The Gas Pixel Detector as an X-ray photoelectric polarimeter with a large field of view
Fabio Muleri, Paolo Soffitta, Ronaldo Bellazzini, Alessandro Brez, Enrico Costa, Sergio Fabiani, Massimo Frutti, Massimo Minuti, Maria Barbara Negri, Michele Pinchera, Alda Rubini, Gloria Spandre
aa r X i v : . [ a s t r o - ph ] O c t The Gas Pixel Detector as an X-ray photoelectric polarimeterwith a large field of view
Fabio Muleri a,b , Paolo Soffitta a , Ronaldo Bellazzini c , Alessandro Brez c , Enrico Costa a ,Sergio Fabiani a , Massimo Frutti a , Massimo Minuti c , Maria Barbara Negri d , Michele Pinchera c ,Alda Rubini a , Gloria Spandre ca Istituto di Astrofisica Spaziale e Fisica Cosmica, Via del Fosso del Cavaliere 100, I-00133Roma, Italy; b Universit`a di Roma Tor Vergata, Dipartimento di Fisica, via della Ricerca Scientifica 1,00133 Roma, Italy c Istituto Nazionale di Fisica Nucleare, Largo B. Pontecorvo 3, I-56127 Pisa, Italy d ASI, Agenzia Spaziale Italiana, Viale Liegi 26, I-00198 Roma, Italy
ABSTRACT
The Gas Pixel Detector (GPD) is a new generation device which, thanks to its 50 µ m pixels, is capable of imagingthe photoelectrons tracks produced by photoelectric absorption in a gas. Since the direction of emission of thephotoelectrons is strongly correlated with the direction of polarization of the absorbed photons, this device hasbeen proposed as a polarimeter for the study of astrophysical sources, with a sensitivity far higher than theinstruments flown to date. The GPD has been always regarded as a focal plane instrument and then it has beenproposed to be included on the next generation space-borne missions together with a grazing incidence optics.Instead in this paper we explore the feasibility of a new kind of application of the GPD and of the photoelectricpolarimeters in general, i.e. an instrument with a large field of view. By means of an analytical treatmentand measurements, we verify if it is possible to preserve the sensitivity to the polarization for inclined beams,opening the way for the measurement of X-ray polarization for transient astrophysical sources. While severesystematic effects arise for inclination greater than about 20 degrees, methods and algorithms to control themare discussed. Keywords:
X-ray polarimetry, photoelectric absorption, large field of view instruments
1. INTRODUCTION
Today polarimetry is the sub-topic of X-Ray Astronomy for which we have the maximum gap between theexpectations deriving from theoretical analysis and the achievements deriving from experiments.
1, 2
Indeedthis branch of astronomy has suffered limitations due to the lack of sensitivity of the previously flown X-raypolarimeters, based on the classical techniques of measurement, namely the Bragg diffraction at nearly 45 degreesand the Thomson scattering at nearly 90 degrees.The development of new devices which can exploit the photoelectric effect to derive the polarization of theabsorbed photons has renewed the interest in this branch of X-ray astronomy. Their operation is based onthe reconstruction of the direction of emission of photoelectrons by means of pairs created by ionization in agas. Since photoelectric absorption is intrinsically wide-band with respect to the Bragg diffraction and can beexploited at lower energies with respect to the Thomson scattering, this kind of devices are characterized by afar higher sensitivity than the X-ray polarimeters built so far.The detection of polarization requires a large number of photons (10 - 10 ) to reach minimum detectablepolarizations of a few percent, i.e. in the range of interest for astrophysical sources. To reach a sufficient collectingarea to perform measurements in a reasonable observing time, these devices can be efficiently employed withX-ray optics, and many proposals have been presented. Two profiles of missions are emerging:
Further author information: (Send correspondence to Fabio Muleri)Fabio Muleri: E-mail: [email protected], Telephone: +39-0649934565 a pathfinder mission, with a medium X-ray optics, which could perform the study of galactic and brightextragalactic sources in a few days; • a large observatory, following the pathfinder mission, which could be dedicated to the study of the faintextragalactic sources with a large area.In both cases, the detector is aligned with the optics, namely the photons are incident nearly orthogonallywith respect to the instrument. Then, the symmetry around the optical axis assures that systematic effects arenegligible, at least at first order.Despite this essential employment of photoelectric polarimeters has not been realized yet, new possibilitiesare already emerging. Indeed it has been proposed to employ this kind of polarimeters to build small and cheapinstruments with large field of view to perform polarimetry of transient and bright sources like Gamma RayBurst. In this paper, we analyze the possible use of the Gas Pixel Detector, one of the most advanced projectin the field of photoelectric polarimetry, as a large field of view instrument by means of theoretical analysisand measurements. We will explore the systematic effects arising when polarized and unpolarized photons areincident at large angle with respect to the perpendicular to the instrument, and will present some basic tools todisentangle the systematics from the actual polarized response. The bases of this analysis were already presentedby Muleri in 2005.
