Energy Calibration of the Pixels of Spectral X-ray ... - Semantic Scholar

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Jul 8, 2014 - Two automated energy calibration techniques for spectral x-ray detectors were proposed and cross-validated. One tech- nique is developed for ...
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Energy Calibration of the Pixels of Spectral X-ray Detectors Raj Kumar Panta*, Michael F Walsh, Stephen T Bell, Nigel G Anderson, Anthony P Butler, and Philip H Butler

Abstract—The energy information acquired using spectral xray detectors allows non-invasive identification and characterization of chemical components of a material. To achieve this, it is important that the energy response of the detector is calibrated. The established techniques for energy calibration are not practical for routine use in pre-clinical or clinical research environment. This is due to the requirements of using monochromatic radiation sources such as synchrotron, radio-isotopes, and prohibitively long time needed to set up the equipment and make measurements. To address these limitations, we have developed an automated technique for calibrating the energy response of the pixels in a spectral x-ray detector that runs with minimal user intervention. This technique uses the x-ray tube voltage (kVp) as a reference energy, which is stepped through an energy range of interest. This technique locates the energy threshold where a pixel transitions from not-counting (off) to counting (on). Similarly, we have developed a technique for calibrating the energy response of individual pixels using x-ray fluorescence (XRF) generated by metallic targets directly irradiated with polychromatic x-rays, and additionally γ-rays from 241 Am. This technique was used to measure the energy response of individual pixels in CdTe-Medipix3RX by characterizing noise performance, threshold dispersion, gain variation and spectral resolution. The comparison of these two techniques shows the energy difference of 1.5 keV at 59.5 keV which is less than the spectral resolution of the detector (FWHM of 8.9 keV at 59.5 keV). Both techniques can be used as quality control tools in a pre-clinical multi-energy CT scanner using spectral x-ray detectors. Index Terms—Energy calibration, x-ray detector, spectral resolution, x-ray fluorescence, Medipix

I. I NTRODUCTION Spectral x-ray detectors can measure the energy of an individual photon at a count rate of approximately 107 counts per second per mm2 [1]. They are used to measure the energy dependence of x-ray attenuation. Each element has a unique xray attenuation property which provides the basis for deriving Raj Kumar Panta* and Nigel G Anderson are with the Department of Radiology, University of Otago, Christchurch 8140, New Zealand (email: [email protected]; [email protected]; [email protected]) Anthony P Butler is with the Department of Radiology, University of Otago, Christchurch 8011, New Zealand, Department of Electrical and Computer Engineering, University of Canterbury, Christchurch 8140, New Zealand and European Organization for Nuclear Research (CERN), Geneva 23, Switzerland (e-mail:[email protected]). Philip H Butler is with the Department of Physics and Astronomy, University of Canterbury, Christchurch 8140, New Zealand and European Organization for Nuclear Research (CERN), Geneva 23, Switzerland (email:[email protected]). Michael F Walsh,, Stephen T Bell, Anthony P Butler and Philip H Butler are with MARS Bioimaging Ltd, Christchurch, New Zealand. (e-mail: [email protected]) Manuscript submitted on: July 8, 2014

quantitative information about the chemical composition of materials non-invasively. Some of the current bio-medical applications in spectral imaging are, differentiating contrast agents such as barium from iodine [2], vascular imaging [3], studying atherosclerotic plaque composition [4], pre-clinical CT [5], K-edge imaging [6], and quantitative soft tissue imaging [7]. Unlike other x-ray detectors, a spectral x-ray detector can be used to measure the x-ray attenuation coefficients of materials at different energies in a single exposure. Optimal selection of the detected energy ranges is highly desirable for maximizing the difference in x-ray attenuation that determines the contrast between the adjacent elements in a material. The accurate selection of energy range requires calibrating the spectral x-ray detector against known reference energies. Accurate and precise energy calibration of a spectral x-ray detector is essential for K-edge imaging applications where the separation of K-edges for many materials of interest is only few keV apart. A. Medipix3RX detector A CdTe-Medipix3RX detector [8] was used for this study. The Medipix3RX ASIC is designed for spectroscopic imaging using 110 µm pixel pitch [8]. Each pixel cell contains an analogue section, followed by a digital section [8]. In the analogue section of the cell, the global energy threshold is set via a reference current, using a digital-to-analogue converter (DAC). In this context we use global to refer to ASIC parameters that are controlled by a single DAC that is applied to all pixels. The discriminator in the analogue section of the pixel cell compares the pulse height of an amplified charge with the reference current set by the energy threshold DAC. If the pulse height of the charge is higher than the reference current, the counter in the digital part of the corresponding pixel is incremented. In this way, the energy threshold DAC can be adjusted to select the range of photon energies that will be counted. It is the ability to use adjustable energy threshold DAC that allows a hybrid pixel detector to be used as a spectral detector. The pixels of the Medipix3RX ASIC can be operated in either Single Pixel Mode (SPM) or Charge Summing Mode (CSM) [8]. Single Pixel Mode is a basic mode of operation in which each pixel works independently of its neighbours. An important factor that distorts the energy response of a small (110 µm) pixel in SPM is the charge sharing effect. Charge sharing occurs when the charge cloud resulting from a photon

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TMI.2014.2337881, IEEE Transactions on Medical Imaging IEEE TRANSACTIONS ON MEDICAL IMAGING

