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In this correspondence maximum-likelihood binary detection theory is applied to an incoherent optical system model employing photodetectors governed by Laguerre counting statistics. It is shown that a maximum-likelihood Laguerre detector corresponds to a count comparison over each signaling interval. Laguerre error probabilities are presented and compared with those for Poisson counting.
Abstract. Ambient aerosol size distributions obtained with a compact scanning mobility analyzer, the “Spider” differential mobility analyzer (DMA), are compared to those obtained with a conventional mobility analyzer, with specific attention to the effect of mobility resolution on the measured size distribution parameters. The Spider is a 12 cm diameter radial differential mobility analyzer that spans the 10–500 nm size range with 30 s mobility scans. It achieves its compact size by operating at a nominal mobility resolution R=3 (sheath flow = 0.9 L min−1; aerosol flow = 0.3 L min−1) in place of the higher ratio of sheath flow to aerosol flow commonly used. The question addressed here is whether the lower resolution is sufficient to capture key characteristics of ambient aerosol size distributions. The Spider, operated at R=3 with 30 s up- and downscans, was co-located with a TSI 3081 long-column mobility analyzer, operated at R=10 with a 360 s sampling duty cycle. Ambient aerosol data were collected over 26 consecutive days of continuous operation, in Pasadena, CA. Over the 17–500 nm size range, the two instruments exhibit excellent correlation in the total particle number concentrations and geometric mean diameters, with regression slopes of 1.13 and 1.00, respectively. Our results suggest that particle sizing at a lower resolution than typically employed may be sufficient to obtain key properties of ambient size distributions, at least for these two moments of the size distribution. Moreover, it enables better counting statistics, as the wider transfer function for a given aerosol flow rate results in a higher counting rate.
For a three-hour period in the magnetotail over which plasma density varied from less than 0.1 to about 1/cu cm, comparisons of ISEE-1 spherical double probe (dawn to dusk) electric field measurements and ISEE-2 plasma flows (converted to electric fields) show the zero lag cross correlation coefficient between 768 second averages of the two data sets to have been 0.93. A statistical relative uncertainty between pairs of points in the two data sets, estimated by only including counting statistics in the plasma measurement and time variations of the observed electric field over the measurement interval, is able to account for at least 75 percent of the deviations between the two data sets. In agreement with simple Langmuir probe theory, it has been found that the spacecraft potential measured over the three-hour interval by the double probe instrument varied as the log of the product of the plasma density and the square root of the electron temperature.
Avalanche photodiodes (APD) are studied for uses as photon counting detectors in spaceborne lidars. Non-breakdown APD photon counters, in which the APD's are biased below the breakdown point, are shown to outperform: (1) conventional APD photon counters biased above the breakdown point; (2) conventional APD photon counters biased above the breakdown point; and (3) APD's in analog mode when the received optical signal is extremely weak. Non-breakdown APD photon counters were shown experimentally to achieve an effective photon counting quantum efficiency of 5.0 percent at lambda = 820 nm with a dead time of 15 ns and a dark count rate of 7000/s which agreed with the theoretically predicted values. The interarrival times of the counts followed an exponential distribution and the counting statistics appeared to follow a Poisson distribution with no after pulsing. It is predicted that the effective photon counting quantum efficiency can be improved to 18.7 percent at lambda = 820 nm and 1.46 percent at lambda = 1060 nm with a dead time of a few nanoseconds by using more advanced commercially available electronic components.
Bonse–Hart ultra-small-angle neutron scattering (USANS) provides access to micrometre-scale structure, but useful measurements often require long counting times. In this work, we test whether the expected smoothness of the scattering profile can be exploited to improve data quality at lower counting statistics. We apply a Gaussian-process-based method to Bonse–Hart USANS data and evaluate its performance on pseudo-measurements generated from high-statistics experiments under Poisson statistics. This provides a stringent test of how well the underlying I(Q) profile can be reconstructed when the available counts are substantially reduced. We further show that, in the counting-limited regime, the reconstruction error follows a universal scaling behaviour that differs from the usual independent-counting expectation. At higher counts, the improvement crosses over to a resolution-limited regime set by analyser-angle discretization and rocking-curve width. These results clarify when correlation-aware inference is useful in USANS and provide a practical basis for improving measurement efficiency and beam-time usage.
