Improving model-data mismatch for photon-counting detector model using global and local model parameters.

BACKGROUND: An energy-discriminating capability of a photon counting detector (PCD) can provide many clinical advantages, but several factors, such as charge sharing (CS) and pulse pileup (PP), degrade the capability by distorting the measured x-ray spectrum. To fully exploit the merits of PCDs, it is important to characterize the output of PCDs. Previously proposed PCD output models showed decent agreement with physical PCDs; however, there were still scopes to be improved: a global model-data mismatch and pixel-to-pixel variations. PURPOSES: In this study, we improve a PCD model by using count-rate-dependent model parameters to address the issues and evaluate agreement against physical PCDs. METHODS: The proposed model is based on the cascaded model, and we made model parameters condition-dependent and pixel-specific to deal with the global model-data mismatch and the pixel-to-pixel variation. The parameters are determined by a procedure for model parameter estimation with data acquired from different thicknesses of water or aluminum at different x-ray tube currents. To analyze the effects of having proposed model parameters, we compared three setups of our model: a model with default parameters, a model with global parameters, and a model with global-and-local parameters. For experimental validation, we used CdZnTe-based PCDs, and assessed the performance of the models by calculating the mean absolute percentage errors (MAPEs) between the model outputs and the actual measurements from low count-rates to high count-rates, which have deadtime losses of up to 24%. RESULTS: The outputs of the proposed model visually matched well with the PCD measurements for all test data. For the test data, the MAPEs averaged over all the bins were 49.2-51.1% for a model with default parameters, 8.0-9.8% for a model with the global parameters, and 1.2-2.7% for a model with the global-and-local parameters. CONCLUSION: The proposed model can estimate the outputs of physical PCDs with high accuracy from low to high count-rates. We expect that our model will be actively utilized in applications where the pixel-by-pixel accuracy of a PCD model is important.

Direct energy binning for photon counting detectors: Simulation study.

BACKGROUND: Photon counting detectors (PCDs) for x-ray computed tomography (CT) face spectral distortion from pulse pileup and charge sharing. The photon counting scheme used by many PCDs is threshold-subtract (TS) with pulse height analysis (PHA), where each counter counts up-crossing events when pulses exceed an energy threshold. PCD data are not Poisson-distributed due to charge sharing and pulse pileup, but the counting statistics have never been studied yet. PURPOSE: The objectives of this study were (1) to propose a modified photon counting scheme, direct energy binning (DB), that is expected to be robust against pulse pileup; (2) to assess the performance of DB compared to TS; and (3) to evaluate its counting statistics. METHODS: With DB scheme, counter k starts a timer upon an up-crossing event of energy threshold k, and adds a count only if the next higher energy threshold (k+1) was not crossed within a short time window (hence, the pulse peak belongs to the energy bin k). We used Monte Carlo (MC) simulation and assessed count-rate curves and count-rate-dependent spectral imaging task performance for conventional CT imaging as well as water thickness estimation, water-bone material decomposition, and K-edge imaging with tungsten as the K-edge material. We also assessed count-rate-dependent measurement statistics such as expectation, variance, and covariance of total counts as well as energy bin outputs. The agreement with counting statistics models was also evaluated. RESULTS: The DB scheme improved the count-rate curve, that is, mean measured counts as a function of input count-rate, and peaked with 59% higher count-rate capability than the TS scheme (3.5 × 108 counts per second (cps)/mm2 versus 2.3 × 108  cps/mm2 ). The Cramér-Rao lower bounds (CRLB) of the variance of basis line integrals estimation for DB was better than those for TS by 2% for the conventional CT imaging, 30% for water-bone material decomposition, and 32% for K-edge imaging at 1000 mA (at 7.3 × 107  cps/sub-pixel after charge sharing). When count-rates were lower, PCD data statistics were dominated by charge sharing: the variance of total counts and lower energy bins was larger than the mean counts; the covariance of bin data was positive and non-zero. When count-rates were higher, PCD data statistics were dominated by pulse pileup: the variance of data was lower than the mean; the covariance of bin data was negative. The transition between the two regimes occurred smoothly, and pulse pileup dominated the statistics ≥400 mA (when the count-rate after charge sharing was 2.9 × 107  cps/sub-pixel and the probability of count-loss for DB was 37%). Both DB and TS had good agreement with Yu-Fessler's models of total counts; however, DB had a better agreement with Wang's variance and covariance models for energy bin data than TS did. CONCLUSIONS: The proposed DB scheme had several advantages over TS. At low to moderate flux, DB could improve the resilience of PCDs to pulse pileup. Counting statistics deviated from the Poisson distribution due to charge sharing for lower count-rate conditions and pulse pileup for higher count-rate conditions.

