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Best approximation to the weighted slab method

The weighted-slab method is modified so that, although it is still not exact, it gives the 'best' approximation in a minimization sense when energy loss cannot be neglected. In this approximation the species-dependent energy-change term that operates on the path-length distribution is 'averaged' over the slab-model solution for that particular energy and path length.

Jones, Frank C.↗

Validating a large geophysical data set - Experiences with satellite-derived cloud parameters

The goal of this study is to validate the global cloud parameters derived from the satellite-borne HIRS2 and MSU atmospheric sounding instrument measurements, and to use the analysis of these data as one prototype for studying large geophysical data sets in general. The HIRS2/MSU data set contains a total of 40 physical parameters, filling 25 MB/day; raw HIRS2/MSU data are available for a period exceeding 10 years. Validation involves developing a quantitative sense for the physical meaning of the derived parameters over the range of environmental conditions sampled. This is accomplished by comparing the spatial and temporal distributions of the derived quantities with similar measurements made using other techniques, and with model results. The need to work with Level 2 (point) data, rather than Level 3 (gridded) data for validation purposes is discussed, and some techniques developed for charting the assumptions made in deriving an algorithm and generating a code to produce geophysical quantities from measured radiances are presented.

Kahn, Ralph↗

Validating a large geophysical data set: Experiences with satellite-derived cloud parameters

We are validating the global cloud parameters derived from the satellite-borne HIRS2 and MSU atmospheric sounding instrument measurements, and are using the analysis of these data as one prototype for studying large geophysical data sets in general. The HIRS2/MSU data set contains a total of 40 physical parameters, filling 25 MB/day; raw HIRS2/MSU data are available for a period exceeding 10 years. Validation involves developing a quantitative sense for the physical meaning of the derived parameters over the range of environmental conditions sampled. This is accomplished by comparing the spatial and temporal distributions of the derived quantities with similar measurements made using other techniques, and with model results. The data handling needed for this work is possible only with the help of a suite of interactive graphical and numerical analysis tools. Level 3 (gridded) data is the common form in which large data sets of this type are distributed for scientific analysis. We find that Level 3 data is inadequate for the data comparisons required for validation. Level 2 data (individual measurements in geophysical units) is needed. A sampling problem arises when individual measurements, which are not uniformly distributed in space or time, are used for the comparisons. Standard 'interpolation' methods involve fitting the measurements for each data set to surfaces, which are then compared. We are experimenting with formal criteria for selecting geographical regions, based upon the spatial frequency and variability of measurements, that allow us to quantify the uncertainty due to sampling. As part of this project, we are also dealing with ways to keep track of constraints placed on the output by assumptions made in the computer code. The need to work with Level 2 data introduces a number of other data handling issues, such as accessing data files across machine types, meeting large data storage requirements, accessing other validated data sets, processing speed and throughput for interactive graphical work, and problems relating to graphical interfaces.

Kahn, Ralph↗

Interacting galaxies resolved by IRAS

We discuss procedures, limitations and results of high resolution processing of interacting galaxies observed by the Infrared Astronomical Satellite (IRAS). Among 56 potentially resolvable interacting groups selected from the IRAS Bright Galaxy Sample, 22 systems have been resolved yielding fluxes for a total of 51 galaxies. In about 2/3 of the resolved pairs, both galaxies were detected in the far-infrared. A set of isolated non-interacting galaxies was chosen from the Bright Galaxy Sample for comparison with the interacting galaxies. For the current sample, which naturally excludes close pairs and ultraluminous merging systems, the primary conclusions are: (1) It is not possible to distinguish individual interacting galaxies from isolated galaxies of similar luminosity on the basis of infrared properties alone. (2) No direct correlation was found between measures of interaction strength and indicators of enhanced star formation within the resolved systems. (3) Comparison of the interacting and isolated samples indicates statistically significant differences between their distributions of far-infrared color ratios, luminosities, and surface brightnesses. Even during the early stages of interaction spanned by these systems, in a statistical sense, tidal perturbations substantially boost far-infrared indicators of star formation compared to non-interacting systems. We also briefly discuss future prospects for pushing the IRAS data to its limits for additional interacting systems.

Mazzarella, Joseph M.↗

BOREAS RSS-11 Ground Network of Sunphotometer Measurements

The BOREAS RSS-11 team operated a network of five automated (Cimel) and two hand-held (Miami) solar radiometers from 1994 to 1996 during the BOREAS field campaigns. The data provide aerosol optical depth measurements, size distribution, phase function, and column water vapor amounts over points in northern Saskatchewan and Manitoba, Canada. The data are useful for the correction of remotely sensed aircraft and satellite images. The data are provided in tabular ASCII files.

