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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Monte Carlo simulations of time-of-flight PET with double-ended readout: calibration, coincidence resolving times and statistical lower bounds

Here, this paper demonstrates through Monte Carlo simulations that a practical positron emission tomograph with (1) deep scintillators for efficient detection, (2) double-ended readout for depth-of-interaction information, (3) fixed-level analog triggering, and (4) accurate calibration and timing data corrections can achieve a coincidence resolving time (CRT) that is not far above the statistical lower bound. One Monte Carlo algorithm simulates a calibration procedure that uses data from a positron point source. Annihilation events with an interaction near the entrance surface of one scintillator are selected, and data from the two photodetectors on the other scintillator provide depth-dependent timing corrections. Another Monte Carlo algorithm simulates normal operation using these corrections and determines the CRT. A third Monte Carlo algorithm determines the CRT statistical lower bound by generating a series of random interaction depths, and for each interaction a set of random photoelectron times for each of the two photodetectors. The most likely interaction times are determined by shifting the depth-dependent probability density function to maximize the joint likelihood for all the photoelectron times in each set. Example calculations are tabulated for different numbers of photoelectrons and photodetector time jitters for three 3 × 3 × 30 mm 3 scintillators: Lu 2 SiO 5 :Ce,Ca (LSO), LaBr 3 :Ce, and a hypothetical ultra-fast scintillator. To isolate the factors that depend on the scintillator length and the ability to estimate the DOI, CRT values are tabulated for perfect scintillator-photodetectors. For LSO with 4000 photoelectrons and single photoelectron time jitter of the photodetector J = 0.2 ns (FWHM), the CRT value using the statistically weighted average of corrected trigger times is 0.098 ns FWHM and the statistical lower bound is 0.091 ns FWHM. For LaBr 3 :Ce with 8000 photoelectrons and J = 0.2 ns FWHM, the CRT values are 0.070 and 0.063 ns FWHM, respectively. For the ultra-fast scintillator with 1 ns decay time, 4000 photoelectrons, and J = 0.2 ns FWHM, the CRT values are 0.021 and 0.017 ns FWHM, respectively. Lastly, the examples also show that calibration and correction for depth-dependent variations in pulse height and in annihilation and optical photon transit times are necessary to achieve these CRT values.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1983

Consistent Tolerance Bounds for Statistical Distributions

Assumption that sample comes from population with particular distribution is made with confidence C if data lie between certain bounds. These "confidence bounds" depend on C and assumption about distribution of sampling errors around regression line. Graphical test criteria using tolerance bounds are applied in industry where statistical analysis influences product development and use. Applied to evaluate equipment life.

Mezzacappa, M. A.↗
DOE OSTI2016

Uncertainty Quantification and Comparison of Weld Residual Stress Measurements and Predictions.

In pressurized water reactors, the prevention, detection, and repair of cracks within dissimilar metal welds is essential to ensure proper plant functionality and safety. Weld residual stresses, which are difficult to model and cannot be directly measured, contribute to the formation and growth of cracks due to primary water stress corrosion cracking. Additionally, the uncertainty in weld residual stress measurements and modeling predictions is not well understood, further complicating the prediction of crack evolution. The purpose of this document is to develop methodology to quantify the uncertainty associated with weld residual stress that can be applied to modeling predictions and experimental measurements. Ultimately, the results can be used to assess the current state of uncertainty and to build confidence in both modeling and experimental procedures. The methodology consists of statistically modeling the variation in the weld residual stress profiles using functional data analysis techniques. Uncertainty is quantified using statistical bounds (e.g. confidence and tolerance bounds) constructed with a semi-parametric bootstrap procedure. Such bounds describe the range in which quantities of interest, such as means, are expected to lie as evidenced by the data. The methodology is extended to provide direct comparisons between experimental measurements and modeling predictions by constructing statistical confidence bounds for the average difference between the two quantities. The statistical bounds on the average difference can be used to assess the level of agreement between measurements and predictions. The methodology is applied to experimental measurements of residual stress obtained using two strain relief measurement methods and predictions from seven finite element models developed by different organizations during a round robin study.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRSDate not supplied

Variational Coupled Loads Analysis using the Hybrid Parametric Variation Method

Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.

