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X-ray polarimetry by means of Compton scattering in the sensor of a hybrid photon counting pixel detector
ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 603 (2009) 384–392
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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
X-ray polarimetry by means of Compton scattering in the sensor of a hybrid photon counting pixel detector T. Michel a,, J. Durst a, J. Jakubek b a b
¨t Erlangen-Nu ¨ rnberg, Erwin-Rommel-Strasse 1, 91058 Erlangen, Germany Erlangen Centre for Astroparticle Physics (ECAP), Friedrich-Alexander-Universita Institute of Experimental and Applied Physics, Czech Technical University in Prague, Horska 3a/22, CZ-12800 Prague 2, Czech Republic
a r t i c l e in f o
a b s t r a c t
Article history: Received 1 September 2008 Received in revised form 19 February 2009 Accepted 19 February 2009 Available online 9 March 2009
For the first time a hybrid semiconductor photon counting pixel detector has been used for measurements of linear X-ray polarization by exploiting the Compton effect in the silicon sensor layer. The time-to-shutter mode of the X-ray imaging detector Timepix was used to identify Comptonscattering events in the sensor layer by the analysis of coincidences. For irradiation with polarized X-ray photons of energies between 27 and 84 keV we were able to measure a large modulation factor of mmeas ¼ ð68:1 16:4Þ% for this type of X-ray polarimeter. Degree and orientation of linear polarization can be determined. This publication describes the experimental setup, data analysis method, measurement and simulation results, and gives first estimations on the polarimetric performance for an application in X-ray astronomy. & 2009 Elsevier B.V. All rights reserved.
Keywords: X-ray Polarization Polarimetry Photon counting pixel detector
1. Introduction We recently reported the possibility to measure the degree of linear X-ray polarization with the Timepix detector by exploiting the photoelectric effect [1]. The results are promising, although the analysing power of the detector is small compared to the analysing power of an X-ray CCD due to the large pixel pitch of the hybrid photon counting detector. Up to now, it has never been shown that a single X-ray imaging detector is able to perform imaging and simultaneously determine the degree of linear X-ray polarization by exploiting the photoelectric and Compton effects. The capability of Timepix detector to exploit both effects to measure the degree of linear X-ray polarization is due to the fine pixelation of the sensor and the possibility to identify coincidences among triggered pixels. In this publication we explain the principle of measuring the degree and orientation of linear X-ray polarization using Compton scattering in the silicon sensor of the Timepix. We discuss the data analysis method and present first measurement and simulation results.
2. The Timepix detector The Timepix detector [2] was developed by the multinational Medipix collaboration with support of the EUDET project to be used in time-projection-chambers or as an X-ray imaging detector when it is combined with a semiconductor sensor layer. The ASIC Corresponding author. Tel.: +49 91318527121.
E-mail address: [email protected] (T. Michel). 0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.02.032
comprises 256 256 electronic cells at a pitch of 55 mm with a preamplifier, discriminator and counter which can be bumpbonded to a pixelated semiconductor sensor layer. For our experiments we used the Timepix detector bump-bonded to a 300 mm-thick silicon sensor. Besides its counting and time-overthreshold modes the Timepix detector can be operated in a timeto-shutter mode. In this mode the counter, which is present in each pixel cell, counts clock pulses upon the detection of an X-ray photon. The counting of the clock pulses stops in all triggered pixels at the occurrence of an external shutter signal which corresponds to the end of the frame exposure. The obtained image contains the detection times of the particles with respect to the end of the frame time. It should be pointed out that, due to the existence of a discriminator in each pixel, there is no electronics noise contribution to the image, as long as the thresholds are properly equalized and the average threshold in the matrix is set well above the noise floor (e.g. 3.5 keV). In our measurements, 21 out of 65 536 pixels (0.032%) were switched off due to high electronics noise.
3. Polarization measurement principle by exploiting Compton scattering in the sensor The differential cross-section for Compton scattering a linearly polarized photon beam with energy E0 off free electrons is described by the Klein–Nishina formula: ds 1 2 E2 E E0 ¼ r0 2 þ 2 sin2 y cos2 f dO 2 E0 E0 E
(1)
ARTICLE IN PRESS T. Michel et al. / Nuclear Instruments and Methods in Physics Research A 603 (2009) 384–392
defined as [3]
where the energy E of the scattered photon is given by E¼
E0 E0 1þ ð1 cos yÞ me c2
385
(2)
m¼
C max C min C min þ C max
(5)
where
and y is the scattering angle, which is the angle between the momentum vectors of the incoming photon to the scattered photon, and the azimuthal angle f is the angle between the electric field vector of the incoming photon and the scattering plane. r 0 denotes the classical electron radius and me is the electron rest mass. For X-ray photons with energies E0 5me c2 and scattering angles y 90 , the scattered X-radiation is almost completely linearly polarized. In our case the measurement of the degree and orientation of linear X-ray polarization can be based on the coincident detection of the Compton-scattered electron and the detection of the scattered photon via photoelectric effect or Compton scattering in another pixel of the matrix. Let us first assume for simplicity that in each of the two detection processes only one pixel is triggered. The angle b of the virtual line connecting these two pixels with respect to a reference axis can be calculated using simple geometry. For the reference axis we chose the direction of the rows of the pixel matrix which is in parallel to the readout zone of the Timepix ASIC. The angle b can be expressed by the scattering angle f in Eq. (1) and an offset angle f0 which depends on the choice of the reference axis and the orientation of the plane of linear polarization:
b ¼ f þ f0 .
(3)
Fig. 1 illustrates the definition of the angle b and shows a typical Compton-scattering event leading to two clusters of coincidently triggered pixels in the Timepix detector. From Eq. (1) one expects that the distribution MðbÞ of the number of detected Compton-scattering events, which depends on the angle b, is modulated: MðbÞ ¼ A cos2 ðb f0 Þ þ B.
(4)
The parameters A, B and f0 can be determined by fitting MðbÞ to the measured distribution. A modulation factor m can be
Pixel 2
C max ¼ A þ B
(6)
and C min ¼ B.
(7)
The modulation factor m100 which would be measured for completely polarized radiation is a key performance indicator of this type of polarimeter. By knowing the modulation factor m100 from simulations or calibration measurements, an unknown degree of linear polarization P can be determined from the measured modulation factor m of the radiation field under investigation via P¼
m . m100
(8)
The orientation of the plane of linear polarization with respect to the reference axis is obtained as f0 .
4. Experimental setup, simulation and data analysis 4.1. Experimental setup
Pixel 3
One row
Readout area of ASIC
The experimental setup is the same as that which was used to determine the potential of the Timepix detector as a polarimeter using the photoelectric effect [1]. Fig. 2 shows the experimental setup. We produced linearly polarized photons between 27 and 84 keV by the Compton scattering of an X-ray tube spectrum off a polymethylacrylate target (PMMA). We used an X-ray tube with a tungsten anode at 100 kV acceleration voltage. The emitted X-ray spectrum was additionally filtered with a 1 mm-thick iron plate in front of the tube’s exit window. A collimator consisting of a lead block with a hole of 10 mm in diameter was equipped with an additional collimator of tungsten with a 2 mm opening and placed between the iron plate and the target. The target had a length of 14 mm in the beam direction and a width of 3 mm in the laboratory plane perpendicular to the beam direction. The height in the vertical direction was 5 mm. The target was fixed by two thin plastic fibres at a distance of 8 cm in front of the Timepix detector and could be moved in a reproducible manner out of the beam. A second arm held only two fibres so that the background contribution could be measured and subtracted from the
r
β α Pixel 1
y
E
x Fig. 1. Illustration of a hit distribution of a Compton-scattering event in the sensor with two clusters of triggered pixels. One cluster consists only of Pixel 1 and the second cluster is formed by Pixels 2 and 3. The definition of the angle b of the event line with respect to the direction of the rows of the pixel matrix is illustrated. The angle of the rows to the plane of linear polarization is denoted as a. The calculated distance between the clusters is r.
Fig. 2. Experimental setup with a collimator, PMMA scattering target and Timepix detector mounted on rotation device. The orientations of the rows and columns of the pixel matrix are indicated. The angle a is 0 in this drawing.
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measured asymmetries. The detector was mounted on an aluminium block that could be rotated around the normal of the sensor surface so that measurements could be taken using different angles a between the rows of the pixel matrix and the direction of linear polarization. The detector was positioned in such a way that mainly photons which were Compton scattered by y 90 in the target were accepted. The scattered X-rays, incident on the detector, were linearly polarized to a high degree in the vertical direction of the laboratory frame. We applied the method described in Ref. [4] to calculate the Compton-scattered spectrum of the X-ray tube incident on the detector and the corresponding degree of linear polarization. This involved numerical integration of the polarized differential Compton-scattering cross-sections over all possible vertices in the target, the angular acceptance of the detector and the filtered emission spectrum of the X-ray tube. We regarded the incoming collimated X-ray beam as unpolarized. Figs. 3 and 4 show the calculated distributions of geometrically accepted Compton-scattering angles y and f for the incoming beam component polarized in the vertical direction (i.e. along the
1
rows of the matrix with a detector rotation angle of a ¼ 0 ). The calculated spectrum impinging on the Timepix in this geometry is shown in Fig. 5. The Timepix detector was operated in the time-to-shutter mode in order to identify coincidences. The discriminator thresholds of the pixels were set to 3.5 keV. The data acquisition programme Pixelman [5] was used to control and read the detector. The minimum clock frequency that could be applied to the Timepix using our version of the MUROS readout interface [6] was 28.9 MHz. Therefore one counted clock pulse corresponded to 34.6 ns. In order to avoid counter overflows for events detected early during the frame, the frame time was set to a very short duration of 311 ms. Due to the very short frame time and a frame rate limited by the serial readout speed of the device, the relative amount of dead time during the measurements was quite large (99.5%). The mean occupancy of the frames of 5.44 triggered pixels was additionally limited by the maximum X-ray tube current. We could allow for a tube current of 15 mA during the long term measurements. Due to these restrictions, our statistical precision was limited but sufficient to prove the capability of Timepix to perform polarimetry by exploiting the Compton effect. We want to point out that with high frame rate readout devices like the PRIAM board [8] or the future USB-2.0-interface [7] the statistical precision can be significantly improved.
