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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Variance components in confocal scanning laser tomography measurements of neuro‐retinal rim area and the effect of repeated measurements on the power to detect loss over time

Abstract Purpose To estimate the variation in measurements of neuro‐retinal rim area (NRA) determined by confocal scanning laser tomography and consequences for clinical follow‐up. Methods Altogether, 24 healthy subjects were randomized on –320 μ m, Moorfields and Standard NRA plane strategies. Additionally, NRA was measured in 32 glaucoma subjects. Variance components for subjects, visits and measurements were estimated with analysis of variance. Sample sizes required to detect a 6.0 × 10 −2 mm 2 NRA change were estimated assuming a significance level of 0.05 and a power of 0.8. Consequences for independent group, and paired comparison design, respectively, were analysed. Further, precision in estimates within subjects over time was investigated. Results The variation of NRA among subjects was considerably larger than the variation among visits and measurements. For glaucoma subjects, the variation among visits and measurements were of the same order but larger than in healthy subjects. It was found that independent group comparisons require inconveniently large sample sizes. Within‐subject paired comparisons over time require sample sizes of below 15 subjects. The estimated variations for glaucoma subjects imply that 54 months of follow‐up is required for detection of change from baseline. Conclusions The variance for subjects is substantial in relation to those for visits and measurements. Cross‐sectional independent group comparisons of levels of NRA are unsuitable, due to considerable subject variation. Levels of NRA differences within subjects between visits can be estimated with acceptable precision. Neuro‐retinal rim area (NRA) measurement can be used for long‐term follow‐up of glaucoma progression.

Sandberg Melin, Camilla↗
NASA NTRS2020

Assessment Of Polsar And Insar Time-Series From The 2019 Nasa Am-Pm Campaign For Above-Ground Biomass Estimation

The forthcoming launch of the NASA-ISRO Synthetic ApertureRadar (NISAR) mission will open the path to a new typeof L-band measurements constituted by dense time-series ofpolarimetric backscatter and interferometric coherence withunprecedented spatial and temporal sampling. Here, we startthe development of a theoretical framework that links L-bandbackscatter time-series with interferometric coherence measurements.The water-cloud-model (WCM) and an extendedversion of the random-motion-over-ground (RMoG) modelare adopted to express radar measurements in terms of forestabove-ground biomass and tree height. Time-series datacollected during the 2019 UAVSAR AM-PM campaign inSoutheastern United States are used to evaluate the correlationof various PolSAR- and InSAR-derived parameters withfield-measured above-ground biomass.

Lavalle, Marco↗
DOE OSTI2015

A partially reflecting random walk on spheres algorithm for electrical impedance tomography

In this work, we develop a probabilistic estimator for the voltage-to-current map arising in electrical impedance tomography. This novel so-called partially reflecting random walk on spheres estimator enables Monte Carlo methods to compute the voltage-to-current map in an embarrassingly parallel manner, which is an important issue with regard to the corresponding inverse problem. Our method uses the well-known random walk on spheres algorithm inside subdomains where the diffusion coefficient is constant and employs replacement techniques motivated by finite difference discretization to deal with both mixed boundary conditions and interface transmission conditions. We analyze the global bias and the variance of the new estimator both theoretically and experimentally. Subsequently, the variance of the new estimator is considerably reduced via a novel control variate conditional sampling technique which yields a highly efficient hybrid forward solver coupling probabilistic and deterministic algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Experimental and Theoretical Study of Azimuth Angle and Polarization Dependences of Sum-Frequency-Generation Vibrational Spectral Features of Uniaxially Aligned Cellulose Crystals