Uncertainty Quantification↗
DOE OSTI2017

High-Density Signal Interface Electromagnetic Radiation Prediction for Electromagnetic Compatibility Evaluation

Radiated power calculation approaches for practical scenarios of incomplete high- density interface characterization information and incomplete incident power information are presented. The suggested approaches build upon a method that characterizes power losses through the definition of power loss constant matrices. Potential radiated power estimates include using total power loss information, partial radiated power loss information, worst case analysis, and statistical bounding analysis. A method is also proposed to calculate radiated power when incident power information is not fully known for non-periodic signals at the interface. Incident data signals are modeled from a two-state Markov chain where bit state probabilities are derived. The total spectrum for windowed signals is postulated as the superposition of spectra from individual pulses in a data sequence. Statistical bounding methods are proposed as a basis for the radiated power calculation due to the statistical calculation complexity to find a radiated power probability density function.

42 ENGINEERING↗
NASA NTRS2016

On the Calculation of Uncertainty Statistics with Error Bounds for CFD Calculations Containing Random Parameters and Fields

This chapter discusses the ongoing development of combined uncertainty and error bound estimates for computational fluid dynamics (CFD) calculations subject to imposed random parameters and random fields. An objective of this work is the construction of computable error bound formulas for output uncertainty statistics that guide CFD practitioners in systematically determining how accurately CFD realizations should be approximated and how accurately uncertainty statistics should be approximated for output quantities of interest. Formal error bounds formulas for moment statistics that properly account for the presence of numerical errors in CFD calculations and numerical quadrature errors in the calculation of moment statistics have been previously presented in [8]. In this past work, hierarchical node-nested dense and sparse tensor product quadratures are used to calculate moment statistics integrals. In the present work, a framework has been developed that exploits the hierarchical structure of these quadratures in order to simplify the calculation of an estimate of the quadrature error needed in error bound formulas. When signed estimates of realization error are available, this signed error may also be used to estimate output quantity of interest probability densities as a means to assess the impact of realization error on these density estimates. Numerical results are presented for CFD problems with uncertainty to demonstrate the capabilities of this framework.

Uncertainty↗
DOE OSTI2024

Positivity from Cosmological Correlators

Abstract Effective field theories in flat space and in anti-de Sitter space are constrained by causality and unitarity, often in the form of positivity bounds. Similar bounds have been harder to demonstrate in cosmological backgrounds, where the roles of unitarity and causality are more obscure. Fortunately, the expansion of the universe ensures that late-time cosmological correlators are effectively classical and the role of unitarity is played by classical statistical inequalities. For multi-field inflation, the resulting positivity constraints have long been known in terms of the Suyama-Yamaguchi inequality. In this paper, we demonstrate that similar statistical bounds imply nontrivial constraints for massive fields in the early universe. We show that any real anomalous dimensions for principal series fields in de Sitter space must be positive. We also derive a limit on the amplitude of particular oscillatory signals from inflation, including those arising in cosmological collider physics. Finally, we demonstrate that these constraints manifest themselves directly in the two-point statistics of matter and galaxies that will be measured in upcoming surveys.

