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DOE OSTI2026

Multi-resolution Arctic Shrub Cover Dataset Derived from UAS and Airborne SfM and LiDAR (2013-2025)

We synthesized 177 unoccupied aerial system flights and 77 airborne flights across the Arctic and created a multi-resolution benchmark data of low-to-tall shrub fractional cover leveraging Structure-from-Motion and Light Detection and Ranging. The resulting dataset covered a total of 1899 km2 across Alaska, Western Canada, Sweden, and Siberian Arctic, including key sites from the Oro Arctic to the High Arctic. The dataset is organized into 6 primary data collection directories (“Abisko,” “AWI,” “ERE,” “Fairbanks,” “NGEE,” “Toolik”), each containing site and flight subdirectories. Flight directories include shrub cover rasters (*.tifs) at 1 m, 5 m, and 30 m resolution, the canopy height model at 1 m resolution (*.tifs), and a bounding box *.kml file. For the AWI, Abisko, NGEE, and Fairbanks collections, we also include the GCC raster at 1 m resolution (*.tif). Files are organized by Collection > Site > Flight Name > Data Files. Flight rasters are in the local UTM zone and the .kml files are in the geographic coordinate system EPSG 4326. We also include a .csv file that details the source datasets for every flight. The Next-Generation Ecosystem Experiments in the Arctic (NGEE Arctic) project is a research effort to reduce uncertainty in the Department of Energy’s Energy Exascale Earth System Model (E3SM) by developing a predictive understanding of Arctic tundra ecosystems underlain by permafrost and to quantify feedbacks from the Arctic tundra to the Earth system. NGEE Arctic is supported by the Department of Energy's Office of Biological and Environmental Research. Over Phases 1–3, observations made by the NGEE Arctic team across a gradient of permafrost landscapes in Arctic Alaska improved the representation of tundra processes in the land surface component of E3SM (the E3SM Land Model, ELM). Model improvements emphasized unique aspects of permafrost environments and explored reductions in model complexity while retaining predictive power. The Arctic-informed ELM developed by NGEE Arctic has been used to make novel predictions on processes ranging from permafrost thaw to soil biogeochemical cycling to Earth system feedbacks associated with the unique characteristics of tundra plants. In Phase 4, the NGEE Arctic team is evaluating our new predictive understanding under novel conditions across the Arctic domain. In collaboration with partners at long-term pan-Arctic research sites we are examining whether an Arctic-informed ELM can faithfully simulate interactions among surface and subsurface processes at site, regional, and pan-Arctic scales. In turn, we are using variety of tools to dynamically extend and evaluate ELM inference, with an emphasis on data synthesis and pan-Arctic model evaluation, reintegration of code with an evolving E3SM, scaling across heterogeneous Arctic landscapes, and the appropriate representation of the impacts of increasingly frequent Arctic disturbances.

canopy height model↗

NASA NTRS1981

Improvements in lake volume predictions using Landsat data

A cumulative error in the water balance budget for Lake Okeechobee produces a one million acre-foot discrepancy in the predicted water volume over a 4-year period. The major source of error appears to be complex shoreline marshes that comprise 20 percent of the lake surface. The water balance budget model presently treats these marshes as open water. Using Landsat data, the vegetation in the lake's littoral zone was classified multispectrally to provide a data base for determining water budget information. First, the acreage of a given plant species in the littoral zone was obtained with satellite data. Second, the surface area occupied by plants (which therefore could not be considered open water) was used to adjust the vegetation acreage giving an effective water surface. Based on this information, more detailed representations of evapotranspiration and total water surface (and hence total lake volume) could be provided to the water balance budget computation.

