Thick Detector Research Articles

Bismuth tri-iodide-polystyrene composite for X-rays switching applications at room temperature

Bismuth tri-iodide is potential low toxic material for fabrication of room-temperature X-rays detector due to its relatively high atomic number and density. However, on increasing the thickness of detector, higher leakage current at low bias voltage and low mechanical strength are major issues in utilizing its full potential in radiation detection and in other practical applications. BiI3-polystyrene composite pellets was prepared to get unique defects tolerance nature of material that improves signal/noise ratio. BiI3-polystyrene composite was prepared by low-cost dry-tumble mixing technique. XRD observations gives information of preferred orientated planes perpendicular to c-axis and morphology study by SEM also confirms the same orientation. X-rays switching response recorded at different voltages (13–100 V) for detector performance measurements. Resistivity of BiI3 (107ohm-cm) is less as compared to polystyrene (1015ohm-cm), it acts as conductive-tips in polystyrene-matrix and improves charge transfer to electrodes. These superior charge transfer properties lead to high photocurrent on-off ratio to 70 and suppress leakage current.

Charge Sharing and Charge Loss in High-Flux Capable Pixelated CdZnTe Detectors.

Cadmium zinc telluride (CdZnTe) detectors are known to suffer from polarization effects under high photon flux due to poor hole transport in the crystal material. This has led to the development of a high-flux capable CdZnTe material (HF-CdZnTe). Detectors with the HF-CdZnTe material have shown promising results at mitigating the onset of the polarization phenomenon, likely linked to improved crystal quality and hole carrier transport. Better hole transport will have an impact on charge collection, particularly in pixelated detector designs and thick sensors (>1 mm). In this paper, the presence of charge sharing and the magnitude of charge loss were calculated for a 2 mm thick pixelated HF-CdZnTe detector with 250 μm pixel pitch and 25 μm pixel gaps, bonded to the STFC HEXITEC ASIC. Results are compared with a CdTe detector as a reference point and supported with simulations from a Monte-Carlo detector model. Charge sharing events showed minimal charge loss in the HF-CdZnTe, resulting in a spectral resolution of 1.63 ± 0.08 keV Full Width at Half Maximum (FWHM) for bipixel charge sharing events at 59.5 keV. Depth of interaction effects were shown to influence charge loss in shared events. The performance is discussed in relation to the improved hole transport of HF-CdZnTe and comparison with simulated results provided evidence of a uniform electric field.

Detector thickness effects on nanosecond-gated imager response.

Hybrid CMOS multi-frame imagers with exposure times down to ∼2ns have made significant impacts in high energy density physics and inertial confinement fusion research. The detector thickness is a key parameter in both detector quantum efficiency and temporal response. The Icarus hybrid CMOS imager has been fabricated with Si detector thicknesses of 8, 25, and 100 µm. The temporal response of imaging sensors with exposure time down to 2ns has been examined and compared to directly measured photodiode current. The 100-μm thick variant displays extended features related to charge carrier collection and is more susceptible to field collapse. We also demonstrate charge collection time effects on spatial response.

Using ambipolar sensitivity in pixelated semiconductor detectors

Significant hole motion has previously been observed in thick pixelated semiconductor detectors such as TlBr. This has been shown to affect depth reconstructions when using simple cathode-to-anode amplitude ratios by altering planar-cathode signals. In this work, a complementary effect altering pixelated-anode signals from a TlBr detector was observed. This effect increases the radiation-sensitive volume of a detector to include the region near the pixelated electrodes. A new depth analog based on the hole-induced pixel signal is introduced for near-pixel events. Applying an additional calibration with this new parameter improved the FWHM at 662 keV of a TlBr detector by 3–4 keV during room-temperature operation. The analysis and techniques are generalizable to ambipolar-sensitive pixelated detectors whose dominant charge carriers are either electrons or holes, allowing extension to promising hole-dominant semiconductors.