Markham, Brian L.↗

BRDF Calibration of Sintered PTFE in the SWIR

Satellite instruments operating in the reflective solar wavelength region often require accurate and precise determination of the Bidirectional Reflectance Distribution Function (BRDF) of laboratory-based diffusers used in their pre-flight calibrations and ground-based support of on-orbit remote sensing instruments. The Diffuser Calibration Facility at NASA's Goddard Space Flight Center is a secondary diffuser calibration standard after NEST for over two decades, providing numerous NASA projects with BRDF data in the UV, Visible and the NIR spectral regions. Currently the Diffuser Calibration Facility extended the covered spectral range from 900 nm up to 1.7 microns. The measurements were made using the existing scatterometer by replacing the Si photodiode based receiver with an InGaAs-based one. The BRDF data was recorded at normal incidence and scatter zenith angles from 10 to 60 deg. Tunable coherent light source was setup. Broadband light source application is under development. Gray-scale sintered PTFE samples were used at these first trials, illuminated with P and S polarized incident light. The results are discussed and compared to empirically generated BRDF data from simple model based on 8 deg directional/hemispherical measurements.

Georgiev, Georgi T.↗

Local Estimators for Spacecraft Formation Flying

A formation estimation architecture for formation flying builds upon the local information exchange among multiple local estimators. Spacecraft formation flying involves the coordination of states among multiple spacecraft through relative sensing, inter-spacecraft communication, and control. Most existing formation flying estimation algorithms can only be supported via highly centralized, all-to-all, static relative sensing. New algorithms are needed that are scalable, modular, and robust to variations in the topology and link characteristics of the formation exchange network. These distributed algorithms should rely on a local information-exchange network, relaxing the assumptions on existing algorithms. In this research, it was shown that only local observability is required to design a formation estimator and control law. The approach relies on breaking up the overall information-exchange network into sequence of local subnetworks, and invoking an agreement-type filter to reach consensus among local estimators within each local network. State estimates were obtained by a set of local measurements that were passed through a set of communicating Kalman filters to reach an overall state estimation for the formation. An optimization approach was also presented by means of which diffused estimates over the network can be incorporated in the local estimates obtained by each estimator via local measurements. This approach compares favorably with that obtained by a centralized Kalman filter, which requires complete knowledge of the raw measurement available to each estimator.

Fathpour, Nanaz↗

The Invasive Species Forecasting System (ISFS): An iRODS-Based, Cloud-Enabled Decision Support System for Invasive Species Habitat Suitability Modeling

The Invasive Species Forecasting System (ISFS) is an online decision support system that allows users to load point occurrence field sample data for a plant species of interest and quickly generate habitat suitability maps for geographic regions of interest, such as a national park, monument, forest, or refuge. Target customers for ISFS are natural resource managers and decision makers who have a need for scientifically valid, model- based predictions of the habitat suitability of plant species of management concern. In a joint project involving NASA and the Maryland Department of Natural Resources, ISFS has been used to model the potential distribution of Wavyleaf Basketgrass in Maryland's Chesapeake Bay Watershed. Maximum entropy techniques are used to generate predictive maps using predictor datasets derived from remotely sensed data and climate simulation outputs. The workflow to run a model is implemented in an iRODS microservice using a custom ISFS file driver that clips and re-projects data to geographic regions of interest, then shells out to perform MaxEnt processing on the input data. When the model completes, all output files and maps from the model run are registered in iRODS and made accessible to the user. The ISFS user interface is a web browser that uses the iRODS PHP client to interact with the ISFS/iRODS- server. ISFS is designed to reside in a VMware virtual machine running SLES 11 and iRODS 3.0. The ISFS virtual machine is hosted in a VMware vSphere private cloud infrastructure to deliver the online service.

Gill, Roger↗

Coupled Inertial Navigation and Flush Air Data Sensing Algorithm for Atmosphere Estimation

This paper describes an algorithm for atmospheric state estimation based on a coupling between inertial navigation and flush air data-sensing pressure measurements. The navigation state is used in the atmospheric estimation algorithm along with the pressure measurements and a model of the surface pressure distribution to estimate the atmosphere using a nonlinear weighted least-squares algorithm. The approach uses a high-fidelity model of atmosphere stored in table-lookup form, along with simplified models propagated along the trajectory within the algorithm to aid the solution. Thus, the method is a reduced-order Kalman filter in which the inertial states are taken from the navigation solution and atmospheric states are estimated in the filter. The algorithm is applied to data from the Mars Science Laboratory entry, descent, and landing from August 2012. Reasonable estimates of the atmosphere are produced by the algorithm. The observability of winds along the trajectory are examined using an index based on the observability Gramian and the pressure measurement sensitivity matrix. The results indicate that bank reversals are responsible for adding information content. The algorithm is applied to the design of the pressure measurement system for the Mars 2020 mission. A linear covariance analysis is performed to assess estimator performance. The results indicate that the new estimator produces more precise estimates of atmospheric states than existing algorithms.

Karlgaard, Christopher D.↗

Low SWaP Onboard Satellite Navigation, Guidance, and Control Technology

Onboard autonomy is a necessity for responsive space operations. Autonomous navigation, guidance, and control (NGC) enables space missions to reduce their dependence on high demand ground assets and costly ground personnel. It also allows for in-situ decision making and higher return on mission data. A flight software and hardware system providing this capability, called “autoNGC,” is currently being developed at NASA Goddard Space Flight Center for infusion into multiple future missions. The first build of autoNGC, providing autonomous navigation for lunar orbiting spacecraft, is targeted for completion by Fall 2024. It provides sensor fusion of multiple measurement types including pseudo-range from a weak signal Global Navigation Satellite Service (GNSS) receiver, 1-way and 2-way direct to Earth (DTE) range and Doppler, bearing and range from optical camera sensed images, and an accelerometer. AutoNGC is also being targeted for future missions that involve small body proximity operations, Sun Earth Libration point orbits, and distributed systems missions (DSMs) including those at outer planets. AutoNGC flight software is being built upon the plug-and-play architecture of the core Flight System (cFS) [Ref. 1]. Figure (Slide 7) shows the message-based software bus layout of various software applications (“apps”) consisting of the standard cFS apps and autoNGC interface apps and libraries. Accurate onboard navigation and timing is obtained through the Goddard Enhanced Onboard Navigation System (GEONS) software library [Ref. 2], which fuses different measurement types through an extended Kalman filter (EKF) framework. Optical measurements that are ingested in GEONS are provided by the cFS Goddard Image Analysis and Navigation Tool (cGIANT) app [Ref. 3]. This app processes optical images to extract the bearing angles of the centroid of the imaged body (near or far), the range to the imaged body, and/or of the features on the surface of a body to perform terrain relative navigation (TRN). Measurement of range to the body’s center of mass can also be derived from the detection of the limb. The first build of autoNGC for a lunar orbiting spacecraft is a minimal size, weight, and power (SWaP) hardware design allowing for inclusion into CubeSats and SmallSat-size class buses. Advancements in miniaturized space processors, such as the SpaceCube 3.0 Mini and the SpaceCube Mini-Z [Ref. 4] are utilized for low SWaP while maintaining a high level of performance. Figure (Slide 11) shows the composition of the first autoNGC build. The current enclosure design has dimensions 12 cm x 17 cm x 13.5 cm. The box mass is expected to be less than 2 kg, and the nominal power is 21 W. The hardware interfaces are designed for flexibility with a variety of sensor inputs. The achievable navigation performance depends on the sensors utilized, including the onboard clock for 1-way pseudo-range measurements. Analysis using a configuration that consists of weak signal GPS, TRN, and 1-way DTE has shown position and velocity accuracies of 10 meters and 2 cm/s (3-σ ) RSS, respectively, with onboard time knowledge estimated to better than 13 ns (3-σ ), for a spacecraft in a representative 12-hour eccentric lunar orbit. Other measurement types such as x-rays from known pulsars (called XNAV) and cross-links can also be processed in GEONS. With the plug-and-play architecture of autoNGC, cFS apps can easily be added and replaced, even after launch. Goddard is actively seeking partners to collaborate in the development of additional capabilities for autoNGC, including industry, academia, and others across the US Government. Plans are being formulated to make the autoNGC software platform available for use by any US government organization to leverage the non-recurring engineering associated with the development of onboard autonomous NGC 3 capabilities. As advancements in space qualified sensors, microprocessors, and algorithms are made, the autoNGC platform provides a ready starting point for inclusion of these technologies.