[A comprehensive review on photon-counting computed tomography: Principles, technical hurdles and analysis of clinical applications].

In recent years, photon-counting computed tomography (PCD-CT) based on photon-counting detectors (PCDs) has become increasingly utilized in clinical practice. Compared with conventional CT, PCD-CT has the potential to achieve micron-level spatial resolution, lower radiation dose, negligible electronic noise, multi-energy imaging, and material identification, etc. This advancement facilitates the promotion of ultra-low dose scans in clinical scenarios, potentially detecting minimal and hidden lesions, thus significantly improving image quality. However, the current state of the art is limited and issues such as charge sharing, pulse pileup, K-escape and count rate drift remain unresolved. These issues could lead to a decrease in image resolution and energy resolution, while an increasing in image noise and ring artifact and so on. This article systematically reviewed the physical principles of PCD-CT, and outlined the structural differences between PCDs and energy integration detectors (EIDs), and the current challenges in the development of PCD-CT. In addition, the advantages and disadvantages of three detector materials were analysed. Then, the clinical benefits of PCD-CT were presented through the clinical application of PCD-CT in the three diseases with the highest mortality rate in China (cardiovascular disease, tumour and respiratory disease). The overall aim of the article is to comprehensively assist medical professionals in understanding the technological innovations and current technical limitations of PCD-CT, while highlighting the urgent problems that PCD-CT needs to address in the coming years.

Exploration of the pulse pileup effects in a clinical CdTe-based photon-counting computed tomography.

BACKGROUND: High tube current generates a high flux of x-rays to photon counting detectors (PCDs) that can potentially result in the piling up of pulses formed by concurrent photons, which can cause count loss and energy resolution degradation. PURPOSE: To evaluate the performance of clinical photon-counting CT (PCCT) systems in high flux, potentially influenced by pulse pileup effects, in terms of task-generic image quality metrics. METHODS: A clinical phantom was scanned on a commercial PCCT scanner (NAEOTOM Alpha, Siemens) at 120 kV under fourteen different tube current levels (40-1000 mA) with a rotation time of 0.25 s and a pitch of 1. The dose levels corresponded to CTDIvol (32 cm phantom) of 0.79-19.8 mGy. CT sinograms were reconstructed using QIR-off mode (noniterative reconstruction algorithm), Br44 kernel, and a voxel size of 0.4102 × 0.4102 × 3 mm 3 $0.4102 \times 0.4102 \times 3{\mathrm{\ mm}}^3$ . imQuest, an open-source MATLAB-based software package was used to calculate noise power spectrum (NPS), task transfer function (TTF), contrast-to-noise ratio (CNR), and CT number according to AAPM Task Group 233 metrology. RESULTS: The 50% cut-off frequency of TTF (f50 ) remained mostly constant across all higher tube currents for all inserts, namely polyethylene, bone, air, and acrylic. Using the lowest two data points (40 and 80 mA), the expected relationship between noise magnitude and tube current was determined to be noise ∝ $ \propto \ $ mA-0.47 . The measured noise magnitude were up to 11.1% higher than the expected value at the highest tube current. The average frequency of NPS (fav ) decreased from 0.32 to 0.29 mm-1 as tube current increased from 40 to 1000 mA. No considerable effects were observed in CT number measurement of any insert; however, CT numbers for air and bone changed almost monotonically as tube current increased. Absolute CNR increased monotonically for all inserts; however, the difference between measured and expected CNRs were approximately -6% to 12% across all tube currents. CONCLUSIONS: Increasing tube currents did not affect the spatial resolution, but slightly affected the CT number and noise measurements of the clinical PCCT system. However, the effects were only considerable at clinically irrelevant tube currents used on a small 20-cm phantom. In general clinical practices, automatic exposure control techniques are used to decrease the variation of flux on the detector, which alleviates the chances of detector saturation due to high count rates. The observed effects could be due to pulse pileup, signal-dependent filtration of the system, or nonlinearities in the reconstruction algorithm. In conclusion, either the deadtime of the detector used in the photon-counting CT system is shorter such that count losses due to pulse pileup are negligible, or pulse pileup has inconsiderable effects on the image quality of clinical photon-counting CT systems in routine clinical practice due to possible corrections applied on the system.