Acceptance [a.u.]
0.8 4.2. Simulation
0.6
0.4
0.2
0 75
80
85
90 θ [degrees]
95
100
105
Fig. 3. Distribution of Compton-scattering angles y of the photons scattered in the target and impinging on the Timepix detector for an incoming beam completely linearly polarized in the vertical direction. The distribution is normalized to its maximum value.
We used the EGS4 and LSCAT based Monte-Carlo environment ROSI to simulate the response of the detector in this experimental setup. In the simulation, the detector (with all relevant parts, like the continuous sensor layer, bump-bonds, ASIC, heat conducting glue and PCB) was irradiated homogeneously with the calculated scattered spectrum coming from the PMMA target (Fig. 5). The transverse diffusion of drifting charge carriers was modelled by projecting released charge carriers to the pixel electrode plane using a probability density function whose width depended on the point of generation of each free charge carrier [9]. Additionally, Coulomb repulsion in the charge carrier cloud was taken into account by an enlarged effective diffusion constant. The number of charge carriers released in each step of the electron track (Compton-scattered electron or photoelectron) was calculated by dividing the energy deposition in the step by the average energy of 3.6 eV which is needed to release an electron–hole pair in
1 1 Spectral density [a.u.]
Acceptance [a.u.]
0.8
0.6
0.4
0.2
0.8
0.6
0.4
0.2 0 75
80
85
90 φ [degrees]
95
100
105
Fig. 4. Distribution of scattering angles f of the photons scattered in the target and impinging on the Timepix detector for an incoming beam completely linearly polarized in the vertical direction. The distribution is normalized to its maximum value.
0 20
30
40
50 60 70 Photon energy [keV]
80
90
100
Fig. 5. Calculated Compton-scattered spectrum impinging on the central region of the detector.
ARTICLE IN PRESS T. Michel et al. / Nuclear Instruments and Methods in Physics Research A 603 (2009) 384–392
0.00016 0.00014 0.00012
Efficiency ε
silicon through the continuous energy loss of ionizing particles. The combined influence of electronics noise (approximately 70 electrons RMS) and the threshold dispersion (approximately 50 electrons RMS) was also taken into account. In the simulation, the impinging X-radiation was completely polarized. Thus, simulated data needed to be corrected for the imperfect degree of linear polarization for comparison with the measurement. The coordinates of all pixels which had detected an event with an energy deposition above 3.5 keV were saved to the disc for every 3000 impinging photons. These images were processed by the same analysis programme that we used to analyse the measured data.
387
0.0001 8e-05 6e-05 4e-05
5. Data analysis The significant amount of multiple triggering of adjacent pixels of the Timepix detector by one photon can be partially attributed to extended track lengths of electrons and the diffusion of released charge carriers during their drift to the pixel electrodes. In a significant fraction of the Compton-scattering events which occur in the sensor layer, the first and/or the second interactions trigger more than one pixel; this leads to coincident clusters of triggered pixels during a single event. Fig. 1 shows an example of such an event. One cluster, triggered for example by the Compton-scattered electron, consists of Pixel 1. The other cluster, triggered for example by the detection of the Comptonscattered photon, comprises two pixels. The position of the pixel centre is used as a measure of the point of interaction if a single pixel is triggered (Pixel 1 in Fig. 1). For a cluster of triggered adjacent pixels the average ðx; yÞcoordinates of all pixels involved in the cluster are used as a measure of the point of interaction (e.g. between Pixels 2 and 3 in Fig. 1). Later we will explain that we accept only those cluster pairs in the analysis separated by a distance of rX8 pixel widths. A minimum calculated distance in the ðx; yÞ-plane of 8 pixels between the cluster centres can occur if the real distance in the ðx; yÞ-plane between the first and second interaction point in the sensor is 7 pixel widths. We can then estimate the minimum (maximum) Compton-scattering angles y to be 37:9 ð142:1 Þ for events to be accepted in our analysis of a Timepix detector with a 300 mm-thick silicon sensor. With this simple geometrical consideration we can estimate the minimum primary photon energy which leads to the detection of a Compton-scattering event in our analysis. If we neglect threshold noise we obtain a minimum photon energy of 33.5 keV for y ¼ 142:1. We define the efficiency as the ratio of the identified Compton-scattered events to the total number of photons impinging homogeneously onto the Timepix detector. Fig. 6 shows simulation results for the efficiency taking into account electronics and threshold noise. The detection efficiency rises between about 30 and 55 keV to the maximum value of only 1:32 104. For higher photon energies the efficiency decreases due to the decreasing detection efficiency of the Compton-scattered photon in the second interaction. Let us discuss the maximum detection time difference which occurs between the first and second interaction due to timewalk of both signals. The maximum delay between the detection of the two hits occurs when the minimum energy is deposited in the first interaction and the maximum energy is deposited during the second interaction. When the discriminator threshold is set to 3.5 keV, the minimum energy to detect the Compton-scattered electron is 3.5 keV. The maximum energy deposition in the second cluster occurs for a primary photon of energy 84 keV scattered in the first interaction by 42:7, giving a photon of 80.5 keV which is then absorbed by photoelectric effect (which is not very likely but possible). Thus the minimum energy deposition to be detected in one of the clusters of the Compton-scattering event is 3.5 keV and
2e-05 0 20
30
40
50
60
70
80
90
100
Primary photon energy [keV] Fig. 6. Efficiency of the detector and analysis method to incoming flux.
the maximum energy deposition is 80.5 keV. Additionally, we assume the absorption of the K-fluorescence photon of the absorbing silicon atom in the same pixel. The peaking time of Timepix for the given DAC-setting is about 150 ns, which corresponds to 4.3 clock cycles. Taking the sampling error of one clock pulse and the fact that the detection time is not well defined for a preamplifier output pulse very close to the threshold, we can assume a reasonable coincidence window length of between 7 and 10 clock cycles. We will later see that after a proper subtraction of random coincidences, the number of detected Compton-scattering events does not depend on the coincidence width for window lengths larger than 8 clock cycles. In the first step of the data analysis the coincidently triggered pixels in a coincidence window of length Dt are identified in each frame. Due to the fact that the time axis does not have a fixed origin, sliding coincidence windows are applied to the measured time-to-shutter values. Next, the spatial distribution of coincidently triggered pixels is analysed and clusters of adjacent pixels are identified. Triggered pixels are not considered to be adjacent if they are separated by at least one untriggered pixel. All coincidently triggered adjacent pixels are considered to belong to the same cluster. The ðx yÞ-coordinates of the cluster are calculated as the average x- and y-positions of all pixel centres in the cluster. These averaged coordinates are used to calculate the angle b of the line connecting the centres of the two clusters with respect to the direction of the rows of the matrix. The smallest time-to-shutter of the pixels is assumed to be the detection time of the cluster. It may be possible to use this information to identify the point of impact of the primary photon. If the number of coincident clusters in the coincidence window is larger than two, these clusters are not taken into account for further analysis. Only coincidence windows with exactly two separated coincidently triggered clusters are considered in the data analysis, assuming that one cluster was caused by the first interaction Compton electron and the second one by either a photoelectron or another Compton electron in the second interaction. The amount of events with more than two clusters in a coincidence window of 311.4 ns (9 clock cycles) is only 1.3% of the number of events with exactly two clusters in the coincidence window. Fig. 7 shows the measured distribution of cluster distances for a coincidence width of 311.4 and 1418.6 ns in comparison to simulation results. The measured data show that random coincidences are characterized by larger distances between the clusters. The prompt events usually have shorter distances
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1.2 Coincidence width 311.4 ns Coincidence width 1418.6 ns Simulation
350
Relative acceptance κ of the angle bin
Number of coincident pairs of clusters
400
300 250 200 150 100 50 0
1.15 1.1 1.05 1 0.95 0.9 0.85 0.8
0
2
4 6 8 10 Distance between clusters [mm]
12
14
0
20
40
60
80
100
120
140
160
180
Angle of event line β [degrees] Fig. 8. Relative geometrical acceptance k of the angle bins in b.
Fig. 7. Measured distributions of the distances between the two clusters in each pair of coincident clusters in the central region of the pixel matrix for two values of the coincidence width in comparison to the simulated distribution. The simulation results are scaled to fit the maximum value of the measurement with the smaller coincidence width.