B. Global energy calibration using x-ray kVp An automated technique for calibrating the global energy threshold using the peak tube voltage (kVp) of an x-ray tube has been proposed. It requires minimal user intervention, and no extra resources in a pre-clinical or clinical CT scanner using spectral x-ray detectors. The kVp of an x-ray tube is the maximum potential difference applied between anode and cathode. According to Duane-Hunt Law [20], the maximum energy in the x-ray emission spectrum is equal to the peak potential applied to the x-ray tube. Fig. 1 illustrates the effect of kVp on the energy end-point of an x-ray emission spectrum as energy end-point shifts to the higher energy while increasing the x-ray kVp. The x-ray spectra were simulated using the Poludniowski model [19]. With the advancement of x-ray detector technology, the kVp of an x-ray tube can be measured using high atomic number (Z) materials like CdTe [13], [21] and CdZnTe [22]. This study hypothesizes that the kVp of an

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interaction with a pixel in the sensor layer is collected across several adjacent pixels. Charge sharing causes both spatial and spectral distortion of the signal, and when unaccounted for, it appears as several lower energy photon interactions in adjacent pixels. The Charge Summing Mode in Medipix3RX ASIC is an advanced mode of operation that is designed to account for the charge sharing effect. Charge Summing Mode operates by summing charges that arrive coincidentally in adjacent pixels of the array to reconstruct the total energy deposited by each interaction. In CSM the Medipix3RX arbitration circuit is used to identify co-incident interactions across clusters of 3x3 pixels and select the 2x2 cluster closest to the site of interaction. The reconstructed charge is the summed charge deposited in this 2x2 pixel cluster. The reconstructed (summed) charge is allocated to the pixel closest to the original site of interaction by the arbitration circuit. To enable charge summing, neighboring pixels communicate on an event-by-event basis. Further details of CSM in Medipix3RX ASIC can be found in elsewhere [8]. Manufacturing variations in the Complementary Metal Oxide Semiconductor (CMOS) ASIC can cause intrinsic interpixel variation in the energy threshold (threshold dispersion) across the pixel matrix [9]. The Medipix3RX ASIC has 9bit (0 - 511) energy threshold DACs. The energy threshold DACs are global current DACs which set the same energy threshold values for all pixels in the matrix. Additionally, each of two discriminators in a pixel contains an independent 5bit (0 - 31) fine adjustment DAC to correct the inter-pixel threshold dispersion. The process of reducing the inter-pixel threshold dispersion by optimising the fine adjustment DAC of each pixel is called threshold equalization. However, the threshold dispersion cannot be completely eliminated by the threshold equalization procedure due to the limited range and resolution of the fine adjustment DAC. The inter-pixel variation of the energy response can be a limiting factor in global spectral resolution, the precision of energy calibration and causes residual fixed pattern noise [8]. Calibrating the energy response of individual pixels is necessary since the residual threshold dispersion can be sufficient to degrade the contrast and spatial resolution [10]. Existing energy calibration techniques employ monochromatic photon sources such as radio-isotopes [11]–[14], synchrotron [15], [16] and X-ray fluorescence (XRF) from metallic targets [8], [17], [18]. Each of these methods has limitations that reduce their usefulness in pre-clinical or clinical applications such as special setup of equipment, long measurement time, and physical space required for maintaining the proper geometry of x-ray or γ-ray source, detector, and target metallic foils. Also, radio-isotopes are not readily available in a small biological laboratory and frequent use of them may not be justifiable from the radiation protection point of view. To address some of the limitations inherent to existing energy calibration techniques, this study aimed to develop pragmatic techniques for both global and pixel-by-pixel energy calibration of a spectral x-ray detector. The second aim of this study was to use the pixel-by-pixel energy calibration approach to measure the energy response of individual pixel in terms of noise performance, threshold dispersion, gain variation and spectral resolution in a CdTe-Medipix3RX detector in CSM.

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Fig. 1: X-ray emission spectra emitted from an x-ray tube simulated using the Poludniowski model [19]. It illustrates the effect of kVp on the energy end-point of a spectrum.

Fig. 2: The workflow of proposed global energy calibration technique using an x-ray kVp.

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TMI.2014.2337881, IEEE Transactions on Medical Imaging IEEE TRANSACTIONS ON MEDICAL IMAGING

x-ray tube can be used as a reference energy to calibrate the spectral x-ray detector since operating kVp of an x-ray tube defines the maximum photon energy hitting the detector. The workflow of the energy calibration technique using xray kVp is shown in Fig. 2. For each energy calibration point, the x-ray kVp is set to the selected calibration energy. The corresponding threshold DAC is estimated and set on the detector. Open-beam frames are acquired at this threshold DAC, and the transition threshold corresponding to the selected calibration energy is found by counting the number of pixels either counting (on) or not counting (off). When calibrating the global energy threshold DAC, the transition threshold is taken to be the threshold DAC where 50% of pixels are counting. This represents the mean of the gaussian threshold dispersion at the selected calibration energy. The slope of pixels counting versus threshold DAC gives an indication of threshold dispersion at the reference energy. For an ideal detector, the discriminator response would be a step function. The calibration algorithm uses an iterative method to locate the threshold values that result in 50% of pixels counting at each kVp setting. If the number of pixels is 50% within our tolerance values (user defined), the energy threshold is assigned to the given kVp and the procedure iterates to the next energy. Otherwise, the iteration re-estimates the threshold DAC that will give 50% within our tolerance values.