A comprehensive review on photon-counting computed tomography: Principles, technical hurdles and analysis of clinical applications / 生物医学工程学杂志

In recent years, photon-counting computed tomography (PCD-CT) based on photon-counting detectors (PCDs) has become increasingly utilized in clinical practice. Compared with conventional CT, PCD-CT has the potential to achieve micron-level spatial resolution, lower radiation dose, negligible electronic noise, multi-energy imaging, and material identification, etc. This advancement facilitates the promotion of ultra-low dose scans in clinical scenarios, potentially detecting minimal and hidden lesions, thus significantly improving image quality. However, the current state of the art is limited and issues such as charge sharing, pulse pileup, K-escape and count rate drift remain unresolved. These issues could lead to a decrease in image resolution and energy resolution, while an increasing in image noise and ring artifact and so on. This article systematically reviewed the physical principles of PCD-CT, and outlined the structural differences between PCDs and energy integration detectors (EIDs), and the current challenges in the development of PCD-CT. In addition, the advantages and disadvantages of three detector materials were analysed. Then, the clinical benefits of PCD-CT were presented through the clinical application of PCD-CT in the three diseases with the highest mortality rate in China (cardiovascular disease, tumour and respiratory disease). The overall aim of the article is to comprehensively assist medical professionals in understanding the technological innovations and current technical limitations of PCD-CT, while highlighting the urgent problems that PCD-CT needs to address in the coming years.

Model-based pulse pileup and charge sharing compensation for photon counting detectors: A simulation study.

PURPOSE: We aim at developing a model-based algorithm that compensates for the effect of both pulse pileup (PP) and charge sharing (CS) and evaluates the performance using computer simulations. METHODS: The proposed PCP algorithm for PP and CS compensation uses cascaded models for CS and PP we previously developed, maximizes Poisson log-likelihood, and uses an efficient three-step exhaustive search. For comparison, we also developed an LCP algorithm that combines models for a loss of counts (LCs) and CS. Two types of computer simulations, slab- and computed tomography (CT)-based, were performed to assess the performance of both PCP and LCP with 200 and 800 mA, (300 µm)2  × 1.6-mm cadmium telluride detector, and a dead-time of 23 ns. A slab-based assessment used a pair of adipose and iodine with different thicknesses, attenuated X-rays, and assessed the bias and noise of the outputs from one detector pixel; a CT-based assessment simulated a chest/cardiac scan and a head-and-neck scan using 3D phantom and noisy cone-beam projections. RESULTS: With the slab simulation, the PCP had little or no biases when the expected counts were sufficiently large, even though a probability of count loss (PCL) due to dead-time loss or PP was as high as 0.8. In contrast, the LCP had significant biases (>±2 cm of adipose) when the PCL was higher than 0.15. Biases were present with both PCP and LCP when the expected counts were less than 10-120 per datum, which was attributed to the fact that the maximum likelihood did not approach the asymptote. The noise of PCP was within 8% from the Cramér-Rao lower bounds for most cases when no significant bias was present. The two CT studies essentially agreed with the slab simulation study. PCP had little or no biases in the estimated basis line integrals, reconstructed basis density maps, and synthesized monoenergetic CT images. But the LCP had significant biases in basis line integrals when X-ray beams passed through lungs and near the body and neck contours, where the PCLs were above 0.15. As a consequence, basis density maps and monoenergetic CT images obtained by LCP had biases throughout the imaged space. CONCLUSION: We have developed the PCP algorithm that uses the PP-CS model. When the expected counts are more than 10-120 per datum, the PCP algorithm is statistically efficient and successfully compensates for the effect of the spectral distortion due to both PP and CS providing little or no biases in basis line integrals, basis density maps, and monoenergetic CT images regardless of count-rates. In contrast, the LCP algorithm, which models an LC due to pileup, produces severe biases when incident count-rates are high and the PCL is 0.15 or higher.