Comprehensive interpretation of vibrational sum-frequency-generation (SFG) spectroscopic features of SFG-active nanodomains interspersed in amorphous bulk requires the knowledge of nonlinear susceptibility, χ ijk (2) , of the SFG-active phase as a function of its spatial arrangement in the bulk as well as the polarizations of the probe lights. Our work reports the full analysis of the azimuth angle and polarization dependence of SFG signals from a control sample consisting of uniaxially aligned cellulose Iβ crystals. The χ ijk (2) terms of cellulose were estimated from quantum mechanics calculations using time-dependent density functional theory (TD-DFT), and a simple structural model was built with truncated glucose dimers. The theoretical azimuth angle and polarization dependences of characteristic CH/CH 2 and OH stretch modes of cellulose were compared with the experimentally observed trends. These comparisons revealed that the relative polarity of crystallites within the SFG coherence length, the random quasi phase-matching of polycrystalline domains, and the preferential packing of crystallites in the bulk play important roles governing the spectral features. Compared to that of small molecules, the difference between chiral and achiral responses in SFG spectra is more difficult to confirm because of the inhomogeneous distribution of crystallites in the bulk sample.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Identification of novel organic polar materials: A machine learning study with importance sampling

Recent advances in the synthesis of polar molecular materials have produced practical alternatives to ferroelectric ceramics, opening up exciting new avenues for their incorporation into modern electronic devices. However, in order to realize the full potential of polar polymer and molecular crystals for modern technological applications, it is paramount to assemble and evaluate all the available data for such compounds, identifying descriptors that could be associated with an emergence of ferroelectricity. In this paper, we utilized data-driven approaches to judiciously shortlist candidate materials from a wide chemical space that could possess ferroelectric functionalities. A machine learning study with importance sampling was employed to address the challenge of having a limited amount of available data on already-known organic ferroelectrics. Sets of molecular- and crystal-level descriptors were combined with a Random Forest Regression algorithm in order to predict the spontaneous polarization of the shortlisted compounds. First-principles simulations were performed to further validate the predictions obtained from the machine learning model.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Unveiling the Milky Way: A new technique for determining the optical color and luminosity of our galaxy

We demonstrate a new statistical method of determining the global photometric properties of the Milky Way (MW) to an unprecedented degree of accuracy, allowing our Galaxy to be compared directly to objects measured in extragalactic surveys. Capitalizing on the high-quality imaging and spectroscopy data set from the Sloan Digital Sky Survey (SDSS), we exploit the inherent dependence of galaxies’ luminosities and colors on their total stellar mass, M{sub ⋆}, and star formation rate (SFR), M-dot {sub ⋆}, by selecting a sample of Milky Way analog galaxies designed to reproduce the best Galactic M{sub ⋆} and M-dot {sub ⋆} measurements, including all measurement uncertainties. Making the Copernican assumption that the MW is not extraordinary among galaxies of similar stellar mass and SFR, we then analyze the photometric properties of this matched sample, constraining the characteristics of our Galaxy without suffering interference from interstellar dust. We explore a variety of potential systematic errors that could affect this method, and find that they are subdominant to random uncertainties. We present both SDSS ugriz absolute magnitudes and colors in both rest-frame z = 0 and z = 0.1 passbands for the MW, which are in agreement with previous estimates but can have up to ∼3× lower errors. We find the MW to have absolute magnitude {sup 0}M{sub r}−5logh=−21.00{sub −0.37}{sup +0.38} and integrated color {sup 0}(g−r)=0.682{sub −0.056}{sup +0.066}, indicating that it may belong to the green-valley region in color–magnitude space and ranking it among the brightest and reddest of spiral galaxies. We also present new estimates of global stellar mass-to-light ratios for our Galaxy. This work will help relate our in-depth understanding of the Galaxy to studies of more distant objects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Machine learning for disruption warnings on Alcator C-Mod, DIII-D, and EAST

