- Email: [email protected]
Compton imager based on a single planar segmented HPGe detector
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 580 (2007) 1075–1078 www.elsevier.com/locate/nima
Compton imager based on a single planar segmented HPGe detector A. Khaplanov, J. Pettersson, B. Cederwall Department of Physics, Royal Institute of Technology, AlbaNova University Center, Roslagstullsbacken 21, SE-106 91 Stockholm, Sweden Available online 1 July 2007
Abstract A collimator-free Compton imaging system has been developed based on a single high-purity germanium detector and used to generate images of radioactive sources emitting g rays. The detector has a planar crystal with one pixellated contact with a total of 25 segments. Pulse shape analysis has been applied to achieve a 3D-position sensitivity of the detector. The first imaging results from this detector are presented, based on the reconstruction of events where a g ray is fully absorbed after scattering between adjacent segments. r 2007 Elsevier B.V. All rights reserved. PACS: 29.40.Gx; 29.85.+c; 87.59.e Keywords: Compton imaging; Gamma-ray imaging; Segmented planar germanium detector; Pulse shape analysis
1. Introduction
2. Experimental set-up
In recent years, 3D-position sensitivity has been achieved in large-volume HPGe detectors using 2D-segmentation of the external electric contacts and pulse shape analysis (PSA) methods. The position sensitivity that has been achieved is typically an order of magnitude smaller than the typical dimensions of the contact segments, below 1 mm for singleinteraction events [1,2]. If the total g-ray energy is collected in the detector and at least two scattering points are present (including the final photo-effect point), the Compton scattering formula may be used to determine a cone of possible directions to the source. In the case of an incomplete energy collection, the first three scattering points are required [3]. A combination of many such cones is used to create an image of the source. This opens up the new possibility of building a g-ray imaging system that combines the excellent energy resolution of HPGe detectors with the high efficiency of a collimator-free Compton imaging system. New applications in medical imaging, environmental monitoring, national security and nuclear safeguards can be developed.
The detector system used in this work is based on a planar segmented HPGe detector manufactured by Canberra Eurisys. The germanium crystal has a 50 50 21 mm sensitive volume. The cathode contact is divided into 251-cm2 segments that are read out with individual charge-sensitive preamplifiers. The anode contact is not segmented. The detector signals were collected by a VMEbased data acquisition system developed by Struck Innovative Systems [4]. The signals were read out synchronously with 14-bit resolution at 100 MHz sampling frequency for all 25 segments. In order to demonstrate the imaging capabilities of the segmented detector, data were collected for events where the central segment triggered in coincidence with any of its eight neighbors. This ensured that none of the hit segments was at the edge of the detector and hence a full set of transient signals was available for both hit segments for all events. Fig. 1 shows the two types of events that were used. A 137 Cs source emitting 662 keV g rays was placed 90 cm away from the detector at two positions—one along the normal to the segmented face of the detector and one at a 45 angle to it.
Corresponding author.
E-mail address: [email protected] (A. Khaplanov). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.06.065
ARTICLE IN PRESS 1076
A. Khaplanov et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 1075–1078
Fig. 1. The two cases of 2-segment events considered in this work. The segments treated by PSA for each case are shown, the triggered segments are shaded.
3. Pulse shape analysis A g ray interacting with the detector material through either Compton scattering or a photo absorption liberates a cloud of charge carriers (electrons and holes). The electric field causes these charges to drift towards the electric contacts on the surface of the detector. While in motion, the charge carriers induce a varying image charge on the contacts (a so-called net charge signal at the contact that will eventually collect the charge and transient charge signals at the other contacts in its vicinity), and it is this effect that assigns a unique signature to an interaction depending on its location. In order to determine the photon interaction locations, PSA based on the matrix method [5] developed at IPNOrsay was used. In this method, an experimental pulse S is decomposed into a linear combination of basis pulses for a set of grid points throughout the detector. These basis pulses may be computed or measured using a scanning setup. If mi is a vector containing basis charge pulses from hit segments and the corresponding transient pulses for their neighbors (a so-called meta-pulse), and the matrix M is the collection of mi for all grid points, an experimental signal S can be represented as S ¼ m1 x1 þ m2 x2 þ þ mn xn ¼ Mx
(1)
where xi is the energy contribution from each basis grid point. Eq. (1) is solved in the least-square sense with a nonnegativity constraint. A further constraint is that most energies are equal to zero. This was solved using the function lsqnonneg in Matlab [6], based on the nonnegative least square algorithm [7]. It is crucial for the success of this method that the experimental and basis pulses are correctly matched in time. Due to the large variation in the pulse shapes, normal constant fraction timing was insufficient. However, the planar geometry proves to be helpful in this case. The weighting potential for a non-segmented contact for an ideal planar detector would vary linearly along the direction perpendicular to the contact. This means that the induced charge on such a contact will also vary linearly as a function of time if the preamplifier response is neglected and the charge velocity is assumed to be constant. For a pixellated electrode, the induced charge is partitioned between the segments. With this in mind, timing of the sampled detector signals was determined by applying a constant fraction algorithm to the sum of the
pulses from all segments for each event. The calculated pulses were then re-sampled to match the measured ones. In this work, the basis signals were calculated for the relevant detector geometry using the weighting field method [8]. The basis pulses were generated on a 2 mm grid, resulting in 250 basis meta-pulses per segment. The validity of the calculated pulses was verified by measuring pulses from collimated 662 keV photons scattered at 900 . This method is commonly used for scanning germanium detectors and is described in Ref. [2]. The measured pulses were found to match the calculated ones to within the uncertainty of the interaction point location, which is limited by the size of the collimators. As mentioned above, we here report on imaging results obtained from selected events where two neighboring segments trigger in coincidence. The basis pulses for the interaction points in the two triggered segments and their neighbors were combined, resulting in a total of 12 pulses in the case of two adjacent segments and 14 pulses in the 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 1
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Fig. 3. Interaction positions and energy deposits assigned (indicated by the area of the dots) returned by the PSA.
ARTICLE IN PRESS A. Khaplanov et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 1075–1078
case of diagonal neighbors, as seen in Fig. 1. In Fig. 2 a measured meta-signal is shown together with the fitted one, and in Fig. 3, the positions that have contributed to this fit are marked with dots inside a sketch of the detector. The area of each dot is proportional to the assigned deposited energy.
In this first attempt to use the detector as a Compton imaging device, some simplifications have been made. Events with more than one interaction inside a segment were treated as single-interaction events. The new position is the weighted average of all positions returned by the PSA, and the energy is the total energy deposited in that segment. Thus all events were treated as one Compton scatter point and a photo absorption point in a neighboring segment. GEANT simulations have shown that this assumption is correct in 28% of the 2-segment events at 662 keV. Furthermore, 2-segment events constitute 43% of all photo-peak events. Simulations have also shown that the segment that contains the larger energy deposit is the one where the first Compton scattering takes place in 80% of the events at this g-ray energy. Accordingly, the larger of the two energy deposits was assumed to be the scattering point in image reconstruction, provided that the Compton scattering formula is fulfilled. The combination of all hits within one segment into a single effective interaction limits the attainable angular resolution of the image. Furthermore, an uncertainty due to the Compton profile of germanium [10] sets a physical limit on the achievable angular resolution, as the relation between the scattering angle and energy is not exact. This is true for any Compton camera (without tracking of Compton electrons). The results of the simulations are shown in Fig. 4a, b for the source positions corresponding to the two measurements. Identical analysis and image reconstruction methods were used for both the simulated and measured data, i.e., 2-segment events were selected and the interactions were treated as single hits in each segment. A 2 keV (FWHM) energy resolution was applied to the simulated interactions. The simulated position uncertainty was varied to produce images with the same angular resolution as the measurement. This yielded a position uncertainty of 1.5 mm (std. dev.). The larger energy deposit was chosen as the first hit in the same way as for the measured data. In Fig. 4c, d, the result of the measurement with a 137 Cs source is shown. The image clearly differentiates between the two source positions. The angular resolution, measured as the FWHM of the spot, is approximately 30 . The overall efficiency, expressed as the fraction of the 662 keV photons that are imaged out of those emitted into the solid angle of the segments used in this measurement is 5.6%. It has been shown in Ref. [11] that imaging using a segmented coaxial HPGe detector where non-neighboring segments are used can provide a significantly better angular resolution. This type of event, however, contributes with an efficiency that is an order of magnitude lower. The
angle θ (degrees)
4. Image reconstruction
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difference in resolution is expected due to the fact that the definition of the cone axis is more sensitive to the position uncertainty when the interaction points are close to each other. For the planar detector used in this study it was found from the simulation that image reconstruction where the hit segments are required to be separated by one segment enhances the angular resolution of the image by a factor of 2.3 while lowering the efficiency by a factor of 3.5. In other words, a significantly higher angular resolution can be achieved at the expense of imaging efficiency. Furthermore, combining the different coincidence criteria will both increase the efficiency as well as the angular resolution compared to the data used in this work. 5. Summary This first attempt to use a single planar pixellated germanium detector as a Compton imager has yielded images of a g-ray emitting radioactive source. PSA based on a least square fit between the measured detector signals and linear combinations of calculated basis pulses proved to be capable of resolving g-ray interaction points in adjacent segments. Images generated using filtered cone back-projection had an angular resolution (FWHM) of 30 with an imaging efficiency of 5.6%. There is a clear tradeoff between the angular resolution and efficiency. This suggests that an appropriate operating mode for a given application may be chosen by setting the coincidence condition and thus requiring a given separation between the first two interaction points for those events that would be used for imaging. The work continues towards resolving multiple interactions in an arbitrary combination of segments and the inclusion of more sophisticated tracking
ARTICLE IN PRESS 1078
A. Khaplanov et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 1075–1078
algorithms in order to improve both the efficiency and the angular resolution. Acknowledgments Enlightening discussions with I.-Y. Lee, P. De´sesquelles and A. Olariu are gratefully acknowledged. We would also like to thank T. Ha¨upke, M. Kirsch and S. Simonsen for making the data acquisition system operational. This work was supported by the Go¨ran Gustafsson Foundation, the Swedish Research Council and the European Commission under contract no. 506065.
References [1] K. Vetter, et al., Nucl. Instr. and Meth. A 452 (2000) 223. [2] L. Milechina, B. Cederwall, Nucl. Instr. and Meth. A 55 (2005) 278. [3] J.D. Kurfess, et al., Nucl. Instr. and Meth. A 505 (2003) 256. [4] hhttp://www.struck.dei. [5] A. Olariu, et al., IEEE Trans. Nucl. Sci. NS53 (3) (2006) 1028. [6] hhttp://www.mathworks.comi. [7] C.L. Lawson, R.J. Hanson (Eds.), Solving Least Square Problems, SIAM, Philadelphia, PA, 1995. [8] Zhong He, Nucl. Instr. Meth. A 463 (2001) 250. [10] D. Brusa, et al., Nucl. Instr. and Meth. A 379 (1996) 167. [11] T. Niedermayr, et al., Nucl. Instr. and Meth. A 553 (2005) 501.
Nuclear Instruments and Methods in Physics Research A 580 (2007) 1075–1078 www.elsevier.com/locate/nima
Compton imager based on a single planar segmented HPGe detector A. Khaplanov, J. Pettersson, B. Cederwall Department of Physics, Royal Institute of Technology, AlbaNova University Center, Roslagstullsbacken 21, SE-106 91 Stockholm, Sweden Available online 1 July 2007
Abstract A collimator-free Compton imaging system has been developed based on a single high-purity germanium detector and used to generate images of radioactive sources emitting g rays. The detector has a planar crystal with one pixellated contact with a total of 25 segments. Pulse shape analysis has been applied to achieve a 3D-position sensitivity of the detector. The first imaging results from this detector are presented, based on the reconstruction of events where a g ray is fully absorbed after scattering between adjacent segments. r 2007 Elsevier B.V. All rights reserved. PACS: 29.40.Gx; 29.85.+c; 87.59.e Keywords: Compton imaging; Gamma-ray imaging; Segmented planar germanium detector; Pulse shape analysis
1. Introduction
2. Experimental set-up
In recent years, 3D-position sensitivity has been achieved in large-volume HPGe detectors using 2D-segmentation of the external electric contacts and pulse shape analysis (PSA) methods. The position sensitivity that has been achieved is typically an order of magnitude smaller than the typical dimensions of the contact segments, below 1 mm for singleinteraction events [1,2]. If the total g-ray energy is collected in the detector and at least two scattering points are present (including the final photo-effect point), the Compton scattering formula may be used to determine a cone of possible directions to the source. In the case of an incomplete energy collection, the first three scattering points are required [3]. A combination of many such cones is used to create an image of the source. This opens up the new possibility of building a g-ray imaging system that combines the excellent energy resolution of HPGe detectors with the high efficiency of a collimator-free Compton imaging system. New applications in medical imaging, environmental monitoring, national security and nuclear safeguards can be developed.
