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X-ray polarimetry with a micropattern TPC
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 581 (2007) 755–760 www.elsevier.com/locate/nima
X-ray polarimetry with a micropattern TPC J.K. Blacka,, R.G. Bakerb, P. Deines-Jonesc, J.E. Hilld,e, K. Jahodac a
Rock Creek Scientific, 1400 East-West Hwy, Suite 807, Silver Spring, MD 20910, USA b Code 660.3, NASA’s Goddard Space Flight Center, Greenbelt, MD 20771, USA c Code 662, NASA’s Goddard Space Flight Center, Greenbelt, MD 20771, USA d Universities Space Research Association, 10211 Wincopin Circle, Columbia, MD 21044, USA e CRESST and NASA’s Goddard Space Flight Center, Greenbelt, MD 20771, USA Received 25 July 2007; accepted 9 August 2007 Available online 19 August 2007
Abstract The micropattern time projection chamber (TPC) offers a novel method of imaging the tracks of photoelectrons as a means of X-ray polarimetry with the potential to simultaneously achieve large modulation factors and high quantum efficiency. Measurements with a simple prototype micropattern TPC polarimeter, with an 18 mm-atm absorption depth of a mixture of 50% neon and 50% dimethyl ether, result in a modulation factor of 45.070.6% with polarized 6.4 keV X-rays. With unpolarized 5.9 keV X-rays, the measured modulation factor is 0.4970.54%, consistent with zero. The geometry of the TPC polarimeter will enable substantial improvements in quantum efficiency without the loss of modulation. r 2007 Elsevier B.V. All rights reserved. PACS: 07.60Fs; 07.85.Fv; 29.40.Gx; 95.55.Ka Keywords: X-ray polarimetry; Particle tracking; GEM; TPC; Pixel readout
1. Introduction Polarization sensitivity depends on both analyzing power and quantum efficiency. The analyzing power is usually described by the modulation factor m, which is the apparent polarization for fully polarized photons, defined as m ¼ ðf max f min Þ=ðf max þ f min Þ where fmax and fmin are the maximum and minimum, respectively, of the measured polarization-dependent angular distribution of the interaction products. For a polarimeter with quantum efficiency e, the sensitivity is pffiffi proportional to m in the background-free limit and proportional to me when background dominates [1]. The photoelectric effect is, in principle, the most sensitive basis for broadband X-ray polarimetry below 100 keV, where photoelectric absorption is the dominant interaction Corresponding author. Tel.: +1 301 286 1231; fax: +1 413 674 5268.
E-mail address: black@rockcreekscientific.com (J.K. Black). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.08.144
mechanism in almost all materials. Not only does the photoelectric effect offer high quantum efficiency, but it is also a powerful polarization analyzer. As a result of the photoionization of an atomic s-orbital, the photoelectron is ejected preferentially in the direction of the electric field of the incident photon with an essentially pure sin2 y cos2 f distribution, where y is the polar angle and f is the polarization-dependent azimuthal angle [2]. This cos2 f dependence gives the photoelectric effect an intrinsically high modulation factor, near unity. The most sensitive photoelectric X-ray polarimeters have been realized with gas-based detectors that determine the photoelectron emission angle by imaging the photoelectron tracks with spatial resolution that is a fraction of the track length. This technique was first demonstrated in 1923 as one of the first applications of the Wilson cloud chamber [3]. Photoelectric polarimeters have been demonstrated in recent years using gas proportional counters with highresolution pixel readout, either optical readout with CCDs of the scintillation light produced [4,5], or direct readout of the charge collected on a pixel anode [6–8].