Physics↗
NASA NTRS2014

Optimizing Integrated Terminal Airspace Operations Under Uncertainty

In the terminal airspace, integrated departures and arrivals have the potential to increase operations efficiency. Recent research has developed geneticalgorithm- based schedulers for integrated arrival and departure operations under uncertainty. This paper presents an alternate method using a machine jobshop scheduling formulation to model the integrated airspace operations. A multistage stochastic programming approach is chosen to formulate the problem and candidate solutions are obtained by solving sample average approximation problems with finite sample size. Because approximate solutions are computed, the proposed algorithm incorporates the computation of statistical bounds to estimate the optimality of the candidate solutions. A proof-ofconcept study is conducted on a baseline implementation of a simple problem considering a fleet mix of 14 aircraft evolving in a model of the Los Angeles terminal airspace. A more thorough statistical analysis is also performed to evaluate the impact of the number of scenarios considered in the sampled problem. To handle extensive sampling computations, a multithreading technique is introduced.

air traffic optimization↗
NASA NTRS2022

Uncertainty Models for the Hybrid Parametric Variation Method of Uncertainty Quantification; Analysis

There is some level of uncertainty in every finite element model (FEM), which flows to a level of uncertainty in predicted results. The purpose of uncertainty quantification (UQ) is to provide statistical bounds on prediction accuracy based on model uncertainty. This is distinct from model updating, which attempts to modify models to improve their accuracy. UQ does not improve the accuracy of models, but accepts that the models are inherently inaccurate and attempts to quantify the impact of that inaccuracy on predicted results. Previously, an alternate method for UQ, called the Hybrid Parametric Variation (HPV) method, was applied to Space Launch System (SLS) Hurty/Craig-Bampton (HCB) components to predict system-level statistics for launch vehicle attitude control transfer functions and core stage section loads due to buffet. The HPV method combines a parametric variation of the HCB fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method that randomly varies the HCB mass and stiffness matrices as Wishart random matrix distributions using random matrix theory (RMT). Alternatively, the most common method for modeling uncertainty in the structural dynamics community is a parametric approach, which varies physical parameters in the model. However, there are several disadvantages associated with the parametric method. Determining a reduced set of parameters that have a significant impact on the system response can be time consuming, and the selected parameter probability distributions are rarely reliably known. Therefore, in practice, the parameters are surrogates for the actual errors, and the link to parameter uncertainty is unknown. Another major drawback is that the uncertainty that can be represented is limited to the form of the nominal FEM. It is the experience of the authors that based on numerous aerospace programs, almost all FEM errors are in form rather than parameter values. This hypothesis is supported by the observation of the authors that it is almost never possible to ‘tune’ a FEM to match modal test results by only modifying model parameters. Model-form uncertainty cannot be directly represented by FEM input parameters nor included in a parametric approach. However, model-form uncertainty can be modeled using RMT, where a probability distribution is developed for the matrix ensemble of interest. The major advantage of the NPV method is that it covers errors in model form. The HPV method anchors uncertainty at the HCB component level to component modal test results by matching the HCB and test modes based on mode descriptions or other methods, and then applying differing levels of frequency variation. The specific variations depend on the confidence to which a component FEM has been validated through modal testing. The NPV method is layered on the frequency variation to match modal test self-orthogonality and cross-orthogonality (XO) results. Once the component uncertainty models are identified, they are assembled, and the uncertainty is propagated to the system level using a Monte Carlo (MC) analysis approach that generates statistics for system-level predictions This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The second example is an application to a component that is design specific to the SLS. Based on this work and other assessments, the HPV method provides another tool to the toolset used for complex system UQ analysis. From experience gathered to date using the HPV method, additional design specific applications must be investigated to provide further confidence in the validity of the HPV method of UQ analysis.

Uncertainty quantification↗
NASA NTRSDate not supplied

SLS Integrated Modal Test Uncertainty Quantification using the Hybrid Parametric Variation Method