A thick semi-monolithic scintillator detector for clinical PET scanners

Both monolithic and semi-monolithic scintillator positron emission tomography (PET) detectors can measure the depth of interaction with single-ended readout. Usually scintillators with a thickness of 10 mm or less are used since the position resolutions of the detectors degrade as the scintillator thickness increases. In this work, the performance of a 20 mm thick long rectangular semi-monolithic scintillator PET detector was measured by using both single-ended and dual-ended readouts with silicon photomultiplier (SiPM) arrays to provide a high detection efficiency. The semi-monolithic scintillator detector consists of nine lutetium–yttrium oxyorthosilicate slices measuring 1.37 × 51.2 × 20 mm3 with erythrocyte sedimentation rate foils of 0.065 mm thickness in between the slices. The SiPM array at each end of the scintillator detector consists of 16 × 4 SiPMs with a pixel size of 3.0 × 3.0 mm2 and a pitch of 3.2 mm. The 64 signals of each SiPM array are processed by using the TOFPET2 application-specific integrated circuit individually. All but the edge slices can be clearly resolved for the detectors with both single-ended and dual-ended readouts. The single-ended readout detector provides an average full width at half maximum (FWHM) Y (continuous direction) position resolution of 2.43 mm, Z (depth direction) position resolution of 4.77 mm, energy resolution of 25.7% and timing resolution of 779 ps. The dual-ended readout detector significantly improves the Y and Z position resolutions, slightly improves the energy and timing resolution at the cost of two photodetectors required for one detector module and provides an average FWHM Y position resolution of 1.97 mm, Z position resolution of 2.60 mm, energy resolution of 21.7% and timing resolution of 718 ps. The energy and timing resolution of the semi-monolithic scintillator detector in this work are worse than those of the segmented scintillator array detector and need to be further improved. The semi-monolithic scintillator detector described in this work reduces costs as compared to the traditional segmented scintillator array detector and reduces the edge effect as compared to the monolithic scintillator detector.

Thin cathode glass gas electron multiplier detector for carbon beam dose imaging

ABSTRACT An optically read-out glass gas electron multiplier (G-GEM) detector is expected to simplify complicated quality assurance measurements for hadron therapies by imaging the dose distribution of the incident beam. However, the effect of secondary particles from the detector itself has not been well studied. In this paper, we evaluate a design that reduces the secondary particles from the cathode of a G-GEM detector. Specifically, we assembled detectors with thin cathodes and assessed their effect on the secondary particle production in simulations and experiments. The experiments were carried out under 290 MeV/u 12C ion bombardment at the Heavy Ion Medical Accelerator in Chiba. The clinical intensity of the thin cathode detector was compared with that of a conventional thick cathode G-GEM detector. The improved chamber design reduced the dose contributions of secondary particles from the cathode without degrading the dose imaging performance.

Confirm Suitability of the 3D Positive Ion Detector to Use in the Field of Radiation Protection, and Gamma Spectrometry Applications

It is well known that the environmental radiation surrounding us consists of various types of radiation that could be dangerous to human health, causes air pollution and also has importance in industry and medicine. There are different types of gamma spectrometry and radiation protection technologies are available. Even though these technologies have been used for several decades; there is a need to improve the sensitivity and selectivity for these detectors. The Multilayer PCB technology based Nanodosimeter was designed to capture positive ions produced by the interaction of ionizing radiation with low pressure gas medium. In order to confirm the signal, the present signal captured under methane medium at 1 to 10 Torr pressure. The indigenously fabricated 3D positive ion detector of thickness 3.483 mm with optimized cathode was using the same Nanodosimeter experimental setup using the Co-60 source. To conform the performance of the 3D positive ion detector as gamma spectrometry and Radiation protection.

Updates to TRACK_TEST and TRACK_VISION Computer Programs.