Fig. 3: Experimental setup for measuring XRF from metallic targets by irradiating with polychromatic x-rays from x-ray tube.

C. Energy calibration of individual pixels using x-ray fluorescence An XRF method was used in order to achieve pixel-bypixel energy calibration in a spectral x-ray detector. This method uses the polychromatic x-ray from the x-ray tube to irradiate the metallic targets directly. The emission of XRF from a metallic target involves the interaction of x-rays with the electrons in a metallic target. When a metallic target is bombarded with the x-rays having the equivalent energy as the binding energy of electrons, the atoms in the metallic target become ionized which creates electronic vacancies in the innermost shell of the atom. These electronic vacancies will be filled by free electrons from the outer shell. When this electronic transition happens, characteristic radiation, or XRF, is emitted with the same energy as the difference in energy between the inner shell and the outer shell of an atom. The

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XRF is specific to an element as the energy levels of electrons in an atom have fixed orbital energy states. This energy calibration technique exploits the XRF emitted from a metallic target that is directly irradiated with x-rays generated from the x-ray tube in a CT scanner. The count rate measured in each pixel is lower than the count rate measured in the whole pixel matrix because photon counts are split over many relatively small areas. For some existing energy calibration techniques, this may lead to a prohibitively long measurement time to obtain sufficient photon-count statistics in a pixel, for example techniques that use radio-isotopes with limited source activity. The proposed energy calibration technique uses the high x-ray flux generated from an x-ray tube to generate XRF photons from target metallic foils at a sufficiently high flux to allow fast energy calibration of individual pixels in a pixel matrix. The metallic target can be mounted either on the exit window of an x-ray source or on the front of the detector as shown in Fig. 3. II. M ETHODS A. MARS camera with Medipix3RX We used a MARS camera [18], [23], [24] fitted with a Medipix3RX ASIC bump-bonded to a standard high resistivity 2 mm thick CdTe pixel sensor layer for this study. The sensitive area of each chip was 1.408 × 1.408 cm2 which is subdivided into a 128 × 128 array of pixels with a pixel pitch of 110 µm. The CdTe sensor layer was configured as a ‘pn junction’ diode supplied with a negative high-voltage bias (-750 V) for collection of electrons. The counter depth was 12-bit providing a dynamic range of 4095 counts per pixel. B. Threshold equalization The detector was equalized using the electronic noise-floor. The noise floor of each pixel is caused by the the overall noise contribution from sensor layer (eg. leakage current) and readout electronics (eg. noise from preamplifier and shaper [25]). This can be used as a reference signal for equalization as the noise floor of each pixel can be considered to be uniform across the whole pixel matrix. The inter-pixel variation in energy response across the entire pixel array was minimized by individually adjusting the offset of the energy discriminator using the ASIC electronic noise floor using the method previously described [26]. After threshold equalization, an integral noise floor scan was run in the absence of radiation flux to establish the noise floor in both SPM and CSM. TABLE I: A summary of metallic targets and reference energies used for energy calibration.

Atomic No. (Z) 42 46 49 73 82

Metallic targets Molybdenum (Mo) Palladium (Pd) Indium (In) Tantalum (Ta) Lead (Pb)

XRF (Kα1 ) energy in keV 17.48 21.18 24.20 57.53 74.97

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are presented in TABLE I. In separate measurements, each foil was placed on the front face of the MARS camera as shown in Fig. 3. A polychromatic x-ray tube (Model SB-120-700-PCW, Source-Ray Inc, Ronkonkoma, NY) was used to irradiate Mo, Pd, In, Ta and Pb foil at a tube voltage of 30 kVp, 35 kVp, 40 kVp, 70 kVp and 90 kVp respectively and the tube current and exposure time were adjusted to get between 1500 - 2000 photon counts per pixel in each measurement. The tube voltage used for measurement with each foil was optimized to maximize the XRF signal, and minimize the Bremsstrahlung transmission and scattering contamination from the direct exposure. A threshold scan is used to acquire the distribution of photon with respect to their deposited energy in the sensor over a range of energy thresholds. The threshold scan can be expressed as: Z ∞ M (ET HL ) = D(E) dE (1)

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Fig. 4: Integral noise floor threshold scan in (a) SPM across 8 counters (C1 - C8) and (b) CSM across 4 counters (C1 - C4) after threshold equalization using the intrinsic noise of front-end of chip.

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C. Experimental Setup and data acquisition The calibration of the global energy threshold using the xray kVp technique was done over the range of (20 - 100) kVp. The workflow of this technique is shown in Fig. 2. Calibration energies of 30 kVp, 40 kVp, 60 kVp and 100 kVp were used. For each of these energies open-beam frames were obtained and used to locate the transition threshold value where 50% pixels are counting (on) and 50% not counting (off), by the iterative method described by Fig. 2. The tube current of 5 µA and exposure of 500 ms were used with a source to detector distance of 20 cm. Energy spectra of individual pixels were measured by two methods. The first method involves the measurement of XRF emitted by metallic foils directly irradiated with a uniform polychromatic x-ray beam. The second method involves the measurement of emission energy spectra from a 241 Am γ-ray source. Different metallic foils of Mo, Pd, In, Ta, Pb with 100 - 300 µm thickness were used to generate the XRF signal. The corresponding XRF (Kα1 ) energy from these metallic targets

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Fig. 5: Distribution of noise floor in individual pixel in first counter in (a) SPM and (b) CSM after threshold equalization based on intrinsic noise of front-end of chip.