In this paper, we report on disruption prediction using a shallow machinelearning method known as Random Forests, trained on large databases containingonly plasma parameters that are available in real-time on Alcator C-Mod, DIII-D, and EAST. The database for each tokamak contains parameters sampled ~10 6 times throughout ~10 4 discharges (disruptive and non-disruptive) over the last 4years of operation. It is found that a number of parameters (e.g.P rad /P input ,l i ,n/n G ,B n=1 /B 0 ) exhibit changes in aggregate as a disruption is approached on one ormore of these tokamaks. However, for each machine, the most useful parameters,as well as the details of their precursor behaviors, are markedly different. When the prediction problem is framed using a binary classification scheme to discriminate between time slices "close to disruption" and "far from disruption," it is found that the prediction algorithms differ substantially in performance among the three machines ona time slice-by-time slice basis, but have similar disruption detection rates (~80-90%) on a shot-by-shot basis after appropriate optimisation. This could have important implications for disruption prediction and avoidance on ITER, for which developmentof a training database of disruptions may be infeasible. The algorithm's output is interpretable using a method that identifies the most strongly contributing inputsignals, which may have implications for avoiding disruptive scenarios. Lastly, to further support its real-time capability, successful applications in inter-shot and real-time environments on EAST and DIII-D are also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Insight into 3D micro-CT data: exploring segmentation algorithms through performance metrics

Three-dimensional (3D) micro-tomography (µ-CT) has proven to be an important imaging modality in industry and scientific domains. Understanding the properties of material structure and behavior has produced many scientific advances. An important component of the 3D µ-CT pipeline is image partitioning (or image segmentation), a step that is used to separate various phases or components in an image. Image partitioning schemes require specific rules for different scientific fields, but a common strategy consists of devising metrics to quantify performance and accuracy. The present article proposes a set of protocols to systematically analyze and compare the results of unsupervised classification methods used for segmentation of synchrotron-based data. Additionally, the proposed dataflow for Materials Segmentation and Metrics (MSM) provides 3D micro-tomography image segmentation algorithms, such as statistical region merging (SRM), k-means algorithm and parallel Markov random field (PMRF), while offering different metrics to evaluate segmentation quality, confidence and conformity with standards. Both experimental and synthetic data are assessed, illustrating quantitative results through the MSM dashboard, which can return sample information such as media porosity and permeability. The main contributions of this work are: (i) to deliver tools to improve material design and quality control; (ii) to provide datasets for benchmarking and reproducibility; (iii) to yield good practices in the absence of standards or ground-truth for ceramic composite analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Vacant niches help predict invasion risk by birds

Abstract Aim If communities have a ceiling determining the number of species that can coexist, then the ability of alien species to establish at any given location should be related to the quantity of vacant niches available. We developed a new approach to estimate the extent to which niches are vacant and then explored the relationship between vacant niches and alien species. Location Global with focal tests in Europe and North America. Taxon Birds. Methods Drawing on a global classification of trophic structures for birds, we calculated a ‘vacant niche ratio’ metric to quantify the expected level of saturation (i.e. number of vacant niches) for each 1° × 1° grid cell globally, based on the difference between expected and observed numbers of bird species for all trophic guilds. Next, we used random forests to examine if the presence of plant‐invertivore (whose food source represents plants, seeds, fruits and invertebrates) and granivore alien bird species was associated with the vacant niche ratio across well‐sampled regions. Results In Europe, we found a significant relationship between alien species and vacant niches, with greater numbers of alien species being found in communities that offered greater numbers of vacant niches overall, and across habitat types. In North America, we found no significant relationship between plant‐invertivores and vacant niches, while for granivores, we found that areas with fewer vacant niches had greater numbers of alien species, especially in forests. However, vacant niches alone correctly predict 69% of the presence of alien bird species when combining both regions and trophic guilds. Main Conclusions Most regions of the world have unsaturated bird communities, with the level of saturation in communities varying within regions and trophic guilds. We found that although often‐neglected, vacant niches are likely to be, at least partially, related with the successful establishment of alien bird species.