Uncertainty in structural loading during launch is a significant concern in the development of spacecraft and launch vehicles. Small variations in launch vehicle and payload mode shapes and their interaction can result in significant variation in system loads. In many cases involving large aerospace systems it is difficult, not economical, or impossible to perform a system modal test. However, it is still vital to obtain test results that can be compared with analytical predictions to validate models. Instead, the “Building Block Approach” is used in which system components are tested individually. Component models are correlated and updated to agree as best they can with test results. The Space Launch System consists of a number of components that are assembled into a launch vehicle. Finite element models of the components are developed, reduced to Hurty/Craig-Bampton models and assembled to represent different phases of flight. The only opportunity to obtain modal test data from an assembled Space Launch System will be during the Integrated Modal Test. There is always uncertainty in every model, which flows into uncertainty in predicted system results. Uncertainty Quantification is used to determine statistical bounds on prediction accuracy based on model uncertainty. For the Space Launch System, model uncertainty is at the Hurty/Craig-Bampton component level. Uncertainty in the Hurty/Craig-Bampton components is quantified using the hybrid parametric variation approach that combines parametric and nonparametric uncertainty. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. This type of uncertainty cannot be represented by variations infinite element model input parameters and thus cannot be included in a parametric approach. However, model-form uncertainty can be modeled using a nonparametric approach based on random matrix theory. The hybrid parametric variation method requires the selection of dispersion values for the Hurty/Craig-Bampton fixed-interface eigenvalues, and the Hurty/Craig-Bampton stiffness matrices. Component test/analysis frequency error is used to identify the fixed-interface eigenvalue dispersions, while test/analysis cross-orthogonality is used to identify stiffness dispersion values. The hybrid parametric variation uncertainty quantification approach is applied to the Space Launch System Integrated Modal Test configuration. Monte Carlo analysis is performed, and statistics are determined for modal correlation metrics, frequency response from Integrated Modal Test shakers to selected accelerometers, as well as other metrics for determining how well target modes are excited and identified. If the predicted uncertainty envelopes future Integrated Modal Test results, then there will be increased confidence in the utility of the component-based hybrid parametric variation uncertainty quantification approach.

Uncertainty Quantification↗
DOE OSTI2024

Improved Statistics for F-theory Standard Models

Much of the analysis of F-theory-based Standard Models boils down to computing cohomologies of line bundles on matter curves. By varying parameters one can degenerate such matter curves to singular ones, typically with many nodes, where the computation is combinatorial and straightforward. The question remains to relate the (a priori possibly smaller) value on the original curve to the singular one. In this work, we introduce some elementary techniques (pruning trees and removing interior edges) for simplifying the resulting nodal curves to a small collection of terminal ones that can be handled directly. When applied to the QSMs, these techniques yield optimal results in the sense that obtaining more precise answers would require currently unavailable information about the QSM geometries. This provides us with an opportunity to enhance the statistical bounds established in earlier research regarding the absence of vector-like exotics on the quark-doublet curve.

Bies, Martin↗
DOE OSTI2020

LANL studies of ESD spark energy discharge through September 2019

Two concentric-sphere apparatuses were used to measure the energies deposited by electric sparks through air to calibrated loads. Both sets of spheres had clean, uninsulated metal surfaces. The 127-mm diameter pair of spheres had a gap of 10 mm and a capacitance of 52 pF. The maximum energy stored on these spheres was 12 mJ and the maximum energy delivered to the 50-mΩ load was 11 µJ, with or without inductance. This load energy amounted to 0.09% of the available input energy; the remainder of the input energy was expended in forming the spark. The second set of spheres was 330 mm in diameter with a gap of 14 mm and a capacitance of 240 pF. The maximum energy stored on these spheres was 71 mJ and the maximum energy delivered to the 50-mΩ load was 150 µJ without added inductance. This load energy was 0.27% of the input energy; again, the remainder of the input energy was expended in forming the spark. The inclusion of 250 nH and 500 nH inductances in the discharge path of the smaller spheres caused the current discharges to resonate, but had little effect on the maximum energies deposited in the loads. At the time of writing, inductances had not yet been added to the larger spheres. The magnitudes of the observed spark discharges were stochastic, so more than 1200 tests were required to develop the statistical bounds of the spark behavior, i.e., to estimate the worst case (highest likely) energy depositions in the loads. The action integrals of the current discharges $∫ i^2dt$ were found to be approximately independent of the load resistances for loads of less than ~1 Ω. Hence the energy deposition scaled with resistance as 207 µJ/Ω and 2.93 mJ/Ω for the two apparatuses.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2022