2. THE GAS PIXEL DETECTOR
The Gas Pixel Detector, developed by the INFN of Pisa, is one of the most advanced X-ray polarimeterbased on the photoelectric effect. It is basically a gas detector with fine 2-D position resolution, made of a gascell with a beryllium X-ray window, a gas electron multiplier (GEM) and, below it, of a pixellated plane whichcollects the charges generated in the gas. Its operating principle is shown in Fig. 1. When a photon crosses thethin beryllium window and is absorbed in the gas, a photoelectron is emitted preferentially along the electricfield of the absorbed photon, i.e. in the direction of polarization. As the photoelectron propagates, it is scatteredby charges in the nuclei and loses its energy by ionization. Its path is traced by the generated electron-ion pairs,which are amplified by the GEM and collected on the fine sub-divided pixel detector. Hence the detector seesthe projection of the track of the photoelectron.When the incident radiation is linearly polarized, the histogram of the angles of emission of a large numberof photoelectrons is modulated with an amplitude proportional to the degree of polarization. The Gas PixelDetector derives the amplitude and the phase of this modulation by analyzing the projection of the track on thedetector and then reconstructing the angle of emission of each photoelectron.This approach is successful only if the tracks are resolved by the detector in many pixels. Indeed, photo-electrons are subjected to nuclear scatterings in the gas and then the first part of the track must be resolved,since it’s the only part that carries memory of the polarization. Moreover, the ejection of the photoelectron isvery likely followed by the production of an Auger electron, which must be distinguished because its directionof emission is isotropic.The current version of the GPD has 105k pixels with 50 µ m pitch in a hexagonal pattern. The versionemployed for the measurements reported below was filled and sealed with a mixture composed by 30% heliumand 70% DME at 1 atm, with a gas cell 1 cm thick and the GEM at 400 µ m from the detector. Since the heliumis nearly transparent for photons at a few keV, the DME acts as quencher and absorber of photons.
3. ANALYSIS OF THE PHOTOELECTRIC DIFFERENTIAL CROSS SECTION
The direction of emission of a photoelectron carries memory of the polarization of the absorbed photon, namelythe probability that a photoelectron is emitted in the direction of polarization is modulated with a cos φ term,where φ is the angle between the direction of emission and polarization (see Fig. 2). igure 1. Principle of operation of the GPD. If we consider only the absorption of shells with spherical symmetry, i.e. 1s and 2s, which give the largercontribution to the photoelectric absorption in the working condition of the GPD, the differential cross sectionof the photoelectric effect is: dσd Ω ∝ sin θ cos φ (1 + β cos θ ) , (1)where θ is the angle between the direction of the photon and that of the photoelectron (see again Fig. 2). PhotonIncomingPlane orthogonal to thedirection of incidence φ Plane parallel to detectorConversion Point Polarization z θ PhotoelectronDetector yx x’ y’ Figure 2. Definition of the emission angle of photoelectrons.
The Eq. 1 includes the relativistic correction β cos θ ) , where β is the velocity of the emitted electron inunits of the speed of light. Without this relativistic correction, the photoelectrons are emitted preferentially intothe plane perpendicular to the direction of incidence, with a symmetry between the emission above and belowhis plane. The lack of this symmetry induced by the relativistic correction makes the emission probability higherin the semi-space opposite with respect to the direction of photon. This effect of “forward folding” is shown inFig. 3, where the energy of photoelectrons is 50 keV to stress the relativistic effects. The photons are absorbedin the center of the sphere of unit radius, in the point (0,0,0), and the directions of emission of photoelectronsare traced by the red points which are concentrated in the semi-space z <
0. Note also that the projection of thedirections of emission on the xy plane is not changed by the relativistic effects, namely it still follows a cos φ dependency and no photoelectrons are emitted orthogonally to the direction of polarization. Figure 3. Forward folding due to the relativistic correction to the differential photoelectric cross section. The directionof incidence of the photons is the black continuous line, while the direction of polarization is gray. The photons areabsorbed in the center of the sphere of unit radius, in the point (0,0,0), and the directions of emission of photoelectronsare traced with the red points on the sphere. The projection of the plot on the xy plane is also shown. The red, greenand blue dashed lines are respectively the x , y and z axes. The energy of the photoelectrons was set to 50 keV to showthe relativistic effects more clearly. The modulation of the direction of emission of photoelectrons, as measured by a polarimeter based on thephotoelectric effect like the GPD, can be derived from Eq. 1. At this aim, we must distinguish between theintrinsic modulation M ′ ( φ ′ ), namely the modulation in the reference frame x’y’z’ of the photons (see Fig. 2 andFig. 4(b)), the intrinsic one in the reference of the detector xyz , M ( φ ), and that measured by a polarimeter M ( φ ).If the hypothesis of absorption from only shells with spherical symmetry is satisfied, the modulation M ′ forpolarized photons can be simply derived from Eq. 1 by integrating over angles θ : pol M ′ ( φ ′ ) = dσ ′ dφ ′ ∝ Z π sin θ ′ cos φ ′ (1 + β cos θ ′ ) sin θ ′ dθ ′ ∝ cos φ ′ , (2)where the term sin θ ′ derives from d Ω ′ = sin θ ′ dθ ′ dφ ′ In the same way, if photons are unpolarized, unpol M ′ ( φ ′ ) = dσ ′ dφ ′ ∝ Z π sin θ ′ (1 + β cos θ ′ ) sin θ ′ dθ ′ ∝ . (3)f the photons are incident orthogonally to the detector, the frames of reference x’y’z’ and xyz are identical(see Fig. 2), and hence: M ( φ ) ≡ M ′ ( φ ′ ) . (4)In the hypothesis that the polarimeter has negligible systematic effects, the direction of the emission willbe reconstructed correctly with a probability, which in general depends on energy, identical in every direction.Hence, the modulation M ( φ ) measured by the detector is proportional to the intrinsic one (in the frame ofreference of the detector), plus a constant which takes into account the errors in the process of measurement,i.e. the probability to reconstruct the direction of emission incorrectly: M ( φ ) = M · M ( φ ) + C with (cid:26) pol M ( φ ) = cos φ unpol M ( φ ) = 1 , (5)where M and C are constants. Eq. 5 is the canonic function employed to fit the modulation of the histogram ofthe direction of photoelectrons with an X-ray polarimeter like the GPD.The modulation factor µ , namely the amplitude of the response of the instrument for completely polarizedphotons, can be derived from Eq. 5: µ = max {M} − min {M} max {M} + min {M} = MM + 2 · C , (6)where the last passage is allowed only if the M ( φ ) function is normalized to unity.
