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Evaluation of a hybrid photon counting pixel detector for X-ray polarimetry
ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 594 (2008) 188–195
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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Evaluation of a hybrid photon counting pixel detector for X-ray polarimetry T. Michel , J. Durst Erlangen Centre for Astroparticle Physics (ECAP), Erwin-Rommel-Strasse 1, 91058 Erlangen, Germany
a r t i c l e in f o
a b s t r a c t
Article history: Received 15 April 2008 Received in revised form 11 June 2008 Accepted 15 June 2008 Available online 2 July 2008
It has already been shown in literature that X-ray sensitive CCDs can be used to measure the degree of linear polarization of X-rays using the effect that photoelectrons are emitted with a non-isotropic angular distribution in respect to the orientation of the electric field vector of impinging photons. Up to now hybrid semiconductor pixel detectors like the Timepix-detector have never been used for X-ray polarimetry. The main reason for this is that the pixel pitch is large compared to CCDs which results in a much smaller analyzing power. On the other hand, the active thickness of the sensor layer can be larger than in CCDs leading to an increased efficiency. Therefore hybrid photon counting pixel detectors may be used for imaging and polarimetry at higher photon energies. For irradiation with polarized X-ray photons we were able to measure an asymmetry between vertical and horizontal double hit events in neighboring pixels of the hybrid photon counting Timepix-detector at room temperature. For the specific spectrum used in our experiment an average polarization asymmetry of ð0:96 0:02Þ% was measured. Additionally, the Timepix-detector with its spectroscopic time-over-threshold-mode was used to measure the dependence of the polarization asymmetry on energy deposition in the detector. Polarization asymmetries between 0.2% at 29 keV and 3.4% at 78 keV energy deposition were determined. The results can be reproduced with our EGS4-based Monte-Carlo simulation. & 2008 Elsevier B.V. All rights reserved.
Keywords: X-ray Polarization Polarimetry Photon counting Medipix Timepix
1. Introduction Charge coupled devices (CCDs) can be used [1] to measure the degree of linear polarization of X-rays. Due to their small depletion depth, CCDs can preferably be used for soft X-ray polarimetry. Due to the fact that the pixel pitch of 55 mm of hybrid photon counting pixel detectors such as Medipix2 [2,3] or Timepix [4] detector are typically larger than the pixel sizes of commercial CCDs together with the fact that the range of photoelectrons in silicon is much smaller than the pixel size, the analyzing power is significantly lower compared to CCDs. On the other hand the typical sensor thickness is significantly larger than the sensitive thickness of a CCD leading to higher efficiency for harder X-rays. Future developments of highly brilliant polarized X-ray sources like synchrotron or free electron laser facilities, also extending their energies to higher values, offer interesting possibilities of using polarized X-ray beams to study material properties. There is a continuous need for X-ray polarimeters with imaging capabilities. Measurements of the degree of linear X-ray polarization of celestial objects would give valuable insights into the production mechanisms or scattering geometries. A very promising and
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efficient device to measure the degree and orientation of linear polarization using the photoelectric effect in a gaseous detector is described in Ref. [5]. This device has a very high analyzing power and high efficiency for low photon energies of 2–10 keV. It should be able to measure even small values of the degree of linear polarization in the low energy range of weak sources in reasonable measuring times. A pixel detector with a semiconductor sensor, like it is presented here, cannot compete with the device described in Ref. [5] at low photon energies due to a lack of analyzing power. Further studies are needed to clarify which performance an optimized semiconductor photon counting pixel detector is able to achieve in X-ray polarimetry in specific applications. Nevertheless, the higher efficiency of the semiconductor sensor for higher photon energies, the high readout speed and the space for improvements in the analyzing power of the hybrid photon counting pixel detector make investigations on its polarimetric performance interesting. The ASIC of the Timepix-detector has been developed to be used in Time-Projection-Chambers. Bump-bonded to a silicon sensor (like the Medipix) it also serves as a tracking detector for charged particles or as an imaging detector for X-rays. This publication shall show that measurements of the degree of linear X-ray polarization can be performed with such a hybrid photon counting pixel detector as a side-effect although the detector is not designed nor optimized for such measurements.
ARTICLE IN PRESS T. Michel, J. Durst / Nuclear Instruments and Methods in Physics Research A 594 (2008) 188–195
For the first time, a hybrid semiconductor photon counting pixel detector has been used to measure polarization asymmetries. The aim of this publication is to show that the hybrid detector is able to measure the degree of linear polarization of X-rays in the energy regime between 27 and 84 keV. In this contribution we will describe a measurement principle of the degree of linear X-ray polarization with the Timepix-detector in counting and in its spectroscopic time-over-threshold mode, prove the applicability in test measurements, compare the measured values to simulation results and discuss advantages and disadvantages of the Timepix for a use in X-ray polarimetry.
2. Polarization signatures of the photoelectric effect and the Compton effect For X-ray energies below about 58 keV the total cross-section of the photoeffect is larger than the total cross-section of Compton scattering in silicon. The ability of the Timepix-detector to measure the degree of linear polarization using the photoeffect is restricted to an energy band where the energy of released photoelectrons is sufficient to cause significant track lengths in silicon and where the photoeffect still significantly contributes to absorption. The polarized radiation that we needed to test the ability of the Timepix to measure the degree of linear polarization was produced by Compton scattering. Therefore we describe the important polarization dependent properties of both effects. 2.1. Photoelectric effect The differential cross-section for the ejection of an electron following photoabsorption of the X-ray photon with energy E0 in the K-shell is given by [6] 7=2 pffiffiffi ds me c2 4 2 sin2 y cos2 f ¼ r 20 Z 5 a4 (1) dO E0 ð1 b cos yÞ4 where f is the polar angle of the momentum of the emitted electron to the y-axis in the reference frame. The reference frame is defined by the direction of the electric field vector of the incoming X-rays (y-axis), the direction of the incoming photon (z-axis) and the direction which is perpendicular to both (x-axis). The angle y is the azimuthal angle of the electron momentum to the z-axis of this frame. r 0 is the classical electron radius, Z the charge of the nucleus, me the electron rest mass, a the fine structure constant and b ¼ v=c is the electron velocity. According to this formula the electron is ejected preferably in the direction of the electric field vector of the incoming X-rays. 2.2. Compton effect The differential cross-section for Compton scattering of a linearly polarized photon beam off a free electron is described by the Klein–Nishina formula: ds 1 2 E2 E E0 2 sin2 y cos2 f ¼ r0 2 þ (2) dO 2 E0 E0 E
E0 1 þ ðE0 =me c2 Þð1 cos yÞ
see that for X-ray photons with energies E0 5me and scattering angles y 90 , where E E0 , the scattered X-radiation is almost completely linearly polarized.
3. The Medipix2 and Timepix-detector The Medipix2 [2,3] and its derivative, the Timepix [4], comprise a sensor layer which is pixelated with a pitch of 55 mm. The Medipix has been designed for X-ray imaging. Each sensor pixel electrode is connected to one electronics cell of the readout ASIC via a bump-bond of a lead–tin alloy. The ASIC has been developed by the Medipix collaboration with its seat at CERN. The pixel cells are organized in a quadratic matrix of 256 rows and 256 columns giving a total side length of about 1.4 cm. Each electronics pixel cell contains an integrating charge sensitive preamplifier, two discriminators in the Medipix2, one discriminator in the Timepix and a pseudo-random counter with a depth of 14 bit. The minimum threshold that can be applied is about 3 keV. If an X-ray photon interacts in the sensitive volume of a sensor pixel the charge carriers, released by the ejected electron, drift towards the pixel electrode. The charge is collected, transferred to the pixel electronics cell and converted into a voltage signal proportional to the amount of collected charge in the preamplifier. If the collected charge, which is a measure of the energy deposition in the pixel volume, exceeds threshold, the photon is counted. This operation mode is called the photon counting mode. It is available in the Medipix2 and the Timepix ASIC. The Medipix2 offers the possibility to count the number of events with energy depositions in an energy window whereas the Timepix-detector can only be operated with one single analogue threshold. The Timepix offers two additional operation modes: the time-over-threshold and the time-to-shutter mode. In the time-over-threshold mode the counter counts the number of clock pulses of a clock signal during the time of the discriminator input pulse being above threshold. This time is proportional to the amount of collected charge and thus proportional to the energy deposition in the sensor pixel. In the time-to-shutter mode the counter of the Timepix counts the number of clock pulses from the moment of detection until the end of the frame. The Medipix2 and Timepix are operated with a shutter signal which stops the detection processes in the pixel matrix at the same time. After having finished all counting activity, the matrix is read out with the pseudo-random-counters acting as shift registers. The whole matrix can be read out serially in about 9 ms or in parallel in about 265 ms thus offering frame rates from several tens of Hertz up to more than a kHz with tolerable dead times. The ASIC is connected to a printed circuit board with a heat conducting glue that contains a significant amount of silver. X-rays which transmit the sensor or even the ASIC can be absorbed in this glue or in the bump-bonds and thus produce fluorescence photons which can be detected again in the sensor layer. Thus the energy deposition spectrum measured with the detector shows strong contributions at the energies of the fluorescence photons of silver and tin. This is important for the interpretation of the energy deposition spectra in this publication.