C. J. Gramling↗

Retrievals of Cloud Droplet Size from the RSP Data: Validation Using in Situ Measurements

We present comparisons of cloud droplet size distributions retrieved from the Research Scanning Polarimeter (RSP) data with correlative in situ measurements made during the North Atlantic Aerosols and Marine Ecosystems Study (NAAMES). This field experiment was based at St. Johns airport, Newfoundland, Canada with the latest deployment in May - June 2016. RSP was onboard the NASA C-130 aircraft together with an array of in situ and other remote sensing instrumentation. The RSP is an along-track scanner measuring polarized and total reflectances in9 spectral channels. Its unique high angular resolution allows for characterization of liquid water droplet size using the rainbow structure observed in the polarized reflectances in the scattering angle range between 135 and 165 degrees. A parametric fitting algorithm applied to the polarized reflectances provides retrievals of the droplet effective radius and variance assuming a prescribed size distribution shape (gamma distribution). In addition to this, we use a non-parametric method, Rainbow Fourier Transform (RFT), which allows us to retrieve the droplet size distribution (DSD) itself. The latter is important in the case of clouds with complex structure, which results in multi-modal DSDs. During NAAMES the aircraft performed a number of flight patterns specifically designed for comparison of remote sensing retrievals and in situ measurements. These patterns consisted of two flight segments above the same straight ground track. One of these segments was flown above clouds allowing for remote sensing measurements, while the other was at the cloud top where cloud droplets were sampled. We compare the DSDs retrieved from the RSP data with in situ measurements made by the Cloud Droplet Probe (CDP). The comparisons show generally good agreement with deviations explainable by the position of the aircraft within cloud and by presence of additional cloud layers in RSP view that do not contribute to the in situ DSDs. In the latter case the distributions retrieved from the RSP data were consistent with the multi-layer cloud structures observed in the correlative High Spectral Resolution Lidar (HSRL) profiles. The comparison results provide a rare validation of polarimetric droplet size retrieval techniques, which can be used for analysis of satellite data on global scale.

cloud droplets↗

Remote sensing of permafrost and geological hazards in Alaska

The author has identified the following significant results. The study of the ERTS-1 imagery of Alaska indicates the following: that areas of different topographic expression affecting the distribution and character of permafrost can be distinguished clearly; that on the Arctic North Slope, regional differences in the distribution and character of permafrost-related oriented thaw lakes can be observed; that the distribution of certain types of geologic materials having a significant effect on the character of permafrost can be delineated on a regional scale; and that the resolution of the imagery is adequate to identify large scale geologic hazards such as landslides, glacier-dammed lakes, aufeis fields, etc. The information concerning the distribution and character of permafrost and geologic hazards to the gained in accomplishing the objectives of this project will be an invaluable aid in solving engineering-geologic and environmental problems related to route and site selection for structures such as roads, railroads, pipelines, and large installations; to distribution of natural construction materials; and to construction and maintenance.

Ferrians, O. J., Jr.↗

Attempts to Localize and Identify the Gravity-sensing Device of Plant Seedlings

The growth hormone asymmetry develops within three minutes following the initiation of the gravitational asymmetry and radio-labeled compounds being transported from the seed to the shoot also show asymmetric distribution. It is found that the target of the gravity stimulus resides primarily in the permability of the vascular tissue that regulates the supply of hormone to the surrounding tissues. It is hypothesized that the gravitational stimulus induces an asymmetric change in the rate of secretion of the growth hormone, IAA, from the vascular tissue into the surrounding cortical cells. More hormone would be secreted from the vascular stele proximal to the lower side of a horizontally placed plant shoot than from the upper side. This results in more growth hormone in the lower cortical (plus epidermal) cells, and ultimately more growth, such that the plant grows asymmetrically and, ultimately attain its normal vertical orientation. A theory was developed of how plants respond to the gravitational stimulus. The theory is based upon the analytical results concerning the effects of gravity on the distribution of the plant growth hormone, IAA, in both its free and conjugated forms, and upon the effect of the growth stimulis on the distribution of externally applied radio-labeled compounds. Its advantage is that it is testable and that it is built upon solid knowledge of the effects of the gravitational stimulus upon the endogenous growth hormone, IAA, and upon the distribution of externally applied radio-labeled compounds.