Gervin, J. C.↗

NASA NTRS1993

Semi-span model testing in the National Transonic Facility

A semi-span testing technique has been proposed for the NASA Langley Research Center's National Transonic Facility (NTF). Semi-span testing has several advantages including (1) larger model size, giving increased Reynolds number capability; (2) improved model fidelity, allowing ease of flap and slat positioning which ultimately improves data quality; and (3) reduced construction costs compared with a full-span model. In addition, the increased model size inherently allows for increased model strength, reducing aeroelastic effects at the high dynamic pressure levels necessary to simulate flight Reynolds numbers. The Energy Efficient Transport (EET) full-span model has been modified to become the EET semi-span model. The full-span EET model was tested extensively at both NASA LRC and NASA Ames Research Center. The available full-span data will be useful in validating the semi-span test strategy in the NTF. In spite of the advantages discussed above, the use of a semi-span model does introduce additional challenges which must be addressed in the testing procedure. To minimize the influence of the sidewall boundary layer on the flow over the semi-span model, the model must be off-set from the sidewall. The objective is to remove the semi-span model from the sidewall boundary layer by use of a stand-off geometry. When this is done however, the symmetry along the centerline of the full-span model is lost when the semi-span model is mounted on the wind tunnel sidewall. In addition, the large semi-span model will impose a significant pressure loading on the sidewall boundary layer, which may cause separation. Even under flow conditions where the sidewall boundary layer remains attached, the sidewall boundary layer may adversely effect the flow over the semi-span model. Also, the increased model size and sidewall mounting requires a modified wall correction strategy. With these issues in mind, the semi-span model has been well instrumented with surface pressure taps to obtain data on the expected complex flow field in the near wall region. This status report summarizes the progress to date on developing the semi-span geometry definition suitable for generating structured grids for the computational research. In addition, the progress on evaluating three state-of-the-art Navier-Stokes codes is presented.

Chokani, Ndaona↗

NASA NTRS1994

A New Reynolds Stress Algebraic Equation Model

A general turbulent constitutive relation is directly applied to propose a new Reynolds stress algebraic equation model. In the development of this model, the constraints based on rapid distortion theory and realizability (i.e. the positivity of the normal Reynolds stresses and the Schwarz' inequality between turbulent velocity correlations) are imposed. Model coefficients are calibrated using well-studied basic flows such as homogeneous shear flow and the surface flow in the inertial sublayer. The performance of this model is then tested in complex turbulent flows including the separated flow over a backward-facing step and the flow in a confined jet. The calculation results are encouraging and point to the success of the present model in modeling turbulent flows with complex geometries.

Shih, Tsan-Hsing↗

NASA NTRS1996

Process Model for Friction Stir Welding

Friction stir welding (FSW) is a relatively new process being applied for joining of metal alloys. The process was initially developed by The Welding Institute (TWI) in Cambridge, UK. The FSW process is being investigated at NASA/MSEC as a repair/initial weld procedure for fabrication of the super-light-weight aluminum-lithium shuttle external tank. The FSW investigations at MSFC were conducted on a horizontal mill to produce butt welds of flat plate material. The weldment plates are butted together and fixed to a backing plate on the mill bed. A pin tool is placed into the tool holder of the mill spindle and rotated at approximately 400 rpm. The pin tool is then plunged into the plates such that the center of the probe lies at, one end of the line of contact, between the plates and the shoulder of the pin tool penetrates the top surface of the weldment. The weld is produced by traversing the tool along the line of contact between the plates. A lead angle allows the leading edge of the shoulder to remain above the top surface of the plate. The work presented here is the first attempt at modeling a complex phenomenon. The mechanical aspects of conducting the weld process are easily defined and the process itself is controlled by relatively few input parameters. However, in the region of the weld, plasticizing and forging of the parent material occurs. These are difficult processes to model. The model presented here addresses only variations in the radial dimension outward from the pin tool axis. Examinations of the grain structure of the weld reveal that a considerable amount of material deformation also occurs in the direction parallel to the pin tool axis of rotation, through the material thickness. In addition, measurements of the axial load on the pin tool demonstrate that the forging affect of the pin tool shoulder is an important process phenomenon. Therefore, the model needs to be expanded to account for the deformations through the material thickness and the forging affect of the shoulder. The energy balance at the boundary of the plastic region with the environment required that energy flow away from the boundary in both radial directions. One resolution to this problem may be to introduce a time dependency into the process model, allowing the energy flow to oscillate across this boundary. Finally, experimental measurements are needed to verify the concepts used here and to aid in improving the model.

Adams, Glynn↗

NASA NTRS2017

Temporal Consistency Between Gross Primary Production and Solar-Induced Chlorophyll Fluorescence in the Ten Most Populous Megacity Areas over Years

The gross primary production (GPP) of vegetation in urban areas plays an important role in the study of urban ecology. It is difficult however, to accurately estimate GPP in urban areas, mostly due to the complexity of impervious land surfaces, buildings, vegetation, and management. Recently, we used the Vegetation Photosynthesis Model (VPM), climate data, and satellite images to estimate the GPP of terrestrial ecosystems including urban areas. Here, we report VPM-based GPP (GPPvpm) estimates for the world's ten most populous megacities during 2000-2014. The seasonal dynamics of GPPvpm during 2007-2014 in the ten megacities track well that of the solar-induced chlorophyll fluorescence (SIF) data from GOME-2 at 0.5deg x 0.5deg resolution. Annual GPPvpm during 2000-2014 also shows substantial variation among the ten megacities, and year-to-year trends show increases, no change, and decreases. Urban expansion and vegetation collectively impact GPP variations in these megacities. The results of this study demonstrate the potential of a satellite-based vegetation photosynthesis model for diagnostic studies of GPP and the terrestrial carbon cycle in urban areas.

urban↗

DOE OSTI2025

Hunga Tonga–Hunga Ha′apai Volcano Impact Model Observation Comparison (HTHH-MOC) project: experiment protocol and model descriptions

The 2022 Hunga volcanic eruption injected a significant amount of water vapor and a moderate amount of sulfur dioxide into the stratosphere, causing observable responses in the climate system. We have developed a model–observation comparison project to investigate the evolution of volcanic water and aerosols and their impacts on atmospheric dynamics, chemistry, and climate, using several state-of-the-art chemistry climate models. The project goals are (1) to evaluate the current chemistry–climate models to quantify their performance in comparison to observations and (2) to understand atmospheric responses in the Earth system after this exceptional event and investigate the potential impacts in the projected future. To achieve these goals, we designed specific experiments for direct comparisons to observations, for example from balloons and the Microwave Limb Sounder satellite instrument. Experiment 1 consists of two sets of free-running ensemble experiments from 2022 to 2031: one with fixed sea-surface temperatures and sea ice and one with coupled ocean. These experiments will help to understand the long-term evolution of water vapor and aerosols; quantify HTHH effects on stratospheric and mesospheric temperatures, dynamics, and transport; understand the impact of dynamic changes on ozone chemistry; quantify the net radiative forcings; and evaluate any surface climate impact. Experiment 2 is a nudged-run experiment from 2022 to 2023 using observed meteorology. To allow participation of more climate models with varying complexities of aerosol simulation, we include two sets of simulations in Experiment 2: Experiment 2a is designed for models with internally generated aerosol, while Experiment 2b is designed for models using prescribed aerosol surface area density. This experiment will help to analyze H 2 O and aerosol evolution, quantify the net radiative forcings, understand the impacts on mid-latitude and polar O 3 chemistry, and allow close comparisons with observations.

Zhu, Yunqian [Univ. of Colorado, Boulder, CO (Unit↗

NASA NTRS1990

Glass sample characterization

The development of in-house integrated optical performance modelling capability at MSFC is described. This performance model will take into account the effects of structural and thermal distortions, as well as metrology errors in optical surfaces to predict the performance of large an complex optical systems, such as Advanced X-Ray Astrophysics Facility. The necessary hardware and software were identified to implement an integrated optical performance model. A number of design, development, and testing tasks were supported to identify the debonded mirror pad, and rebuilding of the Technology Mirror Assembly. Over 300 samples of Zerodur were prepared in different sizes and shapes for acid etching, coating, and polishing experiments to characterize the subsurface damage and stresses produced by the grinding and polishing operations.

Ahmad, Anees↗

DOE OSTI2020

Lagrangian simulations of spray interaction with a surface using a stochastic multi-regime impingement model

Modeling of spray impingement upon the piston or cylinder surface is important for hydrocarbon emission and soot predictions in high-fidelity simulation of internal combustion engines with direct injections. Due to the complexity of the physical process of spray impingement, current computational models heavily rely on the empirical studies which involve large uncertainties. A computational model is presented for spray impingement on solid walls in general computational fluid dynamics (CFD) simulations. The model adopts the Marmanis-Thoroddsen theory for determining the number of secondary droplets and a stochastic method for calculating the velocities of the secondary droplets. The numerical methods and parallel implementation of the impingement model are presented in detail. The model is implemented in Grit, which is a recently developed CPU/GPU performance-portable Lagrangian particle library, for accelerating spray simulations. The model and its implementation are tested for examples of spray impingements on flat and smooth surfaces with different impingement angles.