4. Measurement principle of the degree of linear polarization exploiting the photoelectric effect
where the energy E of the scattered photon is given by E¼
189
(3)
and y is the scattering angle, which is the angle between the momentum vectors of the incoming and the scattered photon and the azimuthal angle f is the angle between the electric field vector of the incoming photon and the scattering plane. One can
The measurement principle of the degree of linear polarization with semiconductor pixel detectors can be based on the fact that the first few microns of the photoelectron track in the sensor material contain information about the original direction of emission of the photoelectron which is correlated with the
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orientation of linear polarization via Eq. (1). The probability to reach the sensitive volume of an adjacent pixel is higher in the direction of ejection. But even if the photoelectron does not reach the border between two pixels, the slightly asymmetric distribution of released charge carriers arriving at the pixel electrode plane prefers the triggering of two adjacent pixels in the direction of linear polarization. During propagation through the silicon sensor the released electrons suffer all kind of scattering processes which cause changes in the direction of propagation. The total path length r of an electron with a kinetic energy Ee of several tens of keV in silicon can be approximated by r ¼ ðEe =10Þ1:75 where the energy Ee given in keV and the range is obtained in mm [1]. For a photon energy of 60 keV the photoelectron, ejected with the energy of 58.2 keV from the silicon K-shell, has a total path length of 21:8 mm. Obviously, in this energy range the total track length of the photoelectrons is comparable to the pixel pitch of the Timepix-detector. Therefore we expect that for a significant number of the events the photoelectron causes energy depositions in adjacent pixels during the randomized part of its track thus reducing the sensitivity to polarization. Additionally the transverse diffusion of released charge carriers during their drift to the pixel electrodes introduces double hits and therefore reduces the polarization sensitivity. We now assume to expose such a photon counting pixel detector with linearly polarized X-rays. The direction of the electric field vector is oriented in parallel to the vertical direction in the laboratory. The rows of the matrix are in parallel to the readout area of the Timepix ASIC. The pixel matrix now can be tilted by a certain angle a between the rows of the pixel matrix and the direction of electric field vector. For a tilt angle of a ¼ 90 the direction of the columns (rows) is parallel (perpendicular) to the direction of the electric field vector. Upon detection of an X-ray photon via photoeffect an electron is ejected preferably in the direction of the columns. Therefore the probability to trigger additionally the neighboring pixel in the same column is higher than the probability to trigger the neighboring pixel in an adjacent column. A difference between the number of double hits among adjacent pixels in the same column N c ða ¼ 90 Þ and the number of double hits between pixels in the same row but in different columns Nr ða ¼ 90 Þ should occur. We define the asymmetry A as AðaÞ:¼
N r ðaÞ Nc ðaÞ N r ðaÞ þ Nc ðaÞ
processes in the silicon sensor have energies between about 1.4 and 11.9 keV corresponding to very short tracks. These track lengths are not large enough to mask the polarization signal emerging from the photoelectrons as one will see later in the data of the polarization asymmetry in dependence on energy deposition.
5. Measurements In order to prove the capability of the Timepix-detector to measure polarization asymmetries we carried out simulations and measurements with polarized X-ray photons in the energy range between 27 and 84 keV. 5.1. Experimental setup In the following we distinguish between the emission spectrum of the X-ray tube which impinges on the target, the spectrum of scattered photons which impinges on the detector, and the spectrum of energy depositions which is measured in the pixels of the detector. We want to point out, that due to the energy dependent absorption of the silicon sensor, charge sharing effects in the sensor layer and detection of fluorescence photons the energy deposition spectrum differs from the spectrum incident on the detector. We performed an experiment using a high intensity medical X-ray tube to produce a linearly polarized X-ray beam by Compton scattering at y 90 off a target of Polymethylacrylate (PMMA). The setup is sketched in Fig. 1. A collimator consisting of a lead block with a hole of 10 mm diameter was equipped with a collimator of tungsten with an opening of 2 mm. It was placed in front of the X-ray tube which was operated at 100 kV acceleration voltage. A 1 mm thick iron plate was placed in front of the exit window of the X-ray tube. The emission spectrum of the tube was measured by performing a threshold scan with a Medipix2 detector placed in the direct beam. A more detailed description of the method to measure the emission spectrum of an X-ray tube with the Medipix2 can be found in Refs. [7,8]. The spectra of the X-ray tube were found to be well represented with the spectra given in Ref. [9] but with an inherent filtration of 1.4 mm aluminum.
(4)
and the polarization asymmetry Apol as Apol :¼
Að0 Þ Að90 Þ . 2
(5)
With this definition the polarization asymmetry Apol does not contain any contributions from apparative asymmetries. A remaining apparative asymmetry can be calculated with Aapp :¼
Að0 Þ þ Að90 Þ . 2
(6)
The polarization asymmetry is proportional to the degree of linear polarization. Thus the measurement of the polarization asymmetry leads to the determination of the degree of linear polarization. At higher X-ray energies the photoelectric cross-section and therefore the count rate is smaller and the Compton effect plays a larger role in the detection process. According to the angular dependencies of Eqs. (1) and (2) the asymmetry signal due to the photoelectric effect may be lowered by the contrary polarization signature of the Compton effect. In the energy range between 27 and 84 keV the electrons, scattered at 90 (where the asymmetry is maximal for low photon energies) in Compton scattering
Fig. 1. Experimental setup consisting of collimator, scattering target and Timepixdetector mounted on rotation device. The orientation of the rows and columns of the pixel matrix is indicated. The angle a is 0 in this case.
ARTICLE IN PRESS T. Michel, J. Durst / Nuclear Instruments and Methods in Physics Research A 594 (2008) 188–195
ds dO
¼ k
1 2 E2 E E0 r0 2 2 þ 4ð1 sin2 y cos2 fÞ þ 4 E0 E0 E
(7)
1
0.8 Acceptance [a.u.]
The scattering target had a length of 14 mm in the beam direction. Its width was 3 mm in the laboratory plane perpendicular to the beam direction and its height in the vertical direction was 5 mm. The target was fixed by two thin plastic fibers in a distance of 8 cm in front of the Timepix-detector. The target could be swept out of the beam. A second arm held only two fibers so that measurements without the PMMA target could be performed in order to remove background contributions. The Timepixdetector was mounted on a rotatable aluminum block. The geometry of the setup was chosen in order to prepare a linearly polarized radiation field impinging on the Timepixdetector. Following the calculation of the degree of linear polarization described in Ref. [10] we calculate the degree of linear polarization by integrating the differential Compton scattering cross-sections ðds=dOÞk and ðds=dOÞ? . The differential cross-section ðds=dOÞk for the direction of the electric field vector of the scattered photons being parallel to the electric field vector of the incoming photons is given by
191
0.6
0.4
0.2
0 75
80
85
90
95
100
105
φ [degrees] Fig. 3. Distribution of accepted Compton scattering angles f for a beam completely linearly polarized in the vertical direction. The distribution is normalized to its maximum value.
The differential cross-section ðds=dOÞ? for the electric field vector of the scattered photons in the orthogonal direction is given by ds dO
¼ ?
1 2 E2 E E0 r0 2 þ 2 . 4 E0 E0 E
1 (8)
These differential cross-sections are integrated numerically over the geometrical acceptance in y of the detector at its position, all directions f of the electric field vector of the incoming unpolarized radiation, the energy dependent scattering probability in the target, the impinging spectrum and all interaction points in the target. The degree of linear polarization is derived from the asymmetry of these two integrated cross-sections. We also took attenuation of the primary beam into account. Photoelectric absorption and additional scattering (Compton- or Rayleighscattering) of Compton scattered photons in the target on their way to the detector was neglected because of the small width of the target. The focal spot size of the X-ray tube was about 1 mm in diameter. Due to the geometry we estimate a beam diameter of about 1.6 mm at the target position. Because of additional small angle scattering in the iron plate and the collimator we assume in our calculation of the Compton scattered spectrum and the degree of linear polarization that the target is illuminated homoge-
0.8
0.6
0.4
0.2
0 20
30
40
50 60 70 Photon energy [keV]
80
90
100
Fig. 4. Calculated Compton scattered spectrum impinging on the detector. Due to the geometrical acceptance of the detector the fluorescence lines are smeared out after Compton scattering in the PMMA target.
neously with a beam of 2 mm in diameter. Fig. 2 shows the Compton scattering angle acceptance (y) of the Timepix in this setup for the incoming unpolarized beam. Fig. 3 shows the Compton scattering angle acceptance ðfÞ for the vertical polarization component of the incoming beam. An average degree of polarization of 98.6% was obtained. Fig. 4 shows the calculated spectrum of the Compton scattered X-rays illuminating the Timepix-detector. The energy range of polarized photons therefore is about 27–84 keV.
1
0.8 Acceptance [a.u.]
Spectral density [a.u.]
0.6
0.4 5.2. Measurement of the asymmetry in photon counting mode
0.2
0 75
80
85
90 θ [degrees]
95
100
105
Fig. 2. Distribution of accepted Compton scattering angles y for a beam completely linearly polarized in the vertical direction. The distribution is normalized to its maximum value.
The measurements were carried out with a tube current of 10 mA and 100 kV acceleration voltage. A Timepix-detector bumpbonded to a 300 mm thick silicon sensor and operated in the photon counting mode was used. The sensor was biased with 150 V. The MUROS [11] was used to read out and control the ASIC. The data acquisition was performed with the Pixelman software [12]. The frame time was set to 60 ms in order to have a tolerable occupancy of about 190 triggered pixels in the pixel matrix in each image. At this occupancy the relative amount of random double
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hits is about 103 . At this level the random double hits can be neglected because they affect horizontal and vertical double hits in the same way. The relative influence on the asymmetry therefore is in the order of 103 which is considerably smaller than the statistical precision we were able to achieve. The neighborhood of pixels with a high noise level was switched off symmetrically in vertical and horizontal direction in order to avoid additional apparative asymmetries. The threshold has been calibrated using different radioactive sources and fluorescence radiation. The threshold has to be set to low energies in order to be sensitive to small amounts of energy deposited in one pixel at the beginning of the track of the photoelectron. The discriminator threshold was set to 3.5 keV. The asymmetry A was measured for different angles a between the plane of linear polarization and the rows of the pixel matrix. The angle was varied by rotating the detector in steps of 151 from 301 to 1201. The measurement of the number of double hits was performed with and without the PMMA target for all angles. For each angle 40 000 images have been taken with the target and additionally without the target. This corresponds to a total beam time of about 3 h for each angle. The series of measurements has caused defects on the surface of the anode of the X-ray tube leading to a harder emission spectrum of the X-ray tube. In order to reduce the influence of increasing beam hardening on the measured asymmetry the target- and no-target-measurements have been carried out in an alternating manner. In the analysis a cluster analyzing algorithm counted the number of double hits in neighboring pixels in the same row Nr and in the same column N c . Clusters of two neighboring triggered pixels were counted in Nr or N c only if the ring of pixels around the two triggered pixels did not detect an event. The numbers of double hits measured without target are subtracted from the corresponding numbers measured with the target inserted in the beam. The asymmetry was calculated using Eq. (4). The statistical error was calculated assuming that the number of double hit events varies according to Poisson statistics.
5.3. Measurement of the asymmetry in dependence on energy deposition In order to measure the energy dependence of the polarization asymmetry Apol we carried out measurements with the same experimental setup but with the Timepix-detector operated in time-over-threshold mode. After a pixelwise calibration with testpulses of the time-over-threshold, we used X-ray emissions from an 241Am source to estimate the energy resolution achieved with the calibration. We obtained an relative energy resolution of 7% at the energy of the decay line at 59.5 keV. Due to the fact that the calibration curve, converting time-over-threshold to energy deposition is not linear for energy depositions close to the threshold, inaccuracies arise for low energy depositions. It has to be pointed out that the calibration procedure for the time-overthreshold used in our analysis did not exploit the full potential of the Timepix. It has been shown in the Medipix collaboration [12] that an energy resolution of about 5.5% at 59.5 keV can be obtained with extensive calibration measurements using radioactive sources and fluorescence photons. The obtained energy resolution is considered to be sufficient to test the energy dependence of the polarization asymmetry. In the analysis the time-over-threshold of the pixels in double hit events was converted using the above-mentioned calibration method to equivalent energy deposition. The energy depositions of the two adjacent pixels in each double hit event were added. The number of double hits (Nc and N r ) were counted in energy bins with a width of 10 keV. Measurements at the angles a ¼ 0 and 90 have
been performed. The polarization asymmetry was calculated for each energy bin according to Eq. (5) in order to remove contributions from remaining apparative asymmetries. Mean energies in the energy bins have been calculated with the measured energy deposition spectrum of the double hit events having a total energy deposition in the bin.
6. Simulation In order to verify our measurements we carried out simulations using our detailed implementation of the relevant physical processes in the Timepix-detector which occur during detection of X-rays. A detailed stochastic modelling of the diffusion and drift process of the holes to the pixel electrodes was included. The Timepix-detector is geometrically implemented with all its important parts affecting its response to radiation, e.g. the bump-bonds, the ASIC, the glue and the printed circuit board. We used the EGS4 and LSCAT based Monte-Carlo simulation package ROSI [14,15] for our simulations. A routine to randomize the distribution of the emission angles of the photoelectrons emerging from the K-shells of the silicon sensor atoms according to Eq. (1) has been implemented. In the tracking routines of our simulation code a change of the direction of propagation of the electron is forced if the continuous energy loss DEe in the current step of the track reaches 1% of the energy Ee of the electron. Therefore the maximum step length during tracking can be estimated with the total stopping power of the highest possible energy of an electron in our energy range. The total stopping power of a photoelectron which is ejected from a silicon K-shell in our experiment is about 82 keV. The total stopping power for this electron energy in silicon is 3:71 MeV cm2 =g according to the database ESTAR [16] of the National Institute of Standards and Technology. With this value and the density of silicon we can calculate a maximum step length of approximately 1 mm. This value seems to be small enough to expect that straggling of the electron is modelled precisely enough in our simulation. We irradiated the Timepix-detector perpendicularly and homogeneously with the calculated spectrum shown in Fig. 4 assuming a degree of polarization of 100%; 120 000 images were simulated with a mean occupancy equal to the mean occupancy in the measurement. The same cluster analysis program was used to analyze the images obtained in the simulation and in the measurement. Special attention is paid to a proper modelling of the drift and diffusion processes in the sensor layer of the Timepix-detector which already has led to good agreement between measurements and simulations of the energy response and imaging properties of the detector [8,17,18]. The influence of Coulomb repulsion among the released charge carriers was taken into account via an enlarged diffusion constant. Drift and diffusion are modelled by a spreading of the released charge carriers onto the pixel grid using Gaussian probability density functions starting with the standard deviations given in Ref. [19] and corrected for the effect of coulombic repulsion. Coulombic repulsion plays an important role because the track lengths of the low energetic electrons are very small leading to a large charge carrier density along the track. In the simulation program the energy deposition along each step of the track is converted to an equivalent number of charge carriers. The average energy which has to be deposited in order to create one electron–hole in silicon is 3.6 eV. Fano noise was neglected due to its weakness compared to the electronics noise of about 100 electrons (RMS). A relative energy resolution due to the use of the time-over-threshold-method of 7% was assumed and modelled with a Gaussian distribution. For the comparison with the measurement the weighted means of the degree of
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polarization in the energy deposition bins were taken into account for each energy deposition bin.
7. Results and discussion 7.1. Measurements in photon counting mode The measured asymmetry as a function of the angle between the rows of the matrix and the plane of linear polarization is shown in Fig. 5. The function AðaÞ ¼ Apol cosð2aÞ þ Aapp was fitted to the data in order to obtain the polarization asymmetry Apol, which is due to the polarization of the incoming radiation, and to determine any remaining apparative asymmetry Aapp. The polarization asymmetry was determined to be Apol ¼ ð0:957 0:019Þ%. An apparative asymmetry of Aapp ¼ ð0:194 0:013Þ% was found. It is obvious that we have successfully measured an non-zero polarization asymmetry due to the linear polarization of the radiation impinging on the detector. Further, the unexpected apparative asymmetry is statistically significant. The mean degree of linear polarization of the spectrum impinging on the detector was calculated to be 98.6%. The average degree of linear polarization of the photons causing double hits in the detector was determined using the calculated degree of linear polarization in dependence on photon energy weighted with the simulated number of detected double hits having this total energy. We obtained an average degree of linear polarization of the detected double hit events of 99.1%. The result of the simulation of the polarization asymmetry for our setup was Apol ¼ ð0:888 0:042Þ% which agrees with the measured value taking uncertainties in the simulation, e.g. changes of the emission spectrum of the X-ray tube, the estimated thickness of the silver containing glue and the estimated diameter of the bump-bonds of the detector into account. A measurement without artificial radiation was carried out in order to determine the influence of cosmic rays which could in principle also result in an asymmetry which is modulated with the rotation angle of the matrix. It was found that the fraction of the number of double hits caused by the natural background to the number of double hits in the measurement with radiation is only about ð1:7 0:5Þ 105 . Thus the ratio of the maximum possible asymmetry caused by cosmic radiation to the asymmetry caused by the linearly polarized X-rays is in the order of 2 103 . Therefore we can neglect the influence of natural background
1.5
Measured asymmetry A [%]
1 0.5
radiation. Natural background cannot be the origin of the apparative asymmetry. Measurements with a 90 kV X-ray tube spectrum scattered to small angles ðy 5 Þ in forward direction were carried out in order to confirm the apparative asymmetry. An apparative asymmetry of Aapp ¼ ð0:182 0:066Þ% was observed in agreement with the previously mentioned value. The origin of the apparative asymmetry is not yet understood and therefore is subject to additional investigations. Possible explanations may for example be patterns in the distribution of the thresholds in the pixel matrix, asymmetric structures in the bump-bond-matrix, nonisotropic pixel pitch or non-isotropic charge collection in the sensor. Non-uniformities of the thresholds in the pixel matrix can in principle influence the measured asymmetries. We will now first discuss the effect of non-uniformities with no pattern. Let us assume for simplicity that one pixel has a slightly lower threshold than the rest of the matrix. Then the efficiency for this pixel and its neighbor in the same row to be triggered by one photoelectron is slightly higher than in the ideal case where all the thresholds exactly have the same value. This results in a slightly increased number N r. On the other hand, the pixel with the lower threshold will also be involved in double hit events with its neighbor in the same column. So we see that also N c will be increased. Therefore this case affects the denominator in Eq. (4) thus reducing the measured asymmetry. In contrast to this, the measured asymmetry is increased, if the threshold of the pixel is slightly higher than the thresholds in the rest of the matrix. This suggests that one can expect that a random non-uniformity of thresholds has a minor net-effect on the measured asymmetry if there is no trend in the thresholds along the rows or the columns. According to Ref. [4] the thresholds of the Timepix are distributed with a standard deviation of about s ¼ 0:13 keV (corresponding to 35 electrons) around the average threshold after threshold equalization. This contribution is small compared to the electronics noise of about s ¼ 0:36 keV (corresponding to 100 electrons). In our simulation we model the combined effect of both noise contributions by introducing a noise of s ¼ 0:4 keV (corresponding to 110 electrons) on the detected charge in each pixel. A threshold non-uniformity having a trend along rows or columns would lead to an apparative asymmetry. The measured polarization asymmetry will not be affected due to the fact that we subtracted the asymmetry measurements at rotation angles a ¼ 0 and 90 of the pixel matrix from each other according to Eq. (5) to obtain the polarization asymmetry. We want to point out that with a faster read-out device like the PRIAM board [20] and with a direct high intensity polarized photon beam the same statistical precision for each data point may have been achieved in less than 3 min, assuming frames with the same occupancy of the matrix like in our measurements.
7.2. Measurements in time-over-threshold mode
0 -0.5 -1 -1.5 -40
193
-20
0
20 40 60 80 Angle of matrix α [degrees]
100
120
Fig. 5. Measured asymmetry A in dependence on the rotation angle a of the detector matrix rows to the plane of linear polarization.
Fig. 6 shows the measured energy deposition spectrum for double hit events with the Timepix-detector in time-over-threshold mode in comparison with the energy deposition spectrum obtained with the Monte-Carlo-simulation. The calculated Compton scattered spectrum in Fig. 4 was used as the impinging spectrum in the simulation. It can be seen that the overall form of the spectra is consistent. The prominent peaks at about 24 keV in the simulation and 22 keV in the measured spectrum are due to fluorescence photons from the silver in the glue between ASIC and chipboard and the tin in the bump-bond material. The peaks at about 11 keV in the simulation and 14 keV in the measurement are
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0.01
1.2 Measurement Simulation
0.008 Apparative asymmetry
Number of events [a.u.]
1 0.8 0.6 0.4 0.2
0
20
40 60 Energy deposition [keV]
80
100
5
Polarization asymmetry [%]
0.002 0
Measurement Simulation
3 2 1 0 -1 10
20
30 40 50 60 Energy deposition [keV]
-0.004 0
10
20
30
40
50
60
70
80
Energy deposition [keV]
Fig. 6. Measured and simulated energy deposition spectrum in the detector for the 100 kV tube spectrum incident on the scattering target.
0
0.004
-0.002
0
4
0.006
70
80
Fig. 7. Measured and simulated polarization asymmetry Apol in dependence on energy deposition. The errorbars are statistical errors only.
due to the L-fluorescence photons of the lead in the bump-bonds. We must assume a systematic error on the photon energy of about 3 keV. The strength of the peaks depends on the diameter of the bump-bonds and the thickness of the glue. Both values are not exactly known, so that the relative height of these peaks cannot be reproduced exactly. Larger deviations are found in the energy deposition spectrum for energy depositions below about 18 keV as it is expected due to the non-linear time-over-threshold measurement for pulse heights closer to the discriminator threshold. For low total energy depositions of the double hit clusters, there is a large fraction of events having one pixel with a pulse height close to the threshold. Due to the fact that the spectrum of X-rays impinging on the detector starts at about 27 keV the influence of the lead, tin and silver fluorescence photons on the measured energy dependence of the asymmetry can be ignored. An additional source of inaccuracies can arise from the measured emission spectrum of the X-ray tube. The exposure times in this experiment were very long so that the X-ray flux decreased during the measurement. This is due to a progressing harshness of the anode surface which leads to hardening of the emitted radiation. Additionally, the influence of scattering in the collimator was neglected in our simulation.
Fig. 8. Measured apparative asymmetry Aapp in dependence on energy deposition. The errorbars represent the statistical error.
Fig. 7 now shows the measured and simulated polarization asymmetry of the detector in dependence on energy deposition. The energy deposition corresponds to the photon energy if we assume that the events are detected via the photoelectric effect. The agreement over a wide energy range is excellent showing that the behavior of the Timepix-detector is well understood and modelled in our simulation. The simulated polarization asymmetry increases from 0.2% at an energy deposition of 29 keV to 3.4% at an energy deposition of 78 keV. This behavior is expected because of the increasing track lengths of the photoelectrons with photon energy. We therefore conclude that the spectroscopic time-overthreshold mode of the Timepix-detector can be used to measure the degree of linear polarization of X-rays in the energy range between 27 and 84 keV in dependence on photon energy. Fig. 8 shows the apparative asymmetry, calculated with Eq. (6) in dependence on energy deposition. We found again an average apparative asymmetry of Aapp ¼ ð0:149 0:066Þ% in consistence with the apparative asymmetries measured in photon counting mode. No statistically significant linear dependence on energy deposition was found for the apparative asymmetry.
8. Summary and outlook We have proven that it is possible to measure the degree of linear polarization in the energy range between 27 and 84 keV with the Timepix-detector. The sensor thickness of 300 mm is very large compared to CCDs which have typically active thicknesses of up to several tens of microns. Therefore hybrid photon counting pixel detectors are an interesting option for polarimetry with higher photon energies. The Timepixdetector, due to its hybrid design, offers the possibility to optimize the pixel pitch, the sensor thickness and the type of sensor material. The Timepix-detector stops counting in the whole matrix at the same time and therefore does not acquire false asymmetries during readout. It is not necessary to cool the Timepix-detector in contrast to many CCD if they are used in X-ray polarimetry. The Timepix-detector can be read out with frame rates of at least 1 kHz [20] using the parallel readout. Additionally the possibility of using very short frame times makes it suitable for high flux polarimetry. The frame time and the frame rate can be chosen independently, making it a very flexible device. The experimental effort and the analysis complex-
ARTICLE IN PRESS T. Michel, J. Durst / Nuclear Instruments and Methods in Physics Research A 594 (2008) 188–195
ity seems to be larger if a CCD is used in X-ray polarimetry. Large potential for improvements in the analyzing power of hybrid photon counting pixel detectors may be found in the suppression of the influence of the charge sharing due to diffusion. Future developments of 3D-sensors, like they have been proposed in Ref. [21] with their electrodes implanted as pillars, may allow the use of very thick sensor layers, while holding the drift length of the charge carriers at a minimum level thus increasing efficiency and analyzing power. The Timepix-detector also offers the possibility to identify Compton scattered events in the sensor by using the time-toshutter mode in each pixel to search for coincidently triggered pixels in each frame. Exploiting Compton scattering in the sensor has the advantage of a significantly higher analyzing power (modulation factor) and the ability to measure the orientation of the plane of linear polarization without rotation of the detector. On the other hand, the efficiency of detecting the Compton scattered photon is low if the standard thin silicon sensor is used. One disadvantage of using Compton scattering in the sensor with the Timepix is that the information about the detection time and the energy deposition is not available simultaneously. Therefore it is not possible to determine the energy of the reacting photon. Additionally it is also not possible to judge which pixel of the triggered pair of pixels corresponds to the point of impact of the primary photon. Thus, imaging polarimetry will be difficult using Compton scattering in the sensor of the Timepix. Assuming a minimum threshold of 3 keV in the pixel, the minimum photon energy, which is necessary to trigger the first pixel in a Compton event at a scattering angle of 901, is about 41 keV. Therefore Compton polarimetry with the Timepix is restricted to energies higher than 41 keV. Nevertheless, Compton polarimetry is subject to current investigations because of the expected high modulation factor. Significant improvements of the analyzing power are necessary in order to ensure that such a hybrid photon counting pixel detector is an option for measurements of the degree of X-ray polarization of celestial sources in reasonable measuring times by exploiting the photoelectric effect.
195
Acknowledgment The authors would like thank the Medipix collaboration for the inspiring atmosphere. A special thank goes to Stanislav Pospisil from the Czech Technical University of Prague for the stimulating discussion during the conference dinner of the 9th International Workshop on Radiation Imaging Detectors (iWoRiD). References [1] H. Tsunemi, K. Hayashida, K. Tamura, S. Nomoto, M. Wada, A. Hirano, E. Miyata, Nucl. Instr. and Meth. A 321 (1992) 629. [2] X. Llopart, M. Campbell, R. Dinapoli, D. San Segundo, E. Pernigotti, IEEE Trans. Nucl. Sci. NS-49 (5) (2002) 2279. [3] X. Llopart, M. Campbell, Nucl. Instr. and Meth. A 509 (2003) 157. [4] X. Llopart, R. Ballabriga, M. Campbell, L. Tlustos, W. Wong, Nucl. Instr. and Meth. A 581 (2007) 485. [5] R. Bellazzini, et al., Nucl. Instr. and Meth. A 560 (2006) 425. [6] R. Bellazzini, L. Baldini, A. Brez, E. Costa, L. Latronico, N. Omodei, P. Soffitta, G. Spandre, Nucl. Instr. and Meth. A 510 (2003) 176. [7] M. Firsching, P. Takoukam Talla, T. Michel, G. Anton, Nucl. Instr. and Meth. A 591 (2008) 19. [8] T. Michel, in: Proceedings of the 16th International Workshop on Vertex Detectors, PoS(Vertex 2007)044. [9] J.H. Aichinger, J. Dierker, S. Joite-Barfuss, M. Sa¨bel, Exposure and Image Quality in X-ray Diagnostic Radiology, Springer, Berlin, 2004. [10] T. Mizuno, T. Kamae, J.S.T. Ng, H. Tajima, J.W. Mitchell, R. Streitmatter, R.C. Fernholz, E. Groth, Y. Fukazawa, Nucl. Instr. and Meth. A 540 (2005) 158. [11] G. Bardelloni, E. Bertolucci, A.L.J. Boerkamp, D. Calvet, M. Conti, M. Maiorino, P. Russo, J.L. Visschers, in: Proceedings of the IEEE Nuclear Science Symposium and Medical Imaging Conference, 2000, pp. 57–60. [12] T. Holy, J. Jakubek, S. Pospisil, J. Uher, D. Vavrik, Z. Vykydal, Nucl. Instr. and Meth. A 563 (2006) 254. [12] J. Jakubek, A. Cejnarova Andrea, S. Pospisil. J. Uher, Ceskoslovensky Casopis pro Fyziku, 1/2008, pp. 37–45. [14] J. Giersch, A. Weidemann, G. Anton, Nucl. Instr. and Meth. A 509 (2003) 151. [15] J. Giersch, J. Durst, Nucl. Instr. and Meth. A 591 (2008) 300. [16] hhttp://physics.nist.gov/PhysRefData/Star/Text/ESTAR.htmli. [17] A. Korn, M. Firsching, G. Anton, M. Hoheisel, T. Michel, Nucl. Instr. and Meth. A 576 (2007) 239. [18] P. Bartl, A. Korn, T. Michel, G. Anton, Nucl. Instr. and Meth. A 591 (2008) 314. [19] H.G. Spieler, E.E. Haller, IEEE Trans. Nucl. Sci. NS-32 (1985) 419. [20] C. Ponchut, J. Clement, J.-M. Rigal, E. Papillon, J. Vallerga, D. LaMarra, B. Mikulec, Nucl. Instr. and Meth. A 377 (2007) 109. [21] C. Kenney, S. Parker, J. Segal, C. Storment, IEEE Trans. Nucl. Sci. NS-46 (1999) 1224.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Evaluation of a hybrid photon counting pixel detector for X-ray polarimetry T. Michel , J. Durst Erlangen Centre for Astroparticle Physics (ECAP), Erwin-Rommel-Strasse 1, 91058 Erlangen, Germany
a r t i c l e in f o
a b s t r a c t
Article history: Received 15 April 2008 Received in revised form 11 June 2008 Accepted 15 June 2008 Available online 2 July 2008
It has already been shown in literature that X-ray sensitive CCDs can be used to measure the degree of linear polarization of X-rays using the effect that photoelectrons are emitted with a non-isotropic angular distribution in respect to the orientation of the electric field vector of impinging photons. Up to now hybrid semiconductor pixel detectors like the Timepix-detector have never been used for X-ray polarimetry. The main reason for this is that the pixel pitch is large compared to CCDs which results in a much smaller analyzing power. On the other hand, the active thickness of the sensor layer can be larger than in CCDs leading to an increased efficiency. Therefore hybrid photon counting pixel detectors may be used for imaging and polarimetry at higher photon energies. For irradiation with polarized X-ray photons we were able to measure an asymmetry between vertical and horizontal double hit events in neighboring pixels of the hybrid photon counting Timepix-detector at room temperature. For the specific spectrum used in our experiment an average polarization asymmetry of ð0:96 0:02Þ% was measured. Additionally, the Timepix-detector with its spectroscopic time-over-threshold-mode was used to measure the dependence of the polarization asymmetry on energy deposition in the detector. Polarization asymmetries between 0.2% at 29 keV and 3.4% at 78 keV energy deposition were determined. The results can be reproduced with our EGS4-based Monte-Carlo simulation. & 2008 Elsevier B.V. All rights reserved.
Keywords: X-ray Polarization Polarimetry Photon counting Medipix Timepix
1. Introduction Charge coupled devices (CCDs) can be used [1] to measure the degree of linear polarization of X-rays. Due to their small depletion depth, CCDs can preferably be used for soft X-ray polarimetry. Due to the fact that the pixel pitch of 55 mm of hybrid photon counting pixel detectors such as Medipix2 [2,3] or Timepix [4] detector are typically larger than the pixel sizes of commercial CCDs together with the fact that the range of photoelectrons in silicon is much smaller than the pixel size, the analyzing power is significantly lower compared to CCDs. On the other hand the typical sensor thickness is significantly larger than the sensitive thickness of a CCD leading to higher efficiency for harder X-rays. Future developments of highly brilliant polarized X-ray sources like synchrotron or free electron laser facilities, also extending their energies to higher values, offer interesting possibilities of using polarized X-ray beams to study material properties. There is a continuous need for X-ray polarimeters with imaging capabilities. Measurements of the degree of linear X-ray polarization of celestial objects would give valuable insights into the production mechanisms or scattering geometries. A very promising and
Corresponding author. Tel.: +49 91318527121.
E-mail address: [email protected] (T. Michel). 0168-9002/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2008.06.024
efficient device to measure the degree and orientation of linear polarization using the photoelectric effect in a gaseous detector is described in Ref. [5]. This device has a very high analyzing power and high efficiency for low photon energies of 2–10 keV. It should be able to measure even small values of the degree of linear polarization in the low energy range of weak sources in reasonable measuring times. A pixel detector with a semiconductor sensor, like it is presented here, cannot compete with the device described in Ref. [5] at low photon energies due to a lack of analyzing power. Further studies are needed to clarify which performance an optimized semiconductor photon counting pixel detector is able to achieve in X-ray polarimetry in specific applications. Nevertheless, the higher efficiency of the semiconductor sensor for higher photon energies, the high readout speed and the space for improvements in the analyzing power of the hybrid photon counting pixel detector make investigations on its polarimetric performance interesting. The ASIC of the Timepix-detector has been developed to be used in Time-Projection-Chambers. Bump-bonded to a silicon sensor (like the Medipix) it also serves as a tracking detector for charged particles or as an imaging detector for X-rays. This publication shall show that measurements of the degree of linear X-ray polarization can be performed with such a hybrid photon counting pixel detector as a side-effect although the detector is not designed nor optimized for such measurements.
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For the first time, a hybrid semiconductor photon counting pixel detector has been used to measure polarization asymmetries. The aim of this publication is to show that the hybrid detector is able to measure the degree of linear polarization of X-rays in the energy regime between 27 and 84 keV. In this contribution we will describe a measurement principle of the degree of linear X-ray polarization with the Timepix-detector in counting and in its spectroscopic time-over-threshold mode, prove the applicability in test measurements, compare the measured values to simulation results and discuss advantages and disadvantages of the Timepix for a use in X-ray polarimetry.
2. Polarization signatures of the photoelectric effect and the Compton effect For X-ray energies below about 58 keV the total cross-section of the photoeffect is larger than the total cross-section of Compton scattering in silicon. The ability of the Timepix-detector to measure the degree of linear polarization using the photoeffect is restricted to an energy band where the energy of released photoelectrons is sufficient to cause significant track lengths in silicon and where the photoeffect still significantly contributes to absorption. The polarized radiation that we needed to test the ability of the Timepix to measure the degree of linear polarization was produced by Compton scattering. Therefore we describe the important polarization dependent properties of both effects. 2.1. Photoelectric effect The differential cross-section for the ejection of an electron following photoabsorption of the X-ray photon with energy E0 in the K-shell is given by [6] 7=2 pffiffiffi ds me c2 4 2 sin2 y cos2 f ¼ r 20 Z 5 a4 (1) dO E0 ð1 b cos yÞ4 where f is the polar angle of the momentum of the emitted electron to the y-axis in the reference frame. The reference frame is defined by the direction of the electric field vector of the incoming X-rays (y-axis), the direction of the incoming photon (z-axis) and the direction which is perpendicular to both (x-axis). The angle y is the azimuthal angle of the electron momentum to the z-axis of this frame. r 0 is the classical electron radius, Z the charge of the nucleus, me the electron rest mass, a the fine structure constant and b ¼ v=c is the electron velocity. According to this formula the electron is ejected preferably in the direction of the electric field vector of the incoming X-rays. 2.2. Compton effect The differential cross-section for Compton scattering of a linearly polarized photon beam off a free electron is described by the Klein–Nishina formula: ds 1 2 E2 E E0 2 sin2 y cos2 f ¼ r0 2 þ (2) dO 2 E0 E0 E
E0 1 þ ðE0 =me c2 Þð1 cos yÞ
see that for X-ray photons with energies E0 5me and scattering angles y 90 , where E E0 , the scattered X-radiation is almost completely linearly polarized.
3. The Medipix2 and Timepix-detector The Medipix2 [2,3] and its derivative, the Timepix [4], comprise a sensor layer which is pixelated with a pitch of 55 mm. The Medipix has been designed for X-ray imaging. Each sensor pixel electrode is connected to one electronics cell of the readout ASIC via a bump-bond of a lead–tin alloy. The ASIC has been developed by the Medipix collaboration with its seat at CERN. The pixel cells are organized in a quadratic matrix of 256 rows and 256 columns giving a total side length of about 1.4 cm. Each electronics pixel cell contains an integrating charge sensitive preamplifier, two discriminators in the Medipix2, one discriminator in the Timepix and a pseudo-random counter with a depth of 14 bit. The minimum threshold that can be applied is about 3 keV. If an X-ray photon interacts in the sensitive volume of a sensor pixel the charge carriers, released by the ejected electron, drift towards the pixel electrode. The charge is collected, transferred to the pixel electronics cell and converted into a voltage signal proportional to the amount of collected charge in the preamplifier. If the collected charge, which is a measure of the energy deposition in the pixel volume, exceeds threshold, the photon is counted. This operation mode is called the photon counting mode. It is available in the Medipix2 and the Timepix ASIC. The Medipix2 offers the possibility to count the number of events with energy depositions in an energy window whereas the Timepix-detector can only be operated with one single analogue threshold. The Timepix offers two additional operation modes: the time-over-threshold and the time-to-shutter mode. In the time-over-threshold mode the counter counts the number of clock pulses of a clock signal during the time of the discriminator input pulse being above threshold. This time is proportional to the amount of collected charge and thus proportional to the energy deposition in the sensor pixel. In the time-to-shutter mode the counter of the Timepix counts the number of clock pulses from the moment of detection until the end of the frame. The Medipix2 and Timepix are operated with a shutter signal which stops the detection processes in the pixel matrix at the same time. After having finished all counting activity, the matrix is read out with the pseudo-random-counters acting as shift registers. The whole matrix can be read out serially in about 9 ms or in parallel in about 265 ms thus offering frame rates from several tens of Hertz up to more than a kHz with tolerable dead times. The ASIC is connected to a printed circuit board with a heat conducting glue that contains a significant amount of silver. X-rays which transmit the sensor or even the ASIC can be absorbed in this glue or in the bump-bonds and thus produce fluorescence photons which can be detected again in the sensor layer. Thus the energy deposition spectrum measured with the detector shows strong contributions at the energies of the fluorescence photons of silver and tin. This is important for the interpretation of the energy deposition spectra in this publication.