Assessment of multi-energy inter-pixel coincidence counters for photon-counting detectors at the presence of charge sharing and pulse pileup: A simulation study.

PURPOSE: Spectral distortion due to charge sharing (CS) and pulse pileup (PP) in photon-counting detectors (PCDs) degrades the quality of PCD data. We recently proposed multi-energy inter-pixel coincidence counters (MEICC) that provided spectral cross-talk information related to CS. When PP was absent, the normalized Cramér-Rao lower bounds (nCRLBs) of 225-µm pixel PCDs with MEICC was comparable to those of 450-µm pixel PCD without MEICC. The aim of this study was to assess the performance of PCDs with MEICC in the presence of both CS and PP using computer simulations. METHODS: An in-house Monte Carlo program was modified to incorporate the following four temporal elements: (1) A pulse shape with a pulse duration of 20 ns, (2) delays of up to 10 ns in anode arrival times when photons were incident on pixel boundaries, (3) offsets proportional to a vertical separation between the primary and secondary charge clouds at the rate of ±4 ns per ±100 µm, and (4) a stochastic fluctuation of anode arrival times for all of the charge clouds with a standard deviation of 2 ns. We assessed the performance of five PCDs, (a)-(f), for three spectral tasks, (A)-(C): (a) The conventional PCD, (b) a PCD with MEICC, (c) a PCD with one coincidence counter (1CC), (d) a PCD with a 3 × 3 analog charge summing scheme (ACS), and (e) a PCD with a 3 × 3 digital count summing scheme (DCS); (A) conventional CT imaging with water (i.e., linear attenuation coefficient maps), (B) water-bone material decomposition, and (C) K-edge imaging with tungsten. The tube current was changed from 1 mA to 1000 mA and the nCRLB was assessed. RESULTS: The recorded count rate curves were fitted by the non-paralyzable detection model with the effective deadtime parameter. The best fit was achieved by 25.8 ns for the conventional PCD, 18.6 ns for MEICC and 1CC, 140.5 ns for ACS, and 209.0 ns for DCS. The nCRLBs were strongly dependent on count rates. MEICC provided the best nCRLBs for all of the imaging tasks over the count rate range investigated except for a few conditions such as K-edge imaging at 1 mA. PP decreased the merit of MEICC over the conventional PCD in addressing CS. Nonetheless, MEICC consistently provided better nCRLBs than the conventional PCD did. The nCRLBs of MEICC were in the range of 49-58% of those of the conventional PCD for K-edge imaging, 45-76% for water-bone material decomposition, and 81-88% for the conventional CT imaging (i.e., linear attenuation coefficient maps). ACS provided better nCRLBs than the conventional PCD did only when the effect of PP was minor (e.g., when the counting efficiency of the conventional PCD was higher than 0.95 with the tube current of up to 100 mA). CONCLUSION: Besides a few cases, MEICC provides the best nCRLBs for all of the tasks at all of the count rates. ACS and DCS provide better nCRLBs than the conventional PCD does only when count rates are very low.