1600
between the clusters. This can also be seen in the distribution obtained with the simulation where we have no random coincidences. This can be explained not only by the Lambert– Beer-attenuation law for Compton-scattered photons, but also the decreasing geometrical angular acceptance in the scattering angle y for increasing cluster distances. In order to improve the statistical precision of our measurements we apply an upper limit on the distance between two coincidently triggered clusters to be identified as a Compton-scattering event in the sensor. We have chosen a maximum distance of 55 pixel widths corresponding to about 3 mm. If we want to obtain a systematic error for b due to the pixelation of the sensor smaller than Db ¼ 10 , then we have to require a minimum distance between the clusters of r min ¼ pffiffiffi 2 55 mm= tanð10 Þ ¼ 0:441 mm, corresponding to about 8 pixel widths. A higher minimum threshold for the distance between the clusters would reduce the efficiency of the analysis but increase the modulation factor by restricting the accepted scattering angles y closer to 90 and by improving the resolution in b. A higher minimum distance will not reduce the amount of random events significantly; this can be seen in Fig. 7. Therefore a trade-off between the statistical precision achieved with the data analysis and the modulation factor has to be found in the future for optimal analysis. In order to reduce the influence of non-isotropic efficiencies to detect the Compton electron and the Compton-scattered photon, we restricted the data analysis to the central area of Timepix, thus emulating a quasi-circular detector with a diameter of 254 pixels to avoid corner effects. The prerequisite for an event to be identified as a potential Compton-scattering event is that both triggered clusters are located in the circular inner region of the pixel matrix. Due to the pixelation of the sensor matrix, the geometrical acceptance of the angle bins in b is nonuniform. We determined the relative acceptance of each angle bin by a simulation with unpolarized radiation impinging on the detector. The relative geometrical acceptance k of each angle bin is defined as the ratio of the number of events detected in this angle bin to the average number of detected events in the bins. Fig. 8 shows the obtained values of k for the 18 angle bins. This choice in the number of angle bins corresponds to an angular resolution of 10 . These
Number of coincident cluster pairs
No subtraction of accidentials With subtraction of accidentials
1400 1200 1000 800 600 400 200 0 0
200
400
600 800 1000 Coincidence width [ns]
1200
1400
Fig. 9. Number of cluster pairs identified to be coincident after background subtraction as a function of the coincidence width before and after random subtraction.
values k are used to correct the number of detected events in the angle bins of the measurement and the simulation for polarized radiation. The strength of this correction ranges between 7% and þ14%. Fig. 9 shows the measured total number of events with coincident cluster pairs with dependence on the width of the sliding coincidence window. The background contribution measured without the target was subtracted from the measurement with the PMMA target. A steep rise in the number of events in the prompt region (small coincidence widths) is visible. Also the number of events increases as expected for larger coincidence width due to random coincidences. The number of additional events between coincidence widths from 553.6 ns (16 clock cycles) to 1072.6 ns (31 clock cycles) was used to calculate an expectation value Nmean random of the total number of random events per nanosecond coincidence width. Fig. 9 also shows the number of events after random subtraction. The number of events corrected for random coincidences is independent of the coincidence window width for window lengths larger than 276.8 ns (8 clock cycles). Therefore we have chosen a coincidence width of 311.4 ns (9 clock cycles) for the analysis.
ARTICLE IN PRESS T. Michel et al. / Nuclear Instruments and Methods in Physics Research A 603 (2009) 384–392
We assume a homogeneous hit distribution of the random hits in the pixel matrix. Therefore we calculate the average number of random coincidences per nanosecond coincidence width for each of the
7. Measurement and simulation of the modulation factor
Nmean random k 18
(9)
which also corrects for the inhomogeneous geometrical acceptance in the different angle bins for random hits. We first prove now that the modulations or asymmetries which we measure are due to the linear polarization of the impinging radiation.
6. Experimental proof of the origin of the measured modulation We define Nh as the number of events with angles b between 45 and 135 . The number Nv is the number of events in complementary directions with angles b from 0 to 45 and from 135 to 180 , respectively. An asymmetry Ameas is defined as Ameas ¼
our measurements which exploit the photoelectric effect in the sensor. This demonstrates the potential of Compton polarimetry.
Nh Nv . Nh þ Nv
(10)
Measurements were carried out for different rotation angles a of the rows of the matrix with respect to the vertical direction (orientation of linear polarization) in the laboratory frame in order to prove that the angular distribution which we measure is due to the linear polarized character of the radiation and not to non-isotropic effects in the detector. Nh ðNv Þ has been determined with and without the PMMA target, and the values have been subtracted from each other in order to remove the influence of background radiation. The asymmetry Ameas was calculated after background subtraction. Random coincidences were not subtracted at this stage. Fig. 10 shows the asymmetry Ameas in dependence on the angle a of the rows to the vertical direction in the laboratory. The behaviour of the asymmetry Ameas ðaÞ is well represented by the expected function f ðaÞ ¼ Amax cosð2 aÞ þ Aapp . We obtained a maximal asymmetry of Amax ¼ ð42:5 2:3Þ%. The apparative asymmetry Aapp ¼ ð2:6 1:9Þ% is not statistically significant showing that the alignment of the setup is precise enough. As expected, the asymmetry reverses its sign at an angle of a ¼ 45 . This measurement proves that the asymmetry stems from the polarized character of the impinging radiation. The measured maximum asymmetry is about 45 times larger than in
The number of events with two clusters, connected by a line with an angle between 0 and þ180 with respect to the rows, was determined with bin widths of Db ¼ 10 for a ¼ 0 and 90 . Target and empty target measurements were subtracted from each other. Fig. 11 shows the resulting distribution of angles b in comparison. The modulation of the signal is clearly visible in both cases. The modulation curve for a ¼ 90 is shifted as expected by 90 compared to the measurement at a ¼ 0 . The measured histograms for a ¼ 0 were then corrected for random coincidences and the non-isotropic angular acceptance k of the angle bins. Fig. 12 shows the resulting measured number of Comptonscattering events for all angle bins in b. The total beam time for this measurement was 8 h. Fig. 13 shows the corresponding simulation results. The modulation of the signal is clearly visible. We fitted the function
160
α = 0 deg α = 90 deg
140 120 Number of events
Nrandom ¼
389
100 80 60 40 20 0 -20 0
20
40
60
80
100
120
140
160
180
Angle of event line β [degrees] Fig. 11. Measured angular distribution of the double cluster event line angles b for the two orientations a ¼ 0 and 90 of the rows of the pixel matrix to the plane of linear polarization. The distributions are not corrected for random coincidences. No correction for the non-isotropic acceptance k of the angle bins was performed.
60 120 40 20
Number of events
Asymmetry A [%]
100
0 -20 -40
80 60 40 20
-60
0 -40
-20
0
20 40 60 80 Angle of matrix α [degrees]
100
120
Fig. 10. Measured asymmetry Ameas with dependence on the angle a of the rows of the pixel matrix with respect to the plane of linear polarization. The dashed curve is an error weighted fit of the function f ðaÞ ¼ Amax cosð2 aÞ þ Aapp to the data.
0
20
40 60 80 100 120 140 Angle of event line β [degrees]
160
180
Fig. 12. Measured modulation curve: distribution of the number of events in dependence on the angle of the event line b.
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1200
Number of events
1000 800 600 400 200 0 0
20
40
60
80
100
120
140
160
180
Angle of event line β [degrees] Fig. 13. Simulated modulation curve for a completely polarized beam in the direction of the rows of the matrix: distribution of the number of events with dependence on the angle of the event line b. The ordinate is enlarged so that the relative dynamic range of the modulation curve in the plot is comparable to Fig. 12.
given in Eq. (4) to the data in order to determine the modulation factor m and the offset angle f0 . For the measurement, we obtained an offset angle f0 ¼ 7:0 3:7 which is consistent with our expectation of f0 ¼ 0 , taking into account inaccuracies of about 2 in the alignment of our setup. The modulation factor is determined to be mmeas ¼ ð68:1 16:4Þ% in the measurement and msim 100 ¼ ð64:7 5:2Þ% in the simulation. In order to compare the simulation to the measurement we estimated the average degree of linear polarization for the detected Compton-scattering events in the sensor. With the detection efficiency (Fig. 6), the impinging spectrum (Fig. 5) and the calculated degree of linear polarization with dependence on photon energy, we estimate that we had an average degree of linear polarization of the impinging photon ensemble (detected as Compton-scattering events) of P ¼ 97:1% in our measurement. In the simulation, we obtain a modulation factor of msim ¼ msim 100 P ¼ ð62:8 5:0Þ% which can be compared to the measured value. The values for the modulation factor in measurement mmeas and simulation msim agree within the statistical errors showing that Timepix is able to measure the degree and orientation of linear polarization by exploiting Compton scattering in the sensor layer.