4. Measurement principle of the degree of linear polarization exploiting the photoelectric effect
where the energy E of the scattered photon is given by E¼
189
(3)
and y is the scattering angle, which is the angle between the momentum vectors of the incoming and the scattered photon and the azimuthal angle f is the angle between the electric field vector of the incoming photon and the scattering plane. One can
The measurement principle of the degree of linear polarization with semiconductor pixel detectors can be based on the fact that the first few microns of the photoelectron track in the sensor material contain information about the original direction of emission of the photoelectron which is correlated with the
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orientation of linear polarization via Eq. (1). The probability to reach the sensitive volume of an adjacent pixel is higher in the direction of ejection. But even if the photoelectron does not reach the border between two pixels, the slightly asymmetric distribution of released charge carriers arriving at the pixel electrode plane prefers the triggering of two adjacent pixels in the direction of linear polarization. During propagation through the silicon sensor the released electrons suffer all kind of scattering processes which cause changes in the direction of propagation. The total path length r of an electron with a kinetic energy Ee of several tens of keV in silicon can be approximated by r ¼ ðEe =10Þ1:75 where the energy Ee given in keV and the range is obtained in mm [1]. For a photon energy of 60 keV the photoelectron, ejected with the energy of 58.2 keV from the silicon K-shell, has a total path length of 21:8 mm. Obviously, in this energy range the total track length of the photoelectrons is comparable to the pixel pitch of the Timepix-detector. Therefore we expect that for a significant number of the events the photoelectron causes energy depositions in adjacent pixels during the randomized part of its track thus reducing the sensitivity to polarization. Additionally the transverse diffusion of released charge carriers during their drift to the pixel electrodes introduces double hits and therefore reduces the polarization sensitivity. We now assume to expose such a photon counting pixel detector with linearly polarized X-rays. The direction of the electric field vector is oriented in parallel to the vertical direction in the laboratory. The rows of the matrix are in parallel to the readout area of the Timepix ASIC. The pixel matrix now can be tilted by a certain angle a between the rows of the pixel matrix and the direction of electric field vector. For a tilt angle of a ¼ 90 the direction of the columns (rows) is parallel (perpendicular) to the direction of the electric field vector. Upon detection of an X-ray photon via photoeffect an electron is ejected preferably in the direction of the columns. Therefore the probability to trigger additionally the neighboring pixel in the same column is higher than the probability to trigger the neighboring pixel in an adjacent column. A difference between the number of double hits among adjacent pixels in the same column N c ða ¼ 90 Þ and the number of double hits between pixels in the same row but in different columns Nr ða ¼ 90 Þ should occur. We define the asymmetry A as AðaÞ:¼
N r ðaÞ Nc ðaÞ N r ðaÞ þ Nc ðaÞ
processes in the silicon sensor have energies between about 1.4 and 11.9 keV corresponding to very short tracks. These track lengths are not large enough to mask the polarization signal emerging from the photoelectrons as one will see later in the data of the polarization asymmetry in dependence on energy deposition.
5. Measurements In order to prove the capability of the Timepix-detector to measure polarization asymmetries we carried out simulations and measurements with polarized X-ray photons in the energy range between 27 and 84 keV. 5.1. Experimental setup In the following we distinguish between the emission spectrum of the X-ray tube which impinges on the target, the spectrum of scattered photons which impinges on the detector, and the spectrum of energy depositions which is measured in the pixels of the detector. We want to point out, that due to the energy dependent absorption of the silicon sensor, charge sharing effects in the sensor layer and detection of fluorescence photons the energy deposition spectrum differs from the spectrum incident on the detector. We performed an experiment using a high intensity medical X-ray tube to produce a linearly polarized X-ray beam by Compton scattering at y 90 off a target of Polymethylacrylate (PMMA). The setup is sketched in Fig. 1. A collimator consisting of a lead block with a hole of 10 mm diameter was equipped with a collimator of tungsten with an opening of 2 mm. It was placed in front of the X-ray tube which was operated at 100 kV acceleration voltage. A 1 mm thick iron plate was placed in front of the exit window of the X-ray tube. The emission spectrum of the tube was measured by performing a threshold scan with a Medipix2 detector placed in the direct beam. A more detailed description of the method to measure the emission spectrum of an X-ray tube with the Medipix2 can be found in Refs. [7,8]. The spectra of the X-ray tube were found to be well represented with the spectra given in Ref. [9] but with an inherent filtration of 1.4 mm aluminum.
(4)
and the polarization asymmetry Apol as Apol :¼
Að0 Þ Að90 Þ . 2
(5)
With this definition the polarization asymmetry Apol does not contain any contributions from apparative asymmetries. A remaining apparative asymmetry can be calculated with Aapp :¼
Að0 Þ þ Að90 Þ . 2
(6)
The polarization asymmetry is proportional to the degree of linear polarization. Thus the measurement of the polarization asymmetry leads to the determination of the degree of linear polarization. At higher X-ray energies the photoelectric cross-section and therefore the count rate is smaller and the Compton effect plays a larger role in the detection process. According to the angular dependencies of Eqs. (1) and (2) the asymmetry signal due to the photoelectric effect may be lowered by the contrary polarization signature of the Compton effect. In the energy range between 27 and 84 keV the electrons, scattered at 90 (where the asymmetry is maximal for low photon energies) in Compton scattering
Fig. 1. Experimental setup consisting of collimator, scattering target and Timepixdetector mounted on rotation device. The orientation of the rows and columns of the pixel matrix is indicated. The angle a is 0 in this case.
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ds dO
¼ k
1 2 E2 E E0 r0 2 2 þ 4ð1 sin2 y cos2 fÞ þ 4 E0 E0 E
(7)
1
0.8 Acceptance [a.u.]
The scattering target had a length of 14 mm in the beam direction. Its width was 3 mm in the laboratory plane perpendicular to the beam direction and its height in the vertical direction was 5 mm. The target was fixed by two thin plastic fibers in a distance of 8 cm in front of the Timepix-detector. The target could be swept out of the beam. A second arm held only two fibers so that measurements without the PMMA target could be performed in order to remove background contributions. The Timepixdetector was mounted on a rotatable aluminum block. The geometry of the setup was chosen in order to prepare a linearly polarized radiation field impinging on the Timepixdetector. Following the calculation of the degree of linear polarization described in Ref. [10] we calculate the degree of linear polarization by integrating the differential Compton scattering cross-sections ðds=dOÞk and ðds=dOÞ? . The differential cross-section ðds=dOÞk for the direction of the electric field vector of the scattered photons being parallel to the electric field vector of the incoming photons is given by
191
0.6
0.4
0.2
0 75
80
85
90
95
100
105
φ [degrees] Fig. 3. Distribution of accepted Compton scattering angles f for a beam completely linearly polarized in the vertical direction. The distribution is normalized to its maximum value.
The differential cross-section ðds=dOÞ? for the electric field vector of the scattered photons in the orthogonal direction is given by ds dO
¼ ?
1 2 E2 E E0 r0 2 þ 2 . 4 E0 E0 E
1 (8)
These differential cross-sections are integrated numerically over the geometrical acceptance in y of the detector at its position, all directions f of the electric field vector of the incoming unpolarized radiation, the energy dependent scattering probability in the target, the impinging spectrum and all interaction points in the target. The degree of linear polarization is derived from the asymmetry of these two integrated cross-sections. We also took attenuation of the primary beam into account. Photoelectric absorption and additional scattering (Compton- or Rayleighscattering) of Compton scattered photons in the target on their way to the detector was neglected because of the small width of the target. The focal spot size of the X-ray tube was about 1 mm in diameter. Due to the geometry we estimate a beam diameter of about 1.6 mm at the target position. Because of additional small angle scattering in the iron plate and the collimator we assume in our calculation of the Compton scattered spectrum and the degree of linear polarization that the target is illuminated homoge-
0.8
0.6
0.4
0.2
0 20
30
40
50 60 70 Photon energy [keV]
80
90
100
Fig. 4. Calculated Compton scattered spectrum impinging on the detector. Due to the geometrical acceptance of the detector the fluorescence lines are smeared out after Compton scattering in the PMMA target.
neously with a beam of 2 mm in diameter. Fig. 2 shows the Compton scattering angle acceptance (y) of the Timepix in this setup for the incoming unpolarized beam. Fig. 3 shows the Compton scattering angle acceptance ðfÞ for the vertical polarization component of the incoming beam. An average degree of polarization of 98.6% was obtained. Fig. 4 shows the calculated spectrum of the Compton scattered X-rays illuminating the Timepix-detector. The energy range of polarized photons therefore is about 27–84 keV.
1
0.8 Acceptance [a.u.]
Spectral density [a.u.]
0.6
0.4 5.2. Measurement of the asymmetry in photon counting mode
0.2
0 75
80
85
90 θ [degrees]
95
100
105
Fig. 2. Distribution of accepted Compton scattering angles y for a beam completely linearly polarized in the vertical direction. The distribution is normalized to its maximum value.