Experimental study of photon-counting CT neural network material decomposition under conditions of pulse pileup.

Purpose: We investigated the performance of a neural network (NN) material decomposition method under varying pileup conditions. Approach: Experiments were performed at tube current settings that provided count rates incident on the detector through air equal to 9%, 14%, 27%, 40%, and 54% of the maximum detector count rate. An NN was trained for each count-rate level using transmission measurements through known thicknesses of basis materials (PMMA and aluminum). The NN trained for each count-rate level was applied to x-ray transmission measurements through test materials and to CT data of a rod phantom. Material decomposition error was evaluated as the distance in basis material space between the estimated thicknesses and ground truth. Results: There was no clear trend between count-rate level and material decomposition error for all test materials except neoprene. As an example result, Teflon error was 0.33 cm at the 9% count-rate level and 0.12 cm at the 54% count-rate level for the x-ray transmission experiments. Decomposition error increased with count-rate level for the neoprene test case, with 0.65-cm error at 9% count-rate level and 1.14-cm error at the 54% count-rate level. In the CT study, material decomposition error decreased with increasing incident count rate. For example, the material decomposition error for Teflon was 0.089, 0.066, 0.054 at count-rate levels of 14%, 27%, and 40%, respectively. Conclusions: Results demonstrate over a range of incident count-rate levels that an NN trained at a specific count-rate level can learn the relationship between photon-counting spectral measurements and basis material thicknesses.

Spectral Photon Counting CT: Imaging Algorithms and Performance Assessment.

Photon counting x-ray detectors (PCDs) with spectral capabilities have the potential to revolutionize computed tomography (CT) for medical imaging. The ideal PCD provides accurate energy information for each incident x-ray, and at high spatial resolution. This information enables material-specific imaging, enhanced radiation dose efficiency, and improved spatial resolution in CT images. In practice, PCDs are affected by non-idealities, including limited energy resolution, pulse pileup, and cross talk due to charge sharing, K-fluorescence, and Compton scattering. In order to maximize their performance, PCDs must be carefully designed to reduce these effects and then later account for them during correction and post-acquisition steps. This review article examines algorithms for using PCDs in spectral CT applications, including how non-idealities impact image quality. Performance assessment metrics that account for spatial resolution and noise such as the detective quantum efficiency (DQE) can be used to compare different PCD designs, as well as compare PCDs with conventional energy integrating detectors (EIDs). These methods play an important role in enhancing spectral CT images and assessing the overall performance of PCDs.

A time-dependent Monte Carlo approach to chance coincidence summing correction factor calculation for high-purity Ge gamma-ray spectroscopy.

The chance (random) coincidence correction factor (CCCF) for the counting geometry of a 137Cs point source placed very close to the end cap of a high-purity Ge coaxial detector with 50% relative efficiency was evaluated by a time-dependent Monte Carlo approach. The probability distributions of gamma-ray and X-ray energy depositions in the detector crystal were obtained by use of the MCNPX code. The signal resolving time of the electronic parts, one of the parameters needed for time-dependent Monte Carlo simulation, was evaluated experimentally by the moving-source method. Another parameter also needed for the simulation is the signal pile-up rejection time interval. A random pulse generator was replaced with the detector for this purpose and the value was calculated iteratively by comparing the spectrum obtained experimentally with the spectrum obtained from the time-dependent Monte Carlo simulation of the random pulse generator. A pulse train with a Poisson distribution in time was created, and these parameters with energy deposition probability distributions were used for theoretical determination of the high-count-rate spectrum and the low-count-rate spectrum. The CCCF for the experiment was calculated as 0.92 by our comparing these two theoretical spectra and agrees well with the experimental result, 0.94. Also, the results of paralyzable and nonparalyzable model approaches for dead time calculations were compared with the experimental results.