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where M is the number of measured events, ET HL is the applied threshold energy, D is the distribution of photons and E is the deposited energy of a photon. The threshold scan was performed by gradually increasing the threshold DAC to acquire the number of photon events as a function of the applied threshold DAC over the range of interest. The threshold scan was repeated 100 times to obtain reliable photon count statistics for each pixel. The registered integral photon counts for each pixel were differentiated with respect to the threshold DAC to obtain the actual photon counts at corresponding energy bin for the pixel. The second method involves the measurement of the emitted energy spectrum from 241 Am. The 241 Am gamma ray source (1.56 GBq, emission γ-ray peak at 59.5 keV) was placed 7 mm away from the CdTe-Medipix3RX detector and 5 second exposures were made at each threshold DAC in the range of 0 - 511 with step size of 3. The threshold scans were repeated 168 times over the period of 20.5 hours. Note that the photon intensity from 241 Am was low which demands a long exposure time to obtain sufficient photon counts in each pixel without affecting the width of the photo - peak. The performance of energy calibration techniques using an x-ray kVp and XRF from metallic targets were compared at the whole chip level. Global energy calibration of x-ray

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Fig. 7: Energy Calibration of the CdTe-Medipix3RX in CSM (a) Energy response function of a pixel measured with XRF of Mo, Pd, In, Ta, Pb and the γ-ray peak from 241 Am. The height of each peak is normalised to one for better visualisation of its relative position in x-axis with other peaks and (b) Establishing the relationship of threshold DAC at XRF-peaks and photo-peak position with the corresponding reference energy for a pixel.

kVp was performed at 18 kVp, 20 kVp, 30 kVp, 40 kVp, 50 kVp, 60 kVp, 70 kVp, 80 kVp, 90 kVp, 100 kVp. To obtain the corresponding threshold DAC at a given kVp, the transition threshold (50% of pixels off) was located. Global energy calibration using XRF and γ-ray was performed at 17.4 keV, 24.2 keV and 59.5 keV using Mo, In metallic targets and 241 Am respectively.

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III. R ESULTS A. Noise Performance

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Fig. 6: Measurement of energy spectra from Mo, In, and (a) SPM and (b) CSM.

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Establishing the noise floor is important since all measurements should be taken above it. Fig. 4(a) and Fig. 4(b) show the integral noise floor scan for both SPM and CSM. The high level of noise apparent in the lower threshold DAC as shown in Fig. 4(a) and Fig. 4(b) is due to limitations of sensor layer and readout ASIC. The noise floor zone and threshold dispersion across all the counters are seen to be similar for both SPM and CSM. The electronic noise dominates below threshold DAC of 25 in both modes of camera operation. Fig. 5(a) and Fig. 5(b) show the distribution of pixels which count more than 10 counts in the absence of radiation in SPM and CSM respectively. The noise floor histograms of SPM and CSM in

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Fig. 5(a) and Fig. 5(b) show the full width at half maximum (FWHM) of 5.3 and 7.4 threshold DAC respectively. All data below threshold DAC of 25 were excluded from further dataanalysis. B. Measurement of energy spectra The energy spectra acquired from the XRF of Mo and In foils and a 241 Am source using the SPM and CSM are shown in Fig. 6(a) and Fig. 6(b) respectively. None of the energy spectra measured in SPM shows the XRF or γ-ray peak. However, the energy spectra acquired in CSM using XRF of Mo and In, and 241 Am shows a well defined peak at 69, 86 and 183 threshold DAC respectively as shown in Fig.6(b). This implies that the spectral resolution in the CSM is superior to that in the SPM. Similarly, additional metallic foils of Pd, Ta and Pb were used to locate the threshold DAC corresponding to the XRF peak. The measured energy spectra from each of the reference energy sources show a positive linear relationship between the XRF peak position and the threshold DAC as shown in Fig. 7(a) and Fig. 7(b). A least-squares method was used to fit the threshold DAC corresponding to the peak position of XRF peak (Kα1 ) and the γ-ray peak against the corresponding

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TABLE II: A summary of threshold dispersion for different counters in Charge Summing Mode.