The computer programs TRACK_TEST and TRACK_VISION were previously developed to model profiles and optical appearances of tracks developed in solid-state nuclear track detectors. The programs were based on a track development model that involved the bulk etch rate Vb and the track etch rate Vt or the V function (i.e., Vt/Vb). The present work reported our work to update and modify these two programs. In the revised TRACK_TEST, two new V functions were added and enabled. Sample results for the CR-39 detector obtained using the three original and the two new V functions were compared. Discrepancies were within ~10% and <14% for incident alpha-particle energies of 1 MeV and >1 MeV, respectively. Another major revision of TRACK_TEST was to enable calculations for the Makrofol detector. In the revised TRACK_VISION, the two new V functions, as well as the option for the Makrofol detector, were also added. The experimental results on the Makrofol detectors were obtained (irradiated with 3.6-MeV alpha particles under normal incidence and then etched to achieve a removed detector thickness of 30 μm) for comparisons with the modeled results using the revised TRACK_VISION. The track diameters obtained from the experiment and model were 24.7 and 23.2 μm, respectively. Moreover, a bright area in the central parts, together with an outer dark ring, were present in both the simulated and experimental tracks. The track-opening diameters and the general optical appearances of the tracks were in good agreement.

Technical Note: A fast and monolithic prototype clinical proton radiography system optimized for pencil beam scanning

To demonstrate a proton-imaging system based on well-established fast scintillator technology to achieve high performance with low cost and complexity, with the potential of a straightforward translation into clinical use. The system tracks individual protons through one (X, Y) scintillating fiber tracker plane upstream and downstream of the object and into a 13-cm -thick scintillating block residual energy detector. The fibers in the tracker planes are multiplexed into silicon photomultipliers (SiPMs) to reduce the number of electronics channels. The light signal from the residual energy detector is collected by 16 photomultiplier tubes (PMTs). Only four signals from the PMTs are output from each event, which allows for fast signal readout. A robust calibration method of the PMT signal to residual energy has been developed to obtain accurate proton images. The development of patient-specific scan patterns using multiple input energies allows for an image to be produced with minimal excess dose delivered to the patient. The calibration of signals in the energy detector produces accurate residual range measurements limited by intrinsic range straggling. We measured the water-equivalent thickness (WET) of a block of solid water (physical thickness of 6.10mm) with a proton radiograph. The mean WET from all pixels in the block was 6.13cm (SD 0.02cm). The use of patient-specific scan patterns using multiple input energies enables imaging with a compact range detector. We have developed a prototype clinical proton radiography system for pretreatment imaging in proton radiation therapy. We have optimized the system for use with pencil beam scanning systems and have achieved a reduction of size and complexity compared to previous designs.

Performance evaluation of a new 30 μm thick GaAs x-ray detector grown by MBE

A circular mesa (400 μm diameter) GaAs p+-i-n+ photodiode with a 30 μm thick i layer was characterized for its performance as a detector in photon counting x-ray spectroscopy at 20 °C. The detector was fabricated from material grown by molecular beam epitaxy (MBE). An earlier MBE-grown detector fabricated using a different fabrication process and material from a different area of the same epiwafer was shown to suffer from: relatively high leakage current at high temperatures; a high effective carrier concentration that limited its depletion layer width; and material imperfections (butterfly defects) [Lioliou et al 2019 Nucl. Instrum. Methods Phys. Res. A 946 162670]. However, the new detector has better performance (lower leakage current and effective carrier concentration within the i layer). Using the new detector and low noise readout electronics, an energy resolution of 750 eV ± 20 eV Full Width at Half Maximum (FWHM) at 5.9 keV was achieved at 20 °C, equal to that reported for high quality GaAs detectors made from high quality material grown by metalorganic vapour phase epitaxy [Lioliou et al 2017 J. Appl. Phys. 122 244506]. The results highlight the substantially different performances of detectors made from the same epiwafer when the wafer qualities are not uniform and the effects of different fabrication processes.

