Pixel Hybrid Photon Detector Magnetic Distortions ... - LHCb - CERN

Abstract - The LHCb experiment requires positive kaon
identification in the momentum range 2 - 100 GeV/c. This is
provided by two Ring Imaging CHerenkov detectors. The
stringent requirements on the photon detectors are fully satisfied
by the novel Pixel Hybrid Photon Detector, HPD. The HPD is a
vacuum tube with a quartz window, S20 photo-cathode, crossfocusing
electron optics and a silicon anode encapsulated within
the tube. The anode is a 32×256 pixels hybrid detector, with a
silicon sensor bump-bonded onto a readout chip containing 8192
channels with analogue front-end and digital read-out circuitry.
An external magnetic field influences the trajectory of the
photoelectrons and could thereby degrade the inherent excellent
space resolution of the HPD. The HPDs must be operational in
the fringe magnetic field of the LHCb magnet. This paper reports
on an extensive experimental characterization of the distortion
effects. The characterization has allowed the development of
parameterisations and of a compensation algorithm. A calibration
procedure based on the imaging of pre-defined test patterns that
has been developed for the RICH detectors is also proposed.
Keywords – Hybrid Photon Detector, magnetic distortions, Sdistortions
correction.
T
Pixel Hybrid Photon Detector Magnetic Distortions
Characterization and Compensation
Gianluca Aglieri Rinella, Tito Flavio Bellunato, Carmelo D’Ambrosio, Roger Forty,
Thierry Gys, Mitesh Patel, Didier Piedigrossi, Ann Van Lysebetten
I. INTRODUCTION
he LHCb experiment [1], [2] is a dedicated B physics
experiment that will run at the LHC Large Hadron Collider
at CERN. It will study CP violation phenomena as well as rare
decays and possibly new physics of b-quarks. The detector
(fig. 1) is a single arm forward spectrometer covering a solid
angle ±300 mrad wide on the bending (horizontal) plane and
±250 mrad on the non-bending (vertical) plane.
LHCb requires efficient positive kaon identification in the
momentum range 2 - 100 GeV/c. This is provided by two
Ring Imaging CHerenkov detectors [3], [4], [5] equipped with
three different radiators: Aerogel [6], C4F10 and CF4.
The hadron identification is based on the accurate
measurement of the Cherenkov photons emission angle, which
is determined from the photon hit position on the detection
planes. A spatial granularity of 2.5 mm is required on the
Manuscript received November 1, 2004.
G. Aglieri Rinella is with the Dept. of Electrical Engineering, University of
Palermo, V.le delle Scienze, Palermo, Italy and with CERN, European
Organization for Nuclear Research, Geneve 23, Switzerland (e-mail:
gianluca.aglieri.rinella@cern.ch).
T. F. Bellunato, is with Dept. of Physics, Università di Milano Bicocca,
Milano and with INFN Sezione di Milano
C.D’Ambrosio, R. Forty, T. Gys, M. Patel, D. Piedigrossi, A. Van
Lysebetten are with CERN, European Organization for Nuclear Research,
Geneve 23, Switzerland.
detection planes in order not to influence the Cherenkov angle
resolution.
Fig. 1. The LHCb detector.
The two RICH detectors share a similar optical design with
spherical mirrors collecting Cherenkov photons. After an
intermediate reflection on plane mirrors the photons are
focused onto rings on the two detection planes located out of
the acceptance angle. The RICH1 detector (fig. 2) is situated
upstream of the spectrometer magnet, while RICH2 is
downstream. They are both located in the fringe field of the
spectrometer magnet. Each LHCb-RICH has two detector
planes. The photon detectors will be contained inside magnetic
shielding boxes made of high magnetic permeability iron. The
design of the boxes is such that the peak magnetic flux density
inside is less than 2.5 mT in RICH1 and less than 1.0 mT in
RICH2.
A balance between the aberrations from the optical system,
Rayleigh scattering, light losses and position resolution sets the
requirements for the photon detectors. Good single photon
detection capabilities with excellent spatial resolution on a
large active area are required. The photon detectors must
operate in the residual magnetic field present inside the
shielding boxes. These stringent requirements are satisfied by
the novel Pixel Hybrid Photon Detector (HPD) developed for
LHCb [7], [8].
