Simulated Performances of Very High Energy ...

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/TNS.2018.2800900, IEEE Transactions on Nuclear Science

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Simulated Performances of Very High Energy Detectors for Non-Destructive CT Characterization of large objects Marc Kistler, Nicolas Estre and Elsa Merle  Abstract— As part of its R&D activities on high-energy X-ray imaging for non-destructive characterization, the Nuclear Measurement Laboratory has started an upgrade of its imaging system currently implemented at the CEA-Cadarache center. The goals are to achieve a sub-millimeter spatial resolution and the ability to perform tomographies on very large objects (more than 100-cm standard concrete or 40-cm steel). This paper presents results on the detection part of the imaging system. The upgrade of the detection part needs a thorough study of the performance of two detectors: a series of CdTe semiconductor sensors and two arrays of segmented CdWO4 scintillators with different pixel sizes. This study consists of a Quantum Accounting Diagram (QAD) analysis coupled with Monte-Carlo simulations. The scintillator arrays should be able to detect millimeter details through 140 cm of concrete, but are limited to 120 cm for smaller ones. CdTe sensors have lower but more homogeneous performance, with a 0.5 mm resolution for 90 cm of concrete. The choice of the detector then depends on the preferred characteristic: the spatial resolution or the use on large volumes. The combination of the features of the source and the studies on the detectors gives the expected performance of the whole equipment, in terms of signal-over-noise ratio (SNR), spatial resolution and acquisition time. Finally, experimental validations are carried out and validate the simulated performances. Index Terms—CdTe, CdWO4, detective quantum efficiency (DQE), high-energy imaging, quantum accounting diagram (QAD), signal-over-noise ratio (SNR), tomography.

I. INTRODUCTION

A

S PART of its R&D activities on high-energy imaging for non-destructive characterization, the Nuclear Measurement Laboratory is working on the upgrade of the tomograph implemented at the CEA-Cadarache Center. This upgrade takes into account the optimization of the detection system. That is why two different types of detectors are studied: a series of CdTe semiconductor sensors and two arrays of segmented CdWO4 scintillators with different pixel sizes.

This paragraph of the first footnote will contain the date on which you submitted your paper for review. M. Kistler and N. Estre are with CEA Cadarache, DEN/Nuclear Measurement Laboratory, F-13108 Saint-Paul-lez-Durance, France (e-mail: [email protected]). E. Merle is with CNRS, IN2P3/Subatomic Physics and Cosmology Laboratory, F-38026 Grenoble, France.

The comparison of the detectors is carried out by three indicators: the detective quantum efficiency (DQE), the spatial resolution and the signal-over-noise ratio (SNR). The DQE and the spatial resolution make it possible to compare the intrinsic performance of the detectors. The DQE can be calculated theoretically using parameters derived from a Quantum Accounting Diagram (QAD) analysis. The spatial resolution of the detector, relative to the object plane, gives the component of the tomograph spatial resolution due to the detection part. Coupled with an X-ray source (up to 20 MeV in the current studies), it allows evaluation of spatial resolution of the complete system. The signal-over-noise ratio, on the other hand, depends on the DQE, but also on the input X-ray flux and on the acquisition time (the flux being determined by the source and the object to be imaged). The acquisition time depends in part on the type of detector used and the associated technique (horizontal scan or fixed object). The goal is therefore to obtain a sub-millimeter spatial resolution, while keeping a significant SNR at the output of the detector, in order to obtain images with sufficient contrast and limited noise. II. DETECTORS SIMULATION AND QAD ANALYSIS The QAD analysis of a detector represents the detection process as a series of cascaded stages of three types: gain stage, spread stage and additive noise stage [1]. This precise and standardized representation allows accurate comparisons and analyses of several detection systems at each stage of the detection process. A. Multi-CdTe Detector In the 1990s, the CEA-Leti has designed a detector based on a series of 25 CdTe sensors1, separated by lead collimators and followed by an electronic acquisition chain [2]. This device still shows remarkable intrinsic performances [3]. Each sensor consists of a thin CdTe semiconductor lamella with a volume of 0.8 mm (width) × 15 mm (height) × 25 mm (thickness). A lead collimation reduces the cross section to 2 mm (width) × 3 mm (height). Its consequent thickness and its high density (ρ = 5.8 g / cm3) allow capture of at least 40% of the incident photons (Fig. 3). Photons deposit an amount of energy during the interaction, leading to the production of 1

CdTe sensors have ohmic contacts [2].

