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NASA NTRS2021

Application of Radon Transform to Multi-Angle Measurements Made by the Research Scanning Polarimeter: A New Approach to Cloud Tomography. Part I: Theory and Tests on Simulated Data.

The Research Scanning Polarimeter (RSP) is an airborne along-track scanner measuring the polarized and total reflectances in 9 spectral channels. The RSP was a prototype for the Aerosol Polarimetry Sensor (APS) launched on-board the NASA Glory satellite. Currently the retrieval algorithms developed for the RSP are being adopted for the measurements of the space-borne polarimeters on the upcoming NASA’s Plankton, Aerosol, Cloud Ocean Ecosystem (PACE)satellite mission. The RSP’s uniquely high angular resolution coupled with the high frequency of measurements allows for characterization of liquid water cloud droplet sizes using the polarized rainbow structure. It also provides geometric constraints on the cumulus cloud’s 2D cross section yielding the cloud’s geometric shape estimates. In this study we further build on the latter technique to develop a new tomographic approach to retrieval of cloud internal structure from remote sensing measurements. While tomography in the strict definition is a technique based on active measurements yielding a tomogram (directional optical thickness as a function of angle and offset of the view ray), we developed a “semi-tomographic” approach in which tomogram of the cloud is estimated from passive observations instead of being measured directly. This tomogram is then converted into 2D spatial distribution of the extinction coefficient using inverse Radon transform (filtered back projection) which is the standard tomographic procedure used e.g., in medical CT scans. This algorithm is computationally inexpensive compared to techniques relying on highly-multi-dimensional least-square fitting; it does not require iterative 3D RT simulations. The resulting extinction distribution is defined up to an unknown constant factor, so we discuss the ways to calibrate it using additional independent measurements. In the next step we use the profile of the droplet size distribution parameters from the cloud’s side (derived by fitting the polarized rainbows) to convert the 2D extinction distribution into that of the droplet number concentration. We illustrate and validate the proposed technique using 3D-RT-simulatedRSP observations of a LES-generated Cu cloud. Quantitative comparisons between the retrieved and the original optical and microphysical parameters are presented.

clouds↗

NASA NTRSDate not supplied

Investigation of Cloud Interior Structure Using a Tomographic Technique Based on Radon Transform. Application to the Measurements Made by the Research Scanning Polarimeter During CAMP2Ex

The Research Scanning Polarimeter (RSP) is an airborne along-track scanner measuring the polarized and total reflectances in 9 spectral channels. The RSP's uniquely high angular resolution coupled with the high frequency of measurements allows for characterization of liquid-water cloud droplet sizes using the rainbow structure observed in the polarized reflectance measurements. The RSP observations also provide for derivation of 2D field of extinction coefficient inside the cloud using a tomographic technique. This technique utilizes the family of cloud shapes derived using "cutout" technique and corresponding to a number of thresholds in total reflectance (separating bright cloud from its darker background). These shapes can be interpreted as level curves of an abstract "reflectance density", which is then used for derivation of the directional cloud optical thickness (dCOT) tomogram. The latter is a collection of dCOTs parameterized by the angles and offsets of the corresponding view rays (chords) relative to the cloud center. After this, the inverse Radon Transform (the mathematical basis of the X-ray com-puter tomography) is applied to the dCOT tomogram yielding 2D spatial distribution of the extinction coefficient. The later can be converted into droplet number concentration using the droplet size profiles derived from the RSP's polarized reflectance measurements. After tests on synthetic data this technique was applied to real RSP measurements from NASA's Cloud, Aerosol and Monsoon Processes Philippines Experiment (CAMP2Ex) conducted in the vicinity of the Philippines during the Southwest Monsoon (August–September 2019). We have investigated the interiors of a number of clouds observed during CAMP2Ex focusing on Cu and CuCg (Tcu) cases. Our retrievals were routinely compared with the correlative measurements by lidar (HSRL-2) and cloud radar (APR-3) that were deployed on the same airborne platform (NASA P-3B) during this field experiment.

Research Scanning Polarimeter↗

NASA NTRSDate not supplied

A Method for Obtaining Surface Flow Vectors and Its Implementation in Interferometric Skin Friction Measurement

A new method was developed to extract surface flow vectors from an oilflow visualization image that has oil streaklines. The method is analogous to the PIV processing where the image is divided into interrogation windows. A representative flow direction is obtained for each interrogation window using image processing with a line-detection algorithm. Repeating the process for the entire image, one can find the surface vector field. The Hough transformation, Radon transformation and Machine Learning were used as line-detection algorithms. The obtained vector field is then postprocessed to filter spurious vectors and to apply smoothing. The method was tested on 2D and 3D models with different flow complexities. The method was able to predict surface flow vectors for all cases tested. The predicted surface flow vectors were used in obtaining the surface skin friction. The successful implementation of the surface flow vectors enables interferometric skin friction measurements on surfaces beneath 3D complex flows. In addition, the surface flow vectors can be superimposed on the oilflow visualization images to better explain the surface flow topology.

Surface flow vectors↗

NASA NTRSDate not supplied

A Method for Obtaining Surface Flow Vectors and Its Implementation in Interferometric Skin Friction Measurement

Surface flow vectors↗

NASA NTRS2017

Baseline-Subtraction-Free (BSF) Damage-Scattered Wave Extraction for Stiffened Isotropic Plates

Lamb waves enable long distance inspection of structures for health monitoring purposes. However, this capability is diminished when applied to complex structures where damage-scattered waves are often buried by scattering from various structural components or boundaries in the time-space domain. Here, a baseline-subtraction-free (BSF) inspection concept based on the Radon transform (RT) is proposed to identify and separate these scattered waves from those scattered by damage. The received time-space domain signals can be converted into the Radon domain, in which the scattered signals from structural components are suppressed into relatively small regions such that damage-scattered signals can be identified and extracted. In this study, a piezoelectric wafer and a linear scan via laser Doppler vibrometer (LDV) were used to excite and acquire the Lamb-wave signals in an aluminum plate with multiple stiffeners. Linear and inverse linear Radon transform algorithms were applied to the direct measurements. The results demonstrate the effectiveