Spectra of clinical CT scanners using a portable Compton spectrometer H. A. Duisterwinkel, J. K. van Abbema, M. J. van Goethem, R. Kawachimaru, L. Paganini, E. R. van der Graaf , and S. Brandenburg Citation: Medical Physics 42, 1884 (2015); doi: 10.1118/1.4915497 View online: http://dx.doi.org/10.1118/1.4915497 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/42/4?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Development of a dynamic quality assurance testing protocol for multisite clinical trial DCE-CT accreditation Med. Phys. 40, 081906 (2013); 10.1118/1.4812429 CT scanner x-ray spectrum estimation from transmission measurements Med. Phys. 38, 993 (2011); 10.1118/1.3547718 Development and performance evaluation of an experimental fine pitch detector multislice CT scanner Med. Phys. 36, 1120 (2009); 10.1118/1.3086117 Commissioning and clinical implementation of a mega-voltage cone beam CT system for treatment localization Med. Phys. 34, 3183 (2007); 10.1118/1.2752374 Cauchois‐type Compton Spectrometer Using X‐ray Image Intensifier AIP Conf. Proc. 705, 901 (2004); 10.1063/1.1757941
Spectra of clinical CT scanners using a portable Compton spectrometer H. A. Duisterwinkela) and J. K. van Abbema KVI-Center for Advanced Radiation Technology (KVI-CART), University of Groningen, Zernikelaan 25, Groningen 9747 AA, The Netherlands
M. J. van Goethem University Medical Center Groningen, University of Groningen, A. Deusinglaan 1, Groningen 9713 AV, The Netherlands
R. Kawachimaru,b) L. Paganini, E. R. van der Graaf, and S. Brandenburg KVI-Center for Advanced Radiation Technology (KVI-CART), University of Groningen, Zernikelaan 25, Groningen 9747 AA, The Netherlands
(Received 30 September 2014; revised 28 January 2015; accepted for publication 3 March 2015; published 25 March 2015) Purpose: Spectral information of the output of x-ray tubes in (dual source) computer tomography (CT) scanners can be used to improve the conversion of CT numbers to proton stopping power and can be used to advantage in CT scanner quality assurance. The purpose of this study is to design, validate, and apply a compact portable Compton spectrometer that was constructed to accurately measure x-ray spectra of CT scanners. Methods: In the design of the Compton spectrometer, the shielding materials were carefully chosen and positioned to reduce background by x-ray fluorescence from the materials used. The spectrum of Compton scattered x-rays alters from the original source spectrum due to various physical processes. Reconstruction of the original x-ray spectrum from the Compton scattered spectrum is based on Monte Carlo simulations of the processes involved. This reconstruction is validated by comparing directly and indirectly measured spectra of a mobile x-ray tube. The Compton spectrometer is assessed in a clinical setting by measuring x-ray spectra at various tube voltages of three different medical CT scanner x-ray tubes. Results: The directly and indirectly measured spectra are in good agreement (their ratio being 0.99) thereby validating the reconstruction method. The measured spectra of the medical CT scanners are consistent with theoretical spectra and spectra obtained from the x-ray tube manufacturer. Conclusions: A Compton spectrometer has been successfully designed, constructed, validated, and applied in the measurement of x-ray spectra of CT scanners. These measurements show that our compact Compton spectrometer can be rapidly set-up using the alignment lasers of the CT scanner, thereby enabling its use in commissioning, troubleshooting, and, e.g., annual performance check-ups of CT scanners. C 2015 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4915497] Key words: Compton spectrometer, spectrum reconstruction, instrument validation, dual energy CT, quality assurance CT scanners
1. INTRODUCTION Dual energy computed tomography (DECT) systems are becoming increasingly more common for diagnostic purposes.1 The computer tomography (CT) images from such systems can also be used advantageously for dose calculations for, e.g., low energy brachytherapy,2 photon therapy,3 and particle therapy.4 In single energy computed tomography (SECT), a calibration is needed to convert CT numbers (Hounsfield units) to the mass or electron density that is used in photon dose calculations.5–7 In DECT systems, in addition to information on the electron density, information on the effective atomic number of the relevant tissues is obtained.8–11 Moreover, with DECT, the use of a CT number to density calibration curve is not necessary.11,12 In therapy planning for proton irradiations, accurate knowledge of proton stopping powers is essential. Proton stopping powers can be determined from the electron density and the effec1884
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tive atomic number.13 In the procedure to obtain the electron density and effective atomic number from the CT images at two tube voltages, the energy spectra of the CT x-ray tube at these voltages are also needed as input.11,12 Ideally, spectra measured at the CT scanner used for the CT images should be used. However, the photon fluxes generated by CT scanners are up to 109 mm−2 s−1 and are orders of magnitude too large to measure the spectrum directly with photon counting xray detectors. To acquire such spectra directly, there are two obvious options to reduce the flux: (1) increase the distance between detector and source or (2) decrease the current of the x-ray tube. The first option is impractical because of the small size of the gantry of a CT scanner which necessitates removal of the x-ray tube from the scanner. The second option is sometimes claimed to alter the shape of the spectrum14,15 and moreover, requires access to the electronics of the scanner, which is generally not allowed in a clinical setting.
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It is also possible to reduce the photon flux at the detector by placing a scatterer in the x-ray beam and detect the scattered photons. With this method, the flux at the detector can easily be reduced with a factor of 105–106. However, this comes at the cost of a procedure to reconstruct the original spectrum from the measured one. Yaffe et al. were the first to describe an instrument (Compton spectrometer) based on this method.14 They used a lucite (PMMA) scatter foil and a germanium detector placed at 90◦ with respect to the incident beam to measure the scattered spectrum. The original spectrum was then reconstructed by using the KleinNishina differential cross section and the Compton formula for the energy of the scattered photon (both at 90◦). Furthermore, corrections were made for absorption in the scatterer and the incomplete detection processes in the detector. This latter correction is also needed in the case of direct detection. Compton spectroscopy was further developed by Matscheko et al.16–19 who systematically studied the influence of various design parameters such as the material, shape, and volume of the scatterer, the distances between source and scatterer and between scatterer and detector and collimator diameters on the energy resolution and detector count rate. It was found that a cylindrical shaped scatterer with a low atomic number and distance between x-ray focus and scatterer of about 200 mm gives a good balance between resolution and detector count rate. The effect of shielding material was studied by Gallardo et al.20 who concluded that it is beneficial to use a combination of lead with aluminum in which the aluminum is in between the lead and the detector to shield for the fluorescence in the lead. The fluorescence from the aluminum produces only very low energy x-rays (2 keV) which are outside the range of clinical importance. In Compton spectroscopy, normally high purity germanium (HPGe) detectors21–23 or cadmium telluride (CdTe) detectors24,25 are used. HPGe detectors have the advantage of a somewhat better energy resolution than CdTe-based detectors, typically 0.7% versus 1.4%, respectively, at 60 keV. However, HPGe detectors need either LN2 or mechanical/electric cooling, which are relatively bulky and expensive making them less practical and economical for application in a portable instrument. CdTe-based x-ray detectors are available with a small thermoelectric cooler which reduces the costs of the setup and makes it much more compact and suitable for a portable device. In reconstructing the original x-ray source spectrum from the measured scattered spectrum, there are various issues to consider. First, the measured spectrum should be corrected for background. This is usually approximated by the spectrum measured without the scatterer. Although this actually overestimates the background, because of scatter in the air volume taken in by the scatterer, this approximation is satisfactory under normal operation, because for most instruments, the background count rate typically accounts for less than a few percent of the count rate with scatterer thanks to the shielding of the detector from direct irradiation by the x-ray source. Second, the effects in the detector that distort the measured spectrum have to be considered. These effects are dominated by detector resolution, detector efficiency, and escape of fluorescence and Medical Physics, Vol. 42, No. 4, April 2015
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Compton scattered photons. Additional spectral distortion is induced by the effects of charge trapping and polarization in CdTe detectors.26 These effects result in some asymmetry in the full energy peaks and some instability in time. However, when using a thin detector with a high bias voltage at a low temperature (−50 ◦C), these effects are small compared to the other effects26–28 and are not taken into account in the spectrum reconstruction. Third, attenuation of the x-ray beam in the materials traversed from source to detector has to be taken into account. Fourth, effects have to be dealt with that are related to the scattering in the material of the scatterer. The latter effects include Rayleigh and multiple Compton scattered photons and the energy shift and intensity modulation due to the 90◦ Compton scattering. In addition, Doppler broadening of the spectrum due to the electron momentum in the scatterer not being zero and geometrical broadening due to the finite opening angles of the collimators influence the shape of the spectrum. A multitude of authors have contributed to Compton spectrometer design and the present state-of-the-art of spectrum reconstruction.14,15,17,20 In this paper, we present a compact portable Compton spectrometer that can be used in a clinical setting. This spectrometer is designed such that background by x-ray fluorescence from its shielding materials is kept to a minimum. Moreover, a systematic, comprehensive, and quantitative treatment is given of all the relevant details of the spectrum reconstruction. All processes that alter the spectrum have been investigated using the Monte Carlo code 2.5 (Ref. 29) to assess their relative importance in the spectrum reconstruction. To validate the instrument, the reconstructed spectrum of a mobile x-ray generator is compared with a directly measured spectrum. Furthermore, the Compton spectrometer has been used to measure spectra of three x-ray tubes of clinical CT scanners at various values of the tube voltage. These spectra are compared with each other, with theoretical spectra, and with spectra obtained from the x-ray tube manufacturer. The paper concludes with a discussion as to whether the instrument can be used in the quality assurance of x-ray tubes. 2. MATERIALS AND METHODS 2.A. Compton spectrometer design
The spectrometer (Fig. 1) is based on a PMMA (C5O2H8) scatterer (length 45 mm, diameter 6 mm). This low Z material favors Compton scattering over the photo-electric effect and reduces the contribution of Rayleigh scattering. The x-ray beam from the source is collimated by two circular (5 mm diameter) apertures that are machined in 8.8 mm thick square (10 × 10 cm2) lead plates that are clad by 3 mm aluminum on both sides to reduce the background due to x-ray fluorescence from the lead. Two identical collimators, as mentioned above, are used between the scatterer and the detector to define the opening angle of the detector. The collimators are placed on a bottom plate that has various slots to change their relative positions. In all experiments, the distance between collimator 1 and the scatterer was 18 cm, while collimator 2 was positioned at 9 cm from the scatterer; the distance
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F. 1. Schematic drawing of the Compton spectrometer.
between the scatterer and collimator 3 and collimator 4 was 9 and 23 cm, respectively. A removable detector shield (8.8 mm lead and 6 mm aluminum) is placed directly after collimator 4. This shield has a circular aperture that is concentric with the aperture of collimator 4. Additional shielding is placed between the source and detector shielding to prevent stray radiation from the source to reach the detector. The unscattered radiation is absorbed in a beam dump that consists of a 1 cm diameter and 1 cm deep cylindrical hole in a block of lead clad with aluminum. The angle between the lines from collimator 1 to scatterer and from scatterer to detector aperture is 90◦. The x-ray detector placed inside the detector shielding is a XR-100 T CdTe 3-stack from Amptek.30 This diode detector consists of three 0.75 mm thick layers of CdTe and has an area of 5 × 5 mm2. The layers are sealed in vacuum with a 250 µm beryllium window in front of the sensitive area of the detector. The efficiency up to 90 keV is essentially 100% and decreases to 55% at 150 keV. The energy resolution is 0.85 keV full width at half maximum (FWHM) at 60 and 1.5 keV FWHM at 122 keV. The detector stack is cooled to approximately −50 ◦C with a thermoelectric cooler to reduce noise. The detector signal is fed to the Amptek PX4 digital pulse processor, which digitizes the preamplifier output, processes the signal, and detects the peak value. The peak values are binned and used to form a spectrum. The PX4 communicates with a PC through a USB interface. The spectra are acquired with a bias of 1200 V on the CdTe stack, with the pile-up rejection logic of the PX4 on, and in 2048 channels using the software of Amptek. In all cases, the rise time and flat top time of the pulse in the slow channel are set at 3.2 and 0.4 µs, respectively. 2.B. Simulations
All Monte Carlo simulations were performed with the code 2.5.0.29 is a multipurpose Monte Carlo radiation transport code that tracks nearly all particles at nearly all energies. It has been issued in the series of Monte Carlo transport codes which have been developed at Los Alamos National Laboratory over the last six decades. All simulations were run in P E mode of which tracks all photons and electrons, until their energy is below the lower energy cutoff (1 keV for both photons and electrons; Medical Physics, Vol. 42, No. 4, April 2015
electron ranges in CdTe for energies lower than 1 keV are less than 0.1 µm). The Amptek CdTe detector was modelled as a 5×5×2.25 mm3 block of CdTe (density of 5.85 g cm−3) with a 250 µm sheet of beryllium (density of 1.848 g cm−3) in front. Dead layers and the electrical contacts of the detector were not included in the model. As their typical dimensions31 are very small compared to the crystal thickness (dead layer: 0.15 µm CdTe; contact: 0.2 µm platinum), it is justified to neglect them. 2.C. Spectrum reconstruction
The spectrum obtained with the Compton spectrometer is influenced by several physical processes along the trajectory of the photon from the source to the detector. For the reconstruction of the initial spectrum from the measured spectrum, simulations have been used to develop an algorithm to correct for these processes, step-by step and in reversed order (see Fig. 2). 2.C.1. Pile-up
The PX4 pile-up rejection logic removes pile-up events by using a fast pulse channel (fast channel resolving time τf = 0.6 µs). Events separated in time by more than τf but less than 4 µs are rejected. This results in a pulse rejection interval τr of 4–0.6 in 3.4 µs. The assumption is made that pu pile-up is a small effect. The pile up corrected spectrum Si (i = 1, ..., Nmax, in which Nmax is the number of energy bins used) can be calculated from the measured spectrum Si (in counts) by (τr + τf ) pu Si = Si *.1 + 2 T ,
N max j=1
τf S j +/ − T -
i−1
S j Si− j ,
(1)
j=1
where T is the acquisition live time. The factor in the first term corrects for the events removed by the pile-up rejection logic and those shifted to higher energy due to pile-up events during τf while the second term accounts for the pile up events in bin i occurring during τf . In all measurements with the Compton spectrometer, the count rate was typically in the order of 2000 counts/s, resulting in corrections for pile-up
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F. 2. Overview of the various reconstruction steps.
rejection and remaining pile-up of 2% and 0.2%, respectively. For some of the directly measured spectra, the count rate was a factor of two higher. 2.C.2. Background
The background of the Compton spectrometer is estimated from a spectrum taken without the scatterer. This background is in principle different for each x-ray tube because of the differences in shielding between tubes and changes also with tube voltage. In general, x-ray tubes used in a clinical environment seem to be better shielded than tubes used in an industrial setting. In all cases, this background should be reduced to values as low as reasonably possible and in the case of our Compton spectrometer, the total count rate of the background was always less than 5% of the spectrum with the scatterer without adding additional shielding for clinical xray tubes. The background could be reduced to less than this 5% with strategically placed extra shielding in case of industrial x-ray tubes. The background is corrected for by subtracting the measured, pile-up corrected background spectrum from the pile-up corrected spectrum. An example of a raw spectrum (before reconstruction) in combination with a background spectrum is shown in Fig. 3. The spectra are taken (1500 s acquisition time) using an industrial x-ray unit (GE Inspection Technologies, ERESCO 42 MF3.1) at 200 kV and 4.5 mA at the industrial irradiation facility of Applus RTD, Veendam, The Netherlands. The raw spectrum clearly shows the two characteristic x-ray peaks originating from the tungsten anode. The total count rate in the background spectrum was 1.5% of the raw spectrum count rate and the peaks in the background spectrum are the characteristic x-rays from the lead of the shielding.
of Compton scattered x-rays. For the CdTe detector, there are eight significant K-line escapes (Kα1, Kα2, K β1, K β2 for both cadmium and tellurium). Simulations were used to estimate the magnitude and shape of the spectral distortion of each of the nine possible incomplete energy deposition events (eight K-line escapes and Compton escape), expressed as a fraction of the number of full energy events. In these simulations, a disk shaped photon source was used facing the front side of the detector. The diameter of the disk was 5 mm and photons were seeded in a direction perpendicular to the disk, thus mimicking the collimated photon beam in the Compton spectrometer. The simulations were done with monoenergetic photons for energies from 10 to 200 keV in 10 keV steps. In the energy range below 10 keV and in the range of the K-edges of cadmium and tellurium, steps of 1 keV were used. For each energy, the energy deposition spectrum in the detector was obtained using the F8 tally. The energy binning of the simulated spectra was 0.1 keV and the
2.C.3. Incomplete energy deposition in the detector
Two types of incomplete energy deposition events may occur in the detector: escapes of K-line x-rays and escapes Medical Physics, Vol. 42, No. 4, April 2015
F. 3. Raw spectrum and background spectrum (×10) taken with the Compton spectrometer in combination with an ERESCO 42 MF3.1 industrial x-ray unit at 200 kV and 4.5 mA.
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edge energy. The distribution of the Compton scattering events was approximated by a rectangle that runs along the energy axis from zero to the Compton edge energy. The height of this rectangle was chosen such that the integral count in the rectangle was equal to the total number of Compton events. A similar stripping procedure as for the K-line escape was used to strip the Compton events from the spectrum and reposition them in the channel with the full energy events. All eight Kescape and the Compton events corrections were executed simultaneously, channel by channel towards lower energy. 2.C.4. Detection efficiency F. 4. Simulated spectrum for 100 keV photons showing the various escape events and the full energy peak.
escape events, Compton events, and full energy events could be clearly separated (Fig. 4). Their contributions to the spectrum have been calculated relative to the full energy events (Fig. 5). The fraction of K-escapes is highest for low energy incoming photons as their point of interaction is close to the surface and the K-line x-rays can escape from the detector before being absorbed. Clearly visible (Fig. 5) are the increases in the Kescape fractions of cadmium at the energy of the K-edge of Te (31.9 keV), due to the decrease in total energy events caused by escaping K-line x-rays of tellurium. These contributions are used to correct the measured spectra with a stripping procedure which starts at the highest energy channel assuming this contains only full energy events. The escape events in the channels corresponding to these events (full energy minus escape line energy) are calculated and subtracted from the spectrum and assigned to the full energy channel. This is repeated channel by channel towards lower energy and ends at the channel corresponding to the K-
F. 5. K -line escape events and Compton escape events as a fraction of the full energy peak (x-axis). Medical Physics, Vol. 42, No. 4, April 2015
In the next step, the spectrum is corrected for the energy efficiency of the Amptek detector by dividing the spectrum by the detector’s total energy efficiency curve, as after the preceding corrections the spectrum is the result of any interaction in the detector. This efficiency curve was determined from the set of detector simulations and is shown in Fig. 6 together with a simulated full energy efficiency curve. Our simulated total efficiency curve is equal (within 1%) with the efficiency curve provided by Amptek32 (calculated on the basis of thicknesses and linear attenuation coefficients of beryllium and CdTe). 2.C.5. Multiple Compton scattering and Rayleigh scattering correction
At this stage, the reconstructed spectrum contains 90◦ Compton scattered photons and photons that were Rayleighscattered or multiple-Compton scattered. The latter contributions that have to be removed before the Klein-Nishina formula for 90◦ scattered photons can be applied. The magnitude of both contributions has been assessed by simulations. In case of multiple Compton scattering, only the contribution of photons that scattered twice were taken into account. The energy range of these photons is bounded on the lower side and the upper side by the energy of photons that have scattered twice over 135◦ and twice over 45◦, respectively. The probability over
F. 6. Total and full energy peak efficiency of the Amptek-100 T CdTe 3-stack detector.
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source and with µair the linear attenuation coefficient of air. The attenuation in the material of the scatterer is accounted for by using a procedure described by Matscheko and Ribberfors.16 They showed that the average distance d s before and after the 90◦ scattering event is 8r/3π with r the radius of the scatterer. For our 6 mm diameter scatterer, this amounts to d s = 2.55 mm. Average correction factors of exp(d s µPMMA (E0)) and exp(d s µPMMA (E)) to correct for the attenuation in the scatterer (µPMMA is the linear attenuation factor of PMMA) are used. These correction factors are relatively small; typically in the order of 1.1–1.2 over the energy range 20–150 keV. 2.C.8. Broadening aspects
F. 7. Contribution of multiple and Rayleigh scattered photons expressed as fractions of the number of 90◦ scattered photons. The error bars are 1σ uncertainties that result from the Monte Carlo statistics.
this range has been found to be constant. Rayleigh scattered photons appear in the energy channel that corresponds to their original (before scattering) energy and can thus easily be identified. The fraction of multiple scattered photons decreases slightly as a function of energy and is in the order of about 10% over the relevant energy range. This also shows that photons that are Compton scattered more than twice will only contribute in the order of 1% and lead to negligible spectrum distortion. Rayleigh scattering is only significant at low energies and is negligible for energies higher than 50 keV (Fig. 7). 2.C.6. 90◦ Compton scattering
The photon energies E0 of the primary spectra were reconstructed by correcting photon energies E of the 90◦ scattered spectra, for the energy shift resulting from the 90◦ scatter by using E0 =
E , 1 − (E/mc2)
(2)
where mc2 is the rest mass of the electron. The primary spectra S0(E0) are reconstructed by using the Klein-Nishina formula at 90◦, 2S(E0)(1 + q)2 , (3) (1 + (q2/(1 + q))) with q = E0/mc2 and S(E0) the spectrum with all corrections except that for the energy dependent cross section of 90◦ Compton scattering. S0(E0) =
2.C.7. Intensity attenuation
The intensity of the x-ray beam will be attenuated due to the air and scatter material through which the beam passes. The attenuation in air is corrected for by multiplying the spectrum before and after the scatterer with a factor exp(d ds µair (E0)) and exp(d ss µair (E)), respectively, with d ds and d ss the distances between detector and scatterer and between scatterer and x-ray Medical Physics, Vol. 42, No. 4, April 2015
There are three processes that cause the reconstructed spectra to be broader than the primary spectra. First, the geometry of the collimators allows photons that are scattered through a range of angles around 90◦ to reach the detector, which will influence the energy of the scattered photons (geometrical broadening). Second, in the reconstruction it is assumed that the electrons, off which the photons scatter, are at rest. Actually, these electrons have a momentum distribution and this will translate in a broadening of the energy distribution of the scattered photons (Doppler broadening). Third, the resolution of the detector itself will broaden the spectrum (detector resolution). The effect of geometrical and Doppler broadening has been estimated from simulations. The detector resolution is taken from the Amptek detector specifications. The geometry of the simulations comprised the 6 mm diameter PMMA scatterer, a 5 mm diameter disk-shaped photon source and the Amptek CdTe detector placed in the 90◦ set up of the Compton spectrometer. Simulations were performed with monoenergetic photons (range 25–200 keV) using two photon physics settings, namely, Doppler effect off and Doppler effect on and using a 0.1 keV energy-binned F4 flux tally on the entrance window of the detector. In the first setting, the spectrum is only broadened due to geometrical effects, in the second setting, both geometrical and Doppler broadening are included. These broadening effects were assessed as a function of photon energy by starting monoenergetic photons from the disk source and determining their FWHM (assuming a Gaussian profile) at the entrance window of the detector. Figure 8 shows the FWHM due to the three processes as a function of energy. The total resolution is largely determined by Doppler broadening and detector resolution; it increases from approximately 1.0 at 25 keV to 3.0 at 150 keV. 2.C.9. Implementation of spectrum reconstruction
All the reconstruction steps shown in Fig. 2 are implemented in a Mathematica 8 (Wolfram research) notebook.33 The notebook starts by reading the raw spectrum, background spectrum, their acquisition times, and the spectrum energy calibration. For indirectly measured spectra, the notebook sequentially performs all reconstruction steps, for directly measured spectra, only corrections for background, detector effects, and attenuation in air are made. No corrections are made for the spectrum broadening.
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F. 8. FWHM, in keV, due to geometrical and Doppler broadening and due to detector resolution as a function of energy. Also, the FWHM resulting from the total of all three contributions is shown (solid line).
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F. 9. A photograph of the Compton spectrometer at the isocenter of the Somatom Definition Flash at Siemens Medical Solutions, Forchheim, Germany.
4. RESULTS AND DISCUSSION 4.A. Validation experiments
3. EXPERIMENTS 3.A. Validation experiments
Direct and indirect spectra were measured using a mobile x-ray source (Siemens Nanomobil) at 100 kV. Exposure times were typically a few 100 s and consisted of pulsed emissions of 0.4 s (the source could not be operated in continuous mode) with a tube current versus time product of 20 mA s. In the case of the directly measured spectrum, the scatterer was removed from the Compton spectrometer. To reduce the flux, the x-ray source was located at 23.95 m from the CdTe detector in the spectrometer that was orientated such that the detector and the two collimators 3 and 4 were in line with the x-ray source. Even at this distance, the flux was too high and further flux reduction was achieved by placing a 0.5 mm diameter tungsten collimator between collimators 3 and 4. The indirect spectrum was measured using the same x-ray source settings but with the source placed at 25 cm before collimator 1 and with the PMMA scatterer in position. 3.B. Clinical CT scanners
Indirect spectra were measured with the scatterer of the Compton spectrometer positioned at the isocentre of a Siemens SOMATOM Definition Flash (dual source CT with two x-ray tubes, A and B) at Siemens Medical Solutions at Forchheim, Germany (Fig. 9) and a Siemens SOMATOM Definition (dual source CT, only one tube measured) at the University Medical Center in Groningen, The Netherlands. For tube A and B of the Definition Flash and the tube of the Definition, spectra were collected at 80, 100, 120, 140 kV with factory supplied filtration; for tube B of the Definition Flash also, a spectrum at 140 kV with an additional filtration of 0.4 mm tin was measured. In all cases, the spectrum acquisition time was 400 s (live time), while a 200 s background spectrum was measured. The x-ray tube current was 25 mA in all measurements. Medical Physics, Vol. 42, No. 4, April 2015
The raw and reconstructed indirect and direct spectra measured for the Siemens Nanomobil are shown in Fig. 10. In both the indirectly and directly measured spectra, the effect of the stripping procedure to correct for the incomplete energy deposition is evident in the lower energy channels where the count rate is markedly decreased by the correction. The reconstructed indirect spectrum is shifted toward higher energy due to the 90◦ Compton scattering correction. In the direct spectrum, the correction for the attenuation in 23.95 m air shifts the weight in the spectrum toward higher energies. Because of the large distance, the correction becomes very large at low energies, e.g., the correction factor is approximately 10 at 20 keV and exponentially decreases to 1.6 at 100 keV. Therefore, the reconstruction is truncated at approximately 20 keV, which explains the discontinuity in the reconstructed spectrum around 20 keV (Fig. 10). Comparison of the reconstructed direct and indirect spectrum (Fig. 11) shows a very good correspondence between both spectra. The ratio between the direct and indirect measured spectra is close to unity (Fig. 11); starting above the discontinuity around 20 keV and up to 100 keV, we find an average (and standard deviation) of this ratio of 0.99(0.07). It is also clear that the peaks of the characteristic x-rays of tungsten have a smaller width in the direct spectrum. This is to be expected, as the direct spectrum is not influenced by geometrical and Doppler broadening of which especially the last contribution has a significant effect on the indirectly measured spectrum. However, the FWHM at the Kα x-ray peak in the direct spectrum (2.8 keV) is more than a factor three larger than expected from the detector resolution (0.9 keV) only. In fact, based on the detector resolution only, the Kα1 (59.3 keV) and Kα2 (58.0 keV) lines should appear resolved in the directly measured spectrum. This extra broadening may have been caused by the still relatively high count rate (a factor two higher than in the indirect measurements), by scatter in the pinhole collimator to reduce this count rate or due to
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F. 11. Comparison of reconstructed direct and indirectly measured spectra from the Siemens Nanomobil portable x-ray source. Bottom figure gives the ratio between the direct and indirect spectrum.
F. 10. Raw and reconstructed spectra from the Siemens Nanomobil portable x-ray source, indirectly (top) and directly (bottom) measured spectra are shown.
scatter in the air between the detector and the x-ray source. The first effect was assessed by measuring the FWHM of the Kα line of terbium (from a terbium-foil under impinging alpha particles) for different count rates obtained by varying the detector source distance. A maximal increase of 15% in FWHM at the acquisition count rate was estimated, thus explaining only a small part of the observed FWHM. From the literature, we found that a long distance between detector and x-ray source seems to negatively affect the energy resolution. Deresch et al. used an Amptek CdTe-stack spectrometer with pinhole collimation and a detector source distance of 16 m and from their spectra, we estimate a FWHM of approximately 3 keV at the tungsten Kα line (unresolved) which is in line with our findings.34 Wanatabe et al. used a similar detector, but instead of pinhole collimation and a large detector to source distance, they used a low-count-rate x-ray generator to reduce the photon flux on the detector.35 In their spectra, the Kα1 and Kα2 lines of tungsten are resolved. Consequently, a combination of rate effects and extra scatter invoked by the large source-detector distance most likely is the cause of the observed extra broadening in our directly measured spectra. Broadening is one of the main limitations in measuring spectra of x-ray tubes. All measured spectra are blurred by the finite resolution of the detection system. However, the x-ray spectrum that enters a tissue that is assessed in a CT scanner is not blurred at all, the only energy blurring expected for the Medical Physics, Vol. 42, No. 4, April 2015
tungsten characteristic x-rays is due to its natural line width with superposed broadening as a result of the temperature of the anode and by scatter in some intermediate materials (filters, air). The first two effects are very small. The broadening due to scatter can be assessed by Monte Carlo simulations and all codes show this also gives almost negligible broadening.36 This suggests that the best choice for an input spectrum for, e.g., a DECT electron density, effective atomic number assessment might be a measured spectrum but with the peak intensities of the characteristic x-ray integrated and artificially (by hand) positioned in the measured spectrum at the energies and in the relative ratios that are known from the literature. The method is further justified by the observation that the shape of a smooth structure like the bremsstrahlung continuum is only slightly influenced by the energy blurring (slightly less steep slopes at the sides of the continuum). 4.B. Clinical CT scanners
The reconstructed unnormalized spectra for all energies (Fig. 12) are rather similar for all three tubes. The characteristic x-rays of tungsten are barely visible in the 80 kV spectra and become more prominent for the higher tube voltages. Also, for all three tubes, a small glitch in the 140 kV spectra is visible at approximately 90 keV, this is due to subtraction of a background spectrum containing Kα x-rays from lead (at 73 and 75 keV, see Fig. 3) from the raw spectrum. These Kα x-rays result directly from interaction of the x-rays from the tube with the shielding of the detector and are thus not energy shifted by the scatterer. Imperfections in this subtraction propagate to higher energies due to the 90◦ Compton energy shift correction. For the spectra at lower energies, because of the much
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F. 13. Zoomed view of the high energy part of the spectra of tube A of the Definition Flash (Top) and of the tube of the Definition (Bottom) at different source voltages.
F. 12. Reconstructed spectra for both tubes ( A and B) of the Definition Flash and of the tube of the Definition.
lower production of Kα x-rays, the effect is too small to be noticeable. The end point energies of the spectra of both tube A and B of the Definition Flash are consistent with the high voltage used (Fig. 13, top). However, for the tube of the Definition, it is clear that for all spectra, the end point energy is about 2 keV higher (Fig. 13, bottom), indicating that deviations from specified high voltage can be readily detected with the Compton spectrometer. The spectra of all three x-ray tubes were re-binned to 1 keV energy bins, normalized and are compared for two high voltage settings (80 and 140 keV) in Fig. 14. Figure 15 shows the re-binned spectrum for tube B at 140 keV with 0.4 mm tin Medical Physics, Vol. 42, No. 4, April 2015
filtration. This comparison shows that the normalized spectra of all three tubes are nearly identical except for the somewhat larger endpoint energy of the tube of the Definition. Theoretical spectra based on a deterministic model of xray production calculated with the software program SpekCalc (Refs. 37–39) are also presented in Figs. 14 and 15. The SpekCalc spectra were computed using a 1 keV grid and a 8◦ anode angle40 and were filtrated with 3 mm aluminum and 0.9 mm titanium (information from the CT scanner manufacturer) and 500 mm air. For tube B of the Definition Flash also, a spectrum with an extra filtration of 0.4 mm tin was calculated. Other parameters, e.g., the ratio between the bremsstrahlung continuum and the characteristic x-rays (P-parameter) were set at their default values. Thereafter, the spectra from SpekCalc were broadened using a Gaussian with an energy dependent FWHM reflecting the combined broadening due to Doppler, geometry, and detector resolution (Fig. 8). The SpekCalc spectra are in very good agreement with the measured spectra with respect to the shape of the bremsstrahlung continuum, the end point energy, and the location of the characteristic x-rays. However, the SpekCalc spectra show higher characteristic x-ray peaks. It is realised that the SpekCalc program does not include any broadening of the spectrum, but it was expected that after broadening, the calculated spectra conform our spectrometer specifications,
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facturer (Siemens Medical Solutions, Forchheim, Germany). These spectra were directly measured a few decades ago and corrected for the intrinsic filtration of the x-ray tube. With respect to characteristic peak height, these spectra are in between our results and the SpekCalc calculations. The rest of the spectrum is in very good agreement with both our results and the SpekCalc spectra. Measurements of x-ray spectra in radiology and radiotherapy are not performed on a regular basis. One of the often mentioned constraints is that these measurements are complex and time consuming.41,42 This constraint has been lifted by our Compton spectrometer design for use at CT scanners as for the positioning of the spectrometer, the alignment lasers of the scanner can be used, leading to setting-up times of typically 10–15 min. Combined with spectrum acquisition times of about 5 min per spectrum, a protocol for measuring spectra at two or three energies will not last more than 30–45 min. In this light, our method does not seem more complex or time-consuming than currently used half-layer thickness41 assessments or recently proposed methods based on direct43 or indirect44 transmission measurements. Measurements with a Compton spectrometer are too involved to be used on a day-to-day basis but the instrument is well suited to be used during, e.g., commissioning, troubleshooting, or yearly CT scanner performance tests in which the instrument is taken of the clinical scheduling for a larger amount of time.
F. 14. Normalized and re-binned (to 1 keV) spectra of all three CT x-ray tubes compared at two high voltages. Also shown are the spectra calculated with SpekCalc and the spectra obtained from Siemens.
the measured and calculated peaks would fall in line. In a search for the reason of the discrepancy, we adjusted the Pparameter of the SpekCalc program and also tried variations in the value of the anode angle, but we did not succeed in a much better match of the SpekCalc results to the measurements. Finally, also output spectra at different voltages of the xray tube used in the Definition were obtained from the manu-
5. CONCLUSION A compact portable Compton spectrometer to indirectly measure the spectra of x-ray tubes has been designed, constructed, and validated. The algorithm to reconstruct the original x-ray spectrum from the indirectly measured spectrum was described step-by-step and the effect of each reconstruction step was quantitatively assessed by Monte Carlo simulations. The measurement and reconstruction procedure was validated by comparing directly and indirectly measured spectra from a mobile x-ray unit. Thereafter, the Compton spectrometer was used in measurements of x-ray spectra of clinical CT scanners. These measurements show that our compact Compton spectrometer can be rapidly set-up using the alignment lasers of the CT scanner, thereby enabling its use in commissioning, troubleshooting and, e.g., annual performance check-ups of CT scanners.
a)Current
F. 15. As Fig. 14 except only tube B at 140 keV with 0.4 mm tin filtration. Medical Physics, Vol. 42, No. 4, April 2015
address: INCAS3, Dr. Nassaulaan 9, 9401 HJ Assen, The Netherlands. b)Permanent address: Department of Medical Physics and Engineering, Osaka University, Osaka, Japan. 1M. Petersilka, H. Bruder, B. Krauss, K. Stierstorfer, and T. G. Flohr, “Technical principles of dual source CT,” Eur. J. Radiol. 68, 362–368 (2008). 2G. Landry, P. V. Granton, B. Reniers, M. C. Öllers, L. Beaulieu, J. E. Wildberger, and F. Verhaegen, “Simulation study on potential accuracy gains from dual energy CT tissue segmentation for low-energy brachytherapy Monte Carlo dose calculations,” Phys. Med. Biol. 56, 6257–6278 (2011). 3M. Saito, “Potential of dual-energy subtraction for converting CT numbers to electron desnity on a single linear relationship,” Med. Phys. 39, 2021–2030 (2012).
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Jiang, J. Seco, and H. Paganetti, “Effects of Hounsfield number conversion on CT based proton Monte Carlo dose calculations,” Med. Phys. 34, 1439–1449 (2007). 5U. Schneider, E. Pedroni, and A. Lomax, “The calibration of CT Hounsfield units for radiotherapy planning,” Phys. Med. Biol. 41, 111–124 (1996). 6J. Seco and P. M. Evans, “Assessing the effect of electron density in photon dose calculations,” Med. Phys. 33, 540–552 (2006). 7B. Vanderstraeten, P. W. Chin, M. Fix, A. Leal, G. Mora, N. Reynart, J. Seco, M. Soukup, E. Spezi, W. De Neve, and H. Thierens, “Conversion of CT numbers into tissue parameters for Monte Carlo dose calculations: A multi-centre study,” Phys. Med. Biol. 52, 539–562 (2007). 8R. A. Rutherford, B. R. Pullan, and I. Isherwood, “Measurement of effective atomic number and electron density using an EMI scanner,” Neuroradiology 11, 15–21 (1976). 9G. Landry, B. Reniers, P. V. Granton, B. Van Rooijen, L. Beaulieu, J. E. Wildberger, and F. Verhaegen, “Extracting atomic numbers and electron densities from a dual source dual energy CT scanner: Experiments and a simulation model,” Radiother. Oncol. 100, 375–379 (2011). 10T. Tsunoo, M. Torikoshi, Y. Ohno, M. Endo, M. Natsuhori, T. Kakizaki, N. Yamada, N. Ito, N. Yagi, and K. Uesugi, “Measurement of electron density and effective atomic number using dual-energy x-ray CT,” Nuclear Science Symposium Conference Record, 2004 IEEE (IEEE, New York, NY, 2004), pp. 3764–3768. 11M. Bazalova, J. F. Carrier, L. Beaulieu, and F. Verhaegen, “Dual-energy CT-based material extraction for tissue segmentation in Monte Carlo dose calculations,” Phys. Med. Biol. 53, 2439–2456 (2008). 12J. K. van Abbema, M.-J. van Goethem, M. J. W. Greuter, A. van der Schaaf, S. Brandenburg, and E. R. van der Graaf, “Relative electron density determination using a physics based parameterization of photon interactions in medical DECT,” Phys. Med. Biol. (2015) (accepted). 13M. Yang, G. Virshup, J. Clayton, X. R. Zhu, R. Mohan, and L. Dong, “Theoretical variance analysis of single- and dual-energy computed tomography methods for calculating proton stopping power ratios of biological tissues,” Phys. Med. Biol. 55, 1343–1362 (2010). 14M. Yaffe, K. W. Taylor, and H. E. Johns, “Spectroscopy of diagnostic x ray by a Compton-scatter method,” Med. Phys. 3, 328–334 (1976). 15A. A. Vieira, A. Linke, E. M. Yoshimura, R. A. Terini, and S. B. Herdade, “A portable Compton spectrometer for clinical X-ray beams in the energy range 20-150 keV,” Appl. Radiat. Isot. 69, 350–357 (2011). 16G. Matscheko and R. Ribberfors, “A Compton scattering spectrometer for determining x-ray photon energy spectra,” Phys. Med. Biol. 32, 577–594 (1987). 17G. Matscheko and R. Ribberfors, “A generalised algorithm for spectral reconstruction in Compton spectroscopy with corrections for coherent scattering,” Phys. Med. Biol. 34, 835–841 (1989). 18G. Matscheko and G. A. Carlsson, “Compton spectroscopy in the diagnostic x-ray range. I. Spectrometer design,” Phys. Med. Biol. 34, 185–197 (1989). 19G. Matscheko, G. A. Carlsson, and R. Ribberfors, “Compton spectroscopy in the diagnostic x-ray range. II. Effects of scattering material and energy resolution,” Phys. Med. Biol. 34, 199–208 (1989). 20S. Gallardo, J. Ródenas, G. Verdú, and J. I. Villaescusa, “Analysis of shielding materials in a Compton spectrometer applied to x-ray tube quality control using Monte Carlo simulation,” Radiat. Prot. Dosim. 115, 375–379 (2005). 21L. E. Wilkinson, P. N. Johnston, and J. C. P. Heggie, “A comparison of mammography spectral measurements with the spectra produced using several different mathematical models,” Phys. Med. Biol. 46, 1575–1589 (2001). 22P. Hammersberg, M. Stenström, H. Hedtjärn, and M. Mångård, “Measurements of absolute energy spectra for an industrial micro focal X-ray source under working conditions using a Compton scattering spectrometer,” J. Xray Sci. Technol. 8, 5–18 (1998).
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23A. Querol, S. Gallardo, J. Ródenas, and G. Verdú, “Application of Tikhonov
and MTSVD methods to unfold experimental X-ray spectra in the radiodiagnostic energy range,” Conference Proceedings of the International Conference of IEEE Engineering in Medicine and Biology Society 2010 (IEEE, New York, NY, 2010), pp. 536–539. 24K. Maeda, M. Matsumoto, and A. Taniguchi, “Compton-scattering measurement of diagnostic x-ray spectrum using high-resolution Schottky CdTe detector,” Med. Phys. 32, 1542–1547 (2005). 25M. Bazalova and F. Verhaegen, “Monte Carlo simulation of a computed tomography x-ray tube,” Phys. Med. Biol. 52, 5945–5955 (2007). 26R. Redus, Charge trapping in XR-100T-CdTe and –CZT detectors, Amptek Application Note ANCZT-2 Rev.3., Amptek, 2007. 27S. Del Sordo, L. Abbene, E. Caroli, A. M. Mancini, A. Zappettini, and P. Ubertini, “Progress in the development of CdTe and CdZnTe semiconductor radiation detectors for astrophysical and medical applications,” Sensors 9, 3491–3526 (2009). 28S. Miyajima, “Thin CdTe detector in diagnostic x-ray spectroscopy,” Med. Phys. 30, 771–777 (2003). 29D. B. Pelowitz, User’s Manual Version 2.50, LA-CP-05–0369, Los Alamos National Laboratory, Los Alamos, NM, 2005. 30R. Redus, A. Huber, J. Pantazis, T. Pantazis, T. Takahashi, and S. Woolf, “Multilelement CdTe stack detectors for gamma-ray spectroscopy,” IEEE Trans. Nucl. Sci. 51, 2386–2394 (2004). 31Amptek, General tutorials, Detector efficiency FAQ, http://www.amptek. com/pdf/efficiency.pdf, last visited on May 25, 2013. 32Amptek, XR-100T-CdTe Cadmium Telluride detector efficiency application note, AN-CdTe-001 Rev.1, 2010. 33Wolfram Research, Inc., Mathematica version 8.0, Wolfram Research, Inc., Champaign, Illinois, 2010. 34A. Deresch, G. J. Jaenisch, C. Bellon, and A. Warrikhoff, “Simulating X-ray spectra: From tube parameters to detector output,” 18th World Conference on Nondestructive testing, Durban, South Africa, 16–20 April (2012). 35M. Wanatabe, E. Sato, P. Abderyim, A. Abudurexiti, O. Hagiwara, H. Matsukiyo, A. Osawa, T. Enomoto, J. Nagao, S. Sato, A. Ogawa, and J. Onagawa, “First demonstration of 10 keV-width energy-discrimination K-edge radiography using a cadmium-telluride X-ray camera with a tungsten target tube,” Nucl. Instrum. Methods Phys. Res., Sect. A 637, 171–177 (2011). 36R. Taleei and M. Shahriari, “Monte Carlo simulation of x-ray spectra and evaluation of filter effect using 4 and Fluka code,” Appl. Radiat. Isot. 67, 266–271 (2009). 37G. Poludniowski, G. Landry, F. deBlois, P. M. Evans, and F. Verhaegen, “SpekCalc: A program to calculate photon spectra from tungsten anode xray tubes,” Phys. Med. Biol. 54, N433–N438 (2009). 38G. G. Poludnoiwski and P. M. Evans, “Calculation of x-ray spectra emerging from an x-ray tube. Part I. Electron penetration characteristics in x-ray targets,” Med. Phys. 34, 2164–2174 (2007). 39G. G. Poludniowski, “Calculation of x-ray spectra emerging from an x-ray tube. Part II. X-ray production and filtration in x-ray targets,” Med. Phys. 34, 2175–2186 (2007). 40T. Flohr and B. Ohnesorge, “Multi-slice CT technology,” in Multi-Slice and Dual Source CT in Cardiac Imaging, 2nd ed. (Springer, New York, NY, 2007), pp. 41–70. 41M. Bhat, J. Pattison, G. Bibbo, and M. Caon, “Diagnostic x-ray spectra: A comparison of spectra generated by different computational methods with a measured spectrum,” Med. Phys. 25, 114–120 (1998). 42ICRU Report 87, “Radiation dose and image-quality assessment in computer tomography,” J. ICRU 12(1) (2012). 43X. Duan, J. Wang, L. Yu, S. Leng, and C. H. McCollough, “CT scanner xray spectrum estimation from transmission measurements,” Med. Phys. 38, 993–997 (2011). 44W. Zhao, K. Niu, S. Schafer, and K. Royalty, “An indirect transmission measurement-based spectrum estimation method for computed tomography,” Phys. Med. Biol. 60, 339–357 (2015).
Spectra of clinical CT scanners using a portable Compton spectrometer H. A. Duisterwinkela) and J. K. van Abbema KVI-Center for Advanced Radiation Technology (KVI-CART), University of Groningen, Zernikelaan 25, Groningen 9747 AA, The Netherlands
M. J. van Goethem University Medical Center Groningen, University of Groningen, A. Deusinglaan 1, Groningen 9713 AV, The Netherlands
R. Kawachimaru,b) L. Paganini, E. R. van der Graaf, and S. Brandenburg KVI-Center for Advanced Radiation Technology (KVI-CART), University of Groningen, Zernikelaan 25, Groningen 9747 AA, The Netherlands
(Received 30 September 2014; revised 28 January 2015; accepted for publication 3 March 2015; published 25 March 2015) Purpose: Spectral information of the output of x-ray tubes in (dual source) computer tomography (CT) scanners can be used to improve the conversion of CT numbers to proton stopping power and can be used to advantage in CT scanner quality assurance. The purpose of this study is to design, validate, and apply a compact portable Compton spectrometer that was constructed to accurately measure x-ray spectra of CT scanners. Methods: In the design of the Compton spectrometer, the shielding materials were carefully chosen and positioned to reduce background by x-ray fluorescence from the materials used. The spectrum of Compton scattered x-rays alters from the original source spectrum due to various physical processes. Reconstruction of the original x-ray spectrum from the Compton scattered spectrum is based on Monte Carlo simulations of the processes involved. This reconstruction is validated by comparing directly and indirectly measured spectra of a mobile x-ray tube. The Compton spectrometer is assessed in a clinical setting by measuring x-ray spectra at various tube voltages of three different medical CT scanner x-ray tubes. Results: The directly and indirectly measured spectra are in good agreement (their ratio being 0.99) thereby validating the reconstruction method. The measured spectra of the medical CT scanners are consistent with theoretical spectra and spectra obtained from the x-ray tube manufacturer. Conclusions: A Compton spectrometer has been successfully designed, constructed, validated, and applied in the measurement of x-ray spectra of CT scanners. These measurements show that our compact Compton spectrometer can be rapidly set-up using the alignment lasers of the CT scanner, thereby enabling its use in commissioning, troubleshooting, and, e.g., annual performance check-ups of CT scanners. C 2015 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4915497] Key words: Compton spectrometer, spectrum reconstruction, instrument validation, dual energy CT, quality assurance CT scanners
1. INTRODUCTION Dual energy computed tomography (DECT) systems are becoming increasingly more common for diagnostic purposes.1 The computer tomography (CT) images from such systems can also be used advantageously for dose calculations for, e.g., low energy brachytherapy,2 photon therapy,3 and particle therapy.4 In single energy computed tomography (SECT), a calibration is needed to convert CT numbers (Hounsfield units) to the mass or electron density that is used in photon dose calculations.5–7 In DECT systems, in addition to information on the electron density, information on the effective atomic number of the relevant tissues is obtained.8–11 Moreover, with DECT, the use of a CT number to density calibration curve is not necessary.11,12 In therapy planning for proton irradiations, accurate knowledge of proton stopping powers is essential. Proton stopping powers can be determined from the electron density and the effec1884
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tive atomic number.13 In the procedure to obtain the electron density and effective atomic number from the CT images at two tube voltages, the energy spectra of the CT x-ray tube at these voltages are also needed as input.11,12 Ideally, spectra measured at the CT scanner used for the CT images should be used. However, the photon fluxes generated by CT scanners are up to 109 mm−2 s−1 and are orders of magnitude too large to measure the spectrum directly with photon counting xray detectors. To acquire such spectra directly, there are two obvious options to reduce the flux: (1) increase the distance between detector and source or (2) decrease the current of the x-ray tube. The first option is impractical because of the small size of the gantry of a CT scanner which necessitates removal of the x-ray tube from the scanner. The second option is sometimes claimed to alter the shape of the spectrum14,15 and moreover, requires access to the electronics of the scanner, which is generally not allowed in a clinical setting.