The detector system used in this work is based on a planar segmented HPGe detector manufactured by Canberra Eurisys. The germanium crystal has a 50 50 21 mm sensitive volume. The cathode contact is divided into 251-cm2 segments that are read out with individual charge-sensitive preamplifiers. The anode contact is not segmented. The detector signals were collected by a VMEbased data acquisition system developed by Struck Innovative Systems [4]. The signals were read out synchronously with 14-bit resolution at 100 MHz sampling frequency for all 25 segments. In order to demonstrate the imaging capabilities of the segmented detector, data were collected for events where the central segment triggered in coincidence with any of its eight neighbors. This ensured that none of the hit segments was at the edge of the detector and hence a full set of transient signals was available for both hit segments for all events. Fig. 1 shows the two types of events that were used. A 137 Cs source emitting 662 keV g rays was placed 90 cm away from the detector at two positions—one along the normal to the segmented face of the detector and one at a 45 angle to it.
Corresponding author.
E-mail address: [email protected] (A. Khaplanov). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.06.065
ARTICLE IN PRESS 1076
A. Khaplanov et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 1075–1078
Fig. 1. The two cases of 2-segment events considered in this work. The segments treated by PSA for each case are shown, the triggered segments are shaded.
3. Pulse shape analysis A g ray interacting with the detector material through either Compton scattering or a photo absorption liberates a cloud of charge carriers (electrons and holes). The electric field causes these charges to drift towards the electric contacts on the surface of the detector. While in motion, the charge carriers induce a varying image charge on the contacts (a so-called net charge signal at the contact that will eventually collect the charge and transient charge signals at the other contacts in its vicinity), and it is this effect that assigns a unique signature to an interaction depending on its location. In order to determine the photon interaction locations, PSA based on the matrix method [5] developed at IPNOrsay was used. In this method, an experimental pulse S is decomposed into a linear combination of basis pulses for a set of grid points throughout the detector. These basis pulses may be computed or measured using a scanning setup. If mi is a vector containing basis charge pulses from hit segments and the corresponding transient pulses for their neighbors (a so-called meta-pulse), and the matrix M is the collection of mi for all grid points, an experimental signal S can be represented as S ¼ m1 x1 þ m2 x2 þ þ mn xn ¼ Mx
(1)
where xi is the energy contribution from each basis grid point. Eq. (1) is solved in the least-square sense with a nonnegativity constraint. A further constraint is that most energies are equal to zero. This was solved using the function lsqnonneg in Matlab [6], based on the nonnegative least square algorithm [7]. It is crucial for the success of this method that the experimental and basis pulses are correctly matched in time. Due to the large variation in the pulse shapes, normal constant fraction timing was insufficient. However, the planar geometry proves to be helpful in this case. The weighting potential for a non-segmented contact for an ideal planar detector would vary linearly along the direction perpendicular to the contact. This means that the induced charge on such a contact will also vary linearly as a function of time if the preamplifier response is neglected and the charge velocity is assumed to be constant. For a pixellated electrode, the induced charge is partitioned between the segments. With this in mind, timing of the sampled detector signals was determined by applying a constant fraction algorithm to the sum of the
pulses from all segments for each event. The calculated pulses were then re-sampled to match the measured ones. In this work, the basis signals were calculated for the relevant detector geometry using the weighting field method [8]. The basis pulses were generated on a 2 mm grid, resulting in 250 basis meta-pulses per segment. The validity of the calculated pulses was verified by measuring pulses from collimated 662 keV photons scattered at 900 . This method is commonly used for scanning germanium detectors and is described in Ref. [2]. The measured pulses were found to match the calculated ones to within the uncertainty of the interaction point location, which is limited by the size of the collimators. As mentioned above, we here report on imaging results obtained from selected events where two neighboring segments trigger in coincidence. The basis pulses for the interaction points in the two triggered segments and their neighbors were combined, resulting in a total of 12 pulses in the case of two adjacent segments and 14 pulses in the 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 1
2
3
4
5
6
7
8
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10 11 12 13 14
Segment number Fig. 2. A fit to a measured event. The pulses from the segments considered are plotted sequentially on the same scale (as a meta-pulse).
20 15 10 5 0 -20 -10 0 10 20
20
10
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-10
-20
Fig. 3. Interaction positions and energy deposits assigned (indicated by the area of the dots) returned by the PSA.
ARTICLE IN PRESS A. Khaplanov et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 1075–1078
case of diagonal neighbors, as seen in Fig. 1. In Fig. 2 a measured meta-signal is shown together with the fitted one, and in Fig. 3, the positions that have contributed to this fit are marked with dots inside a sketch of the detector. The area of each dot is proportional to the assigned deposited energy.
