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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 307 records · Page 17

Development of a Physics-Based Combustion Model for Engine Knock Prediction

The objective of this project is to improve the prediction of engine knock by developing a new combustion modeling framework. Engine knock is a limiting factor to constrain the increase of fuel efficiency for spark ignition (SI) engines in most passenger cars. Efforts to increase fuel efficiency, increasing the compression ratio or downsizing, lead to the increase in the tendency of the knock occurrence. The knock is an undesired ignition of the end-gas, unburned fuel/air mixture ahead of the spark-ignited premixed flame, resulting in rapid in-cylinder pressure rises and engine damages. The combustion modeling framework developed in this project can consider turbulence-chemistry interactions during end-gas ignition, while using a reasonably detailed chemical mechanism developed for ignition and combustion reactions under engine relevant conditions, and the subtle characteristics of spark-ignited flame propagation. It is developed in the context of large eddy simulation (LES), which can capture stochastic in-cylinder processes. The developed model is incorporated into a commercial software for engine simulation, CONVERGE CFD, as a user defined function, and validated. Engine knock and knock-free experiments as well as direct numerical simulation (DNS) of end-gas ignition in homogeneous turbulence are performed to help model development and provide data sets for model validation. With further validation, the developed model is expected to advance the predictive capability for engine knock simulations and thus contribute to improving the fuel efficiency.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Development of a Physics-Based Combustion Model for Engine Knock Prediction

The objective of this project is to improve the prediction of engine knock by developing a new combustion modeling framework. Engine knock is a limiting factor to constrain the increase of fuel efficiency for spark ignition (SI) engines in most passenger cars. Efforts to increase fuel efficiency, increasing the compression ratio or downsizing, lead to the increase in the tendency of the knock occurrence. The knock is an undesired ignition of the end-gas, unburned fuel/air mixture ahead of the spark-ignited premixed flame, resulting in rapid in-cylinder pressure rises and engine damages. The combustion modeling framework developed in this project can consider turbulence-chemistry interactions during end-gas ignition, while using a reasonably detailed chemical mechanism developed for ignition and combustion reactions under engine relevant conditions, and the subtle characteristics of spark-ignited flame propagation. It is developed in the context of large eddy simulation (LES), which can capture stochastic in-cylinder processes. The developed model is incorporated into a commercial software for engine simulation, CONVERGE CFD, as a user defined function, and validated. Engine knock and knock-free experiments as well as direct numerical simulation (DNS) of end-gas ignition in homogeneous turbulence are performed to help model development and provide data sets for model validation. With further validation, the developed model is expected to advance the predictive capability for engine knock simulations and thus contribute to improving the fuel efficiency.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

MELCOR 2.2 Benchmarks of Peach Bottom NUREG/CR 7155 Uncertainty Analysis

The U.S. Nuclear Regulatory Commission (NRC) performed a first-of-a-kind uncertainty analysis (UA) of the accident progression, radiological releases, and offsite consequences for the State-of- the-Art Reactor Consequence Analyses (SOARCA) of an unmitigated long-term station blackout (LTSBO) severe accident scenario at the Peach Bottom Atomic Power Station. The objective of the UA was to evaluate the robustness of the SOARCA deterministic "best estimate results and conclusions documented in NUREG-1935, and to develop insight into the overall sensitivity of the SOARCA results to uncertainty in key modeling inputs. The study was completed in 2015 and documented in NUREG/CR-7155. Since 2015, two other SOARCA UAs were completed for two pressurized water reactor (PWR) plants. The PWR UAs incrementally updated the approach and methodology, including using the latest release of the MELCOR 2.2 computer code. There were also advances made in the state-of-the-art modeling related to NRC efforts using the Peach Bottom model in NUREG-2206, which provided the technical basis for the containment protection and release reduction rulemaking for boiling water reactors with Mark I and Mark II containments. This report documents the input model changes from the NUREG/CR-7155 study and performs a small number of reference calculations to assess the changes of the new computer code and the model input updates. The objective of the work is to verify whether the updated Peach Bottom MELCOR model and updated version of MELCOR support the conclusions formed in the Peach Bottom SOARCA UA by performing these representative calculations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Progenitors and explosion properties of supernova remnants hosting central compact objects: II. A global systematic study with a comparison to nucleosynthesis models