ARTICLE IN PRESS 756
J.K. Black et al. / Nuclear Instruments and Methods in Physics Research A 581 (2007) 755–760
Pixel proportional counters have achieved unprecedented polarization sensitivity, but still realize only a fraction of the intrinsic sensitivity of the photoelectric effect, since, while they achieve large modulation factors, they do so with modest quantum efficiency. In these detector geometries, the modulation factor and the quantum efficiency are competing quantities, linked by the diffusion of the primary ionization electrons as they drift to the pixel readout. Diffusion degrades the image resolution and the accuracy with which the emission angle can be determined, thus reducing the modulation factor. With the X-rays incident normal to the readout plane, the quantum efficiency increases with the detector absorption depth, while the modulation decreases from increased diffusion, caused by the greater average drift distance. For a given gas and absorption depth, the overall sensitivity peaks at an X-ray energy where the quantum efficiency is typically less than 10% [8]. The micropattern time projection chamber (TPC) offers a technique for forming high-resolution images of photoelectron tracks with a detector geometry in which the diffusion is largely independent of the absorption depth. The TPC could thus more fully realize the potential of photoelectric polarimetry by obtaining both high modulation factors and high quantum efficiency. The following sections will describe the TPC polarimeter concept in more detail and present results from a simple prototype device. 2. The TPC polarimeter concept The TPC polarimeter uses a time projection technique to form two-dimensional images of photoelectron tracks from a one-dimensional strip readout. As illustrated in Fig. 1, the polarimeter consists of a micropattern proportional
counter whose active volume is bound between a drift electrode and a gas multiplication stage. Readout strips beneath the multiplication stage are oriented essentially parallel to the incident X-rays. Each strip is instrumented with a charge-sensitive amplifier and a continuously sampling analog-to-digital converter (ADC). A signal from the cathode of the multiplication stage provides a data acquisition trigger. A voltage applied between the drift electrode and the multiplication stage establishes a uniform drift field in the active volume. Voltages on the multiplication stage and readout strips provide the fields necessary for gas avalanche and charge collection on the strips. Each X-ray absorbed in the active gas volume produces a photoelectron, which ionizes the gas along its trajectory. The ionization electrons drift with a constant velocity to the cathode, where the charge is multiplied and collected on the strips. A track image projected onto a plane normal to the X-ray incidence is formed by digitizing the charge pulse waveforms and binning the data into pixels whose coordinates are defined by strip location in one dimension and arrival time multiplied by the drift velocity in the orthogonal dimension. A 6.4 keV photoelectron track formed in this manner is shown in Fig. 1. In this geometry, the quantum efficiency, as governed by the absorption depth of the detector, is independent of the average electron drift distance, at least to the extent that the incident X-ray beam is collimated. The TPC then offers the possibility of a high modulation broadband X-ray polarimeter with unit quantum efficiency. 3. Prototype TPC polarimeter A prototype TPC polarimeter was constructed from readily available, off-the-shelf components. It consists of a
Fig. 1. Photoelectron track imaging with a micropattern TPC. The digitized waveforms are represented as an image in which the areas of the circles are proportional to the charge deposited. The pixels are on a 130 mm spacing, while the waveforms are sampled with a 40 ns period.
ARTICLE IN PRESS J.K. Black et al. / Nuclear Instruments and Methods in Physics Research A 581 (2007) 755–760
757
of 24 channels, 256 before the trigger, and 256 after the trigger. Reconstructed track images and polarization information are displayed in real time. 4. Experimental configuration
Fig. 2. An exploded view of the multiplication stage used in the TPC polarimeter. The electrode structure is like that of a GEM, but is formed from two etched stainless steel foils separated by a teflon spacer. The opening in the spacer defines the active area.