Bandurski, R. S.↗

Optical signal processing of spatially distributed sensor data in smart structures

Smart structures which contain dense two- or three-dimensional arrays of attached or embedded sensor elements inherently require signal multiplexing and processing capabilities to permit good spatial data resolution as well as the adequately short calculation times demanded by real time active feedback actuator drive circuitry. This paper reports the implementation of an in-line optical signal processor and its application in a structural sensing system which incorporates multiple discrete optical fiber sensor elements. The signal processor consists of an array of optical fiber couplers having tailored s-parameters and arranged to allow gray code amplitude scaling of sensor inputs. The use of this signal processor in systems designed to indicate the location of distributed strain and damage in composite materials, as well as to quantitatively characterize that damage, is described. Extension of similar signal processing methods to more complicated smart materials and structures applications are discussed.

Bennett, K. D.↗

Space-Time Controls on Carbon Sequestration Over Large-Scale Amazon Basin

A major research focus of the LBA Ecology Program is an assessment of the carbon budget and the carbon sequestering capacity of the large scale forest-pasture system that dominates the Amazonia landscape, and its time-space heterogeneity manifest in carbon fluxes across the large scale Amazon basin ecosystem. Quantification of these processes requires a combination of in situ measurements, remotely sensed measurements from space, and a realistically forced hydrometeorological model coupled to a carbon assimilation model, capable of simulating details within the surface energy and water budgets along with the principle modes of photosynthesis and respiration. Here we describe the results of an investigation concerning the space-time controls of carbon sources and sinks distributed over the large scale Amazon basin. The results are derived from a carbon-water-energy budget retrieval system for the large scale Amazon basin, which uses a coupled carbon assimilation-hydrometeorological model as an integrating system, forced by both in situ meteorological measurements and remotely sensed radiation fluxes and precipitation retrieval retrieved from a combination of GOES, SSM/I, TOMS, and TRMM satellite measurements. Brief discussion concerning validation of (a) retrieved surface radiation fluxes and precipitation based on 30-min averaged surface measurements taken at Ji-Parana in Rondonia and Manaus in Amazonas, and (b) modeled carbon fluxes based on tower CO2 flux measurements taken at Reserva Jaru, Manaus and Fazenda Nossa Senhora. The space-time controls on carbon sequestration are partitioned into sets of factors classified by: (1) above canopy meteorology, (2) incoming surface radiation, (3) precipitation interception, and (4) indigenous stomatal processes varied over the different land covers of pristine rainforest, partially, and fully logged rainforests, and pasture lands. These are the principle meteorological, thermodynamical, hydrological, and biophysical control paths which perturb net carbon fluxes and sequestration, produce time-space switching of carbon sources and sinks, undergo modulation through atmospheric boundary layer feedbacks, and respond to any discontinuous intervention on the landscape itself such as produced by human intervention in converting rainforest to pasture or conducting selective/clearcut logging operations.

Smith, Eric A.↗

Controls on Variations of Surface Energy, Water, and Carbon Budgets within Large-Scale Amazon Basin

A key research focus of the LBA Research Program is understanding the space-time variations in interlinked surface energy, water, and carbon budgets, the controls on these variations, and the implications of these controls on the carbon sequestering capacity of the large scale forest-pasture system that dominates the Amaz6nia landscape. Quantification of these variations and controls are investigated by a combination of in situ measurements, remotely sensed measurements from space, and a realistically forced hydrometeorological model coupled to a carbon assimilation model, capable of simulating details within the surface energy and water budgets along with the principle processes of photosynthesis and respiration. Herein we describe the results of an investigation concerning the space-time controls of carbon sources and sinks distributed over the large scale Amazon basin. The results are derived from a carbon-water-energy budget retrieval system for the large scale Amazon basin, which uses a coupled carbon assimilation-hydrometeorological model as an integrating system, forced by both in situ meteorological measurements and remotely sensed radiation and precipitation fluxes obtained from a combination of GOES, SSM/I, TOMS, and TRh4M satellite measurements. Results include validation of (a) retrieved surface radiation and precipitation fluxes based on 30-min averaged surface measurements taken at Ji-Parani in Rondania and Manaus in Amazonas, and (b) modeled sensible, latent, and C02 fluxes based on tower measurements taken at Reserva Jaru, Manaus and Fazenda Nossa Senhora. The space-time controls on carbon sequestration are partitioned into sets of factors classified by: (1) above canopy meteorology, (2) incoming surface radiation, (3) precipitation interception, and (4) indigenous stomatal processes varied over the different land covers of pristine rainforest, partially, and fully logged rainforests, and pasture lands. These are the principle meteorological, thermodynamical, hydrological, and biophysical control paths which perturb net carbon fluxes and sequestration, produce time-space switching of carbon sources and sinks, undergo modulation through atmospheric boundary layer feedbacks, and respond to any discontinuous intervention on the landscape itself such as produced by human intervention in converting rainforest to pasture or conducting selective/clearcut logging operations. The results demonstrate how relative carbon sequestration capacity of the Amazonian ecosystem responds to these controls, and how interpretation of space-time heterogeneities in carbon sequestration depends on a fairly exact quantification of the interacting non-linear properties of photosynthesis in response to incoming solar flux, air-canopy temperatures, and leaf water interception -- and soil respiration in response to upper layer soil temperature and water content. The results also show how the interpretation of the control processes is highly sensitive to the scales at which the surface fluxes are analyzed.