ABSTRACT Core-collapse explosions of massive stars leave behind neutron stars, with a known diversity that includes the ‘Central Compact Objects’ (CCOs). Typified by the neutron star discovered near the centre of the Cas A supernova remnant (SNR), CCOs have been observed to shine only in X-rays. To address their supernova progenitors, we perform a systematic study of SNRs that contain a CCO and display X-ray emission from their shock-heated ejecta. We make use of X-ray data primarily using the Chandra X-ray observatory, complemented with XMM–Newton. This study uses a systematic approach to the analysis of each SNR aimed at addressing the supernova progenitor as well as the explosion properties (energy and ambient density). After fitting for the ejecta abundances estimated from a spatially resolved spectroscopic study, we compare the data to six nucleosynthesis models making predictions on supernova ejecta yields in core-collapse explosions. We find that the explosion models commonly used by the astrophysics community do not match the ejecta yields for any of the SNRs, suggesting additional physics, for example multidimensional explosion models or updated progenitor structures, are required. Overall we find low-mass (≤25 solar masses) progenitors among the massive stars population and low-energy explosions (<1051 ergs). We discuss degeneracies in our model fitting, particularly how altering the explosion energy affects the estimate of the progenitor mass. Our systematic study highlights the need for improving on the theoretical models for nucleosynthesis predictions as well as for sensitive, high-resolution spectroscopy observations to be acquired with next generation X-ray missions.

79 ASTRONOMY AND ASTROPHYSICS↗

Marine Corps Base Camp Lejeune Climate Forecasts

Critical military training and testing on lands along the nation’s coastal and estuarine shorelines are increasingly placed at risk because of encroachment pressures in surrounding areas, impairments due to other anthropogenic disturbances, and changes in climate and sea level. The U.S. Department of Defense (DoD) intends to enhance and sustain its training and testing assets and also optimize its stewardship of natural resources through the development and application of an ecosystem-based management approach on DoD installations. To accomplish this goal, particularly for installations in estuarine/coastal environments, the Strategic Environmental Research and Development Program (SERDP) launched the Defense Coastal/Estuarine Research Program (DCERP) as a 10-year effort at Marine Corps Base Camp Lejeune (MCBCL) in North Carolina. The results of the second 5 years of the program (DCERP2) are presented in the DCERP2 Final Report.There were four overarching objectives of DCERP2. The first objective was to understand the effects of climate change impacts, including warming temperatures, variability in the hydrological cycle, storm events, and sea level rise on the coastal ecosystems at MCBCL from observations and measurements made over the 10-year program. The second objective was to understand the carbon cycle of the coastal and terrestrial ecosystems at MCBCL through a highly integrated sampling program. The third objective was to develop models, tools, and indicators to evaluate current and projected future ecosystem state changes and translate scientific findings into actionable information for installation managers. The last objective was to recommend adaptive management strategies to sustain ecosystem natural resources within the context of an active military installation.There are 252 mean change files represented in this dataset (12 months * 3 future time periods * 7 variables ). The mean change is calculated by taking the mean of the differences between the future projected average (e.g., 2046-2065) and the climate model baseline (e.g., 1979-1999). The differences were calculated for each downscaled GCM and then averaged across all models to obtain the mean change. This mean of the differences was calculated for each month, each future time period, and each variable.