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It is also possible to reduce the photon flux at the detector by placing a scatterer in the x-ray beam and detect the scattered photons. With this method, the flux at the detector can easily be reduced with a factor of 105–106. However, this comes at the cost of a procedure to reconstruct the original spectrum from the measured one. Yaffe et al. were the first to describe an instrument (Compton spectrometer) based on this method.14 They used a lucite (PMMA) scatter foil and a germanium detector placed at 90◦ with respect to the incident beam to measure the scattered spectrum. The original spectrum was then reconstructed by using the KleinNishina differential cross section and the Compton formula for the energy of the scattered photon (both at 90◦). Furthermore, corrections were made for absorption in the scatterer and the incomplete detection processes in the detector. This latter correction is also needed in the case of direct detection. Compton spectroscopy was further developed by Matscheko et al.16–19 who systematically studied the influence of various design parameters such as the material, shape, and volume of the scatterer, the distances between source and scatterer and between scatterer and detector and collimator diameters on the energy resolution and detector count rate. It was found that a cylindrical shaped scatterer with a low atomic number and distance between x-ray focus and scatterer of about 200 mm gives a good balance between resolution and detector count rate. The effect of shielding material was studied by Gallardo et al.20 who concluded that it is beneficial to use a combination of lead with aluminum in which the aluminum is in between the lead and the detector to shield for the fluorescence in the lead. The fluorescence from the aluminum produces only very low energy x-rays (2 keV) which are outside the range of clinical importance. In Compton spectroscopy, normally high purity germanium (HPGe) detectors21–23 or cadmium telluride (CdTe) detectors24,25 are used. HPGe detectors have the advantage of a somewhat better energy resolution than CdTe-based detectors, typically 0.7% versus 1.4%, respectively, at 60 keV. However, HPGe detectors need either LN2 or mechanical/electric cooling, which are relatively bulky and expensive making them less practical and economical for application in a portable instrument. CdTe-based x-ray detectors are available with a small thermoelectric cooler which reduces the costs of the setup and makes it much more compact and suitable for a portable device. In reconstructing the original x-ray source spectrum from the measured scattered spectrum, there are various issues to consider. First, the measured spectrum should be corrected for background. This is usually approximated by the spectrum measured without the scatterer. Although this actually overestimates the background, because of scatter in the air volume taken in by the scatterer, this approximation is satisfactory under normal operation, because for most instruments, the background count rate typically accounts for less than a few percent of the count rate with scatterer thanks to the shielding of the detector from direct irradiation by the x-ray source. Second, the effects in the detector that distort the measured spectrum have to be considered. These effects are dominated by detector resolution, detector efficiency, and escape of fluorescence and Medical Physics, Vol. 42, No. 4, April 2015
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Compton scattered photons. Additional spectral distortion is induced by the effects of charge trapping and polarization in CdTe detectors.26 These effects result in some asymmetry in the full energy peaks and some instability in time. However, when using a thin detector with a high bias voltage at a low temperature (−50 ◦C), these effects are small compared to the other effects26–28 and are not taken into account in the spectrum reconstruction. Third, attenuation of the x-ray beam in the materials traversed from source to detector has to be taken into account. Fourth, effects have to be dealt with that are related to the scattering in the material of the scatterer. The latter effects include Rayleigh and multiple Compton scattered photons and the energy shift and intensity modulation due to the 90◦ Compton scattering. In addition, Doppler broadening of the spectrum due to the electron momentum in the scatterer not being zero and geometrical broadening due to the finite opening angles of the collimators influence the shape of the spectrum. A multitude of authors have contributed to Compton spectrometer design and the present state-of-the-art of spectrum reconstruction.14,15,17,20 In this paper, we present a compact portable Compton spectrometer that can be used in a clinical setting. This spectrometer is designed such that background by x-ray fluorescence from its shielding materials is kept to a minimum. Moreover, a systematic, comprehensive, and quantitative treatment is given of all the relevant details of the spectrum reconstruction. All processes that alter the spectrum have been investigated using the Monte Carlo code 2.5 (Ref. 29) to assess their relative importance in the spectrum reconstruction. To validate the instrument, the reconstructed spectrum of a mobile x-ray generator is compared with a directly measured spectrum. Furthermore, the Compton spectrometer has been used to measure spectra of three x-ray tubes of clinical CT scanners at various values of the tube voltage. These spectra are compared with each other, with theoretical spectra, and with spectra obtained from the x-ray tube manufacturer. The paper concludes with a discussion as to whether the instrument can be used in the quality assurance of x-ray tubes. 2. MATERIALS AND METHODS 2.A. Compton spectrometer design
The spectrometer (Fig. 1) is based on a PMMA (C5O2H8) scatterer (length 45 mm, diameter 6 mm). This low Z material favors Compton scattering over the photo-electric effect and reduces the contribution of Rayleigh scattering. The x-ray beam from the source is collimated by two circular (5 mm diameter) apertures that are machined in 8.8 mm thick square (10 × 10 cm2) lead plates that are clad by 3 mm aluminum on both sides to reduce the background due to x-ray fluorescence from the lead. Two identical collimators, as mentioned above, are used between the scatterer and the detector to define the opening angle of the detector. The collimators are placed on a bottom plate that has various slots to change their relative positions. In all experiments, the distance between collimator 1 and the scatterer was 18 cm, while collimator 2 was positioned at 9 cm from the scatterer; the distance
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F. 1. Schematic drawing of the Compton spectrometer.
between the scatterer and collimator 3 and collimator 4 was 9 and 23 cm, respectively. A removable detector shield (8.8 mm lead and 6 mm aluminum) is placed directly after collimator 4. This shield has a circular aperture that is concentric with the aperture of collimator 4. Additional shielding is placed between the source and detector shielding to prevent stray radiation from the source to reach the detector. The unscattered radiation is absorbed in a beam dump that consists of a 1 cm diameter and 1 cm deep cylindrical hole in a block of lead clad with aluminum. The angle between the lines from collimator 1 to scatterer and from scatterer to detector aperture is 90◦. The x-ray detector placed inside the detector shielding is a XR-100 T CdTe 3-stack from Amptek.30 This diode detector consists of three 0.75 mm thick layers of CdTe and has an area of 5 × 5 mm2. The layers are sealed in vacuum with a 250 µm beryllium window in front of the sensitive area of the detector. The efficiency up to 90 keV is essentially 100% and decreases to 55% at 150 keV. The energy resolution is 0.85 keV full width at half maximum (FWHM) at 60 and 1.5 keV FWHM at 122 keV. The detector stack is cooled to approximately −50 ◦C with a thermoelectric cooler to reduce noise. The detector signal is fed to the Amptek PX4 digital pulse processor, which digitizes the preamplifier output, processes the signal, and detects the peak value. The peak values are binned and used to form a spectrum. The PX4 communicates with a PC through a USB interface. The spectra are acquired with a bias of 1200 V on the CdTe stack, with the pile-up rejection logic of the PX4 on, and in 2048 channels using the software of Amptek. In all cases, the rise time and flat top time of the pulse in the slow channel are set at 3.2 and 0.4 µs, respectively. 2.B. Simulations
All Monte Carlo simulations were performed with the code 2.5.0.29 is a multipurpose Monte Carlo radiation transport code that tracks nearly all particles at nearly all energies. It has been issued in the series of Monte Carlo transport codes which have been developed at Los Alamos National Laboratory over the last six decades. All simulations were run in P E mode of which tracks all photons and electrons, until their energy is below the lower energy cutoff (1 keV for both photons and electrons; Medical Physics, Vol. 42, No. 4, April 2015
electron ranges in CdTe for energies lower than 1 keV are less than 0.1 µm). The Amptek CdTe detector was modelled as a 5×5×2.25 mm3 block of CdTe (density of 5.85 g cm−3) with a 250 µm sheet of beryllium (density of 1.848 g cm−3) in front. Dead layers and the electrical contacts of the detector were not included in the model. As their typical dimensions31 are very small compared to the crystal thickness (dead layer: 0.15 µm CdTe; contact: 0.2 µm platinum), it is justified to neglect them. 2.C. Spectrum reconstruction
The spectrum obtained with the Compton spectrometer is influenced by several physical processes along the trajectory of the photon from the source to the detector. For the reconstruction of the initial spectrum from the measured spectrum, simulations have been used to develop an algorithm to correct for these processes, step-by step and in reversed order (see Fig. 2). 2.C.1. Pile-up
The PX4 pile-up rejection logic removes pile-up events by using a fast pulse channel (fast channel resolving time τf = 0.6 µs). Events separated in time by more than τf but less than 4 µs are rejected. This results in a pulse rejection interval τr of 4–0.6 in 3.4 µs. The assumption is made that pu pile-up is a small effect. The pile up corrected spectrum Si (i = 1, ..., Nmax, in which Nmax is the number of energy bins used) can be calculated from the measured spectrum Si (in counts) by (τr + τf ) pu Si = Si *.1 + 2 T ,
N max j=1
τf S j +/ − T -
i−1
S j Si− j ,
(1)
j=1
where T is the acquisition live time. The factor in the first term corrects for the events removed by the pile-up rejection logic and those shifted to higher energy due to pile-up events during τf while the second term accounts for the pile up events in bin i occurring during τf . In all measurements with the Compton spectrometer, the count rate was typically in the order of 2000 counts/s, resulting in corrections for pile-up
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F. 2. Overview of the various reconstruction steps.
rejection and remaining pile-up of 2% and 0.2%, respectively. For some of the directly measured spectra, the count rate was a factor of two higher. 2.C.2. Background
The background of the Compton spectrometer is estimated from a spectrum taken without the scatterer. This background is in principle different for each x-ray tube because of the differences in shielding between tubes and changes also with tube voltage. In general, x-ray tubes used in a clinical environment seem to be better shielded than tubes used in an industrial setting. In all cases, this background should be reduced to values as low as reasonably possible and in the case of our Compton spectrometer, the total count rate of the background was always less than 5% of the spectrum with the scatterer without adding additional shielding for clinical xray tubes. The background could be reduced to less than this 5% with strategically placed extra shielding in case of industrial x-ray tubes. The background is corrected for by subtracting the measured, pile-up corrected background spectrum from the pile-up corrected spectrum. An example of a raw spectrum (before reconstruction) in combination with a background spectrum is shown in Fig. 3. The spectra are taken (1500 s acquisition time) using an industrial x-ray unit (GE Inspection Technologies, ERESCO 42 MF3.1) at 200 kV and 4.5 mA at the industrial irradiation facility of Applus RTD, Veendam, The Netherlands. The raw spectrum clearly shows the two characteristic x-ray peaks originating from the tungsten anode. The total count rate in the background spectrum was 1.5% of the raw spectrum count rate and the peaks in the background spectrum are the characteristic x-rays from the lead of the shielding.
of Compton scattered x-rays. For the CdTe detector, there are eight significant K-line escapes (Kα1, Kα2, K β1, K β2 for both cadmium and tellurium). Simulations were used to estimate the magnitude and shape of the spectral distortion of each of the nine possible incomplete energy deposition events (eight K-line escapes and Compton escape), expressed as a fraction of the number of full energy events. In these simulations, a disk shaped photon source was used facing the front side of the detector. The diameter of the disk was 5 mm and photons were seeded in a direction perpendicular to the disk, thus mimicking the collimated photon beam in the Compton spectrometer. The simulations were done with monoenergetic photons for energies from 10 to 200 keV in 10 keV steps. In the energy range below 10 keV and in the range of the K-edges of cadmium and tellurium, steps of 1 keV were used. For each energy, the energy deposition spectrum in the detector was obtained using the F8 tally. The energy binning of the simulated spectra was 0.1 keV and the
2.C.3. Incomplete energy deposition in the detector
Two types of incomplete energy deposition events may occur in the detector: escapes of K-line x-rays and escapes Medical Physics, Vol. 42, No. 4, April 2015
F. 3. Raw spectrum and background spectrum (×10) taken with the Compton spectrometer in combination with an ERESCO 42 MF3.1 industrial x-ray unit at 200 kV and 4.5 mA.