A Multistage Stochastic Transmission Expansion Algorithm for Wide-Area Planning under Uncertainty

The overall objective for this project was to develop and demonstrate a set of methods for solving the transmission investment problem for a large network considering many possible scenarios of future conditions and multiple decision points when investments can be made. Project sub-objectives achieved this goal through a succession of extending the methods to apply to problems with increasing complexity or additional features, including the number of decision points, whether generation and transmission are co-optimized, and whether AC or DC power flow is used. A transmission model was developed for the Western Electric Coordinating Council (WECC) region, the high-voltage transmission system that serves the western third of the continental U.S. Using a dataset provided by WECC and by researchers from John Hopkins University, we have validated and demonstrated the model and used it to compare the new method for solving multi-stage stochastic transmission planning to several state-of-the-art techniques. The project has resulted in several key outcomes and achievements: The covariance-based method for choosing a small set of hours to represent short-term variability has superior performance in terms of accuracy to existing methods, including K-means clustering and Importance Sampling; The combined partitioning method for long-term uncertainty with the nested clustering approach for choosing representative hours for each long-term group has superior accuracy for equivalent computational effort compared with existing methods; Using the partitioning/clustering method combined with Sample Average Approximation provides both statistical bounds on the quality of the solution and at the same time, a complete investment plan for all contingencies in the full uncertainty set; no existing methods can provide both at the same time; The method is demonstrated to work well for choosing both transmission and generation investments; A variant on the method allows for both scenario selection and simultaneous correction for the error from the DC power flow approximation to provide a tractable method for AC power flow-based transmission planning under uncertainty; The method applied to the WECC case study demonstrates the additional value to the system operator and the consumer of identifying flexible investment options in the near-term decisions. In particular, the case study exhibits significant option value in postponing some transmission additions that appear useful but in some long-term system states create new congestion problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1971

New understanding of fiber composite materials

Statistical bounding approach to study of filamentary composites provides understanding of their fracture mechanics. Comparison shows that bounds are in good agreement with data from several fiber-matrix systems, and that they can be used to interpret strength data and provide fracture behavior information leading to improved strength.

Zweben, C.↗
NASA NTRS1994

The Accuracy of Parameter Estimation in System Identification of Noisy Aircraft Load Measurement

This thesis focuses on the subject of the accuracy of parameter estimation and system identification techniques. Motivated by a complicated load measurement from NASA Dryden Flight Research Center, advanced system identification techniques are needed. The objective of this problem is to accurately predict the load experienced by the aircraft wing structure during flight determined from a set of calibrated load and gage response relationship. We can then model the problem as a black box input-output system identification from which the system parameter has to be estimated. Traditional LS (Least Square) techniques and the issues of noisy data and model accuracy are addressed. A statistical bound reflecting the change in residual is derived in order to understand the effects of the perturbations on the data. Due to the intrinsic nature of the LS problem, LS solution faces the dilemma of the trade off between model accuracy and noise sensitivity. A method of conflicting performance indices is presented, thus allowing us to improve the noise sensitivity while at the same time configuring the degredation of the model accuracy. SVD techniques for data reduction are studied and the equivalence of the Correspondence Analysis (CA) and Total Least Squares Criteria are proved. We also looked at nonlinear LS problems with NASA F-111 data set as an example. Conventional methods are neither easily applicable nor suitable for the specific load problem since the exact model of the system is unknown. Neural Network (NN) does not require prior information on the model of the system. This robustness motivated us to apply the NN techniques on our load problem. Simulation results for the NN methods used in both the single load and the 'warning signal' problems are both useful and encouraging. The performance of the NN (for single load estimate) is better than the LS approach, whereas no conventional approach was tried for the 'warning signals' problems. The NN design methodology is also presented. The use of SVD, CA and Collinearity Index methods are used to reduce the number of neurons in a layer.