54 ENVIRONMENTAL SCIENCES↗

Onslow Beach Washover Fan Morphology from 2012 to 2015

Critical military training and testing on lands along the nation’s coastal and estuarine shorelines are increasingly placed at risk because of encroachment pressures in surrounding areas, impairments due to other anthropogenic disturbances, and changes in climate and sea level. The U.S. Department of Defense (DoD) intends to enhance and sustain its training and testing assets and also optimize its stewardship of natural resources through the development and application of an ecosystem-based management approach on DoD installations. To accomplish this goal, particularly for installations in estuarine/coastal environments, the Strategic Environmental Research and Development Program (SERDP) launched the Defense Coastal/Estuarine Research Program (DCERP) as a 10-year effort at Marine Corps Base Camp Lejeune (MCBCL) in North Carolina. The results of the second 5 years of the program (DCERP2) are presented in the DCERP2 Final Report.There were four overarching objectives of DCERP2. The first objective was to understand the effects of climate change impacts, including warming temperatures, variability in the hydrological cycle, storm events, and sea level rise on the coastal ecosystems at MCBCL from observations and measurements made over the 10-year program. The second objective was to understand the carbon cycle of the coastal and terrestrial ecosystems at MCBCL through a highly integrated sampling program. The third objective was to develop models, tools, and indicators to evaluate current and projected future ecosystem state changes and translate scientific findings into actionable information for installation managers. The last objective was to recommend adaptive management strategies to sustain ecosystem natural resources within the context of an active military installation.These grid files were created from data collected using a Riegl 3-D laser scanner. Millions of x, y, and z points from the F2 Washover Fan on Onslow Beach were processed using the MARS software package to define a bare-earth model. Grid files were imported into Golden Software Surfer version 19 for editing and exported from that application as .grd files. Files can be opened in Surfer or ArcMap, but the coordinate system information will be lost if opened in ArcMap. These data were collected to quantify the morphological changes that occur on a washover fan through time.

54 ENVIRONMENTAL SCIENCES↗

Multidisciplinary design optimization in Architecture, Engineering, and Construction: a detailed review and call for collaboration

The design of buildings has become a complex and multidisciplinary problem involving multiple conflicting objectives as architects and designers address competing technical, economic, environmental, and societal concerns. This has been driving research in Architecture, Engineering, and Construction (AEC) toward rigorous multidisciplinary decision-making frameworks that generate and evaluate numerous design alternatives using multi-objective optimization in concert with simulation and analysis models of varying fidelity and computational expense. While such frameworks are well known and widely employed in the aerospace and systems engineering domains, efforts by design professionals and researchers in the AEC field are scattered at best. In this paper, we provide a detailed review of recent developments in optimization frameworks in the AEC field and subsequently highlight how such developments are largely compartmentalized into separate domains such as structural, energy, daylighting, and other performance factors. Herein, we further discuss the technical challenges involved in concurrent coupled multidisciplinary design optimization (MDO) in the AEC field such as interoperability issues between Building Information Modeling (BIM) environments, analysis/simulation tools, and optimization frameworks. We conclude by outlining research needed for more unified modeling and simulation-based optimization frameworks to aid in complex and multidisciplinary building design processes. We also highlight the need for the identification and development of multi-fidelity simulation tools for use across multiple design phases. As such, this paper contributes a novel roadmap to leverage aerospace and systems engineering research in MDO into the field of AEC, along with a call for researchers in the MDO community to seek collaborations in AEC field.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Scalability analysis of heavy-duty gas turbines using data-driven machine learning

With the increasing integration of variable renewable energy sources into power systems, the role of flexible power generation technologies like gas turbines (GT) in rapid grid balancing remains crucial. This sustained importance underscores the need for scaled and precise modeling of GT to ensure effective integration within evolving energy frameworks. While physics-driven GT models integrate thermodynamics, fluid dynamics, and combustion principles, they often rely on approximate mathematical representations to accommodate scaling that may not capture the actual complex dynamics for GTs and inertial effects associated to GTs with different ratings. In this study, a data-driven model is proposed using machine learning (ML) techniques to conduct GT scalability analysis and performance evaluation with high accuracy. The ML model, trained on data from various operating conditions and performance parameters, aims to uncover intricate relationships and patterns, resembling GT characteristics at different scales (ratings). The model is developed to capture complex system interaction and to adapt to changing operational scenarios at different capacities, providing valuable insights of power system dynamics. In this study, the real-time digital simulator platform was employed to generate training data for the ML model and assess its dynamic characteristics. The ultimate objective was to develop a detailed modeling framework based on governing equations and data-driven ML capable of predicting key performance indicators, in thermal systems such as GTs, including power output, speed, fuel consumption, and exhaust temperature under diverse operating conditions at different scales. The developed ML framework demonstrated high accuracy, with mean relative errors for GT power prediction, reference speed, exhaust temperature, and compressor pressure ratio (CPR) parameters consistently below 0.1% across typical load fluctuation scenarios. Maximum deviations were limited to approximately 0.5 K for exhaust temperature and 0.009 for CPR, underscoring the model’s ability to replicating dynamic GT behavior with high precision. The adaptability of the ML model enables its application across diverse operational conditions and its extension to other thermal systems. By leveraging advanced ML techniques, this study presents a robust and scalable modeling framework that enhances GT simulation precision, facilitating improved integration into evolving power systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Optimal Portfolio Design of Distributed Energy Resources on Puerto Rico Distribution Feeders with Long Outages after Hurricane Maria