4. EXPECTED MODULATION FOR INCLINED PHOTONS
If the GPD is employed as narrow field instrument with an X-ray optics, the photons are incident nearly per-pendicularly to the plane of detector, with an angle determinated by the focusing of the optics but always of theorder of a few degrees. In this case, systematic effects are small and also reduced, even out of the optical axis,since the azimuthal angles are different for each photon and hence different systematic effects sum incoherently(see Fig. 4(a)). Instead, for instruments with large field of view, photons coming from a source are all incidentwith a large and identical inclination.Here we want to explore the systematic effects arising when the inclination angle δ is greater than a fewdegrees, for polarized and unpolarized radiation. We limit ourself to the condition of inclination orthogonal tothe direction of polarization with the following assumptions:1. the direction of polarization is along the x axis;2. the inclination of an angle δ is performed around y axis (see Fig. 4(b)).The function M ( φ ) can be derived with the same procedure presented in Sec. 3, with the important differencethat, in this case, the references x’y’z’ and xyz are not identical. We must first transform the functions: dσ ′ d Ω ′ | pol ∝ sin θ ′ cos φ ′ (1+ β cos θ ′ ) dσ ′ d Ω ′ | unpol ∝ sin θ ′ (1+ β cos θ ′ ) , (7)from the x’y’z’ reference to the xyz one and then perform the integration over θ . Since the relativistic correctionis not easily integrable, we approximated this term at its first order:1(1 + β cos θ ) ≈ − β cos θ. (8) a) direction of incidencePlane orthogonal to the Photon Incident z δ x y Polarization y’ Detector Plane parallel to the detectorConversion point x’ (b)Figure 4. ( a ) Differences between the narrow and the large field of view instruments. ( b ) Angles which define the directionof incidence of photons. Eventually, we obtain: pol M ( φ, δ, β ) = (cid:0) − πβ sin δ cos δ (cid:1) cos φ + (cid:0) cos δ (cid:1) cos φ + (cid:2) π β (cid:0) δ − δ (cid:1)(cid:3) cos φ ++ (cid:0) sin δ (cid:1) ; unpol M ( φ, δ, β ) = (cid:0) πβ sin δ (cid:1) cos φ + (cid:0) − sin δ (cid:1) cos φ + (cid:2) πβ (cid:0) sin δ cos δ − δ (cid:1)(cid:3) cos φ ++ (cid:0) − cos δ (cid:1) . (9)Note that the functions pol M ( φ, δ, β ) and unpol M ( φ, δ, β ) are quite complex, but depend only on theparameters β , δ , namely on the velocity and on the inclination of the photons. Note also that, when δ = 0 ◦ , thefunctions are proportional to the functions reported in Eq. 5, obtained when photons are incident perpendicularlyto the detector.The function pol M ( φ, δ, β ) expresses the presence of a intrinsic constant term in the modulation curve forcompletely polarized and inclined photons, namely a costant contribution not due to the errors of measurement: pol M ( φ = 90 ◦ , δ, β ) = 23 sin δ = 0 if δ = 0 . (10)Moreover, when β = 0 and hence the relativistic correction is introduced, there is an asymmetry between thetwo peaks corresponding to the direction of polarization, which instead are identical when photons are orthogonalto the detector, deriving from the terms proportional to cos φ and cos φ .Inclined systematic effects can be visualized with the projection of the directions of emission of photoelectronsin the xy plane. While for orthogonal photons no photoelectrons tracks are projected in the y direction, namelyin the direction orthogonal to the polarization (see Fig. 3), in case of inclined photons there is emission even inthis direction (see Fig. 5). Moreover, the emission on the left is more probable than that on the right (see againFig. 5) and this induces the asymmetry between the peaks of the modulation cuve. igure 5. The same as Fig. 3, but for photons which are inclined of 30 degrees. Note that in this case there are tracks ofphotoelectrons which are projected along the y axis, namely orthogonally to the direction of polarization. Note also thedifferent intensities of projections on the left and on the right, which indicate a different probability of emission. In the case of unpolarized photons, a spurious modulation appears. In absence of the relativistic correction,this contribution would be of the same form as a polarized signal: unpol M ( φ, δ, β = 0) = (cid:18) −
43 sin δ (cid:19) cos φ + (cid:18) −
23 cos δ (cid:19) . (11)However the presence of the relativistic correction introduces an asymmetry that allows, at least in principle,to distinguish it from the signal of polarized radiation.