We measure the impact of source galaxy clustering on higher order summary statistics of weak gravitational lensing data. By comparing simulated data with galaxies that either trace or do not trace the underlying density field, we show that this effect can exceed measurement uncertainties for common higher order statistics for certain analysis choices. We evaluate the impact on different weak lensing observables, finding that third moments and wavelet phase harmonics are more affected than peak count statistics. Using Dark Energy Survey (DES) Year 3 (Y3) data, we construct null tests for the source-clustering-free case, finding a p-value of p = 4 × 10 −3 (2.6σ) using third-order map moments and p = 3 × 10 −11 (6.5σ) using wavelet phase harmonics. The impact of source clustering on cosmological inference can be either included in the model or minimized through ad hoc procedures (e.g. scale cuts). We verify that the procedures adopted in existing DES Y3 cosmological analyses were sufficient to render this effect negligible. Failing to account for source clustering can significantly impact cosmological inference from higher order gravitational lensing statistics, e.g. higher order N-point functions, wavelet-moment observables, and deep learning or field-level summary statistics of weak lensing maps.
To evaluate radioactive tracer dilution and gamma spectroscopy as a safeguards technique for monitoring the mass of liquid salt in molten salt systems, the gamma spectroscopy data of salt samples from the pyroprocessing facilities in Idaho National Laboratory were acquired and analyzed. The primary focus is the uncertainty analysis of the gamma radioactivity of 154 Eu isotope in the molten salts. The facilities include an electrorefiner for pyroprocessing spent oxide fuels (SOF-ER) and Mark-IV ER for processing the metallic fuels from Experimental Breeder Reactor-II (EBR-II). The relative gamma radioactivity uncertainty was consistently at 3% for 137 Cs for both Mark-IV ER and SOF-ER salts. However, for 154 Eu, it was 8% for SOF-ER salt and 7% for Mark-IV ER salt. Here, the main reason for the higher uncertainty for 154 Eu is believed to be the lower counting statistics in gamma spectroscopy. To improve the gamma radioactivity uncertainty of isotope 154 Eu, a longer data acquisition time (12 h instead of 4 h) and a higher count rate gamma detector for gamma spectroscopy were tested and it was found that the uncertainty for 154 Eu was significantly improved from 7% or 8–3%.
Gamma-ray spectrometry is one of the most effective ways to determine the activity of 239 Pu, depending on activity levels. However, often high backgrounds in complex spectra with low amounts of 239 Pu can increase detection limits. The effectiveness of the use of gamma-gamma spectrometry in the characterization of 239 Pu was studied for the first time. Using the XIA Pixie-16 digital pulse processor, the gamma-gamma system was studied to establish unshielded background radiation, source to detector distances, Poisson statistics and gating of several gamma-rays from 239 Pu. The results clearly show that the distance between gamma ray spectrometers has a much bigger effort in counting statistics for the gamma-gamma coincidence detectors than a single detector. In addition, measurements demonstrated the background radiation to be virtually negligible, meaning gammagamma spectroscopy can still be very effective without requiring the usual lead shielding. Other measurements were taken to assure Poisson statistics were attained in the digital system. Preliminary measurements revealed 3 orders of magnitude background reduction for the measurement of 239 Pu using gated gamma-rays.