González‐del‐Pliego, Pamela↗
DOE OSTI2022

Improved quantitation of SIMS depth profile measurements of niobium via sample holder design improvements and characterization of grain orientation effects

The importance of SIMS analyses for “N-doped” impurity alloyed niobium and other surface-alloyed materials continues to increase. A major hurdle is the uncertainty of instrument calibration due to changes in sample height either from sample surface topography or from the sample holder itself. The CAMECA sample holder design allows for many types of samples to be analyzed. However, a drawback is that the holder faceplate can bend, contributing an uncertainty in the relative sensitivity factor (RSF) used to quantify the SIMS results. Here, we describe an improved sample holder having a reinforced faceplate, which prevents deflection and reduces uncertainty. Simulations show that the new design significantly reduces deflection from 10 μm to 5 nm. Sample measurements show a reduction of RSF uncertainty from this source from 4.1% to 0.95%. Grain orientation has long been suspected to affect RSF measurement as well. A bicrystal implant standard, consisting of randomly oriented and [001] grains, was successively rotated 15° between analyses. It was observed that 20% of the analyses performed on the randomly oriented grain exhibited anomalously high RSF values as well as slow sputter rates. These features were associated with the changing grain normal orientation with respect to the primary Cs + beam. The grain orientation associated with the rise in RSF was simulated and determined to be the [101] crystallographic plane, thus indicating that ion channeling was responsible for the significantly increased RSF. Focused ion beam analysis confirmed slower sputter rates for the cardinal crystallographic orientations, indicating that ion channeling occurred for each.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Structure–activity relationship-based chemical classification of highly imbalanced Tox21 datasets

Abstract The specificity of toxicant-target biomolecule interactions lends to the very imbalanced nature of many toxicity datasets, causing poor performance in Structure–Activity Relationship (SAR)-based chemical classification. Undersampling and oversampling are representative techniques for handling such an imbalance challenge. However, removing inactive chemical compound instances from the majority class using an undersampling technique can result in information loss, whereas increasing active toxicant instances in the minority class by interpolation tends to introduce artificial minority instances that often cross into the majority class space, giving rise to class overlapping and a higher false prediction rate. In this study, in order to improve the prediction accuracy of imbalanced learning, we employed SMOTEENN, a combination of Synthetic Minority Over-sampling Technique (SMOTE) and Edited Nearest Neighbor (ENN) algorithms, to oversample the minority class by creating synthetic samples, followed by cleaning the mislabeled instances. We chose the highly imbalanced Tox21 dataset, which consisted of 12 in vitro bioassays for > 10,000 chemicals that were distributed unevenly between binary classes. With Random Forest (RF) as the base classifier and bagging as the ensemble strategy, we applied four hybrid learning methods, i.e., RF without imbalance handling (RF), RF with Random Undersampling (RUS), RF with SMOTE (SMO), and RF with SMOTEENN (SMN). The performance of the four learning methods was compared using nine evaluation metrics, among which F 1 score, Matthews correlation coefficient and Brier score provided a more consistent assessment of the overall performance across the 12 datasets. The Friedman’s aligned ranks test and the subsequent Bergmann-Hommel post hoc test showed that SMN significantly outperformed the other three methods. We also found that a strong negative correlation existed between the prediction accuracy and the imbalance ratio (IR), which is defined as the number of inactive compounds divided by the number of active compounds. SMN became less effective when IR exceeded a certain threshold (e.g., > 28). The ability to separate the few active compounds from the vast amounts of inactive ones is of great importance in computational toxicology. This work demonstrates that the performance of SAR-based, imbalanced chemical toxicity classification can be significantly improved through the use of data rebalancing.

Idakwo, Gabriel↗
NASA NTRS1998

Physics of Hard Spheres Experiment (PhaSE) or "Making Jello in Space"