Ge, Wenjun↗

NASA NTRS2017

Improvements to Wire Bundle Thermal Modeling for Ampacity Determination

Abstract - Determining current carrying capacity (ampacity) of wire bundles in aerospace vehicles is critical not only to safety but also to efficient design. Published standards provide guidance on determining wire bundle ampacity but offer little flexibility for configurations where wire bundles of mixed gauges and currents are employed with various external insulation jacket surface properties. Thermal modeling has been employed in an attempt to develop techniques to assist in ampacity determination for these complex configurations. An earlier tool allowed analysis of wire bundle configurations but was constrained to configurations comprised of less than 50 elements. Additionally, for vacuum analyses, configurations with very low emittance external jackets suffered from numerical instability in the solution. A new thermal modeler is presented allowing for larger configurations and is not constrained by low bundle jacket surface infrared emittance calculations. Formulation of key internal radiation and interface conductance parameters is discussed including the effects of temperature and ambient air pressure on wire-to-wire thermal conductance. Test cases comparing model-predicted ampacity and that calculated from standards documents are presented.

Steven L Rickman↗

NASA NTRSDate not supplied

The Application of Artificial Intelligence Deep Learning to Visually Identify Micrometeoroid and Orbital Debris Impacts

Recent advances in Artificial Intelligence (AI) are changing the World. Novel approaches to training AI systems have led to dramatic reductions in the amount of time required. Training an AI system could take years and teams of people using traditional methods, but with the advancements of Deep Learning (DL) models this training can now be accomplished by an individual in a matter of minutes. The development of “fast AI” libraries has delivered AI to essentially everyone. Democratization of AI power has inspired many to revisit past problems that will benefit from DL approaches. For example, the application of AI has improved detection of breast cancer by 20% compared to traditional detection methods. Computer vision and machine learning are being used to identify soil deficiencies and provide planting recommendations to farmers. Success stories like these and many others have provided inspiration to see if AI can help improve one of our needed capabilities – that of visually identifying micrometeoroid and orbital debris (MMOD) impact damage to spacecraft from images of the spacecraft exterior. The need to visually locate and characterize spacecraft MMOD impact damage has been present since the early days of space travel. This is often done by either having a crew member take photographs of the spacecraft through a window using a hand-held camera or ground personnel directing externally-mounted cameras. The photographs are then transmitted back to Earth for visual analysis. This method of MMOD damage inspection works well and has been used on various spacecraft including the Space Shuttle and the International Space Station (ISS). One of the issues with the current method that we believe AI could improve is the speed and possibly the accuracy in identifying MMOD impacts. Note that detecting MMOD impacts in images can be very difficult. The visual appearance of an MMOD impact can change dramatically with lighting conditions, size of impact, depth of penetration, material types, surface waviness, fabric coverings, camera & lens, distance to surface, spacecraft orientation, analyst experience, and many other factors. Currently, this takes a team of highly-experienced specialists in both the fields of Image Analysis and MMOD impacts. This paper documents our initial research in training an AI DL model using the fast-AI library to identify actual and simulated MMOD impacts and perforations into exposed flat surfaces. While we recognize that this initial goal seems modest, it must be noted that what we have done would have taken teams of individuals and years of training just ten years ago. Our long-term goal is to add complexity and use-cases to the DL model being trained to expand the capabilities of this model so that it can be used to identify MMOD impacts on all types of spacecraft surfaces.

Cameron M Collins↗

DOE OSTI2021

Doppler-Lidar Evaluation of HRRR-Model Skill at Simulating Summertime Wind Regimes in the Columbia River Basin during WFIP2