drift electrode, micropattern multiplication stage, strip readout plane and encoding electronics. The multiplication stage has an electrode structure similar to the gas electron multiplier (GEM) [9], but was assembled with two etched stainless steel meshes that form the cathode and anode, separated by an insulating spacer as shown in Fig. 2. The meshes are approximately 50 mm thick with 75 mm diameter holes on a 150 mm hexagonal spacing [10]. The meshes were electropolished and then mounted on frames under tension with their holes aligned and separated by a 100 mm thick teflon spacer. The active area is defined by a 30 mm 12.7 mm opening in the spacer. The drift electrode was placed 20 mm above the cathode. The readout strips were mounted 0.5 mm beneath the meshes. The strips are on a pitch of 130 mm and were aligned with the mesh holes along one of the 601 symmetry axes of the hexagonal array of holes. The readout plane is a standard printed circuit board with 96 strips, each 30 mm in length, that are grouped into four sets of 24 by connecting every 24th strip together. In this way, 24 electronics channels can read out the 96 strips and photoelectron tracks that cross fewer than 24 strips can be unambiguously reconstructed. This readout scheme can be expanded in both length (detector depth) and width (number of sets of strips). Each channel of readout electronics consists of a charge sensitive preamplifier, a broadband variable gain amplifier, and an ADC. The preamplifier is a commercial chargesensitive device with a gain of 0.8 V/pC, a few ns rise time, and a 25 ms decay time. The variable gain amplifiers have a 150 MHz bandwidth and so present a largely unfiltered preamplifier signal to the ADC. The ADCs are 8-channel, 12-bit, continuously sampling, 50 MHz devices that were operated at 25 MHz in these measurements. Each ADC is read out with a field-programmable gate array, which transfers the data to a host PC via a USB 2.0 interface. The system trigger is taken from a bipolar-shaped cathode signal using a zero-cross timing discriminator. When triggered, the system stores 512 ADC samples from each
The TPC polarimeter was tested in a gas mixture of 50% neon, 50% dimethyl ether (DME) at 460 Torr. The X-ray beam was collimated and entered the active volume in a direction parallel to the readout strips at a height of 4 mm above the multiplication stage. The TPC was mounted on a stage so that it could be rotated around the axis of the X-ray beam. The multiplication stage was operated at an apparent gain of 3000. The energy resolution was typical for proportional counters, about 20% full width at half maximum at 6 keV. The electronics noise in each encoding channel was less than 1000 electrons rms. In order to construct square pixels in the image, the electron drift velocity was set so that the electron drift distance during an ADC sampling period (40 ns) was equal to the readout strip spacing (130 mm). The drift field was initially set to approximately the required 0.33 cm/ms using drift velocities calculated with the Magboltz extension of the Garfield simulation package [11]. Since this prototype did not have an independent means of measuring the drift velocity, unpolarized 5.9 keV X-rays from an 55Fe source were used to make final, few percent level, adjustments to obtain the correct drift field. With an incorrect drift velocity, the track images will be distorted such that a false modulation will occur in unpolarized data at either 01 or 901. Histograms of the reconstructed photoelectron emission angles of unpolarized X-rays were fit to the functional form a cos2 f+b sin2 f and the voltage on the drift electrode was adjusted to equalize the parameters a and b. This technique is valid as long as other sources of asymmetry are negligible, which can be confirmed by observing an equal modulation at 01 and 901 with polarized X-rays once the drift velocity is properly set. Data from nearly 100% polarized iron Ka (6.4 keV) X-rays were taken with the plane of polarization oriented at 01, 451, and 901 with respect to the electron drift direction. The polarized X-rays were produced by Bragg scattering through 901 off a silicon crystal. Unpolarized 5.9 keV data were collected both before and after the polarized data. The entire data set presented here was collected over a 2-h period with typical event rates of 20 Hz for polarized X-rays and 40 Hz for unpolarized. 5. Data analysis and results Images were formed as an array of 24 24 pixels centered on the event barycenter. The response of the charge-sensitive amplifiers is approximately a step function, so that the charge in a time bin, n, was calculated simply as qnvnvn1, where vn is the digitized voltage at time bin n. Strip number and time bin defined the pixel
ARTICLE IN PRESS 758
J.K. Black et al. / Nuclear Instruments and Methods in Physics Research A 581 (2007) 755–760
Fig. 3. The TPC is able to resolve complex photoelectron track trajectories. Shown are photoelectron track images from 6.4 keV X-ray interactions with arrows indicating the reconstructed emission directions. The pixels are on a 130 mm spacing formed from strip location (vertical) and drift time (40 ns/bin, horizontal).