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CdWO4 scintillator

20 mm Fig. 1. Multi-CdTe detector, with the collimators [3]. TABLE I SUMMARY OF THE GAINS AND POISSON EXCESSES FOR THE STAGES OF THE CDTE DETECTOR #

Description

1

X-ray interaction

2 3 4

X/Deposited energy conversion (MeV/ph-X) Energy spread in the sensor Conversion in e-/e+ pairs

Symbol

Gain gi

Poisson excess 𝜀𝑔𝑖

g1

0.399

-0.399

Gain

g2

1.72

Spread

𝑇3 (𝜔)

Gain

g4

Type of process Binomial gain

TABLE II SUMMARY OF THE GAINS AND POISSON EXCESSES FOR THE STAGES OF THE CDWO4 DETECTOR Description

-0.446

1

X-ray interaction

1

-1

2

2.31 × 10⁵

-0.85

Electrons collection

Binomial gain

g5

0.78

-0.78

6

Additive electronic noise

Noise

𝜎𝑎2 ⁄̅̅̅ 𝑁6

1

-1

3 4 5 6

electron-hole pairs. The voltage created at the output of the integrator circuit is proportional to the number of collected charges. The QAD analysis is in this case composed of six stages, summarized in Table I. See reference [1] for the parameters definition. Since the sensors are non-continuous, the complete acquisition of a tomographic section requires a translation of the object, in addition to its rotation and a precise synchronization of the acquisition with the object displacement and the firing frequency of the X-ray source. This results in an acquisition time per tomographic slice close to 30 min. Moreover, in order to avoid any afterglow effect, a real-time offset is subtracted before each X-ray pulse. B. Segmented CdWO4 Scintillator Array As crystal scintillators promise also great performance, we studied hypothetical linear detectors based on segmented CdWO4 scintillator, forming needles, coupled by optical fiber to a linear matrix of photodiodes. The detector has been studied for two different needle sizes, 20-mm thick with a section of 0.4 mm × 0.6 mm and 0.8 mm × 1.2 mm respectively. Current industrial techniques allow to build such detectors long enough to measure in half-field 140 cm diameter objects without having to translate the object. Moreover, according to Ref. [4], afterglow effects are expected to be negligible (afterglow < 0.1% after 3 ms, while the maximal acquisition frequency is 250 Hz). The detection process combines a high-density scintillator material (ρ = 7.9 g/cm3) and therefore a high X-ray interaction efficiency, with small continuous pixels. The QAD analysis consists of seven stages. The values have been evaluated by Monte Carlo simulations (parameters 1 to 3 with MCNP6.1[5], parameter 5 with Geant4[6]) or correspond to industrial devices

Photodiode

Fig. 2. Segmented CdWO4 scintillator diagram.

#

5

Optical fiber

7

X/Deposited energy conversion (MeV/ph-X) Energy spread in the needles Conversion to optical quanta (ph/MeV) Optical fiber efficiency Quantum efficiency of the photodiodes Additive electronic noise

Symbol

Gain gi

Poisson excess 𝜀𝑔𝑖

g1

0.436

-0.436

Gain

g2

0.85 / 1.55

-0.71 / -0.61

Spread

𝑇3 (𝜔)

1

-1

g4

1.50 × 10⁴

0

g5

0.31

-0.31

g6

0.48

-0.48

𝜎𝑎2 ⁄̅̅̅ 𝑁7

1

-1

Type of process Binomial gain

Gain Binomial gain Binomial gain Noise

Fig. 3. X-ray interaction efficiency g1 of each detector as a function of incident photon energy.

Fig. 4. Mean single interaction energy deposition g2 of each detector as a function of incident photon energy.