The measurements were carried out with a tube current of 10 mA and 100 kV acceleration voltage. A Timepix-detector bumpbonded to a 300 mm thick silicon sensor and operated in the photon counting mode was used. The sensor was biased with 150 V. The MUROS [11] was used to read out and control the ASIC. The data acquisition was performed with the Pixelman software [12]. The frame time was set to 60 ms in order to have a tolerable occupancy of about 190 triggered pixels in the pixel matrix in each image. At this occupancy the relative amount of random double
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hits is about 103 . At this level the random double hits can be neglected because they affect horizontal and vertical double hits in the same way. The relative influence on the asymmetry therefore is in the order of 103 which is considerably smaller than the statistical precision we were able to achieve. The neighborhood of pixels with a high noise level was switched off symmetrically in vertical and horizontal direction in order to avoid additional apparative asymmetries. The threshold has been calibrated using different radioactive sources and fluorescence radiation. The threshold has to be set to low energies in order to be sensitive to small amounts of energy deposited in one pixel at the beginning of the track of the photoelectron. The discriminator threshold was set to 3.5 keV. The asymmetry A was measured for different angles a between the plane of linear polarization and the rows of the pixel matrix. The angle was varied by rotating the detector in steps of 151 from 301 to 1201. The measurement of the number of double hits was performed with and without the PMMA target for all angles. For each angle 40 000 images have been taken with the target and additionally without the target. This corresponds to a total beam time of about 3 h for each angle. The series of measurements has caused defects on the surface of the anode of the X-ray tube leading to a harder emission spectrum of the X-ray tube. In order to reduce the influence of increasing beam hardening on the measured asymmetry the target- and no-target-measurements have been carried out in an alternating manner. In the analysis a cluster analyzing algorithm counted the number of double hits in neighboring pixels in the same row Nr and in the same column N c . Clusters of two neighboring triggered pixels were counted in Nr or N c only if the ring of pixels around the two triggered pixels did not detect an event. The numbers of double hits measured without target are subtracted from the corresponding numbers measured with the target inserted in the beam. The asymmetry was calculated using Eq. (4). The statistical error was calculated assuming that the number of double hit events varies according to Poisson statistics.
5.3. Measurement of the asymmetry in dependence on energy deposition In order to measure the energy dependence of the polarization asymmetry Apol we carried out measurements with the same experimental setup but with the Timepix-detector operated in time-over-threshold mode. After a pixelwise calibration with testpulses of the time-over-threshold, we used X-ray emissions from an 241Am source to estimate the energy resolution achieved with the calibration. We obtained an relative energy resolution of 7% at the energy of the decay line at 59.5 keV. Due to the fact that the calibration curve, converting time-over-threshold to energy deposition is not linear for energy depositions close to the threshold, inaccuracies arise for low energy depositions. It has to be pointed out that the calibration procedure for the time-overthreshold used in our analysis did not exploit the full potential of the Timepix. It has been shown in the Medipix collaboration [12] that an energy resolution of about 5.5% at 59.5 keV can be obtained with extensive calibration measurements using radioactive sources and fluorescence photons. The obtained energy resolution is considered to be sufficient to test the energy dependence of the polarization asymmetry. In the analysis the time-over-threshold of the pixels in double hit events was converted using the above-mentioned calibration method to equivalent energy deposition. The energy depositions of the two adjacent pixels in each double hit event were added. The number of double hits (Nc and N r ) were counted in energy bins with a width of 10 keV. Measurements at the angles a ¼ 0 and 90 have
been performed. The polarization asymmetry was calculated for each energy bin according to Eq. (5) in order to remove contributions from remaining apparative asymmetries. Mean energies in the energy bins have been calculated with the measured energy deposition spectrum of the double hit events having a total energy deposition in the bin.
6. Simulation In order to verify our measurements we carried out simulations using our detailed implementation of the relevant physical processes in the Timepix-detector which occur during detection of X-rays. A detailed stochastic modelling of the diffusion and drift process of the holes to the pixel electrodes was included. The Timepix-detector is geometrically implemented with all its important parts affecting its response to radiation, e.g. the bump-bonds, the ASIC, the glue and the printed circuit board. We used the EGS4 and LSCAT based Monte-Carlo simulation package ROSI [14,15] for our simulations. A routine to randomize the distribution of the emission angles of the photoelectrons emerging from the K-shells of the silicon sensor atoms according to Eq. (1) has been implemented. In the tracking routines of our simulation code a change of the direction of propagation of the electron is forced if the continuous energy loss DEe in the current step of the track reaches 1% of the energy Ee of the electron. Therefore the maximum step length during tracking can be estimated with the total stopping power of the highest possible energy of an electron in our energy range. The total stopping power of a photoelectron which is ejected from a silicon K-shell in our experiment is about 82 keV. The total stopping power for this electron energy in silicon is 3:71 MeV cm2 =g according to the database ESTAR [16] of the National Institute of Standards and Technology. With this value and the density of silicon we can calculate a maximum step length of approximately 1 mm. This value seems to be small enough to expect that straggling of the electron is modelled precisely enough in our simulation. We irradiated the Timepix-detector perpendicularly and homogeneously with the calculated spectrum shown in Fig. 4 assuming a degree of polarization of 100%; 120 000 images were simulated with a mean occupancy equal to the mean occupancy in the measurement. The same cluster analysis program was used to analyze the images obtained in the simulation and in the measurement. Special attention is paid to a proper modelling of the drift and diffusion processes in the sensor layer of the Timepix-detector which already has led to good agreement between measurements and simulations of the energy response and imaging properties of the detector [8,17,18]. The influence of Coulomb repulsion among the released charge carriers was taken into account via an enlarged diffusion constant. Drift and diffusion are modelled by a spreading of the released charge carriers onto the pixel grid using Gaussian probability density functions starting with the standard deviations given in Ref. [19] and corrected for the effect of coulombic repulsion. Coulombic repulsion plays an important role because the track lengths of the low energetic electrons are very small leading to a large charge carrier density along the track. In the simulation program the energy deposition along each step of the track is converted to an equivalent number of charge carriers. The average energy which has to be deposited in order to create one electron–hole in silicon is 3.6 eV. Fano noise was neglected due to its weakness compared to the electronics noise of about 100 electrons (RMS). A relative energy resolution due to the use of the time-over-threshold-method of 7% was assumed and modelled with a Gaussian distribution. For the comparison with the measurement the weighted means of the degree of
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polarization in the energy deposition bins were taken into account for each energy deposition bin.
7. Results and discussion 7.1. Measurements in photon counting mode The measured asymmetry as a function of the angle between the rows of the matrix and the plane of linear polarization is shown in Fig. 5. The function AðaÞ ¼ Apol cosð2aÞ þ Aapp was fitted to the data in order to obtain the polarization asymmetry Apol, which is due to the polarization of the incoming radiation, and to determine any remaining apparative asymmetry Aapp. The polarization asymmetry was determined to be Apol ¼ ð0:957 0:019Þ%. An apparative asymmetry of Aapp ¼ ð0:194 0:013Þ% was found. It is obvious that we have successfully measured an non-zero polarization asymmetry due to the linear polarization of the radiation impinging on the detector. Further, the unexpected apparative asymmetry is statistically significant. The mean degree of linear polarization of the spectrum impinging on the detector was calculated to be 98.6%. The average degree of linear polarization of the photons causing double hits in the detector was determined using the calculated degree of linear polarization in dependence on photon energy weighted with the simulated number of detected double hits having this total energy. We obtained an average degree of linear polarization of the detected double hit events of 99.1%. The result of the simulation of the polarization asymmetry for our setup was Apol ¼ ð0:888 0:042Þ% which agrees with the measured value taking uncertainties in the simulation, e.g. changes of the emission spectrum of the X-ray tube, the estimated thickness of the silver containing glue and the estimated diameter of the bump-bonds of the detector into account. A measurement without artificial radiation was carried out in order to determine the influence of cosmic rays which could in principle also result in an asymmetry which is modulated with the rotation angle of the matrix. It was found that the fraction of the number of double hits caused by the natural background to the number of double hits in the measurement with radiation is only about ð1:7 0:5Þ 105 . Thus the ratio of the maximum possible asymmetry caused by cosmic radiation to the asymmetry caused by the linearly polarized X-rays is in the order of 2 103 . Therefore we can neglect the influence of natural background
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radiation. Natural background cannot be the origin of the apparative asymmetry. Measurements with a 90 kV X-ray tube spectrum scattered to small angles ðy 5 Þ in forward direction were carried out in order to confirm the apparative asymmetry. An apparative asymmetry of Aapp ¼ ð0:182 0:066Þ% was observed in agreement with the previously mentioned value. The origin of the apparative asymmetry is not yet understood and therefore is subject to additional investigations. Possible explanations may for example be patterns in the distribution of the thresholds in the pixel matrix, asymmetric structures in the bump-bond-matrix, nonisotropic pixel pitch or non-isotropic charge collection in the sensor. Non-uniformities of the thresholds in the pixel matrix can in principle influence the measured asymmetries. We will now first discuss the effect of non-uniformities with no pattern. Let us assume for simplicity that one pixel has a slightly lower threshold than the rest of the matrix. Then the efficiency for this pixel and its neighbor in the same row to be triggered by one photoelectron is slightly higher than in the ideal case where all the thresholds exactly have the same value. This results in a slightly increased number N r. On the other hand, the pixel with the lower threshold will also be involved in double hit events with its neighbor in the same column. So we see that also N c will be increased. Therefore this case affects the denominator in Eq. (4) thus reducing the measured asymmetry. In contrast to this, the measured asymmetry is increased, if the threshold of the pixel is slightly higher than the thresholds in the rest of the matrix. This suggests that one can expect that a random non-uniformity of thresholds has a minor net-effect on the measured asymmetry if there is no trend in the thresholds along the rows or the columns. According to Ref. [4] the thresholds of the Timepix are distributed with a standard deviation of about s ¼ 0:13 keV (corresponding to 35 electrons) around the average threshold after threshold equalization. This contribution is small compared to the electronics noise of about s ¼ 0:36 keV (corresponding to 100 electrons). In our simulation we model the combined effect of both noise contributions by introducing a noise of s ¼ 0:4 keV (corresponding to 110 electrons) on the detected charge in each pixel. A threshold non-uniformity having a trend along rows or columns would lead to an apparative asymmetry. The measured polarization asymmetry will not be affected due to the fact that we subtracted the asymmetry measurements at rotation angles a ¼ 0 and 90 of the pixel matrix from each other according to Eq. (5) to obtain the polarization asymmetry. We want to point out that with a faster read-out device like the PRIAM board [20] and with a direct high intensity polarized photon beam the same statistical precision for each data point may have been achieved in less than 3 min, assuming frames with the same occupancy of the matrix like in our measurements.