coordinate. Only pixels having charge greater than 2500 electrons, or about 2.5 times the rms noise, were included in the image. Each photoelectron emission angle was estimated from the track image using a two-stage moments analysis [12]. The first iteration estimated the direction from the entire track, while the second iteration refined the estimate by using only the first half of the track, where the initial direction is less obscured by scattering. With proportional counter energy resolution, the X-ray interaction point could be distinguished from the track endpoint, where most of the energy is deposited. The angle f was estimated as the angle of the major axis of the charge distribution of the track, which is the angle that minimizes the second moment, M, of the charge distribution with barycenter coordinates (xb,yb) P q ½ðy yb Þ cos f ðxi xb Þ sin f2 P M¼ i i i i qi P P q xi qy xb ¼ Pi i ; yb ¼ Pi i i q i i i qi where qi is the charge in the pixel with coordinates (xi,yi). In the first iteration, events for which the major and minor
axis could not be distinguished with 95% confidence were rejected (less than 6% of the 6.4 keV events). In the second iteration, the angle was estimated as in the first, but using only the pixels on the side of the barycenter with the lower charge density, as identified by the sign of the third moment. Fig. 3 shows individual 6.4 keV event images with the reconstructed emission directions. Histograms of the emission angles were fit to the expected functional form: N(f) ¼ A+B cos2 (ff0), where f0 is the angle of the plane of polarization with respect to the electron drift direction. The modulation factor is then given by: m ¼ B/(2A+B). The results are shown in Fig. 4 and Table 1. The data fit the functional form and peak at the expected polarization phase angles. All the polarized data sets are consistent with the average modulation of 45.070.6%, while the unpolarized data are consistent with no modulation. 6. Conclusions and future work A simple micropattern TPC made from readily available components has been demonstrated as photoelectric X-ray polarimeter. At 6.4 keV, the measured modulation factor is 45.070.6% that is uniform over polarization phase angles.
ARTICLE IN PRESS J.K. Black et al. / Nuclear Instruments and Methods in Physics Research A 581 (2007) 755–760
759
Fig. 4. Histograms of reconstructed emission angles for unpolarized 5.9 keV photons (upper left), and for polarized 6.4 keV X-rays with polarization phase at 01 (upper right), 451 (lower left), and 901 (lower right) with respect to the TPC drift direction. The lines are the fits to the data. The fit parameters are listed in Table 1.
Table 1 Fit results to the reconstructed emission angles with reduced chi squared values Polarization phase
Unpolarized 01 451 901
Measured parameters Modulation (%)
Phase (degrees)
wn2
0.4970.54 45.071.1 45.371.1 44.771.1
44.6728.7 0.370.6 45.270.6 89.970.6
1.2 1.1 1.0 1.4
The errors stated are one standard deviation.
Unpolarized 5.9 keV X-rays show no false modulation, with a measured modulation of 0.4970.54%. The quantum efficiency of this prototype is only about 6% at 6 keV, but there are no identified features that would prevent a
much deeper and thus more efficient detector from having the same modulation. Significantly more effort will be required to understand the broadband response and ultimate sensitivity that can be achieved with a TPC polarimeter. In addition to statistical limits, systematic errors in a TPC polarimeter may arise from its inherent rotational asymmetry, since the orthogonal coordinates of the track images are measured in fundamentally different ways. Care will be required in both construction and operation to prevent the sensitivity from being ultimately limited by systematic errors. Efforts are currently underway to develop a nextgeneration TPC polarimeter with both greater absorption depth and finer pixel pitch, which will be tested over a range of X-ray energies. This polarimeter will also include a system for direct, in situ measurements of electron drift velocity and spatial response to control systematic errors.
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Acknowledgments This work was funded in part by NASA contract number NNG05EC04C. We would like to thank Richard Koenecke, Ken Simms and Norman Dobson of the Astrophysics Science Division at the Goddard Space Flight Center for their skilled assembly of this detector. References [1] R. Novick, in: T. Gehrels (Ed.), Planets, Stars and Nebulae Studied with Photopolarimetry, University of Arizona Press, 1972, p. 262.
[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
J.W. Cooper, Phys. Rev. A 47 (1993) 1841. C.T.R. Wilson, Roy. Soc. Proc. A 85 (1923) 1. A.A. Austin, B.D. Ramsey, Opt. Eng. 32 (1993) 1990. H. Sakurai, et al., Nucl. Instr. and Meth. A 525 (2004) 6. E. Costa, P. Soffitta, R. Bellazzini, A. Brez, N. Lumb, G. Spande, Nature 411 (2001) 662. J.K. Black, et al., Nucl. Instr. and Meth. A 513 (2003) 639. R. Bellazzini, et al., Nucl. Instr. and Meth. A 566 (2006) 552. F. Sauli, Nucl. Instr. and Meth. A 522 (2004) 93. Internet Inc., Micro-etch Stainless Steel Screen, part number BE 0201. S. Biagi, Nucl. Instr. and Meth. A 421 (1999) 234. R. Bellazzini, et al., Proc. SPIE 4843 (2003) 383.