We have developed an optical scanning system that generates maps of the spatial distributions of defects in single and polycrystalline silicon wafers. This instrument, called Scanning Defect Mapping System, utilizes differences in the scattering characteristics of dislocation etch pits and grain boundaries from a defect-etched sample to identify and count them. This system simultaneously operates in the dislocation mode and the grain boundary (GB) mode. In the 'dislocation mode,' the optical scattering from the etch pits is used to statistically count dislocations, while ignoring the GB's. Likewise, in the 'grain boundary mode' the system only recognizes the local scattering from the GB's to generate grain boundary distributions. The information generated by this instrument is valuable for material quality control, identifying mechanisms of defect generation and the nature of thermal stresses during the crystal growth, and the solar cell process design.
Catalytic reaction events occurring on the surface of a nanoparticle constitute a complex stochastic process. Although advances in modern single-molecule experiments enable direct measurements of individual catalytic turnover events occurring on a segment of a single nanoparticle, we do not yet know how to measure the number of catalytic sites in each segment or how the catalytic turnover counting statistics and the catalytic turnover time distribution are related to the microscopic dynamics of catalytic reactions. Here, we address these issues by presenting a stochastic kinetics for nanoparticle catalytic systems. We propose a new experimental measure of the number of catalytic sites in terms of the mean and variance of the catalytic event count. By considering three types of nanocatalytic systems, we investigate how the mean, the variance, and the distribution of the catalytic turnover time depend on the catalytic reaction dynamics, the heterogeneity of catalytic activity, and communication among catalytic sites. This work enables accurate quantitative analyses of single-molecule experiments for nanocatalytic systems and enzymes with multiple catalytic sites.
The multivariate method for statistical analysis of crater-filling classes, as presently applied to craters of more than 10-km diameter on Mercury, is noted to be superior to current techniques due to the obviation of any amalgamation of data from regions with different histories in order to arrive at the pertinent counting statistics. In this application to the Mercury intercrater plains, the process responsible for emplacement is constrained to be one that leaves the crater class distribution unaltered from that observed on the densely cratered terrain. The analysis explicitly eliminates the viability of the pulse emplacement of volcanics or basin ejecta.
Absolute gas counting (AGC) was applied to two gas blends of 85Kr in argon-methane (P10) counting gas to establish a high-precision specific activity (Bq/cm3) reference value for characterizing 85Kr detection efficiency for groundwater age dating measurements. The AGC or length-compensated technique has been utilized by the metrology community for decades and is an accepted method for developing radioactive gas standards. The AGC capability at Pacific Northwest National Laboratory (PNNL) uses a set of nine unequal-length proportional counters with precisely-measured internal volumes, and a gas loading system with high-precision pressure and temperature sensors. A series of AGC measurements were collected at multiple pressures to determine the inverse pressure relationship (1/P) for 85Kr and define a wall-effect correction that accounts for events decaying into the detector wall and not depositing sufficient energy in the gas to be detected. In addition to the wall-effect, two additional corrections were evaluated and are discussed in detail. Specifically, the threshold effect which accounts for events deposited below the analysis threshold and a detection efficiency as a function of detector volume effect that was observed during analysis. A robust uncertainty model was developed using the Guide to the expression of Uncertainty in Measurements (GUM) approach. The combination of carefully scrutinized correction factors, precise measurements of pressure, temperature and detector volume, and robust counting statistics resulted in the determination of high-precision specific activity values with 0.50% or less total combined uncertainty for two Kr-in-P10 reference gas standards (KP10) that will enable new groundwater age-dating measurements at PNNL.
