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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Model Inputs, Outputs, and Scripts associated with: “Spatial microbial respiration variations in the hyporheic zones within the Columbia River Basin”

This data package is associated with the publication “Spatial microbial respiration variations in the hyporheic zones within the Columbia River Basin” published in the Journal of Geophysical Research: Biogeosciences (Son et al. 2022) available at doi: 10.1029/2021JG006654. This data package includes the key model inputs/outputs of the river corridor model for the Columbia River Basin (CRB) and the model source codes, which were used in the manuscript. The model is a carbon-nitrogen-coupled river corridor model (RCM), and the model is used to quantify hyporheic zone (HZ) aerobic and anaerobic respiration at the NHDPLUS stream reach scales. The RCM used in this study combines empirical substrate models derived from observations and three microbially driven reactions to compute respiration of the HZ for each National Hydrography Dataset (NHD) reach within the CRB. The reactions in HZs of each NHD reach include anaerobic respiration and two-step anaerobic respiration via denitrification. Our HZ respiration estimates are limited to the lotic (or flowing) stream/river systems, and do not account for the respiration process in water column. Note that the RCM only simulates the HZ’s contribution to the dissolved carbon dioxide (CO2) concentrations in the streams, and the CO2 emissions to the atmosphere are not modelled. The model computes at hourly timesteps because of the fast reaction rates. The key input data of the model are exchange flux, residence time, and stream solute (dissolved organic carbon (DOC), dissolved oxygen (DO), and nitrate concentrations). These inputs are constant over time and represent long-term averaged values.This modeling framework successfully quantified HZ respiration components over multiple scales. It revealed key mechanisms driving the spatial variation of HZ aerobic and anaerobic respiration in reaches with varying hydrologic and substrate conditions. Thus, this modeling study offers a testing hypothesis in different river system (e.g., climate and biomes) for the HZ respiration processes, and can be used as a sampling design tool for large-scale HZ experimental studies.This dataset contains five folders: (1) model_inputs, (2) model_outputs, (3) Rscripts, (4) figures, and (5) model_codes. It also contains a readme, file level metadata (FLMD), and data dictionary (dd). Please see the FLMD for a list of all the files contained in this data package and descriptions for each. The model_inputs folder contains the model inputs used to drive the model simulations. The model_outputs folder contains key model output files from the river corridor model. The Rscripts folder contains the Rscripts for pre- and post- processing model results. The figures folder contains the raw figures associated with the manuscript. The model_codes folder includes key model source codes/input files. All files are .jpg, .jpeg, .out, .e, .od, .dat, .sub, .F90, .0, .R, .sbx, .cpg, .sbn, .shx, .shp, .dbf, .prj, .tfw, .tif, .xml, .pdf, or .csv.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Forecasting generative amplification

Generative networks are perfect tools to enhance the speed and precision of LHC simulations. Especially when generating events beyond the size of the training dataset, it is important to understand their statistical precision. We present two complementary methods to estimate the amplification factor without large holdout datasets. Averaging amplification uses Bayesian networks or ensembling to estimate amplification from the precision of integrals over given phase-space volumes. Differential amplification uses hypothesis testing to quantify amplification without any resolution loss. Applied to state-of-the-art event generators, both methods indicate that amplification is already possible in specific regions of phase space.

Bahl, Henning [Heidelberg Univ. (Germany)] (ORCID:↗
DOE OSTI2015

Multi-Channel Correlation Detectors: Accounting for and Reducing Non-target Detections [Slides]

Overwhelming non-target detections require more representative hypothesis test to target real events. Implicit signal model with convex-cone geometry includes both target waveforms and non-targets. New detector screens target waveforms from convex cone members that correlation detectors return. Proto-type detector returns analyst-equivalent detections, requires minimal modification from correlation detector, and has quantifiable detection performance, and satisfies all solution requirements to reduce false detections for GNDD.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Evaluation of Pre- and Post- Redevelopment Groundwater Chemical Analyses from LM Monitoring Wells

This report documents the efforts and analyses conducted for the Applied Studies and Technology (AS&T) Ancillary Work Plan (AWP) project titled Evaluation of Pre- and Post- Redevelopment Groundwater Sample Laboratory Analyses from Selected LM Groundwater Monitoring Wells. This effort entailed compiling an inventory of nearly 500 previous well redevelopment events at 16 U.S. Department of Energy Office of Legacy Management (LM) sites, searching the literature for impacts of well redevelopment on groundwater sample quality, and—the focus of this report—evaluating the impacts of well redevelopment on field measurements and sample analytical results. Study Catalyst Monitoring well redevelopment, the surging or high-volume pumping of a well to loosen and remove accumulated sediment and biological build-up from a well, is considered an element of monitoring well maintenance that is implemented periodically during the lifetime of the well to mitigate its gradual deterioration. Well redevelopment has been conducted fairly routinely at a few LM sites in the western United States (e.g., the Grand Junction office site and the Gunnison processing site in Colorado), but at most other sites in this region it is not a routine practice. Also, until recently (2014–2015), there had been no specific criteria for implementing well redevelopment, and documentation of redevelopment events has been inconsistent. A catalyst for this evaluation was the self-identification of these inconsistencies by the Legacy Management Support contractor. As a result, in early 2015 Environmental Monitoring Operations (EMO) staff began collecting and documenting additional field measurements during well redevelopment events. In late 2015, AS&T staff undertook an independent internal evaluation of EMO's well redevelopment records and corresponding pre- and post-well-redevelopment groundwater analytical results. Study Findings Although literature discussions parallel the prevailing industry-wide assumption that well redevelopment is necessary to increase production or to extend the life of a well, no data in the literature indicate that redevelopment affects chemical signatures in monitoring wells. The comprehensive evaluation undertaken for this study also yielded no evidence that redevelopment has any quantifiable or predictable effect on groundwater sample quality. Both short-term and long-term changes in groundwater chemistry were assessed relative to preceding and subsequent well redevelopment events. Although short-term changes in specific conductance or contaminant concentrations likely attributable to well redevelopment were found at some sites, these cases were limited to a small subset of wells in which chemical stratification had been observed. Redevelopment causes mixing of the well water, resulting in short-term impacts, but not in a consistent direction. Long-term groundwater concentration trends of uranium, the primary contaminant of concern at most LM Uranium Mill Tailings Radiation Control Act (UMTRCA) sites, were evaluated for all 16 sites addressed in this study. Based on the data evaluated, there are no apparent impacts of well redevelopment on uranium trends. In most cases where deviations in trends were found, these could be attributed to water level fluctuations or other factors. A few exceptions were found where spikes or marked decreases in uranium concentrations could potentially be related to the preceding well redevelopment, but apparent impacts were neither predictable nor quantifiable. Summary and Recommendations A catalyst for this project was a concern that there was a need for strict criteria for a program-wide approach to well redevelopment at LM sites. There was also an implicit question as to whether well redevelopment was a necessary practice that was being overlooked at some sites. The primary objective of this study was to determine if there are significant differences in laboratory analytical results between pre- and post-redevelopment groundwater samples. Results of this evaluation indicate that this is not the case—groundwater concentrations of uranium, the primary contaminant of concern at most LM UMTRCA sites, generally remained unchanged pre- and post-well-redevelopment. The literature supports redevelopment of monitoring and municipal wells if signs of reduced productivity, biofouling, sediment buildup, or other conditions potentially affecting long-term well integrity are observed. In these cases, use of a downhole camera to examine the condition of the well screen and casing may be useful. However, based on the data sets examined for this study, there is no evidence that well redevelopment is needed in order to obtain samples that have the same chemical concentrations as those in the groundwater. To conclusively demonstrate that point—that is, to define chemical effects—the underlying mechanisms have to be understood. For example, if biofouling is observed in a well and is considered a potential cause of spurious or invalid chemical data, appropriate hypothesis-testing ethodology should be used to test the validity of this claim. Until late 2014, the onset of this project, there was no standard procedure for documenting well redevelopment events; some (perhaps many) had not been captured in the historical record. EMO has made notable progress in this regard since 2015, having established a format for documenting well redevelopment events and associated field measurements, as well as a data repository for capturing those records. This policy should be continued to ensure that all well redevelopment events and associated field observations are recorded and easily tracked.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Quality Control of and Analysis Enabling Use of MARCUS and MICRE data for Scientific Applications

The primary objective of this project was to provide a preliminary investigation of data collected during the MARCUS/MICRE field experiments and to produce products and analysis for the scientific community that will enable future scientific investigations and hypothesis testing. Further, the goal was to assist those in the scientific community to understand the strengths and caveats of the MARCUS/MICRE data so that members of the scientific community could use the data in their publications.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Systems Analysis of the Physiological and Molecular Mechanisms of Sorghum Nitrogen Use Efficiency, Water Use Efficiency and Interactions with the Soil Microbiome (Final Report for DE-SC0014395)

The specific project objectives were to: 1) Conduct deep census surveys of root microbiomes concurrent with phenotypic characterizations of a diverse panel of sorghum genotypes across multiple years to define the microbes associated with the most productive lines under drought and low nitrogen conditions. 2) Associate systems-level genotypic, microbial, and environmental factors with improved sorghum performance using robust statistical approaches. 3) Develop culture collections of sorghum root/leaf associated microbes that recapitulate root-enriched sequences defined in the census. 4) Perform controlled environment experiments for in-depth characterization and hypothesis testing of G sorghum x G microbe x E interactions . Validate physiological mechanisms, map genetic loci for stress tolerance, and determine the persistence of optimal microbial strains under greenhouse and field conditions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

3P Program: Phenotyping X Prediction = Productivity (Final Scientific/Technical Report)

The goal of the 3P Program was to establish integrated, real-time phenotyping and to analyze above- and below-ground plant architecture and total carbon partitioning and allocation to predict heterosis and develop superior crop hybrids by fully leveraging the Sorghum gene pool. There were two overarching themes: 1) the development of a new crop improvement approach utilizing advances in high-throughput phenotyping (HTP), computing, and genomics for public dissemination and 2) leveraging this platform for sorghum crop improvement and commercialization. The Clemson team worked on creating genomic resources and using both statistical learning and high-throughput phenotyping in genomics-assisted breeding. Research was broadly interested in the genetics of carbon partitioning, with the aim of improving crop performance and achieving sustainability. The technology and resources created can be readily found in the public domain and serve to advance scientific understanding of crop genomics and breeding. Genomic prediction was able to identify top crosses to be made, and a hybrid prediction pipeline is in place to drive year-over-year genetic gain. Roots have long been ignored by plant breeders and agronomists, not because they are unimportant but because they are hard to measure. This is an untapped white space of potential insight and innovation. To address this, Hi Fidelity Genetics developed the RootTracker to measure roots in the field on a continuous basis. A database system called RootTracker Tracker was developed to handle data coming from the RootTrackers. In using this device, valuable data was observed for plant breeding, hydrochemical development, and other agricultural biology applications. Carnegie Mellon’s goal was developing new techniques to generate high-resolution 3D models of plants from data collected in the field. The idea was that more useful and more informative phenotypes could be extracted by resolving small features, such as seeds and flowers, and that by modeling in 3D, the spatial structure of plants could be examined. To achieve this, multiple images collected by a new small format structured light stereo imager were fused together. A sorghum panicle modeling pipeline was developed to allow the collection and processing of data. Carolina Seed Systems is an agricultural technology company focused on decarbonizing the agricultural system. Their technology pipeline serves to drive fundamental progress towards creation and distribution of carbon negative crops. The genomic and the engineering technology developed through the 3P Program was leveraged to deliver both value and sustainability from the grower to the consumer. Promising sorghum hybrids were scaled up and commercialized. The overall goal of our research was to integrate, create, and deploy genetic and engineering concepts and technologies to enhance crop productivity in a sustainable fashion. The combination of public and private partners allowed the basic research and hypothesis testing to be quickly accelerated for commercial application by the companies yet maintained that the core framework and academic insights remain in the public domain for continued market disruption, competition, and innovation.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Integration of Waveform Simulation Methods

The generation of synthetic seismograms through simulation is a fundamental tool of seismology required to run quantitative hypothesis tests. A variety of approaches have been developed throughout the seismological community and each has their own specific user interface based on their implementation. This causes a challenge to researchers who will need to learn new interfaces with each new software they wish to use and create substantial challenges when attempting to compare results from different tools. Here we provide a unified interface that facilitates interoperability amongst several simulation tools through a modern containerized Python package. Further, this package includes post-processing analysis modules designed to facilitate end-to-end analysis of synthetic seismograms. In this report we present the conceptual guidance and an example implementation of the new Waveform Simulation Framework.