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TABLE III RESOLUTION LIMITS IN DETECTOR AND OBJECT PLANES FOR EACH DETECTOR

Detector plane Object plane

CdWO4 0.4

CdTe

CdWO4 0.8

2 mm-1

1.5 mm-1

1 mm-1

3.2 mm-1

2.4 mm-1

1.6 mm-1

Fig. 5. Simulated Line Spread Function (LSF) of each detector.

Fig. 6. Simulated Modulation Transfer Function (MTF) of each detector.

(parameters 4[7], 62[8] and 7[9]). Fig. 3 and 4 show that both detectors have an equivalent interaction efficiency higher than 40% and that each photon deposits an energy of a few MeV. Due to its smaller section, the CdWO4 0.4 model has the lowest energy deposition values. III. RESULTS A. Spatial Resolution and MTF The spreading stages are materialized by the effect of signal spreading on the average number of quanta. This effect is directly characterized by the square of the Modulation Transfer Function (MTF) [1]. In order to evaluate the MTF, we first calculate the Line Spread Function (LSF), which is the one-dimension signal spread distribution. In this study, the LSF is evaluated by Monte-Carlo simulation (code MCNP6.1). The MTF is then obtained by Fourier Transform of the LSF and can be included in the QAD calculations. The MTF also provides the resolution limit that we define as the spatial frequency at which the MTF is 10%. Beyond this frequency, it is considered that the signal is not exploitable. The LSF and MTF obtained for the two detectors are shown in Fig. 5 and 6 respectively. The LSF of the CdTe detectors is close to a sensor width rectangular function, thanks to the lead collimation. CdWO4 arrays have more complex distributions, with a fine central part 2 For λ=475 nm, the CdWO4 maximum emission wavelength, the spectral response of a p-i-n silicon detector is 0.2 A/W, corresponding to a quantum efficiency of 0.48.

Fig. 7. Spatial-frequency dependent QAD of each detector. The stage refers to the detection steps described in Tables I and II.

and a wider peripheral part, which reflects the spreading of the signal in the adjacent needles due to the absence of collimation. The resolution limit of the small CdWO4 needles remains better than the CdTe one in spite of a larger signal spreading. The large CdWO4 needles (which have the same width as the CdTe sensors) have the poorest resolution. These LSF and MTF curves show the intrinsic detector resolution, for an object placed near the detector (detector plane). These values are corrected by the radiographic magnification factor (1.6 in our setup), in order to obtain the



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Fig. 8. Intrinsic Detective Quantum Efficiency (DQE) of each detector.

resolution at the center of the tomograph (object plane). These values are summarized in Table III. B. QAD As QAD parameters are evaluated by simulation, the diagrams can then be computed (Fig. 7). For the three detectors, they represent the evolution of the number of quanta 𝑃𝑖 (𝜔) at each detection stage i and for different spatial frequencies 𝜔: 2

𝑃𝑖 (𝜔) = ∏𝑖𝑗=1 ̅̅̅ 𝑔𝑗 |𝑇𝑗 (𝜔)|

(1)

The diagrams show that the detection processes are equivalent: first a loss of signal in the first stage, then a spreading that appears through the separation of the curves according to the spatial frequencies, followed by a significant gain of several decades, and finally a small decrease due to the electrons or visible photons collecting efficiency. The larger separation of the curves for the large CdWO4 suggests a higher sensitivity of its DQE to the spatial frequency. C. DQE The formulas of the DQE for each detector are obtained from the theoretical equation [10]. The three curves are plotted in Fig. 8. CdTe: 𝐷𝑄𝐸(𝜔) =

𝑔1 𝑔2 |𝑇3 (𝜔)|2

̅̅̅̅̅ 𝜖𝑔4 1+𝜎2 6 𝑎 ⁄𝑁 + 𝑔4 𝑔4 𝑔5

1+(𝑔2 +𝜖𝑔2 )|𝑇3 (𝜔)|2 +

CdWO4: 𝐷𝑄𝐸(𝜔) =

𝑔1 𝑔2 |𝑇3 (𝜔)|2

1+𝜎2 𝑁7 𝑎 ⁄̅̅̅̅̅ 𝑔4 𝑔5 𝑔6

1+(𝑔2 +𝜖𝑔2 )|𝑇3 (𝜔)|2 +

(2)