Nuclear Instruments and Methods in Physics Research A 581 (2007) 755–760 www.elsevier.com/locate/nima
X-ray polarimetry with a micropattern TPC J.K. Blacka,, R.G. Bakerb, P. Deines-Jonesc, J.E. Hilld,e, K. Jahodac a
Rock Creek Scientific, 1400 East-West Hwy, Suite 807, Silver Spring, MD 20910, USA b Code 660.3, NASA’s Goddard Space Flight Center, Greenbelt, MD 20771, USA c Code 662, NASA’s Goddard Space Flight Center, Greenbelt, MD 20771, USA d Universities Space Research Association, 10211 Wincopin Circle, Columbia, MD 21044, USA e CRESST and NASA’s Goddard Space Flight Center, Greenbelt, MD 20771, USA Received 25 July 2007; accepted 9 August 2007 Available online 19 August 2007
Abstract The micropattern time projection chamber (TPC) offers a novel method of imaging the tracks of photoelectrons as a means of X-ray polarimetry with the potential to simultaneously achieve large modulation factors and high quantum efficiency. Measurements with a simple prototype micropattern TPC polarimeter, with an 18 mm-atm absorption depth of a mixture of 50% neon and 50% dimethyl ether, result in a modulation factor of 45.070.6% with polarized 6.4 keV X-rays. With unpolarized 5.9 keV X-rays, the measured modulation factor is 0.4970.54%, consistent with zero. The geometry of the TPC polarimeter will enable substantial improvements in quantum efficiency without the loss of modulation. r 2007 Elsevier B.V. All rights reserved. PACS: 07.60Fs; 07.85.Fv; 29.40.Gx; 95.55.Ka Keywords: X-ray polarimetry; Particle tracking; GEM; TPC; Pixel readout
1. Introduction Polarization sensitivity depends on both analyzing power and quantum efficiency. The analyzing power is usually described by the modulation factor m, which is the apparent polarization for fully polarized photons, defined as m ¼ ðf max f min Þ=ðf max þ f min Þ where fmax and fmin are the maximum and minimum, respectively, of the measured polarization-dependent angular distribution of the interaction products. For a polarimeter with quantum efficiency e, the sensitivity is pffiffi proportional to m in the background-free limit and proportional to me when background dominates [1]. The photoelectric effect is, in principle, the most sensitive basis for broadband X-ray polarimetry below 100 keV, where photoelectric absorption is the dominant interaction Corresponding author. Tel.: +1 301 286 1231; fax: +1 413 674 5268.
E-mail address: black@rockcreekscientific.com (J.K. Black). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.08.144
mechanism in almost all materials. Not only does the photoelectric effect offer high quantum efficiency, but it is also a powerful polarization analyzer. As a result of the photoionization of an atomic s-orbital, the photoelectron is ejected preferentially in the direction of the electric field of the incident photon with an essentially pure sin2 y cos2 f distribution, where y is the polar angle and f is the polarization-dependent azimuthal angle [2]. This cos2 f dependence gives the photoelectric effect an intrinsically high modulation factor, near unity. The most sensitive photoelectric X-ray polarimeters have been realized with gas-based detectors that determine the photoelectron emission angle by imaging the photoelectron tracks with spatial resolution that is a fraction of the track length. This technique was first demonstrated in 1923 as one of the first applications of the Wilson cloud chamber [3]. Photoelectric polarimeters have been demonstrated in recent years using gas proportional counters with highresolution pixel readout, either optical readout with CCDs of the scintillation light produced [4,5], or direct readout of the charge collected on a pixel anode [6–8].