In this first attempt to use the detector as a Compton imaging device, some simplifications have been made. Events with more than one interaction inside a segment were treated as single-interaction events. The new position is the weighted average of all positions returned by the PSA, and the energy is the total energy deposited in that segment. Thus all events were treated as one Compton scatter point and a photo absorption point in a neighboring segment. GEANT simulations have shown that this assumption is correct in 28% of the 2-segment events at 662 keV. Furthermore, 2-segment events constitute 43% of all photo-peak events. Simulations have also shown that the segment that contains the larger energy deposit is the one where the first Compton scattering takes place in 80% of the events at this g-ray energy. Accordingly, the larger of the two energy deposits was assumed to be the scattering point in image reconstruction, provided that the Compton scattering formula is fulfilled. The combination of all hits within one segment into a single effective interaction limits the attainable angular resolution of the image. Furthermore, an uncertainty due to the Compton profile of germanium [10] sets a physical limit on the achievable angular resolution, as the relation between the scattering angle and energy is not exact. This is true for any Compton camera (without tracking of Compton electrons). The results of the simulations are shown in Fig. 4a, b for the source positions corresponding to the two measurements. Identical analysis and image reconstruction methods were used for both the simulated and measured data, i.e., 2-segment events were selected and the interactions were treated as single hits in each segment. A 2 keV (FWHM) energy resolution was applied to the simulated interactions. The simulated position uncertainty was varied to produce images with the same angular resolution as the measurement. This yielded a position uncertainty of 1.5 mm (std. dev.). The larger energy deposit was chosen as the first hit in the same way as for the measured data. In Fig. 4c, d, the result of the measurement with a 137 Cs source is shown. The image clearly differentiates between the two source positions. The angular resolution, measured as the FWHM of the spot, is approximately 30 . The overall efficiency, expressed as the fraction of the 662 keV photons that are imaged out of those emitted into the solid angle of the segments used in this measurement is 5.6%. It has been shown in Ref. [11] that imaging using a segmented coaxial HPGe detector where non-neighboring segments are used can provide a significantly better angular resolution. This type of event, however, contributes with an efficiency that is an order of magnitude lower. The
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difference in resolution is expected due to the fact that the definition of the cone axis is more sensitive to the position uncertainty when the interaction points are close to each other. For the planar detector used in this study it was found from the simulation that image reconstruction where the hit segments are required to be separated by one segment enhances the angular resolution of the image by a factor of 2.3 while lowering the efficiency by a factor of 3.5. In other words, a significantly higher angular resolution can be achieved at the expense of imaging efficiency. Furthermore, combining the different coincidence criteria will both increase the efficiency as well as the angular resolution compared to the data used in this work. 5. Summary This first attempt to use a single planar pixellated germanium detector as a Compton imager has yielded images of a g-ray emitting radioactive source. PSA based on a least square fit between the measured detector signals and linear combinations of calculated basis pulses proved to be capable of resolving g-ray interaction points in adjacent segments. Images generated using filtered cone back-projection had an angular resolution (FWHM) of 30 with an imaging efficiency of 5.6%. There is a clear tradeoff between the angular resolution and efficiency. This suggests that an appropriate operating mode for a given application may be chosen by setting the coincidence condition and thus requiring a given separation between the first two interaction points for those events that would be used for imaging. The work continues towards resolving multiple interactions in an arbitrary combination of segments and the inclusion of more sophisticated tracking
ARTICLE IN PRESS 1078
A. Khaplanov et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 1075–1078
algorithms in order to improve both the efficiency and the angular resolution. Acknowledgments Enlightening discussions with I.-Y. Lee, P. De´sesquelles and A. Olariu are gratefully acknowledged. We would also like to thank T. Ha¨upke, M. Kirsch and S. Simonsen for making the data acquisition system operational. This work was supported by the Go¨ran Gustafsson Foundation, the Swedish Research Council and the European Commission under contract no. 506065.
References [1] K. Vetter, et al., Nucl. Instr. and Meth. A 452 (2000) 223. [2] L. Milechina, B. Cederwall, Nucl. Instr. and Meth. A 55 (2005) 278. [3] J.D. Kurfess, et al., Nucl. Instr. and Meth. A 505 (2003) 256. [4] hhttp://www.struck.dei. [5] A. Olariu, et al., IEEE Trans. Nucl. Sci. NS53 (3) (2006) 1028. [6] hhttp://www.mathworks.comi. [7] C.L. Lawson, R.J. Hanson (Eds.), Solving Least Square Problems, SIAM, Philadelphia, PA, 1995. [8] Zhong He, Nucl. Instr. Meth. A 463 (2001) 250. [10] D. Brusa, et al., Nucl. Instr. and Meth. A 379 (1996) 167. [11] T. Niedermayr, et al., Nucl. Instr. and Meth. A 553 (2005) 501.