8. Estimation of the polarimetric performance for a use in X-ray astronomy Using an imaging detector for X-ray polarimetry offers the interesting possibility to combine imaging of celestial sources with the measurement of the degree of polarization. Therefore we estimate the performance limit of a Timepix like detector array that can theoretically be achieved in an application such as an imaging polarimeter on X-ray satellite missions. The following considerations shall only give a feeling of the best performance that could be achieved in the future. At this stage we ignore the influence of background radiation, the problem of powering and cooling a large array of photon counting detectors and the challenge of reducing and transmitting a large amount of data. Therefore these considerations investigate more the potential of using a highly segmented silicon sensor array than using the Timepix detector itself. It is understood that such an application requires a dedicated design of the photon counting ASIC. Some of the requirements for such a detector would be lower power consumption in the analogue electronics of the pixel cell, readout
of triggered pixels only (sparse, event based readout), deadtime free readout, self-triggered readout, and the simultaneous measurement of energy deposition and time-of-detection in each pixel. The current low lifetime of the detector in the test measurements was due to the external triggering of the matrix readout with a fixed frame rate. A self-triggering readout ASIC together with a deadtime free measurement scheme (e.g. multihit capability in each pixel) would solve this problem. The presence of high-Z materials (which can produce fluorescence photons that can be detected in the sensor) in the bump-bonds of such a hybrid pixel detector is not an inherent problem of the technology for this application. In our simulations the detector was modelled with realistic dimensions and composition (eutectic led-tin) of the bump-bond underneath each sensor pixel. As can be seen in the results for the modulation factor, the impact is not severe. The polarimetric performance of a polarimeter in a specific application can be quantified by the Minimum Detectable Polarization (MDP). The MDP is the degree of linear polarization that a source has and that can be measured to not stem from unpolarized radiation at a certain confidence level in a given measuring time T, with a certain photon rate from the source to the whole detector S, with a certain background rate B, with an detection efficiency , and with a modulation factor m100 of the polarimeter. For a confidence level of 99% one obtains [10] MDP99
4:29 ¼ m100 S
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðS þ BÞ . T
(11)
In order to estimate the theoretical limit of the MDP 99 that can be achieved with a highly segmented silicon sensor like the one that was used with the Timepix detector (pixel pitch 55 mm, silicon sensor, planar geometry), we neglect the background contribution and obtain MDP99 ¼
4:29 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi .
m100 S T
(12)
It is not possible to give a realistic estimation of the background contribution at this stage. The background strongly depends on the exact setup of the satellite instrumentation, the existence of veto-detectors to suppress the influence of charged particles and the design of the imaging system, e.g. a coded-mask. Due to the fact that we want to estimate the theoretical limit for the best performance that can be achieved, we neglect the background, with the knowledge that we would find an increased MDP in the experiment. We carried out simulations of the efficiency and modulation factor m100 for silicon sensor thicknesses d of 300, 1000 and 2000 mm for irradiation of a Timepix detector with X-ray photons in the energy range between 40 and 100 keV from the Crab nebula. For the flux of photons from the Crab nebula we used the _ ¼ 9:7 ðE=1 keVÞ2:1 g=cm2 =s=keV [11]. The sensor power law FðEÞ bias voltage was adapted to the sensor thickness so that the field strength in the sensor was equal to the 300 mm-thick silicon sensor biased with 150 V. The modulation factor m100 was determined neglecting the influence of random coincidences. It will be explained later why this is justified. S was calculated for an array of Timepix detectors with a sensor area of one square metre which corresponds to about 5000 Timepix detectors. Additionally we assumed that a coded mask in front of the detector array reduces the incoming flux by 50%. Table 1 gives the values for the detection efficiency of the detectors, the modulation factor m100 and the MDP 99 calculated for a measuring time of 106 s of the Crab nebula spectrum between 40 and 100 keV. We want to point out that such a measurement would lead only to one value for the overall degree of linear
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Table 1 Simulation results on the polarimetric performance of a large array of Timepix detectors.
m100 ð%Þ
300
1:08 104
63:5 3:7
2.92
1000
6:36 104
66:5 2:6
1.15
2000
1:57 103
59:7 0:7
0.81
d ðmmÞ
MDP 99 ð%Þ
The MDP 99 is calculated for a 106 s long exposure to the Crab nebula spectrum from 40 to 100 keV.
polarization in this energy range. As expected, the efficiency increases with increasing sensor thickness. The modulation factor seems to be lower for a thick silicon sensor which may be due to the increased acceptance in the scattering angle y especially at short distances between the clusters. We find a better polarimetric performance for thicker sensor layers. To justify the negligence of random coincidences we determined the rate of random coincidences caused by photons from the Crab nebula itself. The detection rate (single hits) in the central ring of one single Timepix sensor (2000 mm-thick silicon) behind the coded mask for irradiation with the spectrum of the Crab nebula between 3 and 100 keV was determined with the _ detected ¼ 1:7 Hz. A random Monte-Carlo simulation. We obtained N coincidence that cannot be distinguished from a Comptonscattering event occurs if two pixels with a minimum distance of 0.44 mm and a maximum distance of 3 mm are triggered during the coincidence width of 311.4 ns. Taking these areas, the single _ detected and the coincidence width into account we estimated rate N _ random ¼ 1:6 107 Hz for the rate of random coincidences to be N a coincidence width of 311.4 ns. The rate of detected Comptonscattering events (the signal) can be estimated by calculating the flux of photons to the Timepix sensor area from the emission spectrum of the Crab nebula between 40 and 100 keV and multiplying this flux with the efficiency given in Table 1. We _ signal ¼ 1:6 104 Hz for the detected obtained a rate of N Compton-scattering events. We can see that the relative amount of random coincidences in this case is about 0.1% of the signal rate. Therefore we can neglect the influence of random coincidences at this stage of the analysis. This estimated rate of random coincidences includes random coincidences among low energy photons. With a dedicated photon counting pixel detector capable of measuring detection time and energy deposition, the relative amount of random coincidences can be reduced by ignoring coincidences with a small total energy deposition in the analysis. The theoretical limit for the MDP that can be achieved (neglecting technical feasibility and the influence of background) with this large planar detector array of 1 m2 is in the same range as some instruments that have been proposed for polarization measurements in gamma-ray astronomy (Table 4.4 in Ref. [12]).
391
proved to be a polarimeter for X-rays by exploiting the polarization signatures of the photoelectric and Compton effect simultaneously. A drawback of the current version of the Timepix is that it is not possible to determine both, the energy deposition and the detection time simultaneously in each triggered pixel. Therefore it is not possible to determine the degree of linear polarization with dependence on the impinging photon energy. Additionally, the information on the point of impact of the impinging photon is only accessible using the detection time difference due to the timewalk between two interactions in the sensor layer. Thus combining imaging and polarimetry is not straightforward as it is when the photoelectric effect is used. But even with the measurement of the energy deposition in the coincident clusters, it is only possible to determine the point of impact securely if the Compton-scattered photon is absorbed in the second interaction via the photoelectric effect in silicon. The next generation of a hybrid photon counting pixel detector should therefore be able to measure time of detection and energy deposition at the same time. The first point of interaction is then most likely found in the cluster with the smaller total energy deposition. This is a reasonable option only for X-ray energies below 60 keV where the absorption due to the photo electric effect is larger than for relevant Compton-scattering interactions. The lack of the possibility to identify the first interaction does not affect the modulation curve between 0 and 180 , because the Comptonscattering cross-section in Eq. (1) is invariant under a shift of f by 180 . Therefore this has no influence on the determination of the plane of linear polarization. Further investigations are needed to adapt the pixel pitch, sensor thickness and geometry of the detector arrangement to specific experiments where the measurement of X-ray polarization is of importance, such as in X-ray astronomy. It is clear that this type of imaging polarimeter will never be able to compete with the imaging polarimeter described in Ref. [13], due to the low efficiency. On the other hand, the micro-pattern gas-detector based polarimeter in Ref. [13] addresses lower photon energies. The X-ray polarimeter described here will be able to measure X-ray polarization at much higher energies. It has to be pointed out that even one single measured value for the X-ray polarization of strong celestial sources in the energy range between 40 and 100 keV would have value for the astronomical community. At the moment the only measurement of the degree of linear polarization has been carried out on the Crab nebula at 2.6 and 5.2 keV [14] and in the energy range between 100 keV and 1 MeV [15]. Therefore a measurement of the degree of linear X-ray polarization for higher photon energies would help in understanding the emission processes of celestial sources. The advantage of the choice of hybrid photon counting detector technology for polarimetry in X-ray astronomy lies in measurements in the energy range between 40 and 100 keV, where the exploitation of Compton scattering is only possible with the dense pixelation of a sensor. This detector technology can address the energy range between the energy range of micro-pattern gas-detector and single-crystal array gamma-ray detectors.
9. Conclusion and outlook We have shown that the Timepix detector bump-bonded to a silicon sensor of 300 mm thickness can be used as an X-ray polarimeter for photon energies between about 40 and 100 keV by exploiting Compton scattering in the sensor layer. A modulation factor of m ¼ ð68:1 16:4Þ% was measured with an X-ray tube spectrum scattered by 90 off a plastic target. Experimental and simulated modulation factors are in agreement. Thus the degree and orientation of the plane of linear polarization of impinging X-rays can be measured simultaneously with this hybrid photon counting semiconductor pixel detector. As far as we know, the Timepix detector is the only X-ray imaging detector that has
Acknowledgements This work was carried out within the Medipix collaboration. The authors would like to thank the collaboration for the inspiring atmosphere and the fruitful discussions. References [1] T. Michel, J. Durst, Nucl. Instr. and Meth. A 594 (2008) 188. [2] X. Llopart, R. Ballabriga, M. Campbell, L. Tlustos, W. Wong, Nucl. Instr. and Meth. A 581 (2007) 485.
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[3] P. Soffitta, E. Costa, G. di Persio, E. Morelli, A. Rubini, R. Bellazzini, A. Brez, R. Raffo, G. Spandre, D. Joy, Nucl. Instr. and Meth. A 469 (2001) 164. [4] 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. [5] T. Holy, J. Jakubek, S. Pospisil, J. Uher, D. Vavrik, Z. Vykydal, Nucl. Instr. and Meth. A 563 (2006) 254. [6] 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. [7] M. Platkevic, V. Bocarov, J. Jakubek, S. Pospisil, V. Tichy, Z. Vykydal, Nucl. Instr. and Meth. A 591 (2008) 245.