Complex-terrain locations often have repeatable near-surface wind patterns, such as synoptic gap flows and local thermally forced flows. An example is the Columbia River Valley in east-central Oregon-Washington, a significant wind-energy-generation region and the site of the Second Wind-Forecast Improvement Project (WFIP2). Data from three Doppler lidars deployed during WFIP2 define and characterize summertime wind regimes and their large-scale contexts, and provide insight into NWP model errors by examining differences in the ability of a model [NOAA’s High-Resolution Rapid-Refresh (HRRR-version1)] to forecast wind-speed profiles for different regimes. Seven regimes were identified based on daily time series of the lidar-measured rotor-layer winds, which then suggested two broad categories. First, in three regimes the primary dynamic forcing was the large-scale pressure gradient. Second, in two regimes the dominant forcing was the diurnal heating-cooling cycle (regional sea-breeze-type dynamics), including the marine intrusion previously described, which generates strong nocturnal winds over the region. The other two included a hybrid regime and a non-conforming regime. For the large-scale pressure-gradient regimes, HRRR had wind-speed biases of ~1 m s -1 and RMSEs of 2-3 m s -1 . Errors were much larger for the thermally forced regimes, owing to the premature demise of the strong nocturnal flow in HRRR. Thus, the more dominant the role of surface heating in generating the flow, the larger the errors. Major errors could result from surface heating of the atmosphere, boundary-layer responses to that heating, and associated terrain interactions. Finally, measurement/modeling research programs should be aimed at determining which modeled processes produce the largest errors, so those processes can be improved and errors reduced.

17 WIND ENERGY↗

NASA NTRS1991

Chemical models of interstellar gas-grain processes. II - The effect of grain-catalysed methane on gas phase evolution

The effects on gas phase chemistry which result from the continuous desorption of methane molecules from grain surfaces are studied. Significant and sustained enhancements in the abundances of several complex hydrocarbon molecules are found, in good agreement with their observed values in TMC-1. The overall agreement is, however, just as good for the case of zero CH4 desorption efficiency. It is thus impossible to determine from the models whether or not the grain-surface production of methane is responsible for the observed abundances of some hydrocarbon molecules.

Brown, Paul D.↗

NASA NTRS1994

An evaluation with the Fourier Amplitude Sensitivity Test (FAST) of which land-surface parameters are of greatest importance in atmospheric modeling

Land-surface parameterizations based on a statistical-dynamical have been suggested recently to improve the representation of the surface forcing from heterogeneous land in atmospheric models. With this approach, land-surface characteristics are prescribed by probability density functions (PDFs) rather than single 'representative' values as in 'big-leaf' parameterizations. Yet the use of many PDFs results in an increased computational burden and requires the complex problem of representing covariances between PDFs to be addressed. In this study, a sensitivity analysis of a land-surface parameterization for atmospheric modeling was performed to evaluate the surface parameters most important to the variability of surface heat fluxes. The Fourier amplitude sensitivity test (FAST) used for this analysis determines the relative contribution of individual input parameters to the variance of energy fluxes resulting from a heterogeneous surface. By simultaneously varying all parameters according to their individual probability density functions, the number of computations needed is very much reduced by this technique. This analysis demonstrates that most of the variability of surface heat fluxes may be described by the distributions of relative stomatal conductance and surface roughness. Thus, the statistical-dynamical approach may be simplified by the use of only these two probability density functions.

Collins, Dan C.↗

NASA NTRS2022

Implementation and Evaluation of Irrigation Techniques in the Community Land Model

Several previous studies have highlighted the irrigation-induced impacts on the global and regional water cycle, energy budget, and near-surface climate. While land models are widely used to address this question, the implementations of irrigation in these models vary in complexity. Here, we expand the representation of irrigation in Community Land Model to enable six different irrigation methods. We find that using a combination of irrigation methods, including default, sprinkler, flood and paddy techniques performs best as determined by evaluating the simulated irrigation water withdrawals against observations, and therefore select this combination as the new irrigation scheme. Then, the impact of the new irrigation scheme on surface fluxes is evaluated and detected using single-point simulations. Finally, the global and regional irrigation-induced impacts on surface energy and water fluxes are compared using both the original and the new irrigation scheme. The new irrigation scheme substantially reduces the bias and root-mean-square error of simulated irrigation water withdrawal in the USA and other countries, but considerably overestimates withdrawals in Central China. Results of single-point experiments show that different irrigation methods have different effects on surface fluxes, while the magnitudes are small. At the global scale, the new scheme enlarges the irrigation-induced impacts on water and energy variables relative to the original scheme, with varying magnitudes across regions. Overall, our results suggest that this newly developed scheme is a better tool for simulating irrigation-induced impacts on climate, and highlight the added value of incorporating human water management in Earth system models.