58 GEOSCIENCES↗
DOE OSTI2024

Pore architecture controls on mineral reactivity

Mineral dissolution rates measured in natural environments are much slower than those measured in laboratory settings. This project tested the hypothesis that the way fluid flows through rocks in natural systems creates areas where mineral dissolution is fast and areas where mineral dissolution is slow. This hypothesis was tested with a combination of laboratory experiments and numerical simulation. We demonstrated a separation of fluid flow pathways and rates of mineral dissolution in laboratory experiments for the first time using an experimental approach where we created synthetic rocks that have different ratios of connected and dead-end pathways for fluid flow. In laboratory experiments with higher proportions of dead-end pathways, the mineral dissolution rates were slower. We found that where fluid flows through connected pathways the continuous refreshing of fluid at the mineral surface creates conditions where dissolution is fast. In contrast, where fluid either flows slowly through poorly connected pathways or is stagnant in dead-end pathways, mineral dissolution is slow. The results from this project suggest that the overall slowing of rates of mineral dissolution is important when the proportion of dead-end pathways is greater than ~40%. This project informs our understanding of the way that fluids react with rocks in carbon dioxide sequestration and enhanced geothermal projects where fluids are purposefully injected into rocks for energy applications.

58 GEOSCIENCES↗
DOE OSTI2025

Formation of Organic Compounds Through Meteoritic Atmospheric Shock

This document is a Final Technical Report for DoE award DE-SC0023375 “Formation of Organic Compounds Through Meteoritic Atmospheric Shock”. The document includes a summary of topics studied, specific tasks completed, challenges, and results from the project. The main goal of this project was to investigate the production of organic molecules and/or complex inorganic precursor molecules in a plasma environment reminiscent of the environment surrounding meteoroids during atmospheric entries. The specific hypothesis tested in this project was that meteoroid ablation during the entry and the chemical reactions in the meteoroid plasma tail could have produced significant amounts of organics or precursor inorganics in the Early Earth’s atmosphere. Investigation of these processes is essential in understanding the origins of life on Earth and the search for life beyond our planet. This project was focused on a set of experiments conducted at the Utilizing the DIII-D tokamak in San Diego, CA. The experiments aimed to study the interaction of carbonaceous and silica materials (typically found in meteoroids) with mixtures of hot plasma gases (mimicking atmospheric entry conditions. The material samples and gas mixtures were selected to investigate the synthesis of the organic compound urea – a key ingredient in the origin of life – or one of its precursor, the complex inorganic compound ammonia.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Estuarine nutrient pollution impact reduction assessment through euphotic zone avoidance/bypass considerations

The feasibility of reducing nutrient pollution impact by redirecting the effluent to depths below the euphotic zone was investigated for the deep estuarine Puget Sound region of the Salish Sea in the Pacific Northwest of America. The hypothesis tested was that the thickness of the outflow layer in deep estuaries may be greater than the euphotic zone depth, allowing a fraction of nutrients to be exported out passively through the layers immediately below. The euphotic zone depth in Puget Sound varies from 8 to 25 m while the depth of the outflow layer can reach up to ≈ 60 m. Outfall relocation strategies were tested on 99% of the anthropogenic nutrient loads currently delivered to Puget Sound. The impact was quantified using the previously established biophysical Salish Sea Model, using gross primary production and exposure to low dissolved oxygen (DO) levels as the metric (< 2 mg/L for hypoxia and < 5 mg/L for impairment). Eliminating nutrient pollution (above natural) from rivers and wastewater reduced hypoxia exposure by 8.1% and 11.2%, respectively. Relocating the outfalls to deeper waters resulted in improvements, but only in the sill-less sub-basins such as Whidbey, where hypoxia and DO impairment exposure decreased (7.9% and 6.8%, respectively). The presence of multiple sills and circulation cells in Puget Sound resulted in increased exposure and rendered nutrient bypass goals unfeasible as originally envisioned. However, an alternate nutrient export pathway was identified through bottom exchange flow out of Puget Sound via Whidbey Basin and Deception Pass. An unexpected reduction in the exchange outflow magnitude (≈ 4%) due additional (22%) freshwater discharged to the estuary bottom was also noted. The potential loss in circulation strength due to rerouting of natural surface freshwater through submerged deep-water outfalls is identified as a new unforeseen anthropogenic impact.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Detection of DoS Attacks Using ARFIMA Modeling of GOOSE Communication in IEC 61850 Substations