Identification of the Ambient Response Relationship in Neutron Counting and Scintillation Measurement Systems

Radiation detection for nuclear security frequently employs neutron counting and scintillation systems simultaneously. One potential issue, particularly when searching a large area, is understanding the ambient (or background) response of these systems throughout the operation. This is easily mitigated for the scintillation system but remains a problem for neutron counting systems. Operational data and previous research have shown that a correlation appears between the neutron count rate and the count rate at high energies in the scintillation system (energies greater than 4 MeV) in background conditions. To understand the cause of the correlation, background measurements were performed using sodium iodide (NaI) and polyvinyl toluene (PVT) scintillation systems. These detectors were calibrated to high energy scales such that their spectra would show energies up to 70 MeV and 85 MeV, respectively. Results show that at least one statistical mode appeared in the spectra on these energy scales (particularly between 5 MeV and 60 MeV). The energy and maximum probability of these modes varied with orientation, and they were dependent upon the detector thickness with respect to the vertical axis and the detector area perpendicular to that axis, respectively. The modes’ energies also matched the expected energy deposition from background muons in the detectors with path lengths equal to one of the detectors’ dimensions. These data matched results from simulations of background muons interacting with these detectors calculated using MCNP, and they similarly matched muon energy spectra calculated from possible path lengths through the detectors using Python. These results indicate that scintillation measurements at energies higher than those employed in typical nuclear security operations are the result of background muons. Since these muons are produced similar processes as background neutrons, the count rate of these particles could potentially be applied to better characterize the background in neutron counting systems.

Optimising sensor geometry of a photodiode based detector for the direct detection of strontium 90 in groundwater

Strontium-90, as one of the primary beta emitting radionuclides produced during nuclear fission, strontium-90 contaminates groundwater at nuclear decommissioning sites after leaks and spills. Its presence in the groundwater presents a long-term site risk, and its activity must be routinely monitored. Existing techniques see groundwater samples collected from deep underground boreholes and sent to remote labs for analysis [1]. These procedures are expensive, time consuming and produce chemical waste, whereby eliminating the need for sample collection and treatment, the net lifetime monitoring costs of strontium 90 can be reduced [2]. In this paper authors present an optimisation of a beta detector, based on submersible photodetector, which can be used in real-time, in-situ beta detection. In order to directly detect and characterise strontium 90 in groundwater, it is essential to maximise the number of beta particles incident on the photodiode surface and ensure that they are fully absorbed within the sensitive region of the detector. This work has developed a Geant4 software framework for investigating the energy deposition by beta particles on photodiode detectors. A series of simulations have been performed to investigate radiation absorption in silicon, cadmium telluride and gallium arsenide detectors. Variations in sensitive area and detector thickness were modeled to determine their suitability for strontium-90 detection in groundwater. The optimal detector geometry of gallium arsenide photodiodes was further investigated. The simulation results and analysis suggest that the optimal detector will feature a large surface area, at least 1 cm2, and an intrinsic layer approximately 400 m thick.

Performance comparison of dual-ended readout depth-encoding PET detectors based on BGO and LYSO crystals

The performance of dual-ended readout depth-encoding positron emission tomography (PET) detectors based on bismuth germanate (BGO) coupled to silicon photomultipliers (SiPM) arrays was measured for the first time and compared to lutetium-yttrium oxyorthosilicate (LYSO)-based detectors using the same readout. The BGO and LYSO crystal arrays all had a crystal pitch of 2.2 mm and were coupled to 8 × 8 SiPM arrays with a matching pitch of 2.2 mm, using a one-to-one coupling configuration. Three types of crystals with Toray reflector were used: polished LYSO, polished BGO, and unpolished BGO, and for two different crystal thicknesses of 20 mm and 30 mm. All the crystal elements in the BGO arrays were clearly resolved in the flood histogram. Better flood histograms were obtained using the LYSO arrays for a selected crystal thickness, and better flood histograms were obtained using the 20 mm thick crystal arrays for a selected crystal type. The average crystal level energy resolution and timing resolution for 20 mm polished LYSO, polished BGO and unpolished BGO crystals at their optimal SiPM bias voltage were 18.6 ± 1.3% and 1.19 ± 0.20 ns, 17.8 ± 0.8% and 4.43 ± 0.47 ns, and 18.0 ± 1.0% and 4.68 ± 1.0 ns, respectively. Depth-of-interaction (DOI) resolution of the 20 mm polished LYSO array was 2.31 ± 0.17 mm and for the 20 mm unpolished BGO array was 3.53 ± 0.25 mm. However, polished BGO arrays with Toray reflector did not provide DOI information. Our key conclusion is that dual-ended readout depth-encoding 20 mm thick unpolished BGO detectors are good candidates for low-activity PET systems with small field-of-view and low timing performance requirements, such as preclinical or compact organ-dedicated PET systems, with the advantage over LYSO of having no background radiation and significantly lower cost.