ARTICLE IN PRESS 756
J.K. Black et al. / Nuclear Instruments and Methods in Physics Research A 581 (2007) 755–760
Pixel proportional counters have achieved unprecedented polarization sensitivity, but still realize only a fraction of the intrinsic sensitivity of the photoelectric effect, since, while they achieve large modulation factors, they do so with modest quantum efficiency. In these detector geometries, the modulation factor and the quantum efficiency are competing quantities, linked by the diffusion of the primary ionization electrons as they drift to the pixel readout. Diffusion degrades the image resolution and the accuracy with which the emission angle can be determined, thus reducing the modulation factor. With the X-rays incident normal to the readout plane, the quantum efficiency increases with the detector absorption depth, while the modulation decreases from increased diffusion, caused by the greater average drift distance. For a given gas and absorption depth, the overall sensitivity peaks at an X-ray energy where the quantum efficiency is typically less than 10% [8]. The micropattern time projection chamber (TPC) offers a technique for forming high-resolution images of photoelectron tracks with a detector geometry in which the diffusion is largely independent of the absorption depth. The TPC could thus more fully realize the potential of photoelectric polarimetry by obtaining both high modulation factors and high quantum efficiency. The following sections will describe the TPC polarimeter concept in more detail and present results from a simple prototype device. 2. The TPC polarimeter concept The TPC polarimeter uses a time projection technique to form two-dimensional images of photoelectron tracks from a one-dimensional strip readout. As illustrated in Fig. 1, the polarimeter consists of a micropattern proportional
counter whose active volume is bound between a drift electrode and a gas multiplication stage. Readout strips beneath the multiplication stage are oriented essentially parallel to the incident X-rays. Each strip is instrumented with a charge-sensitive amplifier and a continuously sampling analog-to-digital converter (ADC). A signal from the cathode of the multiplication stage provides a data acquisition trigger. A voltage applied between the drift electrode and the multiplication stage establishes a uniform drift field in the active volume. Voltages on the multiplication stage and readout strips provide the fields necessary for gas avalanche and charge collection on the strips. Each X-ray absorbed in the active gas volume produces a photoelectron, which ionizes the gas along its trajectory. The ionization electrons drift with a constant velocity to the cathode, where the charge is multiplied and collected on the strips. A track image projected onto a plane normal to the X-ray incidence is formed by digitizing the charge pulse waveforms and binning the data into pixels whose coordinates are defined by strip location in one dimension and arrival time multiplied by the drift velocity in the orthogonal dimension. A 6.4 keV photoelectron track formed in this manner is shown in Fig. 1. In this geometry, the quantum efficiency, as governed by the absorption depth of the detector, is independent of the average electron drift distance, at least to the extent that the incident X-ray beam is collimated. The TPC then offers the possibility of a high modulation broadband X-ray polarimeter with unit quantum efficiency. 3. Prototype TPC polarimeter A prototype TPC polarimeter was constructed from readily available, off-the-shelf components. It consists of a
Fig. 1. Photoelectron track imaging with a micropattern TPC. The digitized waveforms are represented as an image in which the areas of the circles are proportional to the charge deposited. The pixels are on a 130 mm spacing, while the waveforms are sampled with a 40 ns period.
ARTICLE IN PRESS J.K. Black et al. / Nuclear Instruments and Methods in Physics Research A 581 (2007) 755–760
757
of 24 channels, 256 before the trigger, and 256 after the trigger. Reconstructed track images and polarization information are displayed in real time. 4. Experimental configuration
Fig. 2. An exploded view of the multiplication stage used in the TPC polarimeter. The electrode structure is like that of a GEM, but is formed from two etched stainless steel foils separated by a teflon spacer. The opening in the spacer defines the active area.