This work details a project to design reliable, resilient, and cost-effective networked microgrids considering grid constraints and resilience metrics focused on Puerto Rico distribution feeder locations with long outages after Hurricane Maria. The project consisted primarily of modeling and simulation tasks that accomplished the following objectives: 1. Selected 10 distribution feeder models in vulnerable areas. The sample feeders are geographically distributed across Puerto Rico and vary in length to capture the wide variety of feeders on the island. 2. Determined the optimal location and sizing of distributed energy resources (DERs) on the identified distribution feeders. The systems considered as part of the microgrid solutions were solar photovoltaic (PV), battery energy storage systems (BESS) and distributed fossil fuel generation (DFFG). 3. Estimated the cost-benefit of the proposed DER portfolios. 4. Provided a set of final recommendations that inform decision making on how to do targeted planning analysis for microgrids that can supply energy to critical infrastructures.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Development and Validation of a Latent Thermal Energy Storage Model Using Modelica

An abundance of research has been performed to understand the physics of latent thermal energy storage with phase change material. Some analytical and numerical findings have been validated by experiments, but there are few free and open-source models available to the general public for use in systems simulation and analysis. The Modelica programming language is a good avenue to make such models available, because it is object-oriented, equation-based, declarative, and acausal. These characteristics have enabling the creation of component model libraries that can be used to build larger system simulations for design analysis. The authors have previously developed a numerical framework to model phase change thermal storage and have validated model predictions with experiments. The objectives of this paper are to describe the transfer of the numerical framework to an implementation in a Modelica component model and to validate the Modelica model with data from the experiment and the original numerical framework.

25 ENERGY STORAGE↗

Development of physics-consistent conditional diffusion model to overcome data scarcity in critical heat flux

Deep generative modeling provides a powerful pathway to overcome data scarcity in energy-related applications where experimental data are often limited. By learning the underlying probability distribution of the training dataset, deep generative models, such as the diffusion model, can generate high-fidelity synthetic samples that statistically resemble the training data. Such synthetic data generation can significantly enrich the size and diversity of the available training data, and more importantly, improve the robustness of downstream machine learning models in predictive tasks. The objective of this paper is to investigate the effectiveness of diffusion models for overcoming data scarcity in nuclear energy applications. By leveraging a public dataset on critical heat flux which covers a wide range of commercial nuclear reactor operational conditions, we developed a diffusion model that can generate an arbitrary amount of synthetic samples. Since a vanilla diffusion model can only generate samples randomly, we also developed a conditional diffusion model capable of generating targeted critical heat flux data under user-specified thermal-hydraulic conditions. The performance of the diffusion model was evaluated based on its ability to capture empirical feature distributions and pair-wise correlations, as well as to maintain physical consistency. The results showed that both the diffusion model and conditional diffusion model can successfully generate realistic and physics-consistent critical heat flux data. Furthermore, uncertainty quantification results demonstrate that the conditional diffusion model is highly effective in augmenting critical heat flux data while maintaining acceptable levels of uncertainty.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Reprocessing Models for the Optical Light Curves of Hypervariable Quasars from the Sloan Digital Sky Survey Reverberation Mapping Project

We explore reprocessing models for a sample of 17 hypervariable quasars, taken from the Sloan Digital Sky Survey Reverberation Mapping project, which all show coordinated optical luminosity hypervariability with amplitudes of factors ≳2 between 2014 and 2020. We develop and apply reprocessing models for quasar light curves in simple geometries that are likely to be representative of quasar inner environments. In addition to the commonly investigated thin-disk model, we include the thick-disk and hemisphere geometries. The thick-disk geometry could, for instance, represent a magnetically elevated disk, whereas the hemisphere model can be interpreted as a first-order approximation for any optically thick out-of-plane material caused by outflows/winds, warped/tilted disks, and so on. Of the 17 quasars in our sample, 11 are best-fitted by a hemisphere geometry, five are classified as thick disks, and both models fail for just one object. We highlight the successes and shortcomings of our thermal reprocessing models in case studies of four quasars that are representative of the sample. While reprocessing is unlikely to explain all of the variability that we observe in quasars, we present our classification scheme as a starting point for revealing the likely geometries of reprocessing for quasars in our sample and hypervariable quasars in general.