The HPD, shown in fig. 3 and in fig. 4, is a vacuum tube of
80 mm diameter, 115 mm height. A S20 blue enhanced multialkali
photo cathode is deposited on the internal surface of the
quartz entrance window. A peak Quantum Efficiency of 25%
at 240 nm is obtained.

Fig. 2. The LHCb RICH1 detector
optical scheme.
Fig. 3. The LHCb RICH Hybrid
Photon Detector HPD.
The photoelectrons emitted from the cathode are accelerated
towards the anode in a cross-focusing electron optics system
with a demagnification factor around 5. The anode assembly is
fully encapsulated in the vacuum envelope. It consists of a
hybrid silicon detector with a pixel silicon sensor bump
bonded onto a CMOS readout chip, LHCBPIX1 [9]. The latter
has been developed from the ALICE tracker readout chip. The
anode has 32×256 pixels of 500×62.5 µm 2 . They are
connected via the bonds to the chip channels, each of which
contains a full analogue front-end and a 40 MHz digital
section. The device has excellent S/N ratio performance. The
binary data are readout via 32 signal lines fed through the
anode carrier. The channels can be internally ORed to form a
matrix of 32×32 equivalent pixels, corresponding to sensitive
areas of 2.5×2.5 mm 2 on the entrance window. The 484 HPDs
are closed packed to cover efficiently an area of 2.8 m 2 .
The HPD tube electron optics is sensitive to magnetic fields,
in the same way of most image intensifiers [11], [12]. The
Lorentz force due to a field B║ parallel to the tube axis changes
the electron trajectories. It causes them to rotate around the
tube axis in spiral trajectories towards the anode. This effect is
visible as a strong S-distortion of the anode image with respect
to the light pattern incident on the cathode. A transverse
magnetic field with respect to the tube axis B⊥ , causes a lateral
shift of the electronic image. Both effects are sketched in
fig. 4. The largest trajectory distortion takes place in the region
in proximity of the photo-cathode. The RICH detectors
magnetic shielding boxes are insufficient to reduce the
distortions to a manageable level. A local magnetic shielding is
therefore necessary to further reduce the residual field inside
the HPDs. The local shielding is realized surrounding each
HPD with a cylindrical envelope of high magnetic
permeability alloy (Mu Metal).
The reconstruction of the photon hit position requires an
accurate mapping from the pixel hit position on the anode to
the photon hit on the window entrance surface. This
reconstruction will also be required in the presence of the
residual E×B distortions.
The results of a detailed experimental characterization of the
distortions induced by an external magnetic field on the image
of the HPD are presented in the following sections. The
experimental setup and the methods are described in section II.
In section III the results are presented, with a parameterization
of the experimental data. The model can be used to correct an
image even in presence of strong S-distortion, reconstructing
the photon hit position from the pixel hit position if the axial
component of the field is known. An estimator of the axial
magnetic flux density can be realized by projecting a predefined
light test pattern on the HPD window. A proposal of a
calibration procedure for the LHCb RICH photon detectors,
based on the projection of a static image on the full detector
planes, completes section IV.
Fig. 4. A schematic diagram of the HPD tube showing qualitatively the
photo-electron trajectories and the effects of Lorentz force on them. Effect of a
transverse field are shown in blue; effect of an axial field in red.
II. SET-UP AND METHODS
The experimental set-up allowed collimated beams of
visible light to be projected onto the HPD’s entrance window
on a pre-defined set of positions. The HPD was placed in the
magnetic field generated by an Helmholtz coil in order to
measure the effect of E×B distortions. All the elements of the
set-up were contained in a light tight box.
The HPD tube was powered, controlled and read out by a
dedicated test system that allowed the user to control from a
PC all the internal settings of the HPD chip and to read-out the
binary bitmap data corresponding to the photo electron hits on
the anode assembly.
The light source was a common DC LED with a collimator
and was supported by an x-y motorized translation table; the
light beam was parallel to the tube axis and was projected onto
the entrance window. By moving the translation table it was
possible to define the photons hit position on the HPD
window. The set-up was also equipped with a system to project
programmable static light patterns using a digital projector.
A magnetic flux density up to 5.0 mT could be obtained in
the set-up. The Helmholtz coil could be rotated at various
angles with respect to the HPD axis, allowing for changing the

angle between the B field main component and the tube axis. In
this paper, every stated magnetic field value is to be taken as
the value of the field that would be observed in the center of
the coils if the HPD tube and its shield were not there.