Sequential scattering measurements are often performed under a fixed experimental-time budget, even though the expected count rate varies strongly across the measured coordinate. When the dwell time at each measurement position can be controlled independently, this variation creates a general resource-allocation problem: how should the available time be distributed to minimize the uncertainty of the reconstructed profile? We formulate this problem as a constrained variational optimization for measurements governed by Poisson counting statistics. When each measurement is treated independently, minimizing the averaged squared relative uncertainty yields an inverse-square-root intensity allocation. The formulation is then generalized to include correlations between neighboring measurements and an instrumental resolution operator, leading to an allocation criterion that equalizes the marginal reduction in posterior uncertainty per unit measurement time. Bonse–Hart ultra-small-angle neutron scattering (USANS), in which reciprocal space is sampled sequentially through analyzer-angle stepping, provides an experimentally grounded application. Computational benchmarking shows that the optimized allocation outperforms uniform-time and constant-relative-error strategies, while application to an experimentally measured graphite USANS profile from the Spallation Neutron Source, using Poisson resampling under alternative schedules, demonstrates how counting time should be redistributed toward weak-intensity regions under an identical total duration. The resulting framework applies to sequential scattering and related scanning measurements whenever local dwell times are adjustable and directly determine the measurement uncertainties, and when the relevant correlation and instrumental-response models are available.
In this study, in-situ produced cosmogenic nuclide sample preparation and analysis is a complicated, multi-step process with numerous possible sources of error, many of which have not been robustly quantified. Here, we use a liquid reference material (UVM-A) to test whether the analytic precision associated with individual isotopic ratios (n = 96) measured at two Accelerator Mass Spectrometry facilities (Lawrence Livermore National Laboratory and Purdue Rare Isotope Measurement Laboratory) accurately represents the range of values determined for aliquots prepared in a single laboratory over a period of five years. We find that 10 Be/ 9 Be ratios measured at the different accelerator facilities (n = 26 and n = 70) have statistically indistinguishable central tendencies, matching to within 0.1 %. Based on this large dataset, we suggest preliminary consensus values for UVM-A of 1.45 ± 0.06 x 10 -13 for 10 Be/ 9 Be (mean, one standard deviation, n = 96) and 4.47 ± 0.22 x 10 -13 for 26 Al/ 27 Al (mean, one standard deviation, n = 27). For both 10 Be/ 9 Be and 26 Al/ 27 Al, the relative standard deviations of the measured ratios are similar to the reported analytic uncertainties of sample measurement, suggesting that sample preparation introduced little if any additional scatter beyond the uncertainty of isotopic analysis. This dataset demonstrates that robust sample preparation and measurement can generate isotope ratio data reproducible at the level of counting statistics.
Neutron multiplicity counting is the most commonly used nondestructive assay technique for determining the plutonium mass within containers of scrap PuO 2 or mixed oxide (MOX). In multiplicity analysis, the 240 Pu eff mass, leakage multiplication, and alpha ratio (the ratio of [α, n]-to-spontaneous fission neutron production) are the three primary unknown sample properties. They must be determined simultaneously. To solve for these three unknowns in a multiplicity assay, three measured values are needed: the singles, doubles, and triples neutron count rates. While the analysis is limited to solving for three unknowns, there are many additional factors that impact the observed count rates and contribute to the measurement uncertainty. In this study we investigate the various uncertainty contributors for the multiplicity analysis through a combination of traditional uncertainty propagation techniques supplemented by Monte Carlo simulations to address the dependences not explicitly expressed by the point source model. Uncertainties arising from counting statistics, calibration parameters, calibration method, nuclear data, and various material characteristics (isotopic abundances, chemical form, density, and impurities) are considered. A Total Measurement Uncertainty (TMU) estimate is then developed from these uncertainty contributors. This study is confined to multiplicity analysis of items commonly encountered in international safeguards applications. That is, the study focused on Pu oxides and MOX materials for the masses ranging up to 4000 grams total Pu. Multiplicity measurements were simulated using MCNP V6 based on the Plutonium Scrap Multiplicity Counter (PSMC), Epithermal Multiplicity Counter (ENMC), Pyrochemical Multiplicity Counter, and Large Epithermal Multiplicity Counter (LEMC) for this study; however, this report focuses on the parameterization of the uncertainties for the PSMC. The performance differences between the PSMC and the other multiplicity counting systems are relatively small, primarily manifesting in the impact on measurement precision so that the evaluation developed for the PSMC can be applied to the other multiplicity counting systems. Finally an analysis tool, the Multiplicity TMU Estimator, was developed from this study to serve as an aid for evaluation of the total measurement uncertainty of multiplicity assay results obtained from the commonly used INCC acquisition and analysis software.