79 ASTRONOMY AND ASTROPHYSICS↗

A phase-field model of quasi-brittle fracture for pressurized cracks: Application to UO 2 high-burnup microstructure fragmentation

Here, in this paper, we present a phase-field model of quasi-brittle fracture with pressurized cracks, with dedicated applications for polycrystalline materials. The model is formulated as a minimization problem within the variational framework. The external work done by pressure on the crack surfaces is included in the objective function. Several careful modeling choices lead to a regularization-length-independent critical strength. The model is constructed to give a softening response with an underlying linear traction-separation law. The pressure-dependent softening response and the regularization of the prescribed pressure are demonstrated with a (quasi) one-dimensional numerical analysis. In a two-dimensional numerical analysis under plane strain assumptions, the critical stress corresponding to crack propagation (as predicted by our quasi-brittle fracture model) is compared with linear elastic fracture mechanics (LEFM) analytical solutions. Our model is further utilized to simulate fission-gas-induced fragmentation of the UO 2 high-burnup structure (HBS). Simulation results show that pressurized bubbles can cause crack nucleation and propagation, and that the bubble size and the surrounding external pressure affect the critical pressure corresponding to crack nucleation. Simulations of a partial HBS at different recrystallization stages show that different grain structures (due to recrystallization) also influence crack paths and fragmentation morphology.

36 MATERIALS SCIENCE↗

Ionization detail parameters and cluster dose: a mathematical model for selection of nanodosimetric quantities for use in treatment planning in charged particle radiotherapy

Abstract Objective . To propose a mathematical model for applying ionization detail (ID), the detailed spatial distribution of ionization along a particle track, to proton and ion beam radiotherapy treatment planning (RTP). Approach . Our model provides for selection of preferred ID parameters ( I p ) for RTP, that associate closest to biological effects. Cluster dose is proposed to bridge the large gap between nanoscopic I p and macroscopic RTP. Selection of I p is demonstrated using published cell survival measurements for protons through argon, comparing results for nineteen I p : N k , k = 2, 3, …, 10, the number of ionizations in clusters of k or more per particle, and F k , k = 1, 2, …, 10, the number of clusters of k or more per particle. We then describe application of the model to ID-based RTP and propose a path to clinical translation. Main results . The preferred I p were N 4 and F 5 for aerobic cells, N 5 and F 7 for hypoxic cells. Significant differences were found in cell survival for beams having the same LET or the preferred N k . Conversely, there was no significant difference for F 5 for aerobic cells and F 7 for hypoxic cells, regardless of ion beam atomic number or energy. Further, cells irradiated with the same cluster dose for these I p had the same cell survival. Based on these preliminary results and other compelling results in nanodosimetry, it is reasonable to assert that I p exist that are more closely associated with biological effects than current LET-based approaches and microdosimetric RBE-based models used in particle RTP. However, more biological variables such as cell line and cycle phase, as well as ion beam pulse structure and rate still need investigation. Significance . Our model provides a practical means to select preferred I p from radiobiological data, and to convert I p to the macroscopic cluster dose for particle RTP.

Engineering↗

Challenging Practices of Algebraic Battery Life Models through Statistical Validation and Model Identification via Machine-Learning

Various modeling techniques are used to predict the capacity fade of Li-ion batteries. Algebraic reduced-order models, which are inherently interpretable and computationally fast, are ideal for use in battery controllers, technoeconomic models, and multi-objective optimizations. For Li-ion batteries with graphite anodes, solid-electrolyte-interphase (SEI) growth on the graphite surface dominates fade. This fade is often modeled using physically informed equations, such as square-root of time for predicting solvent-diffusion limited SEI growth, and Arrhenius and Tafel-like equations predicting the temperature and state-of-charge rate dependencies. In some cases, completely empirical relationships are proposed. However, statistical validation is rarely conducted to evaluate model optimality, and only a handful of possible models are usually investigated. This article demonstrates a novel procedure for automatically identifying reduced-order degradation models from millions of algorithmically generated equations via bi-level optimization and symbolic regression. Identified models are statistically validated using cross-validation, sensitivity analysis, and uncertainty quantification via bootstrapping. On a LiFePO 4 /Graphite cell calendar aging data set, automatically identified models utilizing square-root, power law, stretched exponential, and sigmoidal functions result in greater accuracy and lower uncertainty than models identified by human experts, and demonstrate that previously known physical relationships can be empirically "rediscovered" using machine learning.