7.2. Measurements in time-over-threshold mode
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Fig. 5. Measured asymmetry A in dependence on the rotation angle a of the detector matrix rows to the plane of linear polarization.
Fig. 6 shows the measured energy deposition spectrum for double hit events with the Timepix-detector in time-over-threshold mode in comparison with the energy deposition spectrum obtained with the Monte-Carlo-simulation. The calculated Compton scattered spectrum in Fig. 4 was used as the impinging spectrum in the simulation. It can be seen that the overall form of the spectra is consistent. The prominent peaks at about 24 keV in the simulation and 22 keV in the measured spectrum are due to fluorescence photons from the silver in the glue between ASIC and chipboard and the tin in the bump-bond material. The peaks at about 11 keV in the simulation and 14 keV in the measurement are
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Fig. 7. Measured and simulated polarization asymmetry Apol in dependence on energy deposition. The errorbars are statistical errors only.
due to the L-fluorescence photons of the lead in the bump-bonds. We must assume a systematic error on the photon energy of about 3 keV. The strength of the peaks depends on the diameter of the bump-bonds and the thickness of the glue. Both values are not exactly known, so that the relative height of these peaks cannot be reproduced exactly. Larger deviations are found in the energy deposition spectrum for energy depositions below about 18 keV as it is expected due to the non-linear time-over-threshold measurement for pulse heights closer to the discriminator threshold. For low total energy depositions of the double hit clusters, there is a large fraction of events having one pixel with a pulse height close to the threshold. Due to the fact that the spectrum of X-rays impinging on the detector starts at about 27 keV the influence of the lead, tin and silver fluorescence photons on the measured energy dependence of the asymmetry can be ignored. An additional source of inaccuracies can arise from the measured emission spectrum of the X-ray tube. The exposure times in this experiment were very long so that the X-ray flux decreased during the measurement. This is due to a progressing harshness of the anode surface which leads to hardening of the emitted radiation. Additionally, the influence of scattering in the collimator was neglected in our simulation.
Fig. 8. Measured apparative asymmetry Aapp in dependence on energy deposition. The errorbars represent the statistical error.
Fig. 7 now shows the measured and simulated polarization asymmetry of the detector in dependence on energy deposition. The energy deposition corresponds to the photon energy if we assume that the events are detected via the photoelectric effect. The agreement over a wide energy range is excellent showing that the behavior of the Timepix-detector is well understood and modelled in our simulation. The simulated polarization asymmetry increases from 0.2% at an energy deposition of 29 keV to 3.4% at an energy deposition of 78 keV. This behavior is expected because of the increasing track lengths of the photoelectrons with photon energy. We therefore conclude that the spectroscopic time-overthreshold mode of the Timepix-detector can be used to measure the degree of linear polarization of X-rays in the energy range between 27 and 84 keV in dependence on photon energy. Fig. 8 shows the apparative asymmetry, calculated with Eq. (6) in dependence on energy deposition. We found again an average apparative asymmetry of Aapp ¼ ð0:149 0:066Þ% in consistence with the apparative asymmetries measured in photon counting mode. No statistically significant linear dependence on energy deposition was found for the apparative asymmetry.
8. Summary and outlook We have proven that it is possible to measure the degree of linear polarization in the energy range between 27 and 84 keV with the Timepix-detector. The sensor thickness of 300 mm is very large compared to CCDs which have typically active thicknesses of up to several tens of microns. Therefore hybrid photon counting pixel detectors are an interesting option for polarimetry with higher photon energies. The Timepixdetector, due to its hybrid design, offers the possibility to optimize the pixel pitch, the sensor thickness and the type of sensor material. The Timepix-detector stops counting in the whole matrix at the same time and therefore does not acquire false asymmetries during readout. It is not necessary to cool the Timepix-detector in contrast to many CCD if they are used in X-ray polarimetry. The Timepix-detector can be read out with frame rates of at least 1 kHz [20] using the parallel readout. Additionally the possibility of using very short frame times makes it suitable for high flux polarimetry. The frame time and the frame rate can be chosen independently, making it a very flexible device. The experimental effort and the analysis complex-
ARTICLE IN PRESS T. Michel, J. Durst / Nuclear Instruments and Methods in Physics Research A 594 (2008) 188–195
ity seems to be larger if a CCD is used in X-ray polarimetry. Large potential for improvements in the analyzing power of hybrid photon counting pixel detectors may be found in the suppression of the influence of the charge sharing due to diffusion. Future developments of 3D-sensors, like they have been proposed in Ref. [21] with their electrodes implanted as pillars, may allow the use of very thick sensor layers, while holding the drift length of the charge carriers at a minimum level thus increasing efficiency and analyzing power. The Timepix-detector also offers the possibility to identify Compton scattered events in the sensor by using the time-toshutter mode in each pixel to search for coincidently triggered pixels in each frame. Exploiting Compton scattering in the sensor has the advantage of a significantly higher analyzing power (modulation factor) and the ability to measure the orientation of the plane of linear polarization without rotation of the detector. On the other hand, the efficiency of detecting the Compton scattered photon is low if the standard thin silicon sensor is used. One disadvantage of using Compton scattering in the sensor with the Timepix is that the information about the detection time and the energy deposition is not available simultaneously. Therefore it is not possible to determine the energy of the reacting photon. Additionally it is also not possible to judge which pixel of the triggered pair of pixels corresponds to the point of impact of the primary photon. Thus, imaging polarimetry will be difficult using Compton scattering in the sensor of the Timepix. Assuming a minimum threshold of 3 keV in the pixel, the minimum photon energy, which is necessary to trigger the first pixel in a Compton event at a scattering angle of 901, is about 41 keV. Therefore Compton polarimetry with the Timepix is restricted to energies higher than 41 keV. Nevertheless, Compton polarimetry is subject to current investigations because of the expected high modulation factor. Significant improvements of the analyzing power are necessary in order to ensure that such a hybrid photon counting pixel detector is an option for measurements of the degree of X-ray polarization of celestial sources in reasonable measuring times by exploiting the photoelectric effect.
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Acknowledgment The authors would like thank the Medipix collaboration for the inspiring atmosphere. A special thank goes to Stanislav Pospisil from the Czech Technical University of Prague for the stimulating discussion during the conference dinner of the 9th International Workshop on Radiation Imaging Detectors (iWoRiD). References [1] H. Tsunemi, K. Hayashida, K. Tamura, S. Nomoto, M. Wada, A. Hirano, E. Miyata, Nucl. Instr. and Meth. A 321 (1992) 629. [2] X. Llopart, M. Campbell, R. Dinapoli, D. San Segundo, E. Pernigotti, IEEE Trans. Nucl. Sci. NS-49 (5) (2002) 2279. [3] X. Llopart, M. Campbell, Nucl. Instr. and Meth. A 509 (2003) 157. [4] X. Llopart, R. Ballabriga, M. Campbell, L. Tlustos, W. Wong, Nucl. Instr. and Meth. A 581 (2007) 485. [5] R. Bellazzini, et al., Nucl. Instr. and Meth. A 560 (2006) 425. [6] R. Bellazzini, L. Baldini, A. Brez, E. Costa, L. Latronico, N. Omodei, P. Soffitta, G. Spandre, Nucl. Instr. and Meth. A 510 (2003) 176. [7] M. Firsching, P. Takoukam Talla, T. Michel, G. Anton, Nucl. Instr. and Meth. A 591 (2008) 19. [8] T. Michel, in: Proceedings of the 16th International Workshop on Vertex Detectors, PoS(Vertex 2007)044. [9] J.H. Aichinger, J. Dierker, S. Joite-Barfuss, M. Sa¨bel, Exposure and Image Quality in X-ray Diagnostic Radiology, Springer, Berlin, 2004. [10] T. Mizuno, T. Kamae, J.S.T. Ng, H. Tajima, J.W. Mitchell, R. Streitmatter, R.C. Fernholz, E. Groth, Y. Fukazawa, Nucl. Instr. and Meth. A 540 (2005) 158. [11] G. Bardelloni, E. Bertolucci, A.L.J. Boerkamp, D. Calvet, M. Conti, M. Maiorino, P. Russo, J.L. Visschers, in: Proceedings of the IEEE Nuclear Science Symposium and Medical Imaging Conference, 2000, pp. 57–60. [12] T. Holy, J. Jakubek, S. Pospisil, J. Uher, D. Vavrik, Z. Vykydal, Nucl. Instr. and Meth. A 563 (2006) 254. [12] J. Jakubek, A. Cejnarova Andrea, S. Pospisil. J. Uher, Ceskoslovensky Casopis pro Fyziku, 1/2008, pp. 37–45. [14] J. Giersch, A. Weidemann, G. Anton, Nucl. Instr. and Meth. A 509 (2003) 151. [15] J. Giersch, J. Durst, Nucl. Instr. and Meth. A 591 (2008) 300. [16] hhttp://physics.nist.gov/PhysRefData/Star/Text/ESTAR.htmli. [17] A. Korn, M. Firsching, G. Anton, M. Hoheisel, T. Michel, Nucl. Instr. and Meth. A 576 (2007) 239. [18] P. Bartl, A. Korn, T. Michel, G. Anton, Nucl. Instr. and Meth. A 591 (2008) 314. [19] H.G. Spieler, E.E. Haller, IEEE Trans. Nucl. Sci. NS-32 (1985) 419. [20] C. Ponchut, J. Clement, J.-M. Rigal, E. Papillon, J. Vallerga, D. LaMarra, B. Mikulec, Nucl. Instr. and Meth. A 377 (2007) 109. [21] C. Kenney, S. Parker, J. Segal, C. Storment, IEEE Trans. Nucl. Sci. NS-46 (1999) 1224.