5. MEASUREMENT OF THE SYSTEMATIC EFFECTS FOR INCLINEDRADIATION
Muleri et al. presented a facility for the calibration of the next generation X-ray polarimeters, which allows tostudy the response of detectors to inclined, polarized and unpolarized radiation. We then employed this facilityto measure the systematic effects presented in Sec. 4 (see Fig. 6).We employed the 105k pixels, 50 µ m pitch, sealed version of the Gas Pixel Detector, described by Bellazziniet al., and filled with 30% helium and 70% DME mixture. Data were analyzed in the standard way, withoutany data selection in the shape of the tracks.In Fig. 7 we report the modulation measured with the GPD in three different situations, fitted with thestandard cos function: M ( φ ) = M · cos ( φ − φ ) + C. (12)In particular, in Fig. 7(a) we show the response of the instrument to 3.7 keV polarized photons which areincident orthogonally to the detector. The fit is very good, as reported in Table 1, and a modulation factorof about 43% is obtained. Instead in Fig. 7(b) we report the modulation when the same kind of photons, i.e.3.7 keV polarized ones, are incident with an inclination of 40 degrees. In this case the fit is extremely poor, the igure 6. The setup employed to perform the measurements at large angle of inclination. A complete description of thefacility used is presented by Muleri et al. peaks are asymmetric and the modulation factor is by far lower, about 21%. These systematic effects were thoseexpected from the analysis performed in the Sec. 4, i.e. a reduction of the modulation due to a intrinsic constantterm and the asymmetry due to the relativistic correction. Eventually in Fig. 7(c) we report the response ofthe instrument to unpolarized 5.9 keV obtained from a Fe radioactive source, inclined with respect to theperpendicular of the detector of 30 degrees. As expected, in this case a spurious and asymmetric modulation ispresent and it mimics the effect of a polarized beam at the level of a few percent. / ndf χ ±
275 C 2.5 ± ± -0.01535 Phi (rad)-3 -2 -1 0 1 2 30100200300400500 / ndf χ ±
275 C 2.5 ± ± -0.01535 Angular Distribution - iteration 1 (a) / ndf χ ± ± ± -0.02049 Phi (rad)-3 -2 -1 0 1 2 30100200300400500600700 / ndf χ ± ± ± -0.02049 Angular Distribution - iteration 1 (b) / ndf χ ± ± ± Phi (rad)-3 -2 -1 0 1 2 3050100150200250300350 / ndf χ ± ± ± Angular Distribution - iteration 1 (c)Figure 7. Response of the GPD to inclined, polarized and unpolarized radiation, fitted with a standard cos function.( a ) Modulation measured when 3.7 keV polarized photons, produced by means of Bragg diffraction at nearly 45 degrees,are incident orthogonally to the detector. ( b ) Response to the same kind of radiation as ( a ) when the beam is inclined40 degrees with respect to the orthogonal of the detector. ( c ) Modulation measured when 5.9 keV unpolarized photonsare incident with an inclination of 30 degrees. In Fig. 8 we report the same data presented in Fig. 7 but fitted with the functions developed in Sec. 4 (Eq. 9).Since we want to verify the systematic effects derived in Sec. 4, we assumed that the inclination and the velocityof the photoelectrons were known. Hence, we assumed that the shape of the modulation is fixed, and only theolarization Energy (keV) Inclination ( ◦ ) function M C µ χ reduced Pol. 3.7 0 ◦ cos ± ± ◦ cos ± ± ◦ cos ± ± ◦ pol M ± ± ◦ pol M ± ± ◦ unpol M ±
11. 196 ±
15 — 0.93
