material for radiators due to its long transmission length, polishability,
moderate dispersion, and its radiation hardness [4]. The bars are 2.4 m long with a cross-section of
17.5 mm x 32 mm. Five bars placed side-by-side with a small air gap in between are comprised by
one module called bar box. The bar boxes are arranged in a barrel of radius 476 mm, surrounding
the beam line. Mirrors are attached to the forward end of the bars to reflect the Cherenkov photons
towards the photo-detector plane where they exit through a focusing lens via a fused silica window
into the expansion volume filled with mineral oil. An array of photo-detectors is placed at the
fused silica back-plane of the expansion volume and the hit pixel and arrival time of the Cherenkov
photons are recorded using several Micro-Channel Plate Photomultiplier Tubes (MCP-PMTs) with
approximately 10-15 k channels in total.
The PID performance is mainly driven by the track Cherenkov angle resolution σC,track defined as
2
2 /N + σ 2
σC,track
= σC,γ
pe
track
where N pe is the number of detected photo-electrons and σC,γ is the single photon Cherenkov
angle resolution. σtrack is the uncertainty of the track direction in the DIRC, dominated by multiple
scattering and the resolution of the PANDA tracking detectors. The single photon Cherenkov angle
resolution σC,γ can be calculated as
–2–
2
2
2
2 = σ2
σC,γ
C,det + σC,bar + σC,trans + σC,chrom
where σC,det is the contribution from the detector pixel size, σC,bar is the error due to optical aberration and imaging errors, σC,trans is the error due to bar imperfections, such as non-squareness, and
σC,chrom is the uncertainty in the photon production angle due to the dispersion n(λ ) of the fused
silica material. The time resolution at the level of 100 ps will allow for partial correction of the
chromatic resolution [5].
The estimated σC,γ ≈ 8-9 mrad is dominated by σC,det = 6.3 mrad and σC,chrom = 5 mrad. The
number of detected photons per track in the PANDA barrel DIRC is expected to be approximately
20. The Cherenkov angle resolution combined with 1 mrad of track polar angle resolution from
the PANDA tracking systems results in a total track Cherenkov angular resolution of σc,track = 22.5 mrad. This resolution will allow a π/K separation of more than 3σ for momenta of 3.5 GeV/c
and better at lower momenta.
Several design options are still being investigated for the barrel and the expansion volume. Two
approaches for the expansion volume are considered: 30 cm deep single tank loaded with mineral
oil, which is a good match to the refractive index of fused silica (Fig. 2 a) and the segmented
prism type expansion volume, separate for each bar box (Fig. 2 b). The second option have better
optical aberration properties and allows to use less photon sensors compared to big single oil tank
geometry. However a lot of additional reflections in the prism complicate the reconstruction of the
θC by adding significant amount of combinatorial background.
However, using wide plates instead of bars (Fig. 2 c) would save 1.5-2 M Euro by building of
just 16 plates instead of 80 narrow bars. However large number of pixels in horizontal and vertical
directions would have to be kept to make it robust against multiple tracks entering one plate and
less dependent on high precision timing. Preliminary estimations indicate that large pixelization
in x and y is expected to loosen constrains on time resolution even up to 200 ps. A time based
likelihood approach is developed to analyze the π/K separation power.
A focusing system to improve the overall track resolution, is also under study. Optimization
of the optics using the ZEMAX, ray tracing and Geant softwares showed that the lens with air
gap between the lens and the expansion volume causes massive photon loss, specially for particle
tracks perpendicular to the bar. Here all the photons are totally internally reflected at the end of the
bar but only few get out through the curved surface of the lens. The potential solution is to use a
compound lens of higher refractive index built of fused silica layer and NLaK, that can be coupled
directly to the bar and the expansion volume. One lens of this type was already used with success
in the prototype experiment, other combinations of materials are being considered also.
The mechanical design follows the general idea from the BaBar DIRC as well. Bar boxes slide
on wheels into slots as shown at the CATIA drawing (Fig. 1), which allows to do staged installation
and will not block other detector subsystems. The carbon structure is made of two rings that have
two sets of openings. The openings at the inner radius are for the DIRC bar boxes and a set of
openings at the outer radius for the scintillation tiles. The vertical ribs allow to slide bar boxes in
and out. A sheet of carbon fiber outside of the ribs adds additional stability.