drift electrode, micropattern multiplication stage, strip readout plane and encoding electronics. The multiplication stage has an electrode structure similar to the gas electron multiplier (GEM) [9], but was assembled with two etched stainless steel meshes that form the cathode and anode, separated by an insulating spacer as shown in Fig. 2. The meshes are approximately 50 mm thick with 75 mm diameter holes on a 150 mm hexagonal spacing [10]. The meshes were electropolished and then mounted on frames under tension with their holes aligned and separated by a 100 mm thick teflon spacer. The active area is defined by a 30 mm 12.7 mm opening in the spacer. The drift electrode was placed 20 mm above the cathode. The readout strips were mounted 0.5 mm beneath the meshes. The strips are on a pitch of 130 mm and were aligned with the mesh holes along one of the 601 symmetry axes of the hexagonal array of holes. The readout plane is a standard printed circuit board with 96 strips, each 30 mm in length, that are grouped into four sets of 24 by connecting every 24th strip together. In this way, 24 electronics channels can read out the 96 strips and photoelectron tracks that cross fewer than 24 strips can be unambiguously reconstructed. This readout scheme can be expanded in both length (detector depth) and width (number of sets of strips). Each channel of readout electronics consists of a charge sensitive preamplifier, a broadband variable gain amplifier, and an ADC. The preamplifier is a commercial chargesensitive device with a gain of 0.8 V/pC, a few ns rise time, and a 25 ms decay time. The variable gain amplifiers have a 150 MHz bandwidth and so present a largely unfiltered preamplifier signal to the ADC. The ADCs are 8-channel, 12-bit, continuously sampling, 50 MHz devices that were operated at 25 MHz in these measurements. Each ADC is read out with a field-programmable gate array, which transfers the data to a host PC via a USB 2.0 interface. The system trigger is taken from a bipolar-shaped cathode signal using a zero-cross timing discriminator. When triggered, the system stores 512 ADC samples from each
The TPC polarimeter was tested in a gas mixture of 50% neon, 50% dimethyl ether (DME) at 460 Torr. The X-ray beam was collimated and entered the active volume in a direction parallel to the readout strips at a height of 4 mm above the multiplication stage. The TPC was mounted on a stage so that it could be rotated around the axis of the X-ray beam. The multiplication stage was operated at an apparent gain of 3000. The energy resolution was typical for proportional counters, about 20% full width at half maximum at 6 keV. The electronics noise in each encoding channel was less than 1000 electrons rms. In order to construct square pixels in the image, the electron drift velocity was set so that the electron drift distance during an ADC sampling period (40 ns) was equal to the readout strip spacing (130 mm). The drift field was initially set to approximately the required 0.33 cm/ms using drift velocities calculated with the Magboltz extension of the Garfield simulation package [11]. Since this prototype did not have an independent means of measuring the drift velocity, unpolarized 5.9 keV X-rays from an 55Fe source were used to make final, few percent level, adjustments to obtain the correct drift field. With an incorrect drift velocity, the track images will be distorted such that a false modulation will occur in unpolarized data at either 01 or 901. Histograms of the reconstructed photoelectron emission angles of unpolarized X-rays were fit to the functional form a cos2 f+b sin2 f and the voltage on the drift electrode was adjusted to equalize the parameters a and b. This technique is valid as long as other sources of asymmetry are negligible, which can be confirmed by observing an equal modulation at 01 and 901 with polarized X-rays once the drift velocity is properly set. Data from nearly 100% polarized iron Ka (6.4 keV) X-rays were taken with the plane of polarization oriented at 01, 451, and 901 with respect to the electron drift direction. The polarized X-rays were produced by Bragg scattering through 901 off a silicon crystal. Unpolarized 5.9 keV data were collected both before and after the polarized data. The entire data set presented here was collected over a 2-h period with typical event rates of 20 Hz for polarized X-rays and 40 Hz for unpolarized. 5. Data analysis and results Images were formed as an array of 24 24 pixels centered on the event barycenter. The response of the charge-sensitive amplifiers is approximately a step function, so that the charge in a time bin, n, was calculated simply as qnvnvn1, where vn is the digitized voltage at time bin n. Strip number and time bin defined the pixel
ARTICLE IN PRESS 758
J.K. Black et al. / Nuclear Instruments and Methods in Physics Research A 581 (2007) 755–760
Fig. 3. The TPC is able to resolve complex photoelectron track trajectories. Shown are photoelectron track images from 6.4 keV X-ray interactions with arrows indicating the reconstructed emission directions. The pixels are on a 130 mm spacing formed from strip location (vertical) and drift time (40 ns/bin, horizontal).