Counter 1 2 3 4

Threshold dispersion (keV) at 24.2 keV 2.30 2.30 2.37 2.30

Threshold dispersion (keV) at 59.5 keV 4.68 4.71 4.65 4.78

reference energies which yields R2 = 0.9972 as shown in Fig. 7(b). In addition to the γ-ray peak in 241 Am spectrum , two other peaks occur at (a) 24.2 keV and (b) 35.2 keV as shown in Fig. 6(b). The peak at 24.2 keV is formed by K-fluorescence x-rays (Kα1 ) from Cd (23.17 keV) and Te (27.47 keV), and the peak at 35.4 keV is formed by photo-electrons from Cd (59.5 - 23.17 = 36.33 keV) and Te (59.5 - 27.47 = 32.03 keV). The individual fluorescence and photo-electron peaks from Cd and Te could not be resolved due to the finite magnitude of spectral resolution of the detector. C. Threshold dispersion and gain variation The threshold DAC corresponding to the XRF peak (24.2 keV) from In foil and γ-ray-peak (59.5 keV) of 241 Am were measured for each pixel across the pixel matrix. The threshold dispersion is a measure of the inter-pixel variation of the threshold DAC corresponding to a reference energy. The threshold dispersion (σ) of 4.77 and 9.73 threshold DAC steps were measured at 24.2 keV and 59.5 keV respectively as shown in Fig. 8(a) and Fig. 8(b). TABLE II shows the threshold dispersion in a pixel matrix of each counter in CSM. Higher threshold dispersion was observed at higher energy. Based on the threshold dispersion across the whole pixel matrix using the XRF from In foil and the γ-ray from 241 Am, the gain variation (threshold DAC/keV), was calculated for each pixel across the matrix and are shown in Fig. 9(a) and Fig. 9(b). TABLE III shows the statistics of gain variation in a pixel matrix of each counter. The co-efficient of gain variation (σx100%/µ) in each counter varies in the range of 6.13% - 6.51%. Similarly, the mean and median gain of whole pixel matrix are 2.08 threshold DAC/keV and 2.10 threshold DAC/keV respectively in each counter. The gain is mainly

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Fig. 8: The distribution of inter-pixel threshold dispersion in CdTeMedipix3RX in CSM across pixel matrix at (a) 24.2 keV and (b) 59.5 keV.

Counter Co-efficient of Gain Variation(%) 1 2 3 4

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Mean of Gain variation (Threshold DAC/keV) 2.08 2.08 2.08 2.09

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Median of Gain variation (Threshold DAC/keV) 2.10 2.10 2.10 2.10

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poor bump-bonding region show zero spectral resolution. The most important factors that affect the spectral resolution in readout electronics are threshold dispersion, gain variation and electronic noise. Similarly, charge sharing, variation in the charge collection efficiency, leakage current and Fano factors are other major factors from sensor that contribute to spectral resolution of the detector [27].

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E. Cross-validation of energy calibration using an x-ray kVp and XRF Fig. 11 shows the number of pixels non-counting (off) and counting (on) as a function of threshold DAC measured at 30 kVp, 40 kVp, 60 kVp and 100 kVp. The ideal curve for 60 kVp is also shown, intersecting through the 50% point of

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controlled by the feedback capacitor in the analogue circuit and this can be cancelled to a large extent with narrow energy range by performing the energy calibration of the detector at the energy of interest [27]. D. Spectral resolution The spectral resolution of each pixel was measured at the 59.5 keV 241 Am γ-ray peak. The spatial variation of spectral resolution of individual pixels is shown in Fig. 10(a) and the distribution of FWHM for each pixel is shown in Fig. 10(b). The average of distribution of FWHM for all pixels is 15% which is equivalent to 8.9 keV at 59.5 keV. The spectral resolution of the individual pixel in CdTe-Medipix3RX varies in the range of (10% - 30%) at 59.5 keV across the whole pixel array. The co-efficient of spectral resolution variation (σx100%/µ)) across the pixel matrix is 21%. The pixels nearby

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Fig. 9: (a) Spatial map of gain (Threshold DAC/keV) across pixel matrix of first counter operated in CSM using CdTe-Medipix3RX. The dead pixels due to poor bump-bonding during manufacturing of the detector show zero gain. (b) distribution of gain of individual pixel across the whole pixel matrix

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Fig. 10: (a) Spatial map of spectral resolution (FWHM) across pixel matrix of first counter operated in CSM using CdTe-Medipix3RX. The spectral resolution was measured using γ-ray (59.5 keV) of 241 Am source. The dead pixels due to poor bump-bonding during manufacturing of the detector show zero spectral resolution. (b) the distribution of spectral resolution (FWHM) of the individual pixel.

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TMI.2014.2337881, IEEE Transactions on Medical Imaging IEEE TRANSACTIONS ON MEDICAL IMAGING

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Fig. 11: Threshold scan showing the fraction of pixels off at 30 kVp, 40 kVp, 60 kVp and 100 kVp using CdTe-Medipix3RX in Charge Summing Mode. The energy calibration technique using x-ray kVp locates the transition threshold where 50% pixels transition from off to on. An ideal detector has no threshold dispersion and it is shown for 60 kVp as a vertical line. The slope of each measurement gives the indication of threshold dispersion at given kVp. The ideal detector at 60 kVp is shown with no threshold dispersion.

Fig. 12: Global energy calibration performance of x-ray kVp technique, and XRF technique in CdTe-Medipix3RX in CSM.

the 60 kVp measurements. These energy calibration points were mapped to threshold DAC of 126, 150, 193 and 273 respectively as shown in Fig. 11. The global energy calibration using an x-ray kVp and XRF techniques provides the good agreement as shown in Fig. 12 across the wide energy range (17 - 100) keV. The difference between these two techniques is 1.5 keV at 59.5 keV which is less than the spectral resolution of the detector (FWHM of 8.9 keV at 59.5 keV). IV. D ISCUSSION The automated energy calibration techniques using an xray kVp and XRF from the metallic targets were developed and cross-validated. The energy difference between these two