The choice of a photo-detector for the DIRC is a challenge due to the expected 20 MHz average
interaction rate during the PANDA operation. Such a high rate demands high rate capability and
long life time of the sensors, also the strong magnetic field of about 1T at the sensor location in
the PANDA experiment is an issue. The recent progress in the photo-sensor R&D [7], shows that
–3–
Figure 2. Geant simulation of considered "radiator + expansion volume" geometry options: a) narrow bars
+ oil tanks, b) narrow bars + compact prisms, c) wide plates + compact prisms.
Figure 3. a) Photon directions leading to same pixel, b) reconstructed Cherenkov angle without time
weighting (red lines) and with time weighting (blue lines).
suitable sensors with higher life times are available for the test experiments and expected to be
commercially available in time for the DIRC construction.
3. Simulation and Reconstruction
Simulation tools for the DIRC detector are developed in the PANDARoot Framework, which is
based on Virtual Monte Carlo engines i.e. GEANT3, GEANT4. Quantum efficiency, collection
efficiency, real reflectivity of the forward mirrors are incorporated to simulate the realistic geometry. Also, dark noise and charge sharing effects are implemented, and the hit position and photon
propagation time are digitized. After simulation and digitization, the Cherenkov angle is reconstructed as described below. The prototype performance parameters are mostly simulated using
independent ray tracing software.
–4–
Figure 4. a) Phase space distribution of the kaons produced due to decay of pp̄->J/ψ->K+ K− γ, b) single
γ
photon resolution (blue circles), Cherenkov angle resolution using likelihood (red circles) and σC /N p (green
stars) for bar+prism geometry with focusing
The DIRC reconstruction approach is similar to the BABAR DIRC’s geometrical reconstruction. In this method, we use pixel position and the bar location to define photon direction at the end
of the bar and store it in a Look-up table. This direction combined with the particle track is then
used to calculate the Cherenkov angle. The pixel and time of the photon hit are observed using the
DIRC, and the particle hit position and momentum at the bar are measured by tracking detectors.
The photon path to reach a given hit pixel is not unique and possible ambiguous solutions add up
to combinatorial background. In addition to 8 possible paths due to reflection inside a rectangular
bar there are many (In Fig. 3 a, see 3 possible paths) possible paths in the prism. The geometrical
approach is to consider all possible paths of the photon for a given pixel hit. A few reflections
in the oil tank expansion volume is a big advantage but at the cost of photon absorption in the
oil and at the cost of more detectors to cover the detection plane. The Look-up table containing
photon direction vectors is generated by illuminating the photo detector plane by a photon gun of
mean wavelength placed at the center of the bar end. All reflections in the expansion volume are
associated with the possible reflections in the bar. In this way, several Cherenkov angles are obtained. The correct solution per photon peaks at the right Cherenkov angle, whereas the ambiguous
solutions due to wrong path create a background as shown in Fig. 3 b.
The difference of the expected Cherenkov angle and the reconstructed Cherenkov angle gives
the single photon resolution. The Cherenkov angle resolution is obtained using a Likelihood approach. The maximum likelihood Cherenkov angle is calculated using the reconstructed Cherenkov
angles. The true value is affected by the background created due to ambiguities. This background
is reduced with the help of true Monte Carlo simulated time information. The time resolution is
path length dependent due to chromatic aberration. The Monte Carlo simulated time is smeared by
100ps detector resolution in the study presented. A time based Gaussian weighting of the reconstructed Cherenkov angles is applied while getting the maximum likelihood Cherenkov angle for
each track (see Fig. 3) b). The difference of the track Cherenkov angle with the expected Cherenkov
angle gives us likelihood based Cherenkov angle resolution. The overall track Cherenkov angle resolution is obtained by combining the Cherenkov angle resolution and the tracking resolution from
the tracking detectors.
–5–
Figure 5. a) Likelihood based Cherenkov angle for decay of pp̄->D0 D̄0 , b) efficiency of kaon detection for
3σ separation (black circles), mis-identification of kaon as pion (blue circles) and mis-identification of kaon
as proton (red squares) for bar+prism geometry.
2 /N but there are several
The Cherenkov angle resolution per track should be equivalent to σC,γ
pe
parameters affecting this value. There is a spread in polar and azimuthal angle of the primary track
inside the bar caused by emission of δ -electrons and multiple scattering. The energy loss of the
particle (≈ 20-30MeV) inside the bar also affect the resolution near Cherenkov threshold.