Community land models↗

DOE OSTI2025

Systematic softening in universal machine learning interatomic potentials

Machine learning interatomic potentials (MLIPs) have introduced a new paradigm for atomic simulations. Recent advancements have led to universal MLIPs (uMLIPs) that are pre-trained on diverse datasets, providing opportunities for universal force fields and foundational machine learning models. However, their performance in extrapolating to out-of-distribution complex atomic environments remains unclear. In this study, we highlight a consistent potential energy surface (PES) softening effect in three uMLIPs: M3GNet, CHGNet, and MACE-MP-0, which is characterized by energy and force underprediction in atomic-modeling benchmarks including surfaces, defects, solid-solution energetics, ion migration barriers, phonon vibration modes, and general high-energy states. The PES softening behavior originates primarily from the systematically underpredicted PES curvature, which derives from the biased sampling of near-equilibrium atomic arrangements in uMLIP pre-training datasets. Our findings suggest that a considerable fraction of uMLIP errors are highly systematic, and can therefore be efficiently corrected. We argue for the importance of a comprehensive materials dataset with improved PES sampling for next-generation foundational MLIPs.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Measurements and Model Improvement: Insight into NWP Model Error Using Doppler Lidar and Other WFIP2 Measurement Systems

Abstract Doppler-lidar wind-profile measurements at three sites were used to evaluate NWP model errors from two versions of NOAA’s 3-km-grid HRRR model, to see whether updates in the latest version 4 reduced errors when compared against the original version 1. Nested (750-m grid) versions of each were also tested to see how grid spacing affected forecast skill. The measurements were part of the field phase of the Second Wind Forecasting Improvement Project (WFIP2), an 18-month deployment into central Oregon–Washington, a major wind-energy-producing region. This study focuses on errors in simulating marine intrusions, a summertime, 600–800-m-deep, regional sea-breeze flow found to generate large errors. HRRR errors proved to be complex and site dependent. The most prominent error resulted from a premature drop in modeled marine-intrusion wind speeds after local midnight, when lidar-measured winds of greater than 8 m s −1 persisted through the next morning. These large negative errors were offset at low levels by positive errors due to excessive mixing, complicating the interpretation of model “improvement,” such that the updates to the full-scale versions produced mixed results, sometimes enhancing but sometimes degrading model skill. Nesting consistently improved model performance, with version 1’s nest producing the smallest errors overall. HRRR’s ability to represent the stages of sea-breeze forcing was evaluated using radiation budget, surface-energy balance, and near-surface temperature measurements available during WFIP2. The significant site-to-site differences in model error and the complex nature of these errors mean that field-measurement campaigns having dense arrays of profiling sensors are necessary to properly diagnose and characterize model errors, as part of a systematic approach to NWP model improvement. Significance Statement Dramatic increases in NWP model skill will be required over the coming decades. This paper describes the role of major deployments of accurate profiling sensors in achieving that goal and presents an example from the Second Wind Forecast Improvement Program (WFIP2). Wind-profile data from scanning Doppler lidars were used to evaluate two versions of HRRR, the original and an updated version, and nested versions of each. This study focuses on the ability of updated HRRR versions to improve upon predicting a regional sea-breeze flow, which was found to generate large errors by the original HRRR. Updates to the full-scale HRRR versions produced mixed results, but the finer-mesh versions consistently reduced model errors.

Meteorology & Atmospheric Sciences↗

NASA NTRS1993

Mathmatical modeling for diffractive optics

We consider a 'diffractive optic' to be a biperiodic surface separating two half-spaces, each having constant constitutive parameters; within a unit cell of the periodic surface and across the transition zone between the two half-spaces, the constitutive parameters can be a continuous, complex-valued function. Mathematical models for diffractive optics have been developed, and implemented as numerical codes, both for the 'direct' problem and for the 'inverse' problem. In problems of the 'direct' class, the diffractive optic is specified, and the full set of Maxwell's equations is cast in a variational form and solved numerically by a finite element approach. This approach is well-posed in the sense that existence and uniqueness of the solution can be proved and specific convergence conditions can be derived. An example of a metallic grating at a Wood anomaly is presented as a case where other approaches are known to have convergence problems. In problems of the 'inverse' class, some information about the diffracted field (e.g., the far-field intensity) is given, and the problem is to find the periodic structure in some optimal sense. Two approaches are described: phase reconstruction in the far-field approximation; and relaxed optimal design based on the Helmholtz equation. Practical examples are discussed for each approach to the inverse problem, including array generators in the far-field case and antireflective structures for the relaxed optimal design.

Dobson, David↗