techniques is 1.5 keV at 59.5 keV which is less than the spectral resolution of the detector (FWHM of 8.9 keV at 59.5 keV). The x-ray kVp based energy calibration technique avoids measurement of monochromatic photons and user intervention. Users can define as many number of energy calibration points as available kVp. However, a large number of energy calibration points requires longer calibration time. Currently, this technique is used for global energy calibration of whole detector. The calibration of global energy threshold based on x-ray kVp technique may be extended to per-pixel energy threshold calibration by locating the transition threshold for individual pixels (instead of the whole pixel matrix for the global energy calibration) based on the probability of the pixels counting at the selected energy calibration points. Energy threshold calibration based on the XRF method needs extra resources like metallic foils of different elements to provide reference energies across the wide energy range of interest. Each metallic foil forms an energy calibration point. The exposure parameters for detecting adequate XRF signal from a foil need to optimized. Currently, this energy calibration using XRF from foil can be used for calibrating the energy response of both whole detector and individual pixel. This technique generates sufficient numbers of XRF photons at the pixel level by using the high x-ray flux from x-ray tube. This allows the XRF based technique to be more efficient and faster when calibrating the energy response of individual pixels than existing techniques such as those using radio-isotopes with limited radioactivity. Both of the energy calibration techniques presented are pragmatic ones which can be used as quality control tools in a daily basis for a pre-clinical multi-energy CT scanner using spectral x-ray detectors. Pixel-by-pixel energy calibration technique using an XRF from metallic targets and γ-ray from 241 Am radio-isotope was used to measure the energy response of individual pixel. The energy response of a pixel in CdTe-Medipix3RX in CSM (Fig. 6(b)) is more clearly defined than that in SPM (Fig. 6(a)). CSM improves the imaging performance by enhancing contrast and spectral resolution of the detector. In SPM, the XRF from different metallic foils and the monochromatic γray emitted from 241 Am are likely to be detected by the adjacent pixels. When the charge cloud generated from photon interaction with sensor drifts across the sensor thickness under electric field strength, it spreads across many small (110µm) pixels in SPM. The charge sharing effect is more severe in the pixel detector with higher sensor thickness and smaller pixel dimension. The splitting of the charge cloud and the false assignment of photon hits to the pixel causes poor energy response of spectral x-ray detector in SPM. However, in CSM, the inter-pixel communication and the assignment of photon hits to the correct pixel take accounts of charge sharing effect. As a consequence, the energy response of a pixel detector is enhanced. The variation of energy threshold with respect to incident photon energy is linear (R2 = 0.9972) across the measured energy range (17.4 keV to 75 keV) in CSM as shown in Fig. 7(b). This linear fit of energy response agrees with the previous findings [7], [12], [17]. The quality of threshold equalization directly affects the

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TMI.2014.2337881, IEEE Transactions on Medical Imaging IEEE TRANSACTIONS ON MEDICAL IMAGING

contrast resolution and the level of fixed pattern noise in an image. The measurement of threshold dispersion across different counters at different energy shows that it increases with energy. The uniformity of the threshold dispersion is directly related to CMOS manufacturing variation and residual threshold dispersion after threshold equalization. Similarly, the gain variation across the whole matrix of pixel array is 6.1 - 6.5% for different counters. This effect is consistent with all the 4 counters in CSM. At higher energies, the higher residual threshold dispersion is more likely to be observed. The threshold equalization is likely to be more effective by using a higher reference energy or equivalent test pulse rather than using the noise floor. However, when using test pulse, the variations in the charge injection capacitor across the pixel matrix can distort the spectroscopic response [27]. So, using higher photon reference energy close to the energy of interest in threshold equalization is the most promising solution even though it takes longer time. The performance of threshold equalization can be enhanced if the new design of readout chips incorporates wider range and finer resolution of adjustment DAC on each pixel. In this study, XRF signal was not used for measuring the spectral resolution of detector because of the possible contamination of scattering and transmission x-rays. The contamination of XRF signal from scattering and transmission x-ray can be avoided by changing the experimental settings that allows only the detection of XRF signal and avoids the direct exposure of x-rays on the detector. However, one should bear in mind in using XRF signal for measuring the spectral resolution of the detector that there are many XRF lines (such as K-series or L-series) at different energies which are overlapped in a XRF peak. Therefore, the FWHM of XRF peak does not represent the true spectral resolution of the detector. We used XRF signal to localise the position of XRF peak with respect to the threshold DAC. Scattering and transmission of x-ray photon do not change the position of XRF peak. We used monochromatic γ-ray from 241 Am for measuring the spectral resolution of the detector. The spectral resolution of the individual pixel in CdTe-Medipix3RX was found to be widely varying (10% - 30%) at 59.5 keV across the whole pixel array. The average FWHM for all pixels is 15% (8.9 keV) as shown in Fig. 10(b). The underlying sources of spectral broadening of the γ-ray peak can be broadly divided into two parts: one from the sensor and the other from Medipix3RX readout ASIC. Higher leakage current, lower charge collection efficiency, thicker sensor layer and the statistical nature of the charge generation (Fano factor) from the sensor layer are the major causes of spectral broadening arising from the sensor layer. Thick layers of CdTe polarize quickly, a wellknown problem in CdTe [28]. The effect of polarization on spectral resolution needs further investigation by refreshing the bias voltage frequently during the data acquisition from CdTe sensor [28]. It is worth noting that without the interaction depth correction, thicker CdTe will inherently cause spectral degradation as the charge carriers originating from interactions at the surface have a longer drift length and will be more likely to encounter material defects in the CdTe. The other sources of spectral broadening arising from the