The required overall track resolution depends on the populated phase space of the interesting
reaction channels. The Phase space of kaons from a radiative decay channel (pp̄->J/ψ->K+ K− γ)
for the DIRC acceptance is shown in Fig. 4. It is clear from Fig. 4 that the highest momenta are
populated around 22◦ . As the number of photons is dependent on the track polar angle (see Fig. 6),
the Cherenkov angle resolution per track also shows a polar angle dependence. The results are
shown for the “bar+prism”geometry with lens and similar trend is observed for the “bar+oil”tank
geometry. It clearly demonstrates that the stringent requirements for the track resolution in the
forward region, are met. The tails in the resolution might be due to viz. spread in primary track
angle due to hadronic interactions, momentum spread due to energy loss etc. In order to analyze
the PID performance, decay of pp̄ to π − π + K− K+ are studied. Clear bands of pions and kaons
are seen(Fig. 5). The efficiency of kaon detection for a pure kaon beam is shown in Fig. 5. The
mis-identification of kaons and protons is quite low for particle momenta below 3.5GeV/C.
The photon yield due to primary kaons of 3.5 GeV/C and due to secondary interactions is
shown in Fig. 6. The secondary photons are produced by particles produced during hadronic interactions, δ -electrons, γ induced e− e+ pairs, neutrons etc. These extra photons deposit extra charge
in the photo-detector sensors, which has an impact on their life time. There is ≈5% increase in the
number of photon hits due back scattering from the electromagnetic calorimeter that surrounds the
Barrel DIRC detector in the PANDA experimental setup. These photons are uncorrelated in time
and angle compared to the Cherenkov photons and create merely a background.
The reconstruction of the plate type barrel is based on time based likelihood method [6]. The
Probability Density Function (PDF) is derived from the simulation in form of histograms instead
of analytic solution. This time based PDF is multiplied with the poissonian PDF of Cherenkov
photons. The separation power for pions and kaons are analysed for many angles and momenta.
The separation power at 3.5GeV/C is shown in Fig. 8. There is more than 4σ separation but the
–6–
Figure 6. a) Photon yield from primary and secondaries for bar+prism geometry without Electro Magnetic
Calorimeter, b) with Electro Magnetic Calorimeter
Figure 7. Separation of pions and kaons at 3.5GeV/C
tails in the distribution has still to be understood.
4. Prototyping of the PANDA Barrel DIRC
The final decision concerning the design and components used in the PANDA Barrel DIRC will be
based on tests of prototypes both, in labs and particle beam experiments. In the following sections,
we describe recent improvements in case of photon sensors, fast timing electronics and radiator bars
challenges. The evolution of the full system prototypes tested in particle beams and a selection of
results are presented.
4.1 Photon Detection
A single photon detection to be performed in a 1 T magnetic field with a fairly good resolution
(millimeter level in space and 100 ps in time) is a challenge. In addition it has to cope with an
experiment of high radiation with rates of in an average 20 MHz at injection range. This results in
a deposition of around 0,5 - 1 Coulomb per square centimeter per year of the PANDA operation on
the anode which this is a big lifetime issue for most of the sensors.
–7–
Figure 8. a) Schematic illustration of the optical setup to measure the transmission of the beam propagating
via total internal reflection. The arrows show the movement degrees of freedom for the motors and mirrors
b)Coefficient of total internal reflection as function of the wavelength with example results for the bar from
the manufacturer Schott Lithotec
The technical challenges concerning sensors were recently solved with a huge improvement
in lifetime of MCP-PMTs [7], which are excellent candidates and are being tested in a setup that
allows to measure quantum efficiency and gain as well as rate tolerance and lifetime.
For data acquisition the HADES trigger and readout board (TRB) [9] has been used. It
fulfills high requirements in case of the amplifications specially for MCP PMTs in order to have
good separation and very fast signal rise time. Two versions of the TRBv2, with and without
amplification, were tested in particle beams. This version uses the TOF add-on based on the NINO
chip and the CERN HPTDC [10] as a discriminator to provide timing with a resolution of 98
ps per count and pulse height information from charge-to-width. New generation of the boards,
TRBv3 [8], with the custom amplify discriminator board were produced and went already through
first successful tests in particle beam experiments at MAMI during summer 2013.
4.2 Radiators
In the PANDA barrel DIRC, Cherenkov photons will be internally reflected for some tracks up
to 200 times and about 20-50 times on average. The optical quality of the surface, in particular
roughness and sub-surface damage, determines the probability of photon losses during total internal
reflection. In order to transport 80% of the photons to sensors, a polishing of the level of 10 Å
is required. Production of large fused silica radiators with extremely high tolerance of flatness
squareness and parallelism with such optical finish is the biggest challenge for any DIRC detector.