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edge energy. The distribution of the Compton scattering events was approximated by a rectangle that runs along the energy axis from zero to the Compton edge energy. The height of this rectangle was chosen such that the integral count in the rectangle was equal to the total number of Compton events. A similar stripping procedure as for the K-line escape was used to strip the Compton events from the spectrum and reposition them in the channel with the full energy events. All eight Kescape and the Compton events corrections were executed simultaneously, channel by channel towards lower energy. 2.C.4. Detection efficiency F. 4. Simulated spectrum for 100 keV photons showing the various escape events and the full energy peak.
escape events, Compton events, and full energy events could be clearly separated (Fig. 4). Their contributions to the spectrum have been calculated relative to the full energy events (Fig. 5). The fraction of K-escapes is highest for low energy incoming photons as their point of interaction is close to the surface and the K-line x-rays can escape from the detector before being absorbed. Clearly visible (Fig. 5) are the increases in the Kescape fractions of cadmium at the energy of the K-edge of Te (31.9 keV), due to the decrease in total energy events caused by escaping K-line x-rays of tellurium. These contributions are used to correct the measured spectra with a stripping procedure which starts at the highest energy channel assuming this contains only full energy events. The escape events in the channels corresponding to these events (full energy minus escape line energy) are calculated and subtracted from the spectrum and assigned to the full energy channel. This is repeated channel by channel towards lower energy and ends at the channel corresponding to the K-
F. 5. K -line escape events and Compton escape events as a fraction of the full energy peak (x-axis). Medical Physics, Vol. 42, No. 4, April 2015
In the next step, the spectrum is corrected for the energy efficiency of the Amptek detector by dividing the spectrum by the detector’s total energy efficiency curve, as after the preceding corrections the spectrum is the result of any interaction in the detector. This efficiency curve was determined from the set of detector simulations and is shown in Fig. 6 together with a simulated full energy efficiency curve. Our simulated total efficiency curve is equal (within 1%) with the efficiency curve provided by Amptek32 (calculated on the basis of thicknesses and linear attenuation coefficients of beryllium and CdTe). 2.C.5. Multiple Compton scattering and Rayleigh scattering correction
At this stage, the reconstructed spectrum contains 90◦ Compton scattered photons and photons that were Rayleighscattered or multiple-Compton scattered. The latter contributions that have to be removed before the Klein-Nishina formula for 90◦ scattered photons can be applied. The magnitude of both contributions has been assessed by simulations. In case of multiple Compton scattering, only the contribution of photons that scattered twice were taken into account. The energy range of these photons is bounded on the lower side and the upper side by the energy of photons that have scattered twice over 135◦ and twice over 45◦, respectively. The probability over
F. 6. Total and full energy peak efficiency of the Amptek-100 T CdTe 3-stack detector.
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source and with µair the linear attenuation coefficient of air. The attenuation in the material of the scatterer is accounted for by using a procedure described by Matscheko and Ribberfors.16 They showed that the average distance d s before and after the 90◦ scattering event is 8r/3π with r the radius of the scatterer. For our 6 mm diameter scatterer, this amounts to d s = 2.55 mm. Average correction factors of exp(d s µPMMA (E0)) and exp(d s µPMMA (E)) to correct for the attenuation in the scatterer (µPMMA is the linear attenuation factor of PMMA) are used. These correction factors are relatively small; typically in the order of 1.1–1.2 over the energy range 20–150 keV. 2.C.8. Broadening aspects
F. 7. Contribution of multiple and Rayleigh scattered photons expressed as fractions of the number of 90◦ scattered photons. The error bars are 1σ uncertainties that result from the Monte Carlo statistics.
this range has been found to be constant. Rayleigh scattered photons appear in the energy channel that corresponds to their original (before scattering) energy and can thus easily be identified. The fraction of multiple scattered photons decreases slightly as a function of energy and is in the order of about 10% over the relevant energy range. This also shows that photons that are Compton scattered more than twice will only contribute in the order of 1% and lead to negligible spectrum distortion. Rayleigh scattering is only significant at low energies and is negligible for energies higher than 50 keV (Fig. 7). 2.C.6. 90◦ Compton scattering
The photon energies E0 of the primary spectra were reconstructed by correcting photon energies E of the 90◦ scattered spectra, for the energy shift resulting from the 90◦ scatter by using E0 =
E , 1 − (E/mc2)
(2)
where mc2 is the rest mass of the electron. The primary spectra S0(E0) are reconstructed by using the Klein-Nishina formula at 90◦, 2S(E0)(1 + q)2 , (3) (1 + (q2/(1 + q))) with q = E0/mc2 and S(E0) the spectrum with all corrections except that for the energy dependent cross section of 90◦ Compton scattering. S0(E0) =
2.C.7. Intensity attenuation
The intensity of the x-ray beam will be attenuated due to the air and scatter material through which the beam passes. The attenuation in air is corrected for by multiplying the spectrum before and after the scatterer with a factor exp(d ds µair (E0)) and exp(d ss µair (E)), respectively, with d ds and d ss the distances between detector and scatterer and between scatterer and x-ray Medical Physics, Vol. 42, No. 4, April 2015
There are three processes that cause the reconstructed spectra to be broader than the primary spectra. First, the geometry of the collimators allows photons that are scattered through a range of angles around 90◦ to reach the detector, which will influence the energy of the scattered photons (geometrical broadening). Second, in the reconstruction it is assumed that the electrons, off which the photons scatter, are at rest. Actually, these electrons have a momentum distribution and this will translate in a broadening of the energy distribution of the scattered photons (Doppler broadening). Third, the resolution of the detector itself will broaden the spectrum (detector resolution). The effect of geometrical and Doppler broadening has been estimated from simulations. The detector resolution is taken from the Amptek detector specifications. The geometry of the simulations comprised the 6 mm diameter PMMA scatterer, a 5 mm diameter disk-shaped photon source and the Amptek CdTe detector placed in the 90◦ set up of the Compton spectrometer. Simulations were performed with monoenergetic photons (range 25–200 keV) using two photon physics settings, namely, Doppler effect off and Doppler effect on and using a 0.1 keV energy-binned F4 flux tally on the entrance window of the detector. In the first setting, the spectrum is only broadened due to geometrical effects, in the second setting, both geometrical and Doppler broadening are included. These broadening effects were assessed as a function of photon energy by starting monoenergetic photons from the disk source and determining their FWHM (assuming a Gaussian profile) at the entrance window of the detector. Figure 8 shows the FWHM due to the three processes as a function of energy. The total resolution is largely determined by Doppler broadening and detector resolution; it increases from approximately 1.0 at 25 keV to 3.0 at 150 keV. 2.C.9. Implementation of spectrum reconstruction
All the reconstruction steps shown in Fig. 2 are implemented in a Mathematica 8 (Wolfram research) notebook.33 The notebook starts by reading the raw spectrum, background spectrum, their acquisition times, and the spectrum energy calibration. For indirectly measured spectra, the notebook sequentially performs all reconstruction steps, for directly measured spectra, only corrections for background, detector effects, and attenuation in air are made. No corrections are made for the spectrum broadening.
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F. 8. FWHM, in keV, due to geometrical and Doppler broadening and due to detector resolution as a function of energy. Also, the FWHM resulting from the total of all three contributions is shown (solid line).
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F. 9. A photograph of the Compton spectrometer at the isocenter of the Somatom Definition Flash at Siemens Medical Solutions, Forchheim, Germany.