25 ENERGY STORAGE↗

Dynamic Rupture Modeling of the 1999 Chi-Chi, Taiwan Earthquake Using 3DFinite Element Method. Sensitivity Analysis of Slip Rate Function to Model Parameters of Crustal Weak-Zone

The main objective of this study was the dynamic rupture modeling of the M7.3 1999 Chi-Chi, Taiwan earthquake. The purpose of the numerical modeling was two folded. First, using models of rupture dynamics, derive kinematic rupture characteristics, including spatial and temporal variations of the slip rate time history and rupture speed, in the long-period ground motion generation area (LMGA), strong motion generation areas (SMGAs) and background fault area for a thrust shallow rupture. Second, investigate the sensitivity of source time function characteristics in the LMGA and SMGA areas to model parameterization of low-velocity weak zone, such as thickness and shear wave velocity.

58 GEOSCIENCES↗

Deep Learning–Assisted Multiobjective Optimization of Geological CO 2 Storage Performance under Geomechanical Risks

In geological CO 2 storage, designing the optimal well control strategy for CO 2 injection to maximize CO 2 storage while minimizing the associated geomechanical risks is not trivial. This challenge arises due to pressure buildup, CO 2 plume migration, the highly nonlinear nature of geomechanical responses to rock-fluid interaction, and the high computational cost associated with coupled flow and geomechanics simulations. In this paper, we introduce a novel optimization framework to address these challenges. The optimization problem is formulated as follows: maximize total CO 2 storage while minimizing geomechanical risks by adjusting the injection schedules within bounded constraints. The geomechanical risks are primarily driven by injection-induced pressure build-up, which is characterized by ground displacement and the induced microseismicity. We used the Fourier neural operator (FNO)-based deep learning model to construct surrogate models, replacing the time-consuming coupled flow and geomechanics simulations for evaluating the aforementioned objective functions. The developed surrogate models have been incorporated into a multiobjective optimization framework through a genetic algorithm to reduce the computational burden. The proposed optimization framework reduces the computational cost from approximately 2,400 hours, when using objective function evaluations based on physics-based simulations, to around 20 minutes. A set of Pareto-optimal solutions of the proposed workflow yields nontrivial optimal decisions, reducing the microseismicity potential and the vertical displacement. This Pareto front highlights the optimal trade-offs between CO 2 storage amount, safety, and ground displacement, emphasizing the need for careful optimization and management of injection strategies to achieve a balanced outcome. The novelty of this work is twofold. First, we demonstrate the importance of incorporating the minimization of the geomechanical risks as objective functions into the CO 2 storage optimization workflow to mitigate the potential risk of induced microseismicity and ground displacement. Second, we leverage the FNO-based surrogate models to optimize a real-field CO 2 storage operation.

42 ENGINEERING↗

Calibration, modeling, parameterization, and verification of the instrument transfer function of an interferometric microscope

Interferometric microscopes are used to measure surface roughness, from which the computed power spectral density function can be used to extract bandwidth-limited values of the various surface properties, such as root-mean-square (rms) height and slope errors. Measurements with a microscope equipped with different objectives that have an overlapping spatial frequency range usually give different rms results over the common frequency bandwidth. This is a result of different instrument transfer functions (ITFs) that attenuate spatial frequencies by different amounts over the overlapping range. We report on the use of binary pseudo-random array (BPRA) standards to characterize the ITF of an interferometric microscope with the various objectives. We use a simple model of a 1D binary Results show that the spectrum for an undersampled array is a cosine function, rather than a straight line, constant white noise spectrum. We have an analytical model of the ITF that includes the effects of an obscured aperture and defocus, in addition to the usual parameters of numerical aperture, wavelength, and sampling period. In addition, the model includes the effect of aliasing of spatial frequency components beyond the Nyquist back into the sub-Nyquist region. We compare the model PSD predictions to the measurements performed with different objectives. Departures of the measured PSDs from the model predictions indicate that there are higher-order ITF corrections yet to be identified and included in the model.

Takacs, PZ↗