(3)

CdTe sensors have the best intrinsic DQE over the entire frequency range. The CdWO4 is more frequency dependent and therefore drops faster, especially the large one after 0.5 mm-1. IV. DISCUSSION For a single incident photon, multi-CdTe detector is therefore the most efficient. But for the acquisition of a

Fig. 9. Output Signal-over-Noise Ratio (SNR) of each detector as a function of the thickness of concrete, for 0.5 and 1 mm-1.

tomographic slice with an identical measurement time, it is necessary to compare the signal-over-noise ratios at the output of the detectors. Indeed, the SNR depends not only on the DQE, but also on the SNR at the detector input: 𝑆𝑁𝑅𝑜𝑢𝑡 = √𝐷𝑄𝐸 × 𝑆𝑁𝑅𝑖𝑛

(4)

The input SNR depends on the photonic flux, the sensors section and the acquisition time of the signal per sensor. These last two values differ between each detector, and can counterbalance a low DQE, finally delivering a readable SNR to the detector output. Fig. 9 shows the output SNR of each detector as a function of the equivalent thickness of concrete imaged with a nominal flux of 10⁶ ph-X / mm² / pulse, for spatial frequencies of 0.5 and 1 mm-1. The readability of an image is arbitrarily fixed for a minimum SNR of 10. With the CdTe detector, it is possible in this setup to discern details up to the millimeter scale (0.5 mm-1) in a 100 cm thick concrete block, and sub-millimeter details through 90 cm of concrete (1 mm-1). For CdWO4, the millimeter resolution is reached for 140 cm of concrete, with better performance for the large needles. Both models have a 500 μm resolution across 120 cm. V. EXPERIMENTAL VALIDATION



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Fig. 12. Evaluated CdWO4 ESF (blue), LSF (green) and MTF (red) with the sharp-edge method. Fig. 10. Lead step-wedge response for multi-CdTe in Analog-to-Digital conversion Unit (ADU). Experimental values (red), simulation without background offset (blue) and simulation with experimental background offset added (green).

Fig. 13. Duplex IQI response. Measurement (blue dots) and simulation using measured MTF (red).

Fig. 11. Lead step-wedge response for CdWO4. Experimental values (red), simulation without background offset (blue) and simulation with experimental background offset added (green).

In the previous sections, some parameters are expected to be correctly simulated (X-ray interaction, deposited energy) whereas others are more difficult to be estimated by simulation (for example, the optical gain variation and optical transmission value in CdWO4 detector). Experimental tests are then needed to compare the global (real) gain and the simulated one, and if needed, correct the simulation parameters. The multi-CdTe detector and a small CdWO4 demonstrator3 have been tested in the CINPHONIE cell with the current 9 MeV tomograph [3]. First, the dynamic range is evaluated by imaging a lead step-wedge (from 0 to 20-cm lead). The multi-CdTe results are compared to the simulation and shown on Fig. 10. We note a detection limit close to 15-cm lead. This is mainly due to a global gamma background in the cell during the irradiation, which is not taken into account in the standard simulation where the detection limit is not reached. If this background offset is artificially added to the simulation, the agreement with the measurement is better than 15%. So, the gains and the electrical parameters used in II.A are validated. In the same way, the lead step-wedge has been imaged with the CdWO4 demonstrator and compared to the simulation4. The results are shown on Fig. 11. In contrast to the Multi-CdTe results, the experimental signal value at 0-cm lead is different from the simulated one. The ratio experimental value over simulation value is 0.36. So we multiply all the simulation points by this calibration factor. With this scale factor, the measurement and the simulation are in good agreement for high 3

The detector needles are 10-mm thick and 0.4-mm width. The simulations presented in part II have been updated to fit the demonstrator geometry. 4