A method to measure the integral vertical intensity and angular distribution of atmospheric muons with a stationary plastic scintillator bar detector

We present a method to measure the integral vertical intensity and angular distribution of atmospheric muons using a stationary thick plastic scintillator bar detector with PMTs at both of its ends over exposures of a few hours in a laboratory setting. The total flux is obtained from the event rate and the angular distribution is inferred from the distribution of the recorded pulse charges, which are correlated with the track length inside the plastic scintillator. A muon generator algorithm was developed and used together with a simple simulation including the effects of the detector resolution, nonlinear saturation of the PMTs, and laboratory building coverage. As a proof of principle we made a measurement assuming a standard cosnθ omnienergetic angular distribution with azimuthal isotropy and different models for the energy spectrum of the source. Using measurements at 5 different azimuthal orientations, we measure an average exponent n=(1.90±0.06(stat)±0.10(syst)), and an average vertical intensity of I0=(101.2±1.8(stat)±5.5(syst))m−2s−1sr−1 at the location with geographic coordinates 19.33°N 99.19°W, altitude 2268 m above sea level, and geomagnetic cut-off of 8.2 GV.

Fabrication of high quantum efficiency p-i-n AlGaN detector and optimization of p-layer and i-layer thickness

In this paper, the fabrication process and structure of AlGaN based p-i-n photodetectors with different layer thicknesses are described. The maximum external quantum efficiency (EQE) of back illumination is 87.87% at zero bias. According to the Poisson equation, the electric field distribution of the devices is analysed, and a detailed method to estimate the reverse bias voltage required for the p-layer and i-layer to be completely depleted is proposed. The reliability of the method is also well proven by the responsivity measurement results under zero bias and reverse bias. Finally, based on the experimental data and theoretical calculation, the optimization method of p-layer and i-layer thickness in p-i-n photodetector is analysed.

Measurements with silicon detectors at extreme neutron fluences1

Thin pad detectors made from 75 μm thick epitaxial silicon on low resistivity substrate were irradiated with reactor neutrons to fluences from 2.5× 1016 n/cm2 to 1× 1017 n/cm2. Edge-TCT measurements showed that the active detector thickness is limited to the epitaxial layer and does not extend into the low resistivity substrate even after the highest fluence. Detector current was measured under reverse and forward bias. The forward current was higher than the reverse at the same voltage but the difference gets smaller with increasing fluence. Rapid increase of current (breakdown) above ∼ 700 V under reverse bias was observed. An annealing study at 60̂C was made to 1200 minutes of accumulated annealing time. It showed that the reverse current anneals with similar time constants as measured at lower fluences. A small increase of forward current due to annealing was seen. Collected charge was measured with electrons from 90Sr source in forward and reverse bias configurations. Under reverse bias the collected charge increased linearly with bias voltage up to 6000 electrons at 2.5× 1016 n/cm2 and 3000 electrons at 1× 1017 n/cm2. Rapid increase of noise was measured above ∼ 700 V reverse bias due to breakdown resulting in worse S/N ratio. At low bias voltages slightly more charge is measured under forward bias compared to reverse. However better S/N is achieved under reverse bias. Effective trapping times were estimated from charge collection measurements under forward bias showing that at high fluences they are much longer than values extrapolated from low fluence measurements—at 1× 1017 n/cm2 a factor of 6 larger value was measured.