Smith, Eric A.↗

Controlling Malaria and Other Diseases Using Remote Sensing

Remote sensing offers the vantage of monitoring a vast area of the Earth continuously. Once developed and launched, a satellite gives years of service in collecting data from the land, the oceans, and the atmosphere. Since the 1980s, attempts have been made to relate disease occurrence with remotely sensed environmental and geophysical parameters, using data from Landsat, SPOT, AVHRR, and other satellites. With higher spatial resolution, the recent satellite sensors provide a new outlook for disease control. At sub-meter to I 10m resolution, surface types associated with disease carriers can be identified more accurately. The Ikonos panchromatic sensor with I m resolution, and the Advanced Land Imager with 1 Om resolution on the newly launched Earth Observing-1, both have displayed remarkable mapping capabilities. In addition, an entire array of geophysical parameters can now be measured or inferred from various satellites. Airborne remote sensing, with less concerns on instrument weight, size, and power consumption, also offers a low-cost alternative for regional applications. NASA/GSFC began to collaborate with the Mahidol University on malaria and filariasis control using remote sensing in late 2000. The objectives are: (1) To map the breeding sites for the major vector species; (2) To identify the potential sites for larvicide and insecticide applications; (3) To explore the linkage of vector population and transmission intensity to environmental variables; (4) To monitor the impact of climate change and human activities on vector population and transmission; and (5) To develop a predictive model for disease distribution. Field studies are being conducted in several provinces in Thailand. Data analyses will soon begin. Malaria data in South Korea are being used as surrogates for developing classification techniques. GIS has been shown to be invaluable in making the voluminous remote sensing data more readily understandable. It will be used throughout this study to clearly demonstrate the spatial relationship between the disease intensities, geophysical variables, and socioeconomic parameters. Asides from malaria and filariasis, application of remote sensing to the control of other diseases have been vigorously pursued by NASA's Environment and Health Initiative. The current program includes projects on Rift Valley fever, St. Louis encephalitis, dengue fever, ebola, African dust and diseases, meningitis, asthma, bartonellosis, cholera, and urban health concerns. Results from these projects indicate that remote sensing will play an increasingly important role in disease control in the future.

Kiang, Richard K.↗

Mapping charge excitations in generalized Wigner crystals

Transition metal dichalcogenide-based moiré superlattices exhibit strong electron-electron correlations, thus giving rise to strongly correlated quantum phenomena such as generalized Wigner crystal states. Evidence of Wigner crystals in transition metal dichalcogenide moire superlattices has been widely reported from various optical spectroscopy and electrical conductivity measurements, while their microscopic nature has been limited to the basic lattice structure. Theoretical studies predict that unusual quasiparticle excitations across the correlated gap between upper and lower Hubbard bands can arise due to long-range Coulomb interactions in generalized Wigner crystal states. However, the microscopic proof of such quasiparticle excitations is challenging because of the low excitation energy of the Wigner crystal. Here, in this study, we describe a scanning single-electron charging spectroscopy technique with nanometre spatial resolution and single-electron charge resolution that enables us to directly image electron and hole wavefunctions and to determine the thermodynamic gap of generalized Wigner crystal states in twisted WS 2 moiré heterostructures. High-resolution scanning single-electron charging spectroscopy combines scanning tunnelling microscopy with a monolayer graphene sensing layer, thus enabling the generation of individual electron and hole quasiparticles in generalized Wigner crystals. We show that electron and hole quasiparticles have complementary wavefunction distributions and that thermodynamic gaps of ~50 meV exist for the 1/3 and 2/3 generalized Wigner crystal states in twisted WS 2 .

36 MATERIALS SCIENCE↗