Kong, Jeffrey↗
NASA NTRS2022

NASA Engineering and Safety Center Technical Bulletin No. 22-04: Uncertainty Quantification of Reduced Order Structural Dynamic Models

Uncertainty quantification (UQ) provides statistical bounds on prediction accuracy based on finite element model (FEM) uncertainty. An alternate method for UQ, called the Hybrid Parametric Variation (HPV) combines a parametric variation of the Hurty/Craig-Bampton (HCB) fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method. This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available.

Uncertainty Quantification↗
NASA NTRS1983

A two step linear statistical technique using leaps and bounds procedure for retrieval of geophysical parameters from microwave radiometric data

A linear statistical technique using a 'leaps and bounds' procedure (Furnival and Wilson, 1974) is developed for retrieving geophysical parameters from remote measurements. It is used for retrieving sea surface temperatures from the Scaning Multichannel Microwave Radiometer (SMMR) on Seasat. The technique uses an efficient algorithm to select the best fixed-size subset of the 10 SMMR channels for linearly retrieving a given geophysical parameter. The 5-channel subset (6.6V, 6.6H 10H, 18V, 21H), where V and H refer to, respectively, the vertical and horizontal polarizations and the numbers are the channel frequencies in gigahertz, gives the minimum rms error in estimating the sea surface temperature. A comparison with ground truth indicates that the algorithm infers the temperature with an rms accuracy of better than 1.5 K under most environmental conditions. A quality control procedure which is seen as holding promise for further improving the accuracy is proposed.

Kakar, R. K.↗
DOE OSTI2015

Monte Carlo calculations of PET coincidence timing: single and double-ended readout

We present Monte Carlo computational methods for estimating the coincidence resolving time (CRT) of scintillator detector pairs in positron emission tomography (PET) and present results for Lu 2 SiO 5 : Ce (LSO), LaBr 3 : Ce, and a hypothetical ultra-fast scintillator with a 1 ns decay time. The calculations were applied to both single-ended and double-ended photodetector readout with constant-fraction triggering. They explicitly include (1) the intrinsic scintillator properties (luminosity, rise time, decay time, and index of refraction), (2) the exponentially distributed depths of interaction, (3) the optical photon transport efficiency, delay, and time dispersion, (4) the photodetector properties (fill factor, quantum efficiency, transit time jitter, and single electron response), and (5) the determination of the constant fraction trigger level that minimizes the CRT. The calculations for single-ended readout include the delayed photons from the opposite reflective surface. The calculations for double-ended readout include (1) the simple average of the two photodetector trigger times, (2) more accurate estimators of the annihilation photon entrance time using the pulse height ratio to estimate the depth of interaction and correct for annihilation photon, optical photon, and trigger delays, and (3) the statistical lower bound for interactions at the center of the crystal. For time-of-flight (TOF) PET we combine stopping power and TOF information in a figure of merit equal to the sensitivity gain relative to whole-body non-TOF PET using LSO. For LSO crystals 3 mm × 3 mm × 30 mm, a decay time of 37 ns, a total photoelectron count of 4000, and a photodetector with 0.2 ns full-width at half-maximum (fwhm) timing jitter, single-ended readout has a CRT of 0.16 ns fwhm and double-ended readout has a CRT of 0.111 ns fwhm. For LaBr 3 : Ce crystals 3 mm × 3 mm × 30 mm, a rise time of 0.2 ns, a decay time of 18 ns, and a total of 7600 photoelectrons the CRT numbers are 0.14 ns and 0.072 ns fwhm, respectively. For a hypothetical ultra-fast scintillator 3 mm × 3 mm × 30 mm, a decay time of 1 ns, and a total of 4000 photoelectrons, the CRT numbers are 0.070 and 0.020 ns fwhm, respectively. Over a range of examples, values for double-ended readout are about 10% larger than the statistical lower bound.

Monte Carlo↗