A position sensitive [formula omitted] coincidence technique for sample analysis with the upgraded PANDA device

PANDA (Particles And Non-Destructive Analysis) is measuring system developed for non-destructive analysis of samples for safety, security and safeguards. The capabilities of the PANDA device were expanded by the addition of a thick silicon detector for β particle detection. The upgraded device can now be used for position-sensitive α−γ and β−γ coincidence measurements of various kinds of radioactive samples. The capability of the PANDA device in using the β−γ coincidence technique was tested using a mixed source of 134Cs and 226Ra. In addition, the ability of PANDA to locate nuclides emitting β particles from samples was tested using a combined sample containing a mixed 134Cs and 226Ra source and a pure 226Ra source placed a few centimeters apart from each other. The construction, commissioning and testing of the upgraded PANDA device is discussed.

Nanodiamond photocathodes for MPGD-based single photon detectors at future EIC

We are developing gaseous photon detectors for Cherenkov imaging applications in the experiments at the future Electron Ion Collider. CsI, converting photons in the far ultraviolet range, is, so far, the only photoconverter compatible with the operation of gaseous detectors. It is very delicate to handle due to its hygroscopic nature: the absorbed water vapour decomposes the CsI molecule. In addition, its quantum efficiency degrades under ion bombardment. These are the key reasons to quest for novel, less delicate materials for photocathodes adequate for gaseous photon detectors. Layers of hydrogenated nanodiamond particles have recently been proposed as an alternative material and have shown promising characteristics. The performance of nanodiamond photocathodes coupled to thick GEM-based detectors is the objects of our ongoing R&D. The first phase of these studies includes the characterization of thick GEM coated with nanodiamond layers and the robustness of its photoconverting properties with respect to the bombardment by ions from the multiplication process in the gaseous detector. The approach is described in detail as well as all the results obtained so far within these exploratory studies.

Silicon Carbide characterization at the n_TOF spallation source with quasi-monoenergetic fast neutrons

Silicon Carbide (SiC) is a relatively new entry in the world of solid-state detectors. Although SiC response to neutrons is more complex than the one obtained with diamonds, the measured energy resolution (FWHM/Ed<4%) makes SiC an interesting alternative to diamond and silicon detectors for fast neutrons. The results obtained from the measurements of the response of a 100μm thick SiC detector to neutrons in the energy range between 3 and 20 MeV at the n_TOF spallation source at CERN are presented in this paper.By selecting the neutron energy by means of the time of flight, the detector response to quasi-mono-energetic neutrons was measured. The main neutron-induced nuclear reactions were identified in the measured pulse height spectrum. Detection efficiency as a function of neutron energy was measured and interpreted based on available neutron cross section and by making use of Monte Carlo simulations.

Comparison of Zr, Bi, Ti, and Ga as Metal Contacts in Inorganic Perovskite CsPbBr₃ Gamma-Ray Detector

We report a performance comparison of Zr, Bi, Ti, and Ga as metal contacts on solution-grown CsPbBr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> single-crystal gamma-ray detectors. The same CsPbBr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> single crystal was repeatedly deposited with different metal contacts for the evaluation of gamma spectral performance to eliminate crystal-to-crystal variation. Leakage current as low as 2-3 nA at -200 V with detector thickness 2-3 mm was consistently achieved with Zr, Bi, Ti, and Ga as Schottky contact metal, which is comparable to the leakage current level of a commercial cadmium zinc telluride (CZT) detector. Gamma energy spectra with a prominent photopeak at 662 keV were consistently acquired with all studied metal contacts. The best resolution at 662 keV is 11% with a peak-to-Compton valley ratio of 2, indicating an improved spectrum shape than previous results. Through Americium-241 ( <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">241</sup> Am) alpha spectra acquisition, the hole mobility of the CsPbBr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> single crystal is evaluated to be 1.78 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> . We also discussed issues related with the CsPbBr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> gamma detector architecture and interface layers, commonly encountered during CsPbBr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> gamma detector fabrication, that is, impact of electron/hole transport layer and surface oxide layer on gamma detector spectral performance, comparison of different metal-perovskite-metal structures. The persistent CsPbBr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> gamma spectral performance marks the good reproducibility of CsPbBr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> gamma detectors, further enabling CsPbBr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> detector field applications.