The HPD tube was surrounded by its local cylindrical
magnetic shield. A gap of ~1.5 mm was left between the HV
electrodes of the HPD and the grounded shield and a high
voltage insulation with layers of Kapton foils was therefore
used.
The measurements consisted of recording the photo electron
hit position on the anode when photons are shone on known
locations while various magnetic field values are applied. A
double cross pattern of 160 points has been used, as shown in
fig 5a. The weighted mean of the light intensity distribution
and the rms spread have been used as measure of the spot
center position on anode and of the error respectively.
III. DATA AND MODEL
A. Experimental results
It has already been said that when a magnetic flux parallel to
the tube axis is applied, the image recorded is characterized by
a non-uniform rotation and a dilation (fig. 5b). A rotational
symmetry is present in this situation, well evident in the
distortion effects. A set of data collected for three different
values of the magnetic flux density is shown in fig. 6a. These
curves are indicated as rotation laws and they clearly depend
on the field value. The error bars are due to the spread of the
light spots. The dilation of the image is not constant along the
radius. This is seen in fig. 6b in which the demagnification
laws are plotted as functions of the B|| field.
The distortion induced by the transverse component (fig. 5c)
is less pronounced and it shows symmetry with respect to the
field direction. Moreover the cylindrical shield is more
effective in reducing the transverse magnetic flux than the axial
one. Table 1 summarizes the maximum displacements
observed in the anode image of the double cross test pattern at
various flux density values with a transverse field.
B. Parameterisation
The plots of the rotation law and demagnification laws show
a regular behavior and a simple model describes data in the
case of an axial field. In presence of the rotational symmetry,
the data points are fitted by polynomial functions. The
demagnification law can be expressed with a second order
polynomial:
ρ +
= ρ1
( B) r
2
ρ 2 ( B)
r
(1)
ρ i ( B) = ∑ ρ i,
j
j≤3
j
B . (2)
in which the coefficients are in turn polynomial functions up to
third degree of the field value.
In a similar fashion the rotation laws are parameterized by:
2
3 (3)
∆ ϕ = ∆ϕ
( B) + ∆ϕ
( B)
r + ∆ϕ
( B)
r
0
2
3
j
∆ϕ
i ( B) = ∑ ∆ϕi
, j B
(4)
j≤3
where a third order (in r) polynomial curve is used and the first
order term is assumed to be zero, imposing the flatness of the
rotation law at small r for physical reasons.
Each of the coefficients ρi,j and ∆ϕi,j in the previous
polynomials have been obtained to best fit the full set of
experimental data, thus providing a simple but complete
parameterization of the demagnification and rotation law and
of their dependence on the magnetic flux density.
(a)
(b) (c)
Fig. 5. (a) Image of the double cross with B=0 mT. (b) Same light
pattern with a 3.0 mT axial B field. (c) With a transverse B field of 5.0 mT
applied.
TABLE 1
Maximum displacements of pattern points on the anode at
various transverse magnetic flux density values in a shielded
HPD.
B⊥ [mT] Max displacement ∆d [mm]
3.0 0.262
4.0 0.373
5.0 0.517

(a)
(b)
Fig. 6. (a) Rotation laws: angle of rotation of the imaged spots on the anode
plane vs. entrance window radial coordinate and for increasing magnetic flux
density. (b) Demagnification law: radial coordinate of focused electrons at the
anode plane vs. radial coordinate of the light spot at the HPD entrance window
plane.
IV. CORRECTION AND ESTIMATION
The photon hit position can be reconstructed from the pixel
hit using the previous model. In order to do this it is necessary
to assume that the B|| field value is known. The estimation of
the magnetic flux density value from the distortions observed
on a pre-defined light pattern projected on the tube window is
discussed in section IV-B.
A. Hit position reconstruction
The rotation and the demagnification laws can be inverted to
reconstruct the radial coordinate and the angular position of a
hit on the window from the position of the pixel hit. The
double cross pattern has been used to evaluate the average
error in the reconstruction process for different values of the
field applied. Fig. 7a shows the original uncorrected data,
namely the weighted centers of the light spots recorded by the
HPD readout. The corresponding reconstructed positions on
the cathode are overlapped to the locations of the DC LED
source in fig 7b. The average reconstruction errors evaluated at
the cathode plane on the 160 points of the double cross are
reported in table 2 for various field values. The error should be
compared to the limited spatial resolution of the HPD due to
the pixel size, which is 2.5 mm / √(12) ≅ 0.72 mm.