[8] C. Ponchut, J. Clement, J.-M. Rigal, E. Papillon, J. Vallerga, D. LaMarra, B. Mikulec, Nucl. Instr. and Meth. A 377 (2007) 109. [9] H.G. Spieler, E.E. Haller, IEEE Trans. Nucl. Sci. NS-32 (1985) 419. [10] M.C. Weisskopf, R.F. Elsner, D. Hanna, V.M. Kaspi, S.L. O’Dell, G.G. Pavlov, B.D. Ramsey hhttp://arxiv.org/abs/astro-ph/0611483i. [11] G.F. Carpenter, M.J. Coe, A.R. Engel, Nature 269 (1976) 99. [12] F. Lei, A.J. Dean, G.L. Hills, Space Sci. Rev. 82 (1997) 309. [13] R. Bellazzini, L. Baldini, A. Brez, E. Costa, L. Latronico, N. Omodei, P. Soffitta, G. Spandre, Nucl. Instr. and Meth. A 510 (2003) 176. [14] M.C. Weisskopf, E.H. Silver, H.L. Kestenbaum, K.S. Long, R. Novick, The Astrophys. J. 220 (Part 2) (1978) L117. [15] A.J. Dean, D.J. Clark, J.B. Stephen, V.A. McBride, L. Bassani, A. Bazzano, A.J. Bird, Science 321 (2008) 1183.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
X-ray polarimetry by means of Compton scattering in the sensor of a hybrid photon counting pixel detector T. Michel a,, J. Durst a, J. Jakubek b a b
¨t Erlangen-Nu ¨ rnberg, Erwin-Rommel-Strasse 1, 91058 Erlangen, Germany Erlangen Centre for Astroparticle Physics (ECAP), Friedrich-Alexander-Universita Institute of Experimental and Applied Physics, Czech Technical University in Prague, Horska 3a/22, CZ-12800 Prague 2, Czech Republic
a r t i c l e in f o
a b s t r a c t
Article history: Received 1 September 2008 Received in revised form 19 February 2009 Accepted 19 February 2009 Available online 9 March 2009
For the first time a hybrid semiconductor photon counting pixel detector has been used for measurements of linear X-ray polarization by exploiting the Compton effect in the silicon sensor layer. The time-to-shutter mode of the X-ray imaging detector Timepix was used to identify Comptonscattering events in the sensor layer by the analysis of coincidences. For irradiation with polarized X-ray photons of energies between 27 and 84 keV we were able to measure a large modulation factor of mmeas ¼ ð68:1 16:4Þ% for this type of X-ray polarimeter. Degree and orientation of linear polarization can be determined. This publication describes the experimental setup, data analysis method, measurement and simulation results, and gives first estimations on the polarimetric performance for an application in X-ray astronomy. & 2009 Elsevier B.V. All rights reserved.
Keywords: X-ray Polarization Polarimetry Photon counting pixel detector
1. Introduction We recently reported the possibility to measure the degree of linear X-ray polarization with the Timepix detector by exploiting the photoelectric effect [1]. The results are promising, although the analysing power of the detector is small compared to the analysing power of an X-ray CCD due to the large pixel pitch of the hybrid photon counting detector. Up to now, it has never been shown that a single X-ray imaging detector is able to perform imaging and simultaneously determine the degree of linear X-ray polarization by exploiting the photoelectric and Compton effects. The capability of Timepix detector to exploit both effects to measure the degree of linear X-ray polarization is due to the fine pixelation of the sensor and the possibility to identify coincidences among triggered pixels. In this publication we explain the principle of measuring the degree and orientation of linear X-ray polarization using Compton scattering in the silicon sensor of the Timepix. We discuss the data analysis method and present first measurement and simulation results.
2. The Timepix detector The Timepix detector [2] was developed by the multinational Medipix collaboration with support of the EUDET project to be used in time-projection-chambers or as an X-ray imaging detector when it is combined with a semiconductor sensor layer. The ASIC Corresponding author. Tel.: +49 91318527121.
E-mail address: [email protected] (T. Michel). 0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.02.032
comprises 256 256 electronic cells at a pitch of 55 mm with a preamplifier, discriminator and counter which can be bumpbonded to a pixelated semiconductor sensor layer. For our experiments we used the Timepix detector bump-bonded to a 300 mm-thick silicon sensor. Besides its counting and time-overthreshold modes the Timepix detector can be operated in a timeto-shutter mode. In this mode the counter, which is present in each pixel cell, counts clock pulses upon the detection of an X-ray photon. The counting of the clock pulses stops in all triggered pixels at the occurrence of an external shutter signal which corresponds to the end of the frame exposure. The obtained image contains the detection times of the particles with respect to the end of the frame time. It should be pointed out that, due to the existence of a discriminator in each pixel, there is no electronics noise contribution to the image, as long as the thresholds are properly equalized and the average threshold in the matrix is set well above the noise floor (e.g. 3.5 keV). In our measurements, 21 out of 65 536 pixels (0.032%) were switched off due to high electronics noise.
3. Polarization measurement principle by exploiting Compton scattering in the sensor The differential cross-section for Compton scattering a linearly polarized photon beam with energy E0 off free electrons is described by the Klein–Nishina formula: ds 1 2 E2 E E0 ¼ r0 2 þ 2 sin2 y cos2 f dO 2 E0 E0 E
(1)
ARTICLE IN PRESS T. Michel et al. / Nuclear Instruments and Methods in Physics Research A 603 (2009) 384–392
defined as [3]
where the energy E of the scattered photon is given by E¼
E0 E0 1þ ð1 cos yÞ me c2
385
(2)
m¼
C max C min C min þ C max
(5)
where
and y is the scattering angle, which is the angle between the momentum vectors of the incoming photon to the scattered photon, and the azimuthal angle f is the angle between the electric field vector of the incoming photon and the scattering plane. r 0 denotes the classical electron radius and me is the electron rest mass. For X-ray photons with energies E0 5me c2 and scattering angles y 90 , the scattered X-radiation is almost completely linearly polarized. In our case the measurement of the degree and orientation of linear X-ray polarization can be based on the coincident detection of the Compton-scattered electron and the detection of the scattered photon via photoelectric effect or Compton scattering in another pixel of the matrix. Let us first assume for simplicity that in each of the two detection processes only one pixel is triggered. The angle b of the virtual line connecting these two pixels with respect to a reference axis can be calculated using simple geometry. For the reference axis we chose the direction of the rows of the pixel matrix which is in parallel to the readout zone of the Timepix ASIC. The angle b can be expressed by the scattering angle f in Eq. (1) and an offset angle f0 which depends on the choice of the reference axis and the orientation of the plane of linear polarization:
b ¼ f þ f0 .
(3)
Fig. 1 illustrates the definition of the angle b and shows a typical Compton-scattering event leading to two clusters of coincidently triggered pixels in the Timepix detector. From Eq. (1) one expects that the distribution MðbÞ of the number of detected Compton-scattering events, which depends on the angle b, is modulated: MðbÞ ¼ A cos2 ðb f0 Þ þ B.
(4)
The parameters A, B and f0 can be determined by fitting MðbÞ to the measured distribution. A modulation factor m can be
Pixel 2
C max ¼ A þ B
(6)
and C min ¼ B.
(7)
The modulation factor m100 which would be measured for completely polarized radiation is a key performance indicator of this type of polarimeter. By knowing the modulation factor m100 from simulations or calibration measurements, an unknown degree of linear polarization P can be determined from the measured modulation factor m of the radiation field under investigation via P¼
m . m100
(8)
The orientation of the plane of linear polarization with respect to the reference axis is obtained as f0 .
4. Experimental setup, simulation and data analysis 4.1. Experimental setup
Pixel 3
One row
Readout area of ASIC
The experimental setup is the same as that which was used to determine the potential of the Timepix detector as a polarimeter using the photoelectric effect [1]. Fig. 2 shows the experimental setup. We produced linearly polarized photons between 27 and 84 keV by the Compton scattering of an X-ray tube spectrum off a polymethylacrylate target (PMMA). We used an X-ray tube with a tungsten anode at 100 kV acceleration voltage. The emitted X-ray spectrum was additionally filtered with a 1 mm-thick iron plate in front of the tube’s exit window. A collimator consisting of a lead block with a hole of 10 mm in diameter was equipped with an additional collimator of tungsten with a 2 mm opening and placed between the iron plate and the target. The target had a length of 14 mm in the beam direction and a width of 3 mm in the laboratory plane perpendicular to the beam direction. The height in the vertical direction was 5 mm. The target was fixed by two thin plastic fibres at a distance of 8 cm in front of the Timepix detector and could be moved in a reproducible manner out of the beam. A second arm held only two fibres so that the background contribution could be measured and subtracted from the
r
β α Pixel 1
y
E
x Fig. 1. Illustration of a hit distribution of a Compton-scattering event in the sensor with two clusters of triggered pixels. One cluster consists only of Pixel 1 and the second cluster is formed by Pixels 2 and 3. The definition of the angle b of the event line with respect to the direction of the rows of the pixel matrix is illustrated. The angle of the rows to the plane of linear polarization is denoted as a. The calculated distance between the clusters is r.
Fig. 2. Experimental setup with a collimator, PMMA scattering target and Timepix detector mounted on rotation device. The orientations of the rows and columns of the pixel matrix are indicated. The angle a is 0 in this drawing.