Integration of Information and Communication Technology (ICT) in modern smart grids (SGs) offers many advantages including the use of renewables and an effective way to protect, control and monitor the energy transmission and distribution. To reach an optimal operation of future energy systems, availability, integrity and confidentiality of data should be guaranteed. Research on the cyber-physical security of electrical substations based on IEC 61850 is still at an early stage. In the present work, we first model the network traffic data in electrical substations, then, we present a statistical Anomaly Detection (AD) method to detect Denial of Service (DoS) attacks against the Generic Object Oriented Substation Event (GOOSE) network communication. According to interpretations on the self-similarity and the Long-Range Dependency (LRD) of the data, an Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) model was shown to describe well the GOOSE communication in the substation process network. Based on this ARFIMA-model and in view of cyber-physical security, an effective model-based AD method is developed and analyzed. Two variants of the statistical AD considering statistical hypothesis testing based on the Generalized Likelihood Ratio Test (GLRT) and the cumulative sum (CUSUM) are presented to detect flooding attacks that might affect the availability of the data. Our work presents a novel AD method, with two different variants, tailored to the specific features of the GOOSE traffic in IEC 61850 substations. The statistical AD is capable of detecting anomalies at unknown change times under the realistic assumption of unknown model parameters. The performance of both variants of the AD method is validated and assessed using data collected from a simulation case study. We perform several Monte-Carlo simulations under different noise variances. The detection delay is provided for each detector and it represents the number of discrete time samples after which an anomaly is detected. In fact, our statistical AD method with both variants (CUSUM and GLRT) has around half the false positive rate and a smaller detection delay when compared with two of the closest works found in the literature. Our AD approach based on the GLRT detector has the smallest false positive rate among all considered approaches. Whereas, our AD approach based on the CUSUM test has the lowest false negative rate thus the best detection rate. Depending on the requirements as well as the costs of false alarms or missed anomalies, both variants of our statistical detection method can be used and are further analyzed using composite detection metrics.

IEC 61850 electrical substations↗
DOE OSTI2023

SNM Radiation Signature Classification Using Different Semi-Supervised Machine Learning Models

The timely detection of special nuclear material (SNM) transfers between nuclear facilities is an important monitoring objective in nuclear nonproliferation. Persistent monitoring enabled by successful detection and characterization of radiological material movements could greatly enhance the nuclear nonproliferation mission in a range of applications. Supervised machine learning can be used to signal detections when material is present if a model is trained on sufficient volumes of labeled measurements. However, the nuclear monitoring data needed to train robust machine learning models can be costly to label since radiation spectra may require strict scrutiny for characterization. Therefore, this work investigates the application of semi-supervised learning to utilize both labeled and unlabeled data. As a demonstration experiment, radiation measurements from sodium iodide (NaI) detectors are provided by the Multi-Informatics for Nuclear Operating Scenarios (MINOS) venture at Oak Ridge National Laboratory (ORNL) as sample data. Anomalous measurements are identified using a method of statistical hypothesis testing. After background estimation, an energy-dependent spectroscopic analysis is used to characterize an anomaly based on its radiation signatures. In the absence of ground-truth information, a labeling heuristic provides data necessary for training and testing machine learning models. Supervised logistic regression serves as a baseline to compare three semi-supervised machine learning models: co-training, label propagation, and a convolutional neural network (CNN). In each case, the semi-supervised models outperform logistic regression, suggesting that unlabeled data can be valuable when training and demonstrating value in semi-supervised nonproliferation implementations.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2021

Bioverse: A Simulation Framework to Assess the Statistical Power of Future Biosignature Surveys