4. RESULTS AND DISCUSSION 4.A. Validation experiments
3. EXPERIMENTS 3.A. Validation experiments
Direct and indirect spectra were measured using a mobile x-ray source (Siemens Nanomobil) at 100 kV. Exposure times were typically a few 100 s and consisted of pulsed emissions of 0.4 s (the source could not be operated in continuous mode) with a tube current versus time product of 20 mA s. In the case of the directly measured spectrum, the scatterer was removed from the Compton spectrometer. To reduce the flux, the x-ray source was located at 23.95 m from the CdTe detector in the spectrometer that was orientated such that the detector and the two collimators 3 and 4 were in line with the x-ray source. Even at this distance, the flux was too high and further flux reduction was achieved by placing a 0.5 mm diameter tungsten collimator between collimators 3 and 4. The indirect spectrum was measured using the same x-ray source settings but with the source placed at 25 cm before collimator 1 and with the PMMA scatterer in position. 3.B. Clinical CT scanners
Indirect spectra were measured with the scatterer of the Compton spectrometer positioned at the isocentre of a Siemens SOMATOM Definition Flash (dual source CT with two x-ray tubes, A and B) at Siemens Medical Solutions at Forchheim, Germany (Fig. 9) and a Siemens SOMATOM Definition (dual source CT, only one tube measured) at the University Medical Center in Groningen, The Netherlands. For tube A and B of the Definition Flash and the tube of the Definition, spectra were collected at 80, 100, 120, 140 kV with factory supplied filtration; for tube B of the Definition Flash also, a spectrum at 140 kV with an additional filtration of 0.4 mm tin was measured. In all cases, the spectrum acquisition time was 400 s (live time), while a 200 s background spectrum was measured. The x-ray tube current was 25 mA in all measurements. Medical Physics, Vol. 42, No. 4, April 2015
The raw and reconstructed indirect and direct spectra measured for the Siemens Nanomobil are shown in Fig. 10. In both the indirectly and directly measured spectra, the effect of the stripping procedure to correct for the incomplete energy deposition is evident in the lower energy channels where the count rate is markedly decreased by the correction. The reconstructed indirect spectrum is shifted toward higher energy due to the 90◦ Compton scattering correction. In the direct spectrum, the correction for the attenuation in 23.95 m air shifts the weight in the spectrum toward higher energies. Because of the large distance, the correction becomes very large at low energies, e.g., the correction factor is approximately 10 at 20 keV and exponentially decreases to 1.6 at 100 keV. Therefore, the reconstruction is truncated at approximately 20 keV, which explains the discontinuity in the reconstructed spectrum around 20 keV (Fig. 10). Comparison of the reconstructed direct and indirect spectrum (Fig. 11) shows a very good correspondence between both spectra. The ratio between the direct and indirect measured spectra is close to unity (Fig. 11); starting above the discontinuity around 20 keV and up to 100 keV, we find an average (and standard deviation) of this ratio of 0.99(0.07). It is also clear that the peaks of the characteristic x-rays of tungsten have a smaller width in the direct spectrum. This is to be expected, as the direct spectrum is not influenced by geometrical and Doppler broadening of which especially the last contribution has a significant effect on the indirectly measured spectrum. However, the FWHM at the Kα x-ray peak in the direct spectrum (2.8 keV) is more than a factor three larger than expected from the detector resolution (0.9 keV) only. In fact, based on the detector resolution only, the Kα1 (59.3 keV) and Kα2 (58.0 keV) lines should appear resolved in the directly measured spectrum. This extra broadening may have been caused by the still relatively high count rate (a factor two higher than in the indirect measurements), by scatter in the pinhole collimator to reduce this count rate or due to
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F. 11. Comparison of reconstructed direct and indirectly measured spectra from the Siemens Nanomobil portable x-ray source. Bottom figure gives the ratio between the direct and indirect spectrum.
F. 10. Raw and reconstructed spectra from the Siemens Nanomobil portable x-ray source, indirectly (top) and directly (bottom) measured spectra are shown.
scatter in the air between the detector and the x-ray source. The first effect was assessed by measuring the FWHM of the Kα line of terbium (from a terbium-foil under impinging alpha particles) for different count rates obtained by varying the detector source distance. A maximal increase of 15% in FWHM at the acquisition count rate was estimated, thus explaining only a small part of the observed FWHM. From the literature, we found that a long distance between detector and x-ray source seems to negatively affect the energy resolution. Deresch et al. used an Amptek CdTe-stack spectrometer with pinhole collimation and a detector source distance of 16 m and from their spectra, we estimate a FWHM of approximately 3 keV at the tungsten Kα line (unresolved) which is in line with our findings.34 Wanatabe et al. used a similar detector, but instead of pinhole collimation and a large detector to source distance, they used a low-count-rate x-ray generator to reduce the photon flux on the detector.35 In their spectra, the Kα1 and Kα2 lines of tungsten are resolved. Consequently, a combination of rate effects and extra scatter invoked by the large source-detector distance most likely is the cause of the observed extra broadening in our directly measured spectra. Broadening is one of the main limitations in measuring spectra of x-ray tubes. All measured spectra are blurred by the finite resolution of the detection system. However, the x-ray spectrum that enters a tissue that is assessed in a CT scanner is not blurred at all, the only energy blurring expected for the Medical Physics, Vol. 42, No. 4, April 2015
tungsten characteristic x-rays is due to its natural line width with superposed broadening as a result of the temperature of the anode and by scatter in some intermediate materials (filters, air). The first two effects are very small. The broadening due to scatter can be assessed by Monte Carlo simulations and all codes show this also gives almost negligible broadening.36 This suggests that the best choice for an input spectrum for, e.g., a DECT electron density, effective atomic number assessment might be a measured spectrum but with the peak intensities of the characteristic x-ray integrated and artificially (by hand) positioned in the measured spectrum at the energies and in the relative ratios that are known from the literature. The method is further justified by the observation that the shape of a smooth structure like the bremsstrahlung continuum is only slightly influenced by the energy blurring (slightly less steep slopes at the sides of the continuum). 4.B. Clinical CT scanners
The reconstructed unnormalized spectra for all energies (Fig. 12) are rather similar for all three tubes. The characteristic x-rays of tungsten are barely visible in the 80 kV spectra and become more prominent for the higher tube voltages. Also, for all three tubes, a small glitch in the 140 kV spectra is visible at approximately 90 keV, this is due to subtraction of a background spectrum containing Kα x-rays from lead (at 73 and 75 keV, see Fig. 3) from the raw spectrum. These Kα x-rays result directly from interaction of the x-rays from the tube with the shielding of the detector and are thus not energy shifted by the scatterer. Imperfections in this subtraction propagate to higher energies due to the 90◦ Compton energy shift correction. For the spectra at lower energies, because of the much
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F. 13. Zoomed view of the high energy part of the spectra of tube A of the Definition Flash (Top) and of the tube of the Definition (Bottom) at different source voltages.
F. 12. Reconstructed spectra for both tubes ( A and B) of the Definition Flash and of the tube of the Definition.
lower production of Kα x-rays, the effect is too small to be noticeable. The end point energies of the spectra of both tube A and B of the Definition Flash are consistent with the high voltage used (Fig. 13, top). However, for the tube of the Definition, it is clear that for all spectra, the end point energy is about 2 keV higher (Fig. 13, bottom), indicating that deviations from specified high voltage can be readily detected with the Compton spectrometer. The spectra of all three x-ray tubes were re-binned to 1 keV energy bins, normalized and are compared for two high voltage settings (80 and 140 keV) in Fig. 14. Figure 15 shows the re-binned spectrum for tube B at 140 keV with 0.4 mm tin Medical Physics, Vol. 42, No. 4, April 2015
filtration. This comparison shows that the normalized spectra of all three tubes are nearly identical except for the somewhat larger endpoint energy of the tube of the Definition. Theoretical spectra based on a deterministic model of xray production calculated with the software program SpekCalc (Refs. 37–39) are also presented in Figs. 14 and 15. The SpekCalc spectra were computed using a 1 keV grid and a 8◦ anode angle40 and were filtrated with 3 mm aluminum and 0.9 mm titanium (information from the CT scanner manufacturer) and 500 mm air. For tube B of the Definition Flash also, a spectrum with an extra filtration of 0.4 mm tin was calculated. Other parameters, e.g., the ratio between the bremsstrahlung continuum and the characteristic x-rays (P-parameter) were set at their default values. Thereafter, the spectra from SpekCalc were broadened using a Gaussian with an energy dependent FWHM reflecting the combined broadening due to Doppler, geometry, and detector resolution (Fig. 8). The SpekCalc spectra are in very good agreement with the measured spectra with respect to the shape of the bremsstrahlung continuum, the end point energy, and the location of the characteristic x-rays. However, the SpekCalc spectra show higher characteristic x-ray peaks. It is realised that the SpekCalc program does not include any broadening of the spectrum, but it was expected that after broadening, the calculated spectra conform our spectrometer specifications,
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facturer (Siemens Medical Solutions, Forchheim, Germany). These spectra were directly measured a few decades ago and corrected for the intrinsic filtration of the x-ray tube. With respect to characteristic peak height, these spectra are in between our results and the SpekCalc calculations. The rest of the spectrum is in very good agreement with both our results and the SpekCalc spectra. Measurements of x-ray spectra in radiology and radiotherapy are not performed on a regular basis. One of the often mentioned constraints is that these measurements are complex and time consuming.41,42 This constraint has been lifted by our Compton spectrometer design for use at CT scanners as for the positioning of the spectrometer, the alignment lasers of the scanner can be used, leading to setting-up times of typically 10–15 min. Combined with spectrum acquisition times of about 5 min per spectrum, a protocol for measuring spectra at two or three energies will not last more than 30–45 min. In this light, our method does not seem more complex or time-consuming than currently used half-layer thickness41 assessments or recently proposed methods based on direct43 or indirect44 transmission measurements. Measurements with a Compton spectrometer are too involved to be used on a day-to-day basis but the instrument is well suited to be used during, e.g., commissioning, troubleshooting, or yearly CT scanner performance tests in which the instrument is taken of the clinical scheduling for a larger amount of time.
F. 14. Normalized and re-binned (to 1 keV) spectra of all three CT x-ray tubes compared at two high voltages. Also shown are the spectra calculated with SpekCalc and the spectra obtained from Siemens.
the measured and calculated peaks would fall in line. In a search for the reason of the discrepancy, we adjusted the Pparameter of the SpekCalc program and also tried variations in the value of the anode angle, but we did not succeed in a much better match of the SpekCalc results to the measurements. Finally, also output spectra at different voltages of the xray tube used in the Definition were obtained from the manu-
5. CONCLUSION A compact portable Compton spectrometer to indirectly measure the spectra of x-ray tubes has been designed, constructed, and validated. The algorithm to reconstruct the original x-ray spectrum from the indirectly measured spectrum was described step-by-step and the effect of each reconstruction step was quantitatively assessed by Monte Carlo simulations. The measurement and reconstruction procedure was validated by comparing directly and indirectly measured spectra from a mobile x-ray unit. Thereafter, the Compton spectrometer was used in measurements of x-ray spectra of clinical CT scanners. These measurements show that our compact Compton spectrometer can be rapidly set-up using the alignment lasers of the CT scanner, thereby enabling its use in commissioning, troubleshooting and, e.g., annual performance check-ups of CT scanners.
a)Current
F. 15. As Fig. 14 except only tube B at 140 keV with 0.4 mm tin filtration. Medical Physics, Vol. 42, No. 4, April 2015
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