The procedure needs an accurate knowledge of the
coordinates of the centres in the two reference frames at
cathode plane and anode plane, from which all the radial
distances and vector angles are evaluated. Uncertainties on
these are believed to be a source of reconstruction error, even
in the case of no field applied.
(a) (b)
Fig 7. (a) Double cross pattern acquired with a 3.0 mT axial field applied,
pixel hit coordinates on anode plane. (b) Reconstruction of photon hits
positions. In red the reconstructed points on entrance plane, in black the real
LED coordinates.
TABLE 2
Photon hit position reconstruction error on the double cross.
B║ [mT] Average bias [mm]
0.0 0.82
1.0 1.24
2.0 1.40
3.0 1.78
B. Field estimation
The previous reconstruction procedure relies on the a priori
knowledge of the field value. Despite its simplicity, the model
allows an estimate of the field applied to be made. The
procedure to make this estimate is based on the projection of a
simple light test pattern. The latter is used to quantify the Sdistortions
by comparing the images read out when no field is
applied and when an unknown axial flux is present.
Fig 8a is the image read-out from the HPD while the test
pattern is being projected onto the window (using the image
projector) and no field is applied. Fig. 8b shows the effects of
the application of a 4.0 mT axial field.
The essential features of the test pattern are a small (five)
number of light spots, a larger central one and a set of smaller
ones at increasing radial distances from the central. The
algorithm evaluates the light spots weighted centres ordering
the data points by the increasing distance from the central spot,
easily identified by its larger size. The procedure is applied to
the undistorted image and to the distorted one, solving the spot
to spot correspondence and then extracting the image angular
rotation at various radial distances from the cathode centre. In

this way a four-point sampling of the rotation law is realized.
The distortion polynomial model with the B-field value as a
free parameter is used to fit the sampled points and then
estimate the field value.
(a)
Fig 8. (a) Test pattern acquired with no field applied. (b) The same pattern
acquired with a 4.0 mT axial magnetic flux density.
Results of the application of this algorithm to test runs with
various magnetic flux densities are reported in table 3. This
shows an estimation error limited to about 0.2 mT. Excluding
the 3.0 mT data set, the algorithm error is less than 0.1 mT.
The magnetic field simulations for the LHCb RICH detector
magnetic shields confirm that different values of the field will
be observed inside distinct HPDs depending on the location in
the detection plane. Given that 484 HPDs will be installed in
the RICHs an automated procedure to measure the field value
in each tube will be used. The test pattern is therefore required
to be simple. The large number of detectors to calibrate
compels the use of image processing to extract the frame
characteristics. Light projection systems properly positioned in
the RICHs are under study to allow projection of test patterns
on the detector planes. They will allow to apply a calibration
procedure similar to the one proposed here, by acquiring
sample data before and after the ramp-up of the LHCb dipole
magnet current.
TABLE 3
Axial field estimator error.
B║ [mT] Estimated field [mT] Bias [mT]
V. CONCLUSION
The innovative Hybrid Photon Detector has been developed
by the LHCb collaboration and industrial partners to fulfil the
Ring Imaging CHerenkov detectors requirements. The device
is a single photon sensitive detector, with large active area and
good spatial resolution, requested to operate in the fringe
magnetic field of the LHCb spectrometer dipole magnet. The
(b)
1.0 0.90 ± 0.20 -0.10
2.0 2.05 ± 0.27 0.05
3.0 3.24 ± 0.27 0.24
4.0 4.08 ± 0.24 0.08
5.0 5.07 ± 0.19 0.07
HPD with a magnetic shield is operational in magnetic flux
densities more than double the required value.
The induced E×B distortions make the accurate
reconstruction of the photon non trivial. This work describes
an experimental characterization of the distortions and presents
a simple parameterisation for them. The model has been used
for testing a basic photon position reconstruction algorithm, in
an axial magnetic field of known value.
A method to estimate the field value from the distortions
induced on a pre-defined test pattern has been described. The
simplicity of the model and of the algorithms for distortion
compensation and field estimation allowed to propose a
procedure for the RICH detectors calibration. The calibration
would be based on the projection of light test patterns on the
484 HPDs of the RICH detectors.
VI. ACKNOWLEDGMENT
The authors wish to thank Asmund Skjaeveland for the
contribution made to this work while studying at CERN in the
framework of the Summer Students Program.
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