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readout ASIC are threshold dispersion, gain variation and the electronic noise and quantization of signals. In CSM, the performance of one pixel is affected by the electronic noise of adjacent pixels. The threshold variation between intercommunicating pixels will be summed which may cause the broadening of γ-ray peak from 241 Am. K-fluorescence x-rays ((Kα1 )) are emitted from Cd (23.17 keV) and Te (27.47 keV) detector and the fluorescent yield in CdTe is 87 %. The mean free path length of those photons is 116 µm and 64 µm respectively, comparable to the dimension of a pixel. These photons can be reabsorbed away from the original site of their generation causing the distortion in the energy spectrum measured by the pixel. Similarly, the photoelectron, whose energy equals to the original photon hitting the sensor minus the fluorescence x-ray energy, is emitted in high Z sensor material which deposits its energy away from the original site of interaction. Generation of fluorescence x-rays from CdTe and photo-electrons are fundamental in nature. Secondary products from photon interaction with highZ sensor materials need to be taken into account for effective material characterization and quantification in spectral x-ray imaging. V. C ONCLUSION Two automated energy calibration techniques for spectral x-ray detectors were proposed and cross-validated. One technique is developed for global energy calibration using an xray kVp of an x-ray tube and the other is developed for pixel-by-pixel energy calibration based on XRF from metallic targets. Both techniques can be used as quality control tools in a pre-clinical multi-energy CT scanner using spectral xray detectors. Measurements of energy response of individual pixel show that the energy response function and the spectral resolution of CdTe-Medipix3RX in CSM is well defined. The energy resolving performance of the detector can be enhanced by minimizing the electronic noise and threshold dispersion. Pixel-by-pixel energy calibration is highly desirable for taking account of gain variation across the pixel matrix and enhancing the global spectral resolution of spectral x-ray detectors that may improve the sensitivity and specificity of tissue characterization in spectral imaging. ACKNOWLEDGMENT The authors would like to acknowledge University of Otago, University of Canterbury, MARS Bioimaging Ltd, Medipix3 collaborations at CERN, and the Canterbury District Health Board for their valuable assistance. R EFERENCES [1] T. Koenig, E. Hamann, S. Procz, R. Ballabriga, A. Cecilia, M. Zuber, X. Llopart, M. Campbell, A. Fauler, T. Baumbach, and M. Fiederle, “Charge summing in spectroscopic x-ray detectors with high-z sensors,” IEEE Transactions on Nuclear Science, vol. 60, no. 6, pp. 4713–4718, Dec. 2013. [2] N. G. Anderson, A. P. Butler, N. J. A. Scott, N. J. Cook, J. S. Butzer, N. Schleich, M. Firsching, R. Grasset, N. d. Ruiter, M. Campbell, and P. H. Butler, “Spectroscopic (multi-energy) CT distinguishes iodine and barium contrast material in mice,” European Radiology, vol. 20, no. 9, pp. 2126–2134, Sep. 2010.

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TMI.2014.2337881, IEEE Transactions on Medical Imaging IEEE TRANSACTIONS ON MEDICAL IMAGING