coordinate. Only pixels having charge greater than 2500 electrons, or about 2.5 times the rms noise, were included in the image. Each photoelectron emission angle was estimated from the track image using a two-stage moments analysis [12]. The first iteration estimated the direction from the entire track, while the second iteration refined the estimate by using only the first half of the track, where the initial direction is less obscured by scattering. With proportional counter energy resolution, the X-ray interaction point could be distinguished from the track endpoint, where most of the energy is deposited. The angle f was estimated as the angle of the major axis of the charge distribution of the track, which is the angle that minimizes the second moment, M, of the charge distribution with barycenter coordinates (xb,yb) P q ½ðy yb Þ cos f ðxi xb Þ sin f2 P M¼ i i i i qi P P q xi qy xb ¼ Pi i ; yb ¼ Pi i i q i i i qi where qi is the charge in the pixel with coordinates (xi,yi). In the first iteration, events for which the major and minor
axis could not be distinguished with 95% confidence were rejected (less than 6% of the 6.4 keV events). In the second iteration, the angle was estimated as in the first, but using only the pixels on the side of the barycenter with the lower charge density, as identified by the sign of the third moment. Fig. 3 shows individual 6.4 keV event images with the reconstructed emission directions. Histograms of the emission angles were fit to the expected functional form: N(f) ¼ A+B cos2 (ff0), where f0 is the angle of the plane of polarization with respect to the electron drift direction. The modulation factor is then given by: m ¼ B/(2A+B). The results are shown in Fig. 4 and Table 1. The data fit the functional form and peak at the expected polarization phase angles. All the polarized data sets are consistent with the average modulation of 45.070.6%, while the unpolarized data are consistent with no modulation. 6. Conclusions and future work A simple micropattern TPC made from readily available components has been demonstrated as photoelectric X-ray polarimeter. At 6.4 keV, the measured modulation factor is 45.070.6% that is uniform over polarization phase angles.
ARTICLE IN PRESS J.K. Black et al. / Nuclear Instruments and Methods in Physics Research A 581 (2007) 755–760
759
Fig. 4. Histograms of reconstructed emission angles for unpolarized 5.9 keV photons (upper left), and for polarized 6.4 keV X-rays with polarization phase at 01 (upper right), 451 (lower left), and 901 (lower right) with respect to the TPC drift direction. The lines are the fits to the data. The fit parameters are listed in Table 1.
Table 1 Fit results to the reconstructed emission angles with reduced chi squared values Polarization phase
Unpolarized 01 451 901
Measured parameters Modulation (%)
Phase (degrees)
wn2
0.4970.54 45.071.1 45.371.1 44.771.1
44.6728.7 0.370.6 45.270.6 89.970.6
1.2 1.1 1.0 1.4
The errors stated are one standard deviation.
Unpolarized 5.9 keV X-rays show no false modulation, with a measured modulation of 0.4970.54%. The quantum efficiency of this prototype is only about 6% at 6 keV, but there are no identified features that would prevent a
much deeper and thus more efficient detector from having the same modulation. Significantly more effort will be required to understand the broadband response and ultimate sensitivity that can be achieved with a TPC polarimeter. In addition to statistical limits, systematic errors in a TPC polarimeter may arise from its inherent rotational asymmetry, since the orthogonal coordinates of the track images are measured in fundamentally different ways. Care will be required in both construction and operation to prevent the sensitivity from being ultimately limited by systematic errors. Efforts are currently underway to develop a nextgeneration TPC polarimeter with both greater absorption depth and finer pixel pitch, which will be tested over a range of X-ray energies. This polarimeter will also include a system for direct, in situ measurements of electron drift velocity and spatial response to control systematic errors.
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J.K. Black et al. / Nuclear Instruments and Methods in Physics Research A 581 (2007) 755–760
Acknowledgments This work was funded in part by NASA contract number NNG05EC04C. We would like to thank Richard Koenecke, Ken Simms and Norman Dobson of the Astrophysics Science Division at the Goddard Space Flight Center for their skilled assembly of this detector. References [1] R. Novick, in: T. Gehrels (Ed.), Planets, Stars and Nebulae Studied with Photopolarimetry, University of Arizona Press, 1972, p. 262.
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