Pulse pileup analysis for a double-sided silicon strip detector using variable pulse shapes.

Due to pulse pileup, photon counting detectors (PCDs) suffer from count loss and energy distortion when operating in high count rate environments. In this paper, we studied the pulse pileup of a double-sided silicon strip detector (DSSSD) to evaluate its potential application in a mammography system. We analyzed the pulse pileup using pulses of varied shapes, where the shape of the pulse depends on the location of photon interaction within the detector. To obtain the shaped pulses, first, transient currents for photons interacting at different locations were simulated using a Technology Computer-Aided Design (TCAD) software. Next, the currents were shaped by a CR-RC2 shaping circuit, calculated using Simulink. After obtaining these pulses, both the different orders of pileup and the energy spectrum were calculated by taking into account the following two factors: 1) spatial distribution of photon interactions within the detector, and 2) time interval distribution between successive photons under a given photon flux. We found that for a DSSSD with thickness of 300 µm, pitch of 25 µm and strip length of 1 cm, under a bias voltage of 50 V, the variable pulse shape model predicts the fraction free of pileup can be > 90 % under a photon flux of 3.75 Mcps/mm2. The double-sided silicon-strip detector is a promising candidate for digital mammography applications.

Spectral resolution and high-flux capability tradeoffs in CdTe detectors for clinical CT.

PURPOSE: Photon-counting detectors using CdTe or CZT substrates are promising candidates for future CT systems but suffer from a number of nonidealities, including charge sharing and pulse pileup. By increasing the pixel size of the detector, the system can improve charge sharing characteristics at the expense of increasing pileup. The purpose of this work is to describe these considerations in the optimization of the detector pixel pitch. METHODS: The transport of x rays through the CdTe substrate was simulated in a Monte Carlo fashion using GEANT4. Deposited energy was converted into charges distributed as a Gaussian function with size dependent on interaction depth to capture spreading from diffusion and Coulomb repulsion. The charges were then collected in a pixelated fashion. Pulse pileup was incorporated separately with Monte Carlo simulation. The Cramér-Rao lower bound (CRLB) of the measurement variance was numerically estimated for the basis material projections. Noise in these estimates was propagated into CT images. We simulated pixel pitches of 250, 350, and 450 microns and compared the results to a photon counting detector with pileup but otherwise ideal energy response and an ideal dual-energy system (80/140 kVp with tin filtration). The modeled CdTe thickness was 2 mm, the incident spectrum was 140 kVp and 500 mA, and the effective dead time was 67 ns. Charge summing circuitry was not modeled. We restricted our simulations to objects of uniform thickness and did not consider the potential advantage of smaller pixels at high spatial frequencies. RESULTS: At very high x-ray flux, pulse pileup dominates and small pixel sizes perform best. At low flux or for thick objects, charge sharing dominates and large pixel sizes perform best. At low flux and depending on the beam hardness, the CRLB of variance in basis material projections tasks can be 32%-55% higher with a 250 micron pixel pitch compared to a 450 micron pixel pitch. However, both are about four times worse in variance than the ideal photon counting detector. The optimal pixel size depends on a number of factors such as x-ray technique and object size. At high technique (140 kVp/500 mA), the ratio of variance for a 450 micron pixel compared to a 250 micron pixel size is 2126%, 200%, 97%, and 78% when imaging 10, 15, 20, and 25 cm of water, respectively. If 300 mg/cm2 of iodine is also added to the object, the variance ratio is 117%, 91%, 74%, and 72%, respectively. Nonspectral tasks, such as equivalent monoenergetic imaging, are less sensitive to spectral distortion. CONCLUSIONS: The detector pixel size is an important design consideration in CdTe detectors. Smaller pixels allow for improved capabilities at high flux but increase charge sharing, which in turn compromises spectral performance. The optimal pixel size will depend on the specific task and on the charge shaping time.

Assessment of the spectral performance of hybrid photon counting x-ray detectors.