Neutron multiplicity counting (NMC) is a technique for the assay of fissile material. In this work, three detection systems are utilized for active interrogation assay of shells of the Rocky Flats shells (highly enriched uranium, 93% 235U) stacked from 13.25-54.92 kg assemblies. The singles ($R_1$) and doubles ($R_2$) rates are calculated with each system to estimate two sample parameters: $M_L$- the leakage multiplication and F - the sample fission rate. The estimated mass, m, is found by dividing F by a constant activity per unit mass. Since we are interrogating HEU, the α ratio of (α; n) to fission neutrons is taken to be zero. The system of equations to calculate these quantities was originally derived. The Neutron Multiplicity 3 He Array Detector (NOMAD) consists of 15 3 He tubes inside polyethylene and is the traditional, capture-based detection system for NMC. The polyethylene moderates incoming neutrons for thermal capture in individual tubes. The low gamma background, discrete capture signals, and high efficiency of the NOMAD are beneficial for NMC. However, the time to slow down neutrons to thermal energies leads to a system die away time on the scale of microseconds. Comparatively, the Rossi-alpha Measurements – Rapid Organic (n, γ) Discrimination Detector (RAMRODD) and the Organic Scintillator Array (OSCAR) are scatter-based detection systems. RAMRODD consists of 8, 5.08 by 5.08 cm EJ-309 liquid scintillators in 4 pairs, evenly-spaced with 90 degrees separation about the center of each assembly. OSCAR consists of a single array of 12, 5.08 by 5.08 cm trans-stilbene crystals aligned with the center of the assembly. Scatter-based systems detect fast neutrons without any moderation, leading to system die away times on the scale of tens of nanoseconds. This allows much shorter timing gate widths compared to thermal systems, thus increasing counting statistics of true correlated fission events. However, scatter-based systems are susceptible to neutron cross-talk when an incident neutron scatters off one detector and interacts in an adjacent detector, causing two seemingly correlated detection signals. The equations developed adjust for cross-talk to conduct NMC with scatter-based systems.
Statistical description of a photoelectric detector is given. The photosensitive surface of the detector is divided into many small areas, and the moment generating function of the photo-counting statistic is derived for large time-bandwidth product. The detection of a specified optical image in the presence of the background light by using the hypothesis test is discussed. The ideal detector based on the likelihood ratio from a set of numbers of photoelectrons ejected from many small areas of the photosensitive surface is studied and compared with the threshold detector and a simple detector which is based on the likelihood ratio by counting the total number of photoelectrons from a finite area of the surface. The intensity of the image is assumed to be Gaussian distributed spatially against the uniformly distributed background light. The numerical approximation by the method of steepest descent is used, and the calculations of the reliabilities for the detectors are carried out by a digital computer.
Advance high density monolithic alloy HALEU fuels have been scanned with a silicon drift detector scanning system to measure low-energy characteristic X-rays emitted by uranium daughters, as well as zirconium present as a foil diffusion barrier. Four peaks were measured across the surfaces of three plates, and are consistent with other thorium and protactinium peaks present in depleted uranium samples that are induced by the decay of 235 U and 238 U. Of the four peaks detected, three are dominated by the decay of 235 U, and one peak at 15.70 keV covers two characteristic X-rays from the zirconium diffusion barrier (Kα 1 ) and from a 231 Th 15.62 keV X-ray induced by 235 U α-decay. The low energies of these lines suggest that they are mostly emitted from the fuel meat surface, and the poor counting statistics caused by strong self-attenuation make these data a poor candidate for 235 U/ 238 U ratio analysis. We suggest, then, that these X-rays could be used for passive measurement of variations in the cladding thickness of these fuels to complement manual thickness measurement methods.