There are only few vendors worldwide capable of fulfilling these requirements.
The technical, dimensional and angular specs are tested in three separate experimental setups.
Two of them provide the shape of the bar quality measurements, by a laser light reflected from
the surface of the bar and other with an auto-collimator, that allows to test angles with a precision
better then 0.1mrad for parallelism and squareness.
The efficiency of the photon transport inside the radiator can be determined from bulk attenuation and reflection coefficient measurements [4] related to the roughness of the radiator by the
scalar scattering theory [11]. A setup (see Fig. 8 a)) with motion-controlled elements was designed
–8–
Figure 9. Schematic outline of the setup in 2012 test beam in CERN T9 with photo of the DIRC prototype.
Figure 10. a) Photo of 3 x 3 MCP-PMTs array. Number of detected photo-electrons per MCP-PMT pixel
for experimental (b) and simulated (c) data. The white pixels in the test beam data plot were caused by dead
TDC channels.
and installed in a dark, temperature-stabilized clean room to qualify the production and polishing
processes of the prototype radiators obtained from different manufacturers.
Previous measurements using lasers of three different wavelengths (Fig. 8 b)) show good
agreement with the model predictions. The measured data are shown with points while model
calculations for different surface roughness values are presented by colored lines. In the recent
setup, it is possible to measure bars up to 2.5 m long with lasers of different wavelength up to UV
range. More sensitivity to subsurface damages inside the bars is , and will significantly improve
the study of prototype bars and plates of various manufacturing qualities.
4.3 PANDA Barrel DIRC Prototypes in Particle Beams
All prototypes consist commonly of: a radiator bar, an expansion volume and photon detectors.
These components of the first Barrel DIRC prototype along with focusing lens are tested with the
proton beam in 2008 and 2009. The Cherenkov photons were recognized and ring segments were
observed. The second prototype was more complex. A stand alone system with a larger deeper
expansion volume loaded with mineral oil [12] mounted on the movable and rotatable support
structure. A larger detector plane allowed to test different types of sensors (MCP-PMTs, SiPM,
and Multi Anode PMT) and focusing lenses with different Anti Reflective (AR) coatings were
used. The data collected from two campaigns in 2011, at GSI and at CERN were used for the
first determination of the Cherenkov angle resolution and the number of photons per track of both
narrow bar and the oil tank designs.
–9–
Figure 11. a) Single photon Cherenkov angle resolution for experimental data. Reconstructed ΘC =
825 mrad, σ = 12 mrad b) Difference in number of photons per track between measurements with AR
coated lens with air gap (red) and compound lens directly coupled to the prism (blue).
Several key aspects of the design options were implemented into the third prototype and tested
in summer 2012 at CERN. A schematic view of the setup and a photo of the prototype components
are shown in Fig. 9. A synthetic fused silica bar (17 x 35 x 1225 mm3 ) with a focusing lens
attached to one end and a mirror attached to the other end were placed into a light-tight container.
A large synthetic fused silica prism with a depth of 30 cm, located about 2 mm from the lens,
served as expansion volume. The hit location and the photon propagation time of photons were
measured with an array of nine Photonis XP85112 MCP-PMTs coupled with optical grease to the
back surface of the prism. The data acquisition for 896 channels was performed using the TRBv2
boards.
The setup was placed into the mixed hadron beam at the T9 area of the CERN PS with momenta varying between 1.5 and 10 GeV/c. The trigger was provided by two scintillator counters.
A time-of-flight system together with two tracking stations based on scintillating fibers are used
for both tagging the pions/protons up to 6 GeV/c momentum and measuring the beam direction.
A total of about 220M triggers were recorded in several configurations. Spherical and cylindrical
focusing lenses with and without anti-reflective coating were tested in combination with bars produced from different manufacturers, including a bar made of acrylic glass. Wide radiator plate as
an alternative to narrow bars, compound lens without a need of an air gap and large fused silica
prism as an expansion volume were used first time. The polar angle between the particle beam and
the bar was varied between 20◦ and 156◦ , and the interception point between beam and bar was
scanned 80 cm along the long bar axis covering the range similar to the PANDA phase space. An
example of the occupancy plot for a 124◦ polar angle is shown in Fig. 10. A complicated hit pattern including position of the ring segments and the overlapping parts corresponding to additional
reflections from the prism sides are consistent with the pixelized simulation data for 10 GeV/c pions provided by the ray tracing software. The gray dots in the background are true hits from the
simulation.