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measured asymmetries. The detector was mounted on an aluminium block that could be rotated around the normal of the sensor surface so that measurements could be taken using different angles a between the rows of the pixel matrix and the direction of linear polarization. The detector was positioned in such a way that mainly photons which were Compton scattered by y 90 in the target were accepted. The scattered X-rays, incident on the detector, were linearly polarized to a high degree in the vertical direction of the laboratory frame. We applied the method described in Ref. [4] to calculate the Compton-scattered spectrum of the X-ray tube incident on the detector and the corresponding degree of linear polarization. This involved numerical integration of the polarized differential Compton-scattering cross-sections over all possible vertices in the target, the angular acceptance of the detector and the filtered emission spectrum of the X-ray tube. We regarded the incoming collimated X-ray beam as unpolarized. Figs. 3 and 4 show the calculated distributions of geometrically accepted Compton-scattering angles y and f for the incoming beam component polarized in the vertical direction (i.e. along the
1
rows of the matrix with a detector rotation angle of a ¼ 0 ). The calculated spectrum impinging on the Timepix in this geometry is shown in Fig. 5. The Timepix detector was operated in the time-to-shutter mode in order to identify coincidences. The discriminator thresholds of the pixels were set to 3.5 keV. The data acquisition programme Pixelman [5] was used to control and read the detector. The minimum clock frequency that could be applied to the Timepix using our version of the MUROS readout interface [6] was 28.9 MHz. Therefore one counted clock pulse corresponded to 34.6 ns. In order to avoid counter overflows for events detected early during the frame, the frame time was set to a very short duration of 311 ms. Due to the very short frame time and a frame rate limited by the serial readout speed of the device, the relative amount of dead time during the measurements was quite large (99.5%). The mean occupancy of the frames of 5.44 triggered pixels was additionally limited by the maximum X-ray tube current. We could allow for a tube current of 15 mA during the long term measurements. Due to these restrictions, our statistical precision was limited but sufficient to prove the capability of Timepix to perform polarimetry by exploiting the Compton effect. We want to point out that with high frame rate readout devices like the PRIAM board [8] or the future USB-2.0-interface [7] the statistical precision can be significantly improved.
Acceptance [a.u.]
0.8 4.2. Simulation
0.6
0.4
0.2
0 75
80
85
90 θ [degrees]
95
100
105
Fig. 3. Distribution of Compton-scattering angles y of the photons scattered in the target and impinging on the Timepix detector for an incoming beam completely linearly polarized in the vertical direction. The distribution is normalized to its maximum value.
We used the EGS4 and LSCAT based Monte-Carlo environment ROSI to simulate the response of the detector in this experimental setup. In the simulation, the detector (with all relevant parts, like the continuous sensor layer, bump-bonds, ASIC, heat conducting glue and PCB) was irradiated homogeneously with the calculated scattered spectrum coming from the PMMA target (Fig. 5). The transverse diffusion of drifting charge carriers was modelled by projecting released charge carriers to the pixel electrode plane using a probability density function whose width depended on the point of generation of each free charge carrier [9]. Additionally, Coulomb repulsion in the charge carrier cloud was taken into account by an enlarged effective diffusion constant. The number of charge carriers released in each step of the electron track (Compton-scattered electron or photoelectron) was calculated by dividing the energy deposition in the step by the average energy of 3.6 eV which is needed to release an electron–hole pair in
1 1 Spectral density [a.u.]
Acceptance [a.u.]
0.8
0.6
0.4
0.2
0.8
0.6
0.4
0.2 0 75
80
85
90 φ [degrees]
95
100
105
Fig. 4. Distribution of scattering angles f of the photons scattered in the target and impinging on the Timepix detector for an incoming beam completely linearly polarized in the vertical direction. The distribution is normalized to its maximum value.
0 20
30
40
50 60 70 Photon energy [keV]
80
90
100
Fig. 5. Calculated Compton-scattered spectrum impinging on the central region of the detector.
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0.00016 0.00014 0.00012
Efficiency ε
silicon through the continuous energy loss of ionizing particles. The combined influence of electronics noise (approximately 70 electrons RMS) and the threshold dispersion (approximately 50 electrons RMS) was also taken into account. In the simulation, the impinging X-radiation was completely polarized. Thus, simulated data needed to be corrected for the imperfect degree of linear polarization for comparison with the measurement. The coordinates of all pixels which had detected an event with an energy deposition above 3.5 keV were saved to the disc for every 3000 impinging photons. These images were processed by the same analysis programme that we used to analyse the measured data.
387
0.0001 8e-05 6e-05 4e-05
5. Data analysis The significant amount of multiple triggering of adjacent pixels of the Timepix detector by one photon can be partially attributed to extended track lengths of electrons and the diffusion of released charge carriers during their drift to the pixel electrodes. In a significant fraction of the Compton-scattering events which occur in the sensor layer, the first and/or the second interactions trigger more than one pixel; this leads to coincident clusters of triggered pixels during a single event. Fig. 1 shows an example of such an event. One cluster, triggered for example by the Compton-scattered electron, consists of Pixel 1. The other cluster, triggered for example by the detection of the Comptonscattered photon, comprises two pixels. The position of the pixel centre is used as a measure of the point of interaction if a single pixel is triggered (Pixel 1 in Fig. 1). For a cluster of triggered adjacent pixels the average ðx; yÞcoordinates of all pixels involved in the cluster are used as a measure of the point of interaction (e.g. between Pixels 2 and 3 in Fig. 1). Later we will explain that we accept only those cluster pairs in the analysis separated by a distance of rX8 pixel widths. A minimum calculated distance in the ðx; yÞ-plane of 8 pixels between the cluster centres can occur if the real distance in the ðx; yÞ-plane between the first and second interaction point in the sensor is 7 pixel widths. We can then estimate the minimum (maximum) Compton-scattering angles y to be 37:9 ð142:1 Þ for events to be accepted in our analysis of a Timepix detector with a 300 mm-thick silicon sensor. With this simple geometrical consideration we can estimate the minimum primary photon energy which leads to the detection of a Compton-scattering event in our analysis. If we neglect threshold noise we obtain a minimum photon energy of 33.5 keV for y ¼ 142:1. We define the efficiency as the ratio of the identified Compton-scattered events to the total number of photons impinging homogeneously onto the Timepix detector. Fig. 6 shows simulation results for the efficiency taking into account electronics and threshold noise. The detection efficiency rises between about 30 and 55 keV to the maximum value of only 1:32 104. For higher photon energies the efficiency decreases due to the decreasing detection efficiency of the Compton-scattered photon in the second interaction. Let us discuss the maximum detection time difference which occurs between the first and second interaction due to timewalk of both signals. The maximum delay between the detection of the two hits occurs when the minimum energy is deposited in the first interaction and the maximum energy is deposited during the second interaction. When the discriminator threshold is set to 3.5 keV, the minimum energy to detect the Compton-scattered electron is 3.5 keV. The maximum energy deposition in the second cluster occurs for a primary photon of energy 84 keV scattered in the first interaction by 42:7, giving a photon of 80.5 keV which is then absorbed by photoelectric effect (which is not very likely but possible). Thus the minimum energy deposition to be detected in one of the clusters of the Compton-scattering event is 3.5 keV and
2e-05 0 20
30
40
50
60
70
80
90
100
Primary photon energy [keV] Fig. 6. Efficiency of the detector and analysis method to incoming flux.
the maximum energy deposition is 80.5 keV. Additionally, we assume the absorption of the K-fluorescence photon of the absorbing silicon atom in the same pixel. The peaking time of Timepix for the given DAC-setting is about 150 ns, which corresponds to 4.3 clock cycles. Taking the sampling error of one clock pulse and the fact that the detection time is not well defined for a preamplifier output pulse very close to the threshold, we can assume a reasonable coincidence window length of between 7 and 10 clock cycles. We will later see that after a proper subtraction of random coincidences, the number of detected Compton-scattering events does not depend on the coincidence width for window lengths larger than 8 clock cycles. In the first step of the data analysis the coincidently triggered pixels in a coincidence window of length Dt are identified in each frame. Due to the fact that the time axis does not have a fixed origin, sliding coincidence windows are applied to the measured time-to-shutter values. Next, the spatial distribution of coincidently triggered pixels is analysed and clusters of adjacent pixels are identified. Triggered pixels are not considered to be adjacent if they are separated by at least one untriggered pixel. All coincidently triggered adjacent pixels are considered to belong to the same cluster. The ðx yÞ-coordinates of the cluster are calculated as the average x- and y-positions of all pixel centres in the cluster. These averaged coordinates are used to calculate the angle b of the line connecting the centres of the two clusters with respect to the direction of the rows of the matrix. The smallest time-to-shutter of the pixels is assumed to be the detection time of the cluster. It may be possible to use this information to identify the point of impact of the primary photon. If the number of coincident clusters in the coincidence window is larger than two, these clusters are not taken into account for further analysis. Only coincidence windows with exactly two separated coincidently triggered clusters are considered in the data analysis, assuming that one cluster was caused by the first interaction Compton electron and the second one by either a photoelectron or another Compton electron in the second interaction. The amount of events with more than two clusters in a coincidence window of 311.4 ns (9 clock cycles) is only 1.3% of the number of events with exactly two clusters in the coincidence window. Fig. 7 shows the measured distribution of cluster distances for a coincidence width of 311.4 and 1418.6 ns in comparison to simulation results. The measured data show that random coincidences are characterized by larger distances between the clusters. The prompt events usually have shorter distances
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1.2 Coincidence width 311.4 ns Coincidence width 1418.6 ns Simulation
350
Relative acceptance κ of the angle bin
Number of coincident pairs of clusters
400
300 250 200 150 100 50 0
1.15 1.1 1.05 1 0.95 0.9 0.85 0.8
0
2
4 6 8 10 Distance between clusters [mm]
12
14
0
20
40
60
80
100
120
140
160
180
Angle of event line β [degrees] Fig. 8. Relative geometrical acceptance k of the angle bins in b.