Table 1. Parameters of the fits shown in the Fig. 7 and in the Fig. 8. normalization is allowed to change. Then, in the case of polarized photons, we employed: pol M ( φ, φ , δ = δ, β = β ) = M · ( − sin δ + πβ (cid:12)(cid:12) sin δ (cid:12)(cid:12) (cid:2) pol M ( φ − φ , δ, β ) (cid:3)) + C, (13)where δ and β are constants. As in the case of Eq. 5, we fitted data with a function which is proportional tothe intrinsic modulation, plus a constant which takes into account the error in the process of measurement. Weintroduced the phase φ and the factor − sin δ + πβ | sin δ | to normalized to unity the function pol M ( φ, δ, β ) sothat we can calculate the modulation factor with the usual formula µ = MM +2 · C .Instead, we employed: unpol M ( φ, φ , δ = δ, β = β ) = M · (cid:8) unpol M ( φ − φ , δ, β ) (cid:9) + C (14)for fitting data for unpolarized radiation. Even in this case the shape of the modulation is fixed and only thenormalization can change.The results of the fits are reported in Table 1. The agreement is quite good for all the measurements done.In particular, taking into account the systematics, we can recover a good modulation factor even at 40 degrees,about 33% against the 43% on axis. Instead the fit with the cos gives a modulation of about 21%, since itdoesn’t take into account that there is a intrinsically unmodulated contribution.Eventually we want also stress that the systematic effects presented are only visible in the unfolded modulationcurve, namely if the directions of photoelectrons are reconstructed on the whole round angle. Indeed, by assumingthat the modulation curve is periodic on 180 degrees, these systematics are confused and often not distinguishablefrom the actual signal. / ndf χ ±
275 C 2.5 ± ± -0.01535 Phi (rad)-3 -2 -1 0 1 2 30100200300400500 / ndf χ ±
275 C 2.5 ± ± -0.01535 Angular Distribution - iteration 1 (a) / ndf χ ±
334 C 5.6 ± ± -0.02281 Phi (rad)-3 -2 -1 0 1 2 30100200300400500600700 / ndf χ ±
334 C 5.6 ± ± -0.02281 Angular Distribution - iteration 1 (b) / ndf χ ± ±
196 Phase 0.0916 ± -0.1118 Phi (rad)-3 -2 -1 0 1 2 3050100150200250300350 / ndf χ ± ±
196 Phase 0.0916 ± -0.1118 Angular Distribution - iteration 1 (c)Figure 8. The same as Fig. 7, but in this case the fits are perfromed with the functions derived in Sec. 4. The parameters β and δ are fixed at their expected values. The results of the fits are reported in Table 1.
6. CONCLUSION
We have presented a feasibility study for testing the possible use of the Gas Pixel Detector as an X-ray photoelec-tric polarimeter with large field of view. Accurately analyzing the differential cross section of the photoelectricbsorption and performing measurements with polarized and unpolarized inclined photons, we have found thatsystematic effects on the measured modulation exist for both polarized and unpolarized radiation when photonsare not incident orthogonally to the detector. For polarized radiation, these systematics induce an intrinsicunmodulated contribution and an asymmetry between the peaks of the modulation curve corresponding to thedirection of polarization. While the former effect arises from the inclination of the photons and tends to reducethe modulation factor, the latter is due to the relativistic correction of the differential photoelectric cross sectionwhich can only be distinguished in the unfolded modulation curve. Instead the systematics in the case of unpo-larized radiation mimic the modulation induced by polarized photons and only a relativistic asymmetry, againvisible only in the unfolded modulation curve, can, in principle, disentangle the two situations.After discussing the systematics arising when polarized or unpolarized inclined beams are incident on thedetector, we have also presented functions to fit the modulation curves and correct the systematic effects. We haveonly restricted the analysis in one of the simplest situation, assuming that the direction of polarization is parallelto the axis of inclination. Even if we can’t today establish the feasibility of photoelectric polarmeter with largefield of view, good results are obtained by assuming that the inclination and the velocity of the photoelectrons areknown. This corresponds to assume that the instrument has both good imaging and spectroscopic capabilities,that is the case of the GPD.
Acknowledgments
FM acknowledges financial support from Agenzia Spaziale Italiana (ASI) under contract ASI I/088/06/0.