The reconstructed Cherenkov angle for the prototype configuration with the narrow bar and the
spherical lens placed 2 mm before the prism is shown in Fig 11 a). The results from 8 particle track
– 10 –
polar angles with an interval of 0.25◦ were combined to decrease pixelization effect. The value of
the reconstructed Cherenkov angle is consistent with Monte Carlo predictions. The difference in
Cherenkov angle resolution comes from beam divergence.
The number of detected photons per track depends not only on the different sizes and qualities
of the used prototype bars but also on the configuration of the setup. Changes in the particle track
polar angle and the orientation of the bar with respect to the prism result in different fractions
of the ring segments lost on the gaps between the sensors. The measurements confirm that there
are not much difference for the different quartz bars. The only significantly different performance
was observed for acrylic glass bar. A 60% larger loss of the photons is observed in comparison
to the quartz bars and smearing of the actual arrival points. Lack of differences between various
quartz bars is expected because of too short photons path that is the sensitive parameter for the
imperfections. More detailed studies of the bars were done in separate high precision measurements
as described in 4.2.
The influence on the photon yield of different focusing lenses is shown Fig. 11 b). A regular,
UV anti-reflective coated, spherical lens with 2 mm air gap was used. It was observed in the
measured data and simulation that the light yield drops dramatically for tracks close to 90o when
using this lens. The reason is that photons are totally internally reflected at the lens interface. This
can be avoided by replacing this lens by lens of high refractive index without air gap. Comparison
of the results for standard UV lens with air gap and this compound lens is shown in Fig. 11 b) for
the angle of 128◦ . Here, the light yield is improved by about 10%. The observed improvement
for this particle track angle is consistent with simulations. Moreover, as expected for incidence
angle close to 90◦ photon yield stays stable for the compound lens while drops close to zero for the
regular one.
5. Conclusions
Simulation and prototyping of the barrel DIRC has been carried out. The PID performance has
been studied in view of various design options. The DIRC design with bars and lenses meet the
requirement of the PANDA Physics to a good extent. Mostly all (98%) of the physics reaction
channels that need good kaon separation are below 3.5GeV/C momentum. The time based likelihood approach of the reconstruction for the plate type barrel are promising and will be continued
to improve further. The lab experiment for reflection coefficient shows good agreement with the
model predictions. The recent progress in increasing the lifetime of photon sensors is promising.
Further tests of new prototype bars will be performed in the new improved setup. The aspects of
different design options were implemented in the prototypes and tested in particle beams. The results of photon yield, and single photon resolution are in good agreement with the predictions from
simulations. Further PID performance evaluation using simulations and prototype experiments is
planed to finalize the design of the Barrel DIRC detector for PANDA.
Acknowledgments
Acknowledgments.
– 11 –
References
[1] PANDA Collaboration, Technical Progress Report, GSI, 2005; PANDA Collaboration, Physics
Performance Report <arXiv:0903.3905v1>, 2009.
[2] C. Schwarz, et al.., Particle identification for the PANDA detector, Nucl. Instr. and Meth. A639 (2011)
169-172; D. Dutta, et al.., Software development for the P?ANDA barrel DIRC,Nucl. Instr. and Meth.
A639 (2011) 264-266.
[3] J. Benitez, et al., Nucl. Instr. and Meth. A595 (2008) 104-357.
[4] J. Cohen-Tanugi, et al.,Nucl. Instr. and Meth. A515 (2003) 680-700.
[5] I. Adam, et al., Nucl. Instr. and Meth. A538 (2005) 281-357.
[6] Y. Enari, et al., Nucl. Instr. and Meth. A494 (2002) 430-435.
[7] A. Lehmann, et al., these proceedings
[8] M. Traxler, et al., these proceedings
[9] I. Fröhlich, et al., IEEE Trans. Nucl. Sci. 55 59 (2008).
[10] F. Anghinolfi, et al., Nucl. Instr. and Meth. A533 183 (2004); J. Christiansen, et al., “High
Performance Time to Digital Converter,” 2004 CERN/EP-MIC;
http://hades-wiki.gsi.de/pub/DaqSlowControl/ DAQUpgradeTOFAddOn/TRB-TOF-AddOn.pdf.
[11] P. Beckmann and A. Spizzichino, “The Scattering of Electromagnetic Waves from Rough Surfaces”,
Pergamon (1963) 1. Edition
[12] ExxonMobil Lubricants & Specialties Europe, Hermeslaan 2, 1831 Machelen, Belgium.
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