Fig. 7. Measured distributions of the distances between the two clusters in each pair of coincident clusters in the central region of the pixel matrix for two values of the coincidence width in comparison to the simulated distribution. The simulation results are scaled to fit the maximum value of the measurement with the smaller coincidence width.
1600
between the clusters. This can also be seen in the distribution obtained with the simulation where we have no random coincidences. This can be explained not only by the Lambert– Beer-attenuation law for Compton-scattered photons, but also the decreasing geometrical angular acceptance in the scattering angle y for increasing cluster distances. In order to improve the statistical precision of our measurements we apply an upper limit on the distance between two coincidently triggered clusters to be identified as a Compton-scattering event in the sensor. We have chosen a maximum distance of 55 pixel widths corresponding to about 3 mm. If we want to obtain a systematic error for b due to the pixelation of the sensor smaller than Db ¼ 10 , then we have to require a minimum distance between the clusters of r min ¼ pffiffiffi 2 55 mm= tanð10 Þ ¼ 0:441 mm, corresponding to about 8 pixel widths. A higher minimum threshold for the distance between the clusters would reduce the efficiency of the analysis but increase the modulation factor by restricting the accepted scattering angles y closer to 90 and by improving the resolution in b. A higher minimum distance will not reduce the amount of random events significantly; this can be seen in Fig. 7. Therefore a trade-off between the statistical precision achieved with the data analysis and the modulation factor has to be found in the future for optimal analysis. In order to reduce the influence of non-isotropic efficiencies to detect the Compton electron and the Compton-scattered photon, we restricted the data analysis to the central area of Timepix, thus emulating a quasi-circular detector with a diameter of 254 pixels to avoid corner effects. The prerequisite for an event to be identified as a potential Compton-scattering event is that both triggered clusters are located in the circular inner region of the pixel matrix. Due to the pixelation of the sensor matrix, the geometrical acceptance of the angle bins in b is nonuniform. We determined the relative acceptance of each angle bin by a simulation with unpolarized radiation impinging on the detector. The relative geometrical acceptance k of each angle bin is defined as the ratio of the number of events detected in this angle bin to the average number of detected events in the bins. Fig. 8 shows the obtained values of k for the 18 angle bins. This choice in the number of angle bins corresponds to an angular resolution of 10 . These
Number of coincident cluster pairs
No subtraction of accidentials With subtraction of accidentials
1400 1200 1000 800 600 400 200 0 0
200
400
600 800 1000 Coincidence width [ns]
1200
1400
Fig. 9. Number of cluster pairs identified to be coincident after background subtraction as a function of the coincidence width before and after random subtraction.
values k are used to correct the number of detected events in the angle bins of the measurement and the simulation for polarized radiation. The strength of this correction ranges between 7% and þ14%. Fig. 9 shows the measured total number of events with coincident cluster pairs with dependence on the width of the sliding coincidence window. The background contribution measured without the target was subtracted from the measurement with the PMMA target. A steep rise in the number of events in the prompt region (small coincidence widths) is visible. Also the number of events increases as expected for larger coincidence width due to random coincidences. The number of additional events between coincidence widths from 553.6 ns (16 clock cycles) to 1072.6 ns (31 clock cycles) was used to calculate an expectation value Nmean random of the total number of random events per nanosecond coincidence width. Fig. 9 also shows the number of events after random subtraction. The number of events corrected for random coincidences is independent of the coincidence window width for window lengths larger than 276.8 ns (8 clock cycles). Therefore we have chosen a coincidence width of 311.4 ns (9 clock cycles) for the analysis.
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We assume a homogeneous hit distribution of the random hits in the pixel matrix. Therefore we calculate the average number of random coincidences per nanosecond coincidence width for each of the
7. Measurement and simulation of the modulation factor
Nmean random k 18
(9)
which also corrects for the inhomogeneous geometrical acceptance in the different angle bins for random hits. We first prove now that the modulations or asymmetries which we measure are due to the linear polarization of the impinging radiation.
6. Experimental proof of the origin of the measured modulation We define Nh as the number of events with angles b between 45 and 135 . The number Nv is the number of events in complementary directions with angles b from 0 to 45 and from 135 to 180 , respectively. An asymmetry Ameas is defined as Ameas ¼
our measurements which exploit the photoelectric effect in the sensor. This demonstrates the potential of Compton polarimetry.
Nh Nv . Nh þ Nv
(10)
Measurements were carried out for different rotation angles a of the rows of the matrix with respect to the vertical direction (orientation of linear polarization) in the laboratory frame in order to prove that the angular distribution which we measure is due to the linear polarized character of the radiation and not to non-isotropic effects in the detector. Nh ðNv Þ has been determined with and without the PMMA target, and the values have been subtracted from each other in order to remove the influence of background radiation. The asymmetry Ameas was calculated after background subtraction. Random coincidences were not subtracted at this stage. Fig. 10 shows the asymmetry Ameas in dependence on the angle a of the rows to the vertical direction in the laboratory. The behaviour of the asymmetry Ameas ðaÞ is well represented by the expected function f ðaÞ ¼ Amax cosð2 aÞ þ Aapp . We obtained a maximal asymmetry of Amax ¼ ð42:5 2:3Þ%. The apparative asymmetry Aapp ¼ ð2:6 1:9Þ% is not statistically significant showing that the alignment of the setup is precise enough. As expected, the asymmetry reverses its sign at an angle of a ¼ 45 . This measurement proves that the asymmetry stems from the polarized character of the impinging radiation. The measured maximum asymmetry is about 45 times larger than in
The number of events with two clusters, connected by a line with an angle between 0 and þ180 with respect to the rows, was determined with bin widths of Db ¼ 10 for a ¼ 0 and 90 . Target and empty target measurements were subtracted from each other. Fig. 11 shows the resulting distribution of angles b in comparison. The modulation of the signal is clearly visible in both cases. The modulation curve for a ¼ 90 is shifted as expected by 90 compared to the measurement at a ¼ 0 . The measured histograms for a ¼ 0 were then corrected for random coincidences and the non-isotropic angular acceptance k of the angle bins. Fig. 12 shows the resulting measured number of Comptonscattering events for all angle bins in b. The total beam time for this measurement was 8 h. Fig. 13 shows the corresponding simulation results. The modulation of the signal is clearly visible. We fitted the function
160
α = 0 deg α = 90 deg
140 120 Number of events
Nrandom ¼
389
100 80 60 40 20 0 -20 0
20
40
60
80
100
120
140
160
180
Angle of event line β [degrees] Fig. 11. Measured angular distribution of the double cluster event line angles b for the two orientations a ¼ 0 and 90 of the rows of the pixel matrix to the plane of linear polarization. The distributions are not corrected for random coincidences. No correction for the non-isotropic acceptance k of the angle bins was performed.
60 120 40 20
Number of events
Asymmetry A [%]
100
0 -20 -40
80 60 40 20
-60
0 -40
-20
0
20 40 60 80 Angle of matrix α [degrees]
100
120
Fig. 10. Measured asymmetry Ameas with dependence on the angle a of the rows of the pixel matrix with respect to the plane of linear polarization. The dashed curve is an error weighted fit of the function f ðaÞ ¼ Amax cosð2 aÞ þ Aapp to the data.
0
20
40 60 80 100 120 140 Angle of event line β [degrees]
160
180
Fig. 12. Measured modulation curve: distribution of the number of events in dependence on the angle of the event line b.
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1200
Number of events
1000 800 600 400 200 0 0
20
40
60
80
100
120
140
160
180
Angle of event line β [degrees] Fig. 13. Simulated modulation curve for a completely polarized beam in the direction of the rows of the matrix: distribution of the number of events with dependence on the angle of the event line b. The ordinate is enlarged so that the relative dynamic range of the modulation curve in the plot is comparable to Fig. 12.
given in Eq. (4) to the data in order to determine the modulation factor m and the offset angle f0 . For the measurement, we obtained an offset angle f0 ¼ 7:0 3:7 which is consistent with our expectation of f0 ¼ 0 , taking into account inaccuracies of about 2 in the alignment of our setup. The modulation factor is determined to be mmeas ¼ ð68:1 16:4Þ% in the measurement and msim 100 ¼ ð64:7 5:2Þ% in the simulation. In order to compare the simulation to the measurement we estimated the average degree of linear polarization for the detected Compton-scattering events in the sensor. With the detection efficiency (Fig. 6), the impinging spectrum (Fig. 5) and the calculated degree of linear polarization with dependence on photon energy, we estimate that we had an average degree of linear polarization of the impinging photon ensemble (detected as Compton-scattering events) of P ¼ 97:1% in our measurement. In the simulation, we obtain a modulation factor of msim ¼ msim 100 P ¼ ð62:8 5:0Þ% which can be compared to the measured value. The values for the modulation factor in measurement mmeas and simulation msim agree within the statistical errors showing that Timepix is able to measure the degree and orientation of linear polarization by exploiting Compton scattering in the sensor layer.