REFERENCES [1] Meszaros, P., Novick, R., Szentgyorgyi, A., Chanan, G. A., and Weisskopf, M. C., “Astrophysical implica-tions and observational prospects of X-ray polarimetry,” ApJ , 1056–1067 (1988).[2] Weisskopf, M. C., Elsner, R. F., Hanna, D., Kaspi, V. M., O’Dell, S. L., Pavlov, G. G., and Ramsey,B. D., “The prospects for X-ray polarimetry and its potential use for understanding neutron stars,”
PaperPresented at the 363rd Heraeus Seminar in Bad Honef, Germany. Springer Lecture Notes, submitted (2006).[3] Bellazzini, R., Baldini, L., Bitti, F., Brez, A., Cavalca, F., Latronico, L., Massai, M. M., Omodei, N.,Pinchera, M., Sgr´o, C., Spandre, G., Costa, E., Soffitta, P., Di Persio, G., Feroci, M., Muleri, F., Pacciani,L., Rubini, A., Morelli, E., Matt, G., and Perola, G. C., “A photoelectric polarimeter for XEUS: a newwindow in x-ray sky,” in [
Proc. SPIE ], , 62663Z (2006).[4] Costa, E., Bellazzini, R., Soffitta, P., Muleri, F., Feroci, M., Frutti, M., Mastropietro, M., Pacciani, L.,Rubini, A., Morelli, E., Baldini, L., Bitti, F., Brez, A., Cavalca, F., Latronico, L., Massai, M. M., Omodei,N., Pinchera, M., Sgr´o, C., Spandre, G., Matt, G., Perola, G. C., Chincarini, G., Citterio, O., Tagliaferri,G., Pareschi, G., and Cotroneo, V., “POLARIX: a small mission of x-ray polarimetry,” in [ Proc. SPIE ], , 62660R (2006).[5] Costa, E., Bellazzini, R., Tagliaferri, G., Baldini, L., Basso, S., Bregeon, J., Brez, A., Citterio, O., Cotroneo,V., Frontera, F., Frutti, M., Matt, G., Minuti, M., Muleri, F., Pareschi, G., Perola, G. C., Rubini, A., Sgro,C., Soffitta, P., and Spandre, G., “An x-ray polarimeter for HXMT mission,” in [ Proc. SPIE ], ,66860Z–66860Z–1 (2007).[6] Hill, J. E., Barthelmy, S., Black, J. K., Deines-Jones, P., Jahoda, K., Sakamoto, T., Kaaret, P., McConnell,M. L., Bloser, P. F., Macri, J. R., Legere, J. S., Ryan, J. M., Smith, Jr., B. R., and Zhang, B., “A burstchasing x-ray polarimeter,” in [ Proc. SPIE ], , 66860Y–66860Y–12 (2007).[7] Muleri, F., Un Polarimetro Fotoelettrico per Astronomia a Raggi X , Master’s thesis, Universit`a di Roma“La Sapienza” (2005).[8] Costa, E., Soffitta, P., Bellazzini, R., Brez, A., Lumb, N., and Spandre, G., “An efficient photoelectric X-raypolarimeter for the study of black holes and neutron stars,” Nature , 662–665 (2001).[9] Bellazzini, R., Spandre, G., Minuti, M., Baldini, L., Brez, A., Cavalca, F., Latronico, L., Omodei, N.,Massai, M. M., Sgro’, C., Costa, E., Soffitta, P., Krummenacher, F., and de Oliveira, R., “Direct readingof charge multipliers with a self-triggering CMOS analog chip with 105 k pixels at 50 µ m pitch,” NuclearInstruments and Methods in Physics Research A , 552–562 (2006).10] Bellazzini, R., Spandre, G., Minuti, M., Baldini, L., Brez, A., Latronico, L., Omodei, N., Razzano, M.,Massai, M. M., Pesce-Rollins, M., Sgr´o, C., Costa, E., Soffitta, P., Sipila, H., and Lempinen, E., “A sealedGas Pixel Detector for X-ray astronomy,”
Nuclear Instruments and Methods in Physics Research A ,853–858 (2007).[11] Muleri, F., Soffitta, P., Bellazzini, R., Brez, A., Costa, E., Frutti, M., Mastropietro, M., Morelli, E.,Pinchera, M., Rubini, A., and Spandre, G., “A versatile facility for the calibration of x-ray polarimeterswith polarized radiation,” in [
Proc. SPIE ],7011-84