[3] S. Feuerlein, E. Roessl, R. Proksa, G. Martens, O. Klass, M. Jeltsch, V. Rasche, H.-J. Brambs, M. H. K. Hoffmann, and J.-P. Schlomka, “Multienergy photon-counting k-edge imaging: Potential for improved luminal depiction in vascular imaging,” Radiology, vol. 249, no. 3, pp. 1010–1016, Jan. 2008. [4] D. P. Cormode, E. Roessl, A. Thran, T. Skajaa, R. E. Gordon, J.-P. Schlomka, V. Fuster, E. A. Fisher, W. J. M. Mulder, R. Proksa, and Z. A. Fayad, “Atherosclerotic plaque composition: Analysis with multicolor CT and targeted gold nanoparticles,” Radiology, vol. 256, no. 3, pp. 774–782, Jan. 2010. [5] J. P. Schlomka, E. Roessl, R. Dorscheid, S. Dill, G. Martens, T. Istel, C. Bumer, C. Herrmann, R. Steadman, G. Zeitler, A. Livne, and R. Proksa, “Experimental feasibility of multi-energy photon-counting k-edge imaging in pre-clinical computed tomography,” Physics in Medicine and Biology, vol. 53, no. 15, pp. 4031–4047, Aug. 2008. [6] E. Roessl and R. Proksa, “K-edge imaging in x-ray computed tomography using multi-bin photon counting detectors,” Physics in medicine and biology, vol. 52, no. 15, pp. 4679–4696, Aug. 2007. [7] J. P. Ronaldson, “Quantitative soft-tissue imaging by spectral CT with medipix3,” Thesis, University of Otago, 2012. [8] R. Ballabriga, J. Alozy, G. Blaj, M. Campbell, M. Fiederle, E. Frojdh, E. H. M. Heijne, X. Llopart, M. Pichotka, S. Procz, L. Tlustos, and W. Wong, “The Medipix3RX: a high resolution, zero dead-time pixel detector readout chip allowing spectroscopic imaging,” Journal of Instrumentation, vol. 8, no. 02, p. C02016, Feb. 2013. [9] M. Pelgrom, A. C. J. Duinmaijer, and A. Welbers, “Matching properties of MOS transistors,” IEEE Journal of Solid-State Circuits, vol. 24, no. 5, pp. 1433–1439, Oct. 1989, 02425. [10] A. Manuilskiy, B. Norlin, H.-E. Nilsson, and C. Frjdh, “Spectroscopy applications for the medipix photon counting x-ray system,” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 531, no. 12, pp. 251–257, Sep. 2004. [11] M. Fiederle, D. Greiffenberg, J. Idrraga, J. Jakbek, V. Krl, C. Lebel, C. Leroy, G. Lord, S. Pospil, V. Sochor, and M. Suk, “Energy calibration measurements of Medipix2,” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 591, no. 1, pp. 75–79, Jun. 2008. [12] T. Koenig, “Exploring coherent phenomena and energy discrimination in x-ray imaging,” Thesis, University of Heidelberg, 2011. [13] E. Guni, J. Durst, B. Kreisler, T. Michel, G. Anton, M. Fiederle, A. Fauler, and A. Zwerger, “The influence of pixel pitch and electrode pad size on the spectroscopic performance of a photon counting pixel detector with CdTe sensor,” IEEE Transactions on Nuclear Science, vol. 58, no. 1, pp. 17–25, Feb. 2011. [14] T. Koenig, J. Schulze, M. Zuber, K. Rink, J. Butzer, E. Hamann, A. Cecilia, A. Zwerger, A. Fauler, M. Fiederle, and U. Oelfke, “Imaging properties of small-pixel spectroscopic x-ray detectors based on cadmium telluride sensors,” Physics in Medicine and Biology, vol. 57, no. 21, p. 6743, Nov. 2012. [15] C. Ponchut, J. Visschers, A. Fornaini, H. Graafsma, M. Maiorino, G. Mettivier, and D. Calvet, “Evaluation of a photon-counting hybrid pixel detector array with a synchrotron x-ray source,” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 484, no. 13, pp. 396–406, May 2002. [16] E. Gimenez, R. Ballabriga, M. Campbell, I. Horswell, X. Llopart, J. Marchal, K. J. S. Sawhney, N. Tartoni, and D. Turecek, “Characterization of Medipix3 with synchrotron radiation,” IEEE Transactions on Nuclear Science, vol. 58, no. 1, pp. 323–332, Feb. 2011. [17] R. Ballabriga, G. Blaj, M. Campbell, M. Fiederle, D. Greiffenberg, E. H. M. Heijne, X. Llopart, R. Plackett, S. Procz, L. Tlustos, D. Turecek, and W. Wong, “Characterization of the Medipix3 pixel readout chip,” Journal of Instrumentation, vol. 6, no. 01, pp. C01 052–C01 052, Jan. 2011. [18] J. P. Ronaldson, M. Walsh, S. J. Nik, J. Donaldson, R. M. N. Doesburg, D. v. Leeuwen, R. Ballabriga, M. N. Clyne, A. P. H. Butler, and P. H. Butler, “Characterization of Medipix3 with the MARS readout and software,” Journal of Instrumentation, vol. 6, no. 01, pp. C01 056–C01 056, Jan. 2011. [19] G. G. Poludniowski and P. M. Evans, “Calculation of x-ray spectra emerging from an x-ray tube. Part I. Electron penetration characteristics in x-ray targets,” Medical Physics, vol. 34, no. 6, pp. 2164–2174, Jun. 2007. [20] E. B. Podgorsak, Radiation Physics for Medical Physicists. Springer, 2010.

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[21] M. Krmar, N. Bucalovic, M. Baucal, and N. Jovancevic, “Possible use of CdTe detectors in kVp monitoring of diagnostic x-ray tubes,” Nuclear instruments & methods in physics research. Section A, Accelerators, spectrometers, detectors and associated equipment, vol. 622, no. 1, pp. 256–260, Oct. 2010. [22] M. Matsumoto, A. Yamamoto, I. Honda, A. Taniguchi, and H. Kanamori, “Direct measurement of mammographic x-ray spectra using a CdZnTe detector,” Medical Physics, vol. 27, no. 7, pp. 1490–1502, Jul. 2000. [23] R. M. Doesburg, “The MARS photon processing cameras for spectral CT,” Thesis, University of Canterbury, 2012. [24] M. F. Walsh, A. M. T. Opie, J. P. Ronaldson, R. M. N. Doesburg, S. J. Nik, J. L. Mohr, R. Ballabriga, A. P. H. Butler, and P. H. Butler, “First CT using Medipix3 and the MARS-CT-3 spectral scanner,” Journal of Instrumentation, vol. 6, no. 01, pp. C01 095–C01 095, Jan. 2011. [25] L. Tlustos, R. Ballabriga, M. Campbell, E. Heijne, K. Kincade, X. Llopart, and P. Stejskal, “Imaging properties of the Medipix2 system exploiting single and dual energy thresholds,” IEEE Transactions on Nuclear Science, vol. 53, no. 1, pp. 367–372, Feb. 2006, 00041. [26] M. F. Walsh, “Spectral CT development,” Ph.D. dissertation, University of Otago, 2013. [27] C. Frojdh, D. Krapohl, S. Reza, E. Frojdh, G. Thungstrom, and B. Norlin, “Spectral resolution in pixel detectors with single photon processing,” vol. 8852, 2013, pp. 88 520O–88 520O–12. [28] S. D. 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 (Basel, Switzerland), vol. 9, no. 5, pp. 3491–3526, May 2009.

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