8. Estimation of the polarimetric performance for a use in X-ray astronomy Using an imaging detector for X-ray polarimetry offers the interesting possibility to combine imaging of celestial sources with the measurement of the degree of polarization. Therefore we estimate the performance limit of a Timepix like detector array that can theoretically be achieved in an application such as an imaging polarimeter on X-ray satellite missions. The following considerations shall only give a feeling of the best performance that could be achieved in the future. At this stage we ignore the influence of background radiation, the problem of powering and cooling a large array of photon counting detectors and the challenge of reducing and transmitting a large amount of data. Therefore these considerations investigate more the potential of using a highly segmented silicon sensor array than using the Timepix detector itself. It is understood that such an application requires a dedicated design of the photon counting ASIC. Some of the requirements for such a detector would be lower power consumption in the analogue electronics of the pixel cell, readout
of triggered pixels only (sparse, event based readout), deadtime free readout, self-triggered readout, and the simultaneous measurement of energy deposition and time-of-detection in each pixel. The current low lifetime of the detector in the test measurements was due to the external triggering of the matrix readout with a fixed frame rate. A self-triggering readout ASIC together with a deadtime free measurement scheme (e.g. multihit capability in each pixel) would solve this problem. The presence of high-Z materials (which can produce fluorescence photons that can be detected in the sensor) in the bump-bonds of such a hybrid pixel detector is not an inherent problem of the technology for this application. In our simulations the detector was modelled with realistic dimensions and composition (eutectic led-tin) of the bump-bond underneath each sensor pixel. As can be seen in the results for the modulation factor, the impact is not severe. The polarimetric performance of a polarimeter in a specific application can be quantified by the Minimum Detectable Polarization (MDP). The MDP is the degree of linear polarization that a source has and that can be measured to not stem from unpolarized radiation at a certain confidence level in a given measuring time T, with a certain photon rate from the source to the whole detector S, with a certain background rate B, with an detection efficiency , and with a modulation factor m100 of the polarimeter. For a confidence level of 99% one obtains [10] MDP99
4:29 ¼ m100 S
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðS þ BÞ . T
(11)
In order to estimate the theoretical limit of the MDP 99 that can be achieved with a highly segmented silicon sensor like the one that was used with the Timepix detector (pixel pitch 55 mm, silicon sensor, planar geometry), we neglect the background contribution and obtain MDP99 ¼
4:29 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi .
m100 S T
(12)
It is not possible to give a realistic estimation of the background contribution at this stage. The background strongly depends on the exact setup of the satellite instrumentation, the existence of veto-detectors to suppress the influence of charged particles and the design of the imaging system, e.g. a coded-mask. Due to the fact that we want to estimate the theoretical limit for the best performance that can be achieved, we neglect the background, with the knowledge that we would find an increased MDP in the experiment. We carried out simulations of the efficiency and modulation factor m100 for silicon sensor thicknesses d of 300, 1000 and 2000 mm for irradiation of a Timepix detector with X-ray photons in the energy range between 40 and 100 keV from the Crab nebula. For the flux of photons from the Crab nebula we used the _ ¼ 9:7 ðE=1 keVÞ2:1 g=cm2 =s=keV [11]. The sensor power law FðEÞ bias voltage was adapted to the sensor thickness so that the field strength in the sensor was equal to the 300 mm-thick silicon sensor biased with 150 V. The modulation factor m100 was determined neglecting the influence of random coincidences. It will be explained later why this is justified. S was calculated for an array of Timepix detectors with a sensor area of one square metre which corresponds to about 5000 Timepix detectors. Additionally we assumed that a coded mask in front of the detector array reduces the incoming flux by 50%. Table 1 gives the values for the detection efficiency of the detectors, the modulation factor m100 and the MDP 99 calculated for a measuring time of 106 s of the Crab nebula spectrum between 40 and 100 keV. We want to point out that such a measurement would lead only to one value for the overall degree of linear
ARTICLE IN PRESS T. Michel et al. / Nuclear Instruments and Methods in Physics Research A 603 (2009) 384–392
Table 1 Simulation results on the polarimetric performance of a large array of Timepix detectors.
m100 ð%Þ
300
1:08 104
63:5 3:7
2.92
1000
6:36 104
66:5 2:6
1.15
2000
1:57 103
59:7 0:7
0.81
d ðmmÞ
MDP 99 ð%Þ
The MDP 99 is calculated for a 106 s long exposure to the Crab nebula spectrum from 40 to 100 keV.
polarization in this energy range. As expected, the efficiency increases with increasing sensor thickness. The modulation factor seems to be lower for a thick silicon sensor which may be due to the increased acceptance in the scattering angle y especially at short distances between the clusters. We find a better polarimetric performance for thicker sensor layers. To justify the negligence of random coincidences we determined the rate of random coincidences caused by photons from the Crab nebula itself. The detection rate (single hits) in the central ring of one single Timepix sensor (2000 mm-thick silicon) behind the coded mask for irradiation with the spectrum of the Crab nebula between 3 and 100 keV was determined with the _ detected ¼ 1:7 Hz. A random Monte-Carlo simulation. We obtained N coincidence that cannot be distinguished from a Comptonscattering event occurs if two pixels with a minimum distance of 0.44 mm and a maximum distance of 3 mm are triggered during the coincidence width of 311.4 ns. Taking these areas, the single _ detected and the coincidence width into account we estimated rate N _ random ¼ 1:6 107 Hz for the rate of random coincidences to be N a coincidence width of 311.4 ns. The rate of detected Comptonscattering events (the signal) can be estimated by calculating the flux of photons to the Timepix sensor area from the emission spectrum of the Crab nebula between 40 and 100 keV and multiplying this flux with the efficiency given in Table 1. We _ signal ¼ 1:6 104 Hz for the detected obtained a rate of N Compton-scattering events. We can see that the relative amount of random coincidences in this case is about 0.1% of the signal rate. Therefore we can neglect the influence of random coincidences at this stage of the analysis. This estimated rate of random coincidences includes random coincidences among low energy photons. With a dedicated photon counting pixel detector capable of measuring detection time and energy deposition, the relative amount of random coincidences can be reduced by ignoring coincidences with a small total energy deposition in the analysis. The theoretical limit for the MDP that can be achieved (neglecting technical feasibility and the influence of background) with this large planar detector array of 1 m2 is in the same range as some instruments that have been proposed for polarization measurements in gamma-ray astronomy (Table 4.4 in Ref. [12]).
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proved to be a polarimeter for X-rays by exploiting the polarization signatures of the photoelectric and Compton effect simultaneously. A drawback of the current version of the Timepix is that it is not possible to determine both, the energy deposition and the detection time simultaneously in each triggered pixel. Therefore it is not possible to determine the degree of linear polarization with dependence on the impinging photon energy. Additionally, the information on the point of impact of the impinging photon is only accessible using the detection time difference due to the timewalk between two interactions in the sensor layer. Thus combining imaging and polarimetry is not straightforward as it is when the photoelectric effect is used. But even with the measurement of the energy deposition in the coincident clusters, it is only possible to determine the point of impact securely if the Compton-scattered photon is absorbed in the second interaction via the photoelectric effect in silicon. The next generation of a hybrid photon counting pixel detector should therefore be able to measure time of detection and energy deposition at the same time. The first point of interaction is then most likely found in the cluster with the smaller total energy deposition. This is a reasonable option only for X-ray energies below 60 keV where the absorption due to the photo electric effect is larger than for relevant Compton-scattering interactions. The lack of the possibility to identify the first interaction does not affect the modulation curve between 0 and 180 , because the Comptonscattering cross-section in Eq. (1) is invariant under a shift of f by 180 . Therefore this has no influence on the determination of the plane of linear polarization. Further investigations are needed to adapt the pixel pitch, sensor thickness and geometry of the detector arrangement to specific experiments where the measurement of X-ray polarization is of importance, such as in X-ray astronomy. It is clear that this type of imaging polarimeter will never be able to compete with the imaging polarimeter described in Ref. [13], due to the low efficiency. On the other hand, the micro-pattern gas-detector based polarimeter in Ref. [13] addresses lower photon energies. The X-ray polarimeter described here will be able to measure X-ray polarization at much higher energies. It has to be pointed out that even one single measured value for the X-ray polarization of strong celestial sources in the energy range between 40 and 100 keV would have value for the astronomical community. At the moment the only measurement of the degree of linear polarization has been carried out on the Crab nebula at 2.6 and 5.2 keV [14] and in the energy range between 100 keV and 1 MeV [15]. Therefore a measurement of the degree of linear X-ray polarization for higher photon energies would help in understanding the emission processes of celestial sources. The advantage of the choice of hybrid photon counting detector technology for polarimetry in X-ray astronomy lies in measurements in the energy range between 40 and 100 keV, where the exploitation of Compton scattering is only possible with the dense pixelation of a sensor. This detector technology can address the energy range between the energy range of micro-pattern gas-detector and single-crystal array gamma-ray detectors.
9. Conclusion and outlook We have shown that the Timepix detector bump-bonded to a silicon sensor of 300 mm thickness can be used as an X-ray polarimeter for photon energies between about 40 and 100 keV by exploiting Compton scattering in the sensor layer. A modulation factor of m ¼ ð68:1 16:4Þ% was measured with an X-ray tube spectrum scattered by 90 off a plastic target. Experimental and simulated modulation factors are in agreement. Thus the degree and orientation of the plane of linear polarization of impinging X-rays can be measured simultaneously with this hybrid photon counting semiconductor pixel detector. As far as we know, the Timepix detector is the only X-ray imaging detector that has
Acknowledgements This work was carried out within the Medipix collaboration. The authors would like to thank the collaboration for the inspiring atmosphere and the fruitful discussions. References [1] T. Michel, J. Durst, Nucl. Instr. and Meth. A 594 (2008) 188. [2] X. Llopart, R. Ballabriga, M. Campbell, L. Tlustos, W. Wong, Nucl. Instr. and Meth. A 581 (2007) 485.
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