Fig. 14. Intrinsic experimental DQE comparison between CdTe and CdWO 4

signal values. For large thicknesses of lead, we must artificially add the experimental offset (background) to the simulation results. Then, the gains and the electrical parameters used in II.B must be corrected by a 0.36 factor. At this stage, it is difficult to know which parameter is over-estimated, but the most probable hypotheses are: - the scintillation light yield value used is 15000 ph-X/MeV, while according to Ref [7], it is between 12000 and 15000 ph-X/MeV; - the optical fiber efficiency is probably inferior, as we did not take into account the drop of the signal while passing through the optical glue, as well as the fill factors at the interfaces between needles and optical fiber and between optical fiber and photodiodes. The second important validation is to measure LSF and MTF in order to compare the results with the simulations in III.A where only the energy spread was taken into account. As it is difficult to measure the LSF on Multi-CdTe detectors (CdTe pixels are not joined), only results on CdWO4 are shown here. Two measurements are carried out in order to evaluate the CdWO4 LSF. First, we use the sharp edge method [11] with a



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perfectly sharp block of copper (5-cm thick) placed in front of the detector. The response (ESF) is then converted into LSF and MTF. Results are shown on Fig. 12. From the MTF we deduce a resolution limit of 0.875 mm-1 in the detector plane (1.4 mm-1 in the object plane). Second, the simulation of the Duplex IQI5 radiography using this MTF curve fits accurately the measurement of the response to a Duplex IQI (Fig. 13). The evaluated MTF is then validated. Thanks to experimental validation of parameters (gain factor, MTF and noise), it is now possible to compare the DQE (Fig. 14). As we can see, the detectors exhibit now more comparable performances, even if CdWO4 have a better DQE at low frequency and CdTe become more interesting after 0.3 mm-1.

efficiency model of signal and noise propagation in cascading imaging systems,” Med. Phys., vol. 21, no. 3, pp. 417-427, Mar. 1994. [11] E. Samei et al., “A method for measuring presampled MTF of digital radiographic systems using an edge test device,” Med. Phys, vol. 25, no. 1, pp. 102-113, Jan. 1998.

VI. CONCLUSION This study of two possible detectors for high energy tomography reveals notable performance, in terms of spatial resolution as well as penetration capacity. According to the simulations, it appears that the multi-CdTe detector has the best intrinsic performance, with a relatively stable DQE, which provides a SNR that is slightly spatial frequency dependent and therefore spatial resolution dependent. For an equal acquisition time, the linear CdWO4 scintillator arrays have a better SNR input, which counterbalances their lower DQE. We can therefore expect a better output SNR. The measurements validate the simulations for the CdTe detector, even if this study should now be completed by the measurement of the CdTe spatial resolution. As a correction factor appears between simulated and experimental results for the CdWO4 detector, further simulations are needed to estimate final performances. Then it will be possible to choose the most appropriate detector for the future upgraded tomograph.

REFERENCES J.-P. Bissonnette et al., “A quantum accounting and detective quantum efficiency analysis for video-based portal imaging,” Med. Phys., vol. 24, no. 6, pp. 815-826, Jun. 1997. [2] F. Glasser et al., “Application of cadmium telluride detectors to high energy computed tomography,” Nucl. Instrum. Methods Phys. Res. A, vol. 322, pp. 619-622, Nov. 1992. [3] N. Estre et al., “High-energy X-ray imaging applied to nondestructive characterization of large nuclear waste drums,” in IEEE Transactions on Nuclear Science, vol. 62, no. 6, pp. 3104-3109, Dec. 2015. [4] G. Blasse and B. C. Grabmaier, “Luminescent Materials”, Springer Science & Business Media, p 183, Dec. 2012. [5] Los Alamos National Laboratory, “MCNP6 Users Manual Code Version 6.1,” Jun. 2014. [6] OpenGATE Collaboration, “GATE Users Guide V7.2,” Feb. 2016. [7] Saint Gobain, “Cadmium Tungstate Scintillation Material,” Jun. 2014. [8] R. E. Simon, “Electro-Optics Handbook,” RCA, Dec. 1974. [9] X-Scan Imaging, “Linear X-Ray Photodiode Detector Array with Signal Amplification,” Dec. 2014. [10] I. A. Cunningham et al., “A spatial-frequency dependent quantum accounting diagram and detective quantum [1]

5 IQI Duplex is a tool used to measure image unsharpness. See norm ISO 19232-5 / EN462-5 / ASTM E2002-99 for more details.