Next-generation space observatories will conduct the first systematic surveys of terrestrial exoplanet atmospheres and search for evidence of life beyond Earth. While in-depth observations of the nearest habitable worlds may yield enticing results, there are fundamental questions about planetary habitability and evolution that can only be answered through population-level studies of dozens to hundreds of terrestrial planets. To determine the requirements for next-generation observatories to address these questions, we have developed Bioverse. Bioverse combines existing knowledge of exoplanet statistics with a survey simulation and hypothesis testing framework to determine whether proposed space-based direct imaging and transit-spectroscopy surveys will be capable of detecting various hypothetical statistical relationships between the properties of terrestrial exoplanets. Following a description of the code, we apply Bioverse to determine whether an ambitious direct imaging or transit survey would be able to determine the extent of the circumstellar habitable zone and study the evolution of Earth-like planets. Given recent evidence that Earth-sized habitable zone planets are likely much rarer than previously believed, we find that space missions with large search volumes will be necessary to study the population of terrestrial and habitable worlds. Moving forward, Bioverse provides a methodology for performing trade studies of future observatory concepts to maximize their ability to address population-level questions, including and beyond the specific examples explored here.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Examination of Extreme Rainfall Events in Two Regions of the United States since the 19th Century

A common hypothesis regarding human-induced climate change is that precipitation processes will accelerate leading to an increasing magnitude of rainfall amounts on a daily time scale as the atmosphere warms. This assertion is supported by two physically demonstrable facts, (1) warmer air accommodates more water vapor, and (2) precipitation processes become more efficient as the cloud environment warms. However, by definition, extreme events are rare, and thus statistics of their occurrence and possible long-term changes present difficult challenges, some herein addressed. In any case, the observational datasets on which hypothesis tests may be carried out should cover the longest periods possible because precipitation can naturally vary considerably on even century time scales. In this study we focus on this temporal issue by building long-term daily precipitation datasets for twenty stations, ten along or near the US Pacific Coast (PC) and ten along or near the coast in the US Southeast (SE). Observations for these stations begin between 1840 and 1890 and end in 2018, using the water year (Oct to Sep) to define the annual period. For some metrics, e.g. the annual total precipitation or the number of days per year measuring greater than 25 mm, there is no discernable change over the most recent 145 years (1874-2018). For other metrics, e.g. the magnitude of the wettest day per year or the temporal distribution of the 29 wettest 2-day events in the past 145 years (i.e. nominal 1-in-5-year occurrence), there appears to be an increase in SE and a decrease in PC. Whether these trends are significant for the relatively short climate record of 145 years will be discussed with the conclusion being the limited time frame of analysis does not lead to decisive claims that these changes are outside of the range of natural variability.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

An Observation Data Driven Simulation and Analysis Framework for Early Stage C. elegans Embryogenesis

Recent developments in cutting-edge live microscopy and image analysis provide a unique opportunity to systematically investigate individual cell’s dynamics as well as simulation-based hypothesis testing. After a summary of data generation and analysis in the observation and modeling efforts related to C. elegans embryogenesis, we develop a systematic approach to model the basic behaviors of individual cells. Next, we present our ideas to model cell fate, division, and movement using 3D time-lapse images within an agent-based modeling framework. Then, we summarize preliminary result and discuss efforts in cell fate, division, and movement modeling. Finally, we discuss the ongoing efforts and future directions for C. elegans embryo modeling, including an inferred developmental landscape for cell fate, a quasi-equilibrium model for cell division, and multi-agent, deep reinforcement learning for cell movement.

3D live images↗
NASA NTRS1972

The resolution of point sources of light as analyzed by quantum detection theory

The resolvability of point sources of incoherent light is analyzed by quantum detection theory in terms of two hypothesis-testing problems. In the first, the observer must decide whether there are two sources of equal radiant power at given locations, or whether there is only one source of twice the power located midway between them. In the second problem, either one, but not both, of two point sources is radiating, and the observer must decide which it is. The decisions are based on optimum processing of the electromagnetic field at the aperture of an optical instrument. In both problems the density operators of the field under the two hypotheses do not commute. The error probabilities, determined as functions of the separation of the points and the mean number of received photons, characterize the ultimate resolvability of the sources.

Helstrom, C. W.↗
NASA NTRS1973

Detection and Estimation of an Optical Image by Photon-Counting Techniques

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.

Wang, Lily Lee↗