The Physics of Hard Spheres Experiment (PHaSE) is a highly successful experiment that flew aboard two shuttle missions to study the transitions involved in the formation of jellolike colloidal crystals in a microgravity environment. A colloidal suspension, or colloid, consists of fine particles, often having complex interactions, suspended in a liquid. Paint, ink, and milk are examples of colloids found in everyday life. In low Earth orbit, the effective force of gravity is thousands of times less than at the Earth's surface. This provides researchers a way to conduct experiments that cannot be adequately performed in an Earth-gravity environment. In microgravity, colloidal particles freely interact without the complications of settling that occur in normal gravity on Earth. If the particle interactions within these colloidal suspensions could be predicted and accurately modeled, they could provide the key to understanding fundamental problems in condensed matter physics and could help make possible the development of wonderful new "designer" materials. Industries that make semiconductors, electro-optics, ceramics, and composites are just a few that may benefit from this knowledge. Atomic interactions determine the physical properties (e.g., weight, color, and hardness) of ordinary matter. PHaSE uses colloidal suspensions of microscopic solid plastic spheres to model the behavior of atomic interactions. When uniformly sized hard spheres suspended in a fluid reach a certain concentration (volume fraction), the particle-fluid mixture changes from a disordered fluid state, in which the spheres are randomly organized, to an ordered "crystalline" state, in which they are structured periodically. The thermal energy of the spheres causes them to form ordered arrays, analogous to crystals. Seven of the eight PHaSE samples ranged in volume fraction from 0.483 to 0.624 to cover the range of interest, while one sample, having a concentration of 0.019, was included for instrument calibration.

Ling, Jerri S.↗
NASA NTRS2006

Estimating Random Errors Due to Shot Noise in Backscatter Lidar Observations

In this paper, we discuss the estimation of random errors due to shot noise in backscatter lidar observations that use either photomultiplier tube (PMT) or avalanche photodiode (APD) detectors. The statistical characteristics of photodetection are reviewed, and photon count distributions of solar background signals and laser backscatter signals are examined using airborne lidar observations at 532 nm using a photon-counting mode APD. Both distributions appear to be Poisson, indicating that the arrival at the photodetector of photons for these signals is a Poisson stochastic process. For Poisson-distributed signals, a proportional, one-to-one relationship is known to exist between the mean of a distribution and its variance. Although the multiplied photocurrent no longer follows a strict Poisson distribution in analog-mode APD and PMT detectors, the proportionality still exists between the mean and the variance of the multiplied photocurrent. We make use of this relationship by introducing the noise scale factor (NSF), which quantifies the constant of proportionality that exists between the root-mean-square of the random noise in a measurement and the square root of the mean signal. Using the NSF to estimate random errors in lidar measurements due to shot noise provides a significant advantage over the conventional error estimation techniques, in that with the NSF uncertainties can be reliably calculated from/for a single data sample. Methods for evaluating the NSF are presented. Algorithms to compute the NSF are developed for the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) lidar and tested using data from the Lidar In-space Technology Experiment (LITE). OCIS Codes:

Liu, Zhaoyan↗
DOE OSTI2017

Comparison of Experimental Methods for Estimating Matrix Diffusion Coefficients for Contaminant Transport Modeling

Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
NASA NTRS1993

X-ray emission from a complete sample of Abell clusters of galaxies

The Rosat all sky survey is used to investigate the X-ray properties of a sample of Abell clusters with measured redshifts and accurate positions. The sample comprises the 145 clusters within a 561 square degree region at high galactic latitude. The mean redshift is 0.17. The sample mean exposure time is higher than average and its mean galactic column density is very low. These together produce a flux limit of about 4.2 x 10(exp -13) erg/sq cm/s in the 0.5 to 2.5 keV energy band. By analyzing the excess of positive fluctuations of the X-ray flux at the cluster positions, compared with the fluctuations of randomly drawn background fields, it is possible to extend these results below the nominal flux limit. It is found that 80 of richness R equal to or greater than 0 and 86 of R equal to or greater than 1 clusters are X-ray emitters with fluxes above 1.10 to the power of minus 13 erg/sq cm/s. Nearly 90 of the clusters meeting the requirements to be in Abell's statistical sample emit above the same level. It is concluded that almost all Abell clusters are real clusters and the Abell catalogue is not strongly contaminated by projection effects. The Kaplan-Meier product limit estimator is used to calculate the cumulative X-ray luminosity function. It is shown that the shape of the luminosity functions are similar for different richness classes, but the characteristic luminosities of richness 2 clusters are about twice of those of richness 1 clusters which are in turn about twice of those of richness zero clusters. This result is another manifestation of the luminosity richness relation for Abell cluster.