PURPOSE: Hybrid Photon Counting (HPC) detectors profoundly improved x-ray diffraction experiments at third generation synchrotron facilities. Enabling the simultaneous measurement of x-ray intensities in multiple energy bins, they also have many potential applications in the field of medical imaging. A prerequisite for this is a clean spectral response. To quantify how efficiently HPC detectors are able to assign photons to the correct energy bin, a quantity called Spectral Efficiency (SE) is introduced. This figure of merit measures the number of x-rays with correctly assigned energy normalized to the number of incoming photons. METHODS: A prototype HPC detector has been used to perform precision measurements of x-ray spectra at the BESSY synchrotron. The detector consists of a novel ASIC with pixels of 75 × 75 µm2 size and a 750 µm thick CdTe sensor. The experimental data are complemented by the results of a Monte-Carlo (MC) simulation, which not only includes the physical detection process but also pulse pile-up at high photon fluxes. The spectra and the measured photon flux are used to infer the Spectral Efficiency. RESULTS: In the energy range from 10 to 60 keV, both the Quantum Efficiency and the Spectral Efficiency were precisely measured and simulated. Good agreement between simulation and experiment has been achieved. For the small pixels of the prototype detector, a SE between 15% and 77% has been determined. The MC simulation is used to predict the SE for various pixel sizes at different photon fluxes. For a typical flux of 5∙107  photons/mm2 /s used in human Computed Tomography (CT), the highest SE is achieved for pixel sizes in the range between 150 × 150 µm2 and 300 × 300 µm2 . CONCLUSIONS: The Spectral Efficiency turns out to be a useful figure of merit to quantify the spectral performance of HPC detectors. It allows a quantitative comparison of detectors with different sensor and ASIC configurations over a broad range of x-ray energies and fluxes. The maximization of the SE is a prerequisite for a successful usage of HPC detectors in the field of medical imaging.

Improving pulse detection in multibin photon-counting detectors.

Energy-discriminating, photon-counting (EDPC) detectors are attractive for their potential for improved detective quantum efficiency and for their spectral imaging capabilities. However, at high count rates, counts are lost, the detected spectrum is distorted, and the advantages of EDPC detectors disappear. Existing EDPC detectors identify counts by analyzing the signal with a bank of comparators. We explored alternative methods for pulse detection for multibin EDPC detectors that could improve performance at high count rates. The detector signal was simulated in a Monte Carlo fashion assuming a bipolar shape and analyzed using several methods, including the conventional bank of comparators. For example, one method recorded the peak energy of the pulse along with the width (temporal extent) of the pulse. The Cramer-Rao lower bound of the variance of basis material estimates was numerically found for each method. At high count rates, the variance in water material (bone canceled) measurements could be reduced by as much as an order of magnitude. Improvements in virtual monoenergetic images were modest. We conclude that stochastic noise in spectral imaging tasks could be reduced if alternative methods for pulse detection were utilized.

Evaluation of models of spectral distortions in photon-counting detectors for computed tomography.

A semi-analytical model describing spectral distortions in photon-counting detectors (PCDs) for clinical computed tomography was evaluated using simulated data. The distortions were due to count rate-independent spectral response effects and count rate-dependent pulse-pileup effects and the model predicted both the mean count rates and the spectral shape. The model parameters were calculated using calibration data. The model was evaluated by comparing the predicted x-ray spectra to Monte Carlo simulations of a PCD at various count rates. The data-model agreement expressed as weighted coefficient of variation [Formula: see text] was better than [Formula: see text] for dead time losses up to 28% and [Formula: see text] or smaller for dead time losses up to 69%. The accuracy of the model was also tested for the purpose of material decomposition by estimating material thicknesses from simulated projection data. The estimated attenuator thicknesses generally agreed with the true values within one standard deviation of the statistical uncertainty obtained from multiple noise realizations.

Benchmarking the repeatability of a pneumatic cyclic neutron activation analysis facility using 16O(n,p)16N for nuclear forensics.

A target was prepared for cyclic neutron activation analysis by heat sealing lithium-carbonate in polyethylene. The target was cyclically irradiated 50 times using a Thermo-Scientific accelerator based deuterium-tritium fusion neutron generator. During counting periods, gamma-rays emitted by (16)N were detected using three high-purity germanium detectors acquiring data in list-mode. Total counts acquired in each spectrum were compared between the three detectors to examine variability in geometric positioning of the target and variability of the generator intensity throughout the experiment. These two effects were determined to be the primary sources of variation in the measured counts. Variation in target positioning and generator intensity were found to increase the standard deviation by 34% and 33%, respectively. Transit times to the detector were found to be slower and more variable than transit to the generator but were well below the half second threshold needed to measure short-lived radionuclides with half-lives on the order of seconds. The standard deviation in irradiation time was found to be less than 1 milliseconds. The impact on statistical variability in the measured counts was negligible relative to the two primary sources of variation. Spectra acquired from each cycle were summed together. The sum of the peak areas from the 6.1 MeV gamma-ray and its corresponding single and double escape peaks were used to measure the half-life of (16)N. The result of 7.108(15)seconds derived from data suggests that the currently published value of 7.13(2)seconds has minimal systematic bias induced by background.

The influence of dead time related distortions on live cell fluorescence lifetime imaging (FLIM) experiments.

Recent developments in the field of fluorescence lifetime imaging microscopy (FLIM) techniques allow the use of high repetition rate light sources in live cell experiments. For light sources with a repetition rate of 20-100 MHz, the time-correlated single photon counting (TCSPC) FLIM systems suffer serious dead time related distortions, known as "inter-pulse pile-up". The objective of this paper is to present a new method to quantify the level of signal distortion in TCSPC FLIM experiments, in order to determine the most efficient laser repetition rate for different FLT ranges. Optimization of the F -value, which is the relation between the relative standard deviation (RSD) in the measured FLT to the RSD in the measured fluorescence intensity (FI), allows quantification of the level of FI signal distortion, as well as determination of the correct FLT of the measurement. It is shown that by using a very high repetition rate (80 MHz) for samples characterized by high real FLT's (4-5 ns), virtual short FLT components are added to the FLT histogram while a F -value that is higher than 1 is obtained. For samples characterized with short real FLT's, virtual long FLT components are added to the FLT histogram with the lower repetition rate (20-50 MHz), while by using a higher repetition rate (80 MHz) the "inter-pulse pile-up" is eliminated as the F -value is close to 1.

High Count Rate Electron Probe Microanalysis.

Reducing the measurement uncertainty of quantitative analyses made using electron probe microanalyzers (EPMA) requires a careful study of the individual uncertainties from each definable step of the measurement. Those steps include measuring the incident electron beam current and voltage, knowing the angle between the electron beam and the sample (takeoff angle), collecting the emitted x rays from the sample, comparing the emitted x-ray flux to known standards (to determine the k-ratio) and transformation of the k-ratio to concentration using algorithms which includes, as a minimum, the atomic number, absorption, and fluorescence corrections. This paper discusses the collection and counting of the emitted x rays, which are diffracted into the gas flow or sealed proportional x-ray detectors. The representation of the uncertainty in the number of collected x rays collected reduces as the number of counts increase. The uncertainty of the collected signal is fully described by Poisson statistics. Increasing the number of x rays collected involves either counting longer or at a higher counting rate. Counting longer means the analysis time increases and may become excessive to get to the desired uncertainty. Instrument drift also becomes an issue. Counting at higher rates has its limitations, which are a function of the detector physics and the detecting electronics. Since the beginning of EPMA analysis, analog electronics have been used to amplify and discriminate the x-ray induced ionizations within the proportional counter. This paper will discuss the use of digital electronics for this purpose. These electronics are similar to that used for energy dispersive analysis of x rays with either Si(Li) or Ge(Li) detectors except that the shaping time constants are much smaller.