Briel, Ulrich G.↗
NASA NTRS2016

X-Ray Computed Tomography of Tranquility Base Moon Rock

X-ray Computed Tomography (CT) was used for the first time on the Apollo 11 Lunar Sample number 10057.30, which had been previously maintained by the White House, then transferred back to NASA under the care of Goddard Space Flight Center. Results from this analysis show detailed images of the internal structure of the moon rock, including vesicles (pores), crystal needles, and crystal bundles. These crystals, possibly the common mineral ilmenite, are found in abundance and with random orientation. Future work, in particular a greater understanding of these crystals and their formation, may lead to a more in-depth understanding of the lunar surface evolution and mineral content.

X-ray computed tomography↗
DOE OSTI2026

An improved dataset for predicting mammal infecting viruses from genetic sequence information

There have been several attempts to develop machine learning (ML) models to identify human infecting viruses from their genomic sequences, with varying degrees of success. Direct comparison between models is problematic, because these models are typically trained and evaluated on different datasets with alternative data splitting schemes, features, and model performance metrics. In this paper we present a standardized dataset of mammal infecting and non-infecting viral pathogens, refined from the previous work of Mollentze et al. to include the latest literature evidence, roughly doubling the number of curated host-virus records available to the community, and new host target labels, primate and mammal. The new host labels were included for several reasons, including previous reports that classification performance is better at broader taxonomic ranks and the idea that there may be more data for primate infection that might serve as a suitable proxy for zoonotic potential and avoidance of false positives for human infection due to absence of evidence. On this dataset, we report the performance of eight machine learning models for predicting mammal-infecting viruses from their genomic sequences. We find that randomly assigning cases in our improved dataset to training/testing sets, when compared to the original assignments into training/testing in Mollentze et al., increases the overall average ROC AUC of prediction of human infection from 0.663 ± 0.070 to 0.784 ± 0.013, consistent with the reduction in phylogenetic distance between train and test sets (relative entropy change from 3.00 to 0.08). The broadest host category of mammal infection can be predicted most reliably at 0.850 ± 0.020. We share our improved dataset and code to enable standardized comparisons of machine learning methods to predict human host infections. Overall, we have presented preliminary evidence that classification of virus host infection is more tractable at higher taxonomic ranks, that unsurprisingly reducing the phylogenetic distance between training and test sets can improve predictive performance, that peptide kmer features appear to be harmful to out of sample model performance, and we are left with the question of whether models for virus host prediction can reasonably be expected to perform well in out of sample scenarios given the likelihood that viruses do not share a common ancestor. Consistent with this concern, when the data is resampled such that there is no overlap between viral families in training and test sets (relative entropy > 24), models perform no better than random chance at prediction of human infection regardless of whether kmers are included (ROC AUC 0.50 ± 0.08) or not (ROC AUC 0.50 ± 0.04).

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2003

Estimating the Average Diameter of a Population of Spheres from Observed Diameters of Random Two-Dimensional Sections

Size distributions of chondrules, volcanic fire-fountain or impact glass spherules, or of immiscible globules in silicate melts (e.g., in basaltic mesostasis, agglutinitic glass, impact melt sheets) are imperfectly known because the spherical objects are usually so strongly embedded in the bulk samples that they are nearly impossible to separate. Hence, measurements are confined to two-dimensional sections, e.g. polished thin sections that are commonly examined under reflected light optical or backscattered electron microscopy. Three kinds of approaches exist in the geologic literature for estimating the mean real diameter of a population of 3D spheres from 2D observations: (1) a stereological approach with complicated calculations; (2) an empirical approach in which independent 3D size measurements of a population of spheres separated from their parent sample and their 2D cross sectional diameters in thin sections have produced an array of somewhat contested conversion equations; and (3) measuring pairs of 2D diameters of upper and lower surfaces of cross sections each sphere in thin sections using transmitted light microscopy. We describe an entirely probabilistic approach and propose a simple factor of 4/x (approximately equal to 1.27) to convert the 2D mean size to 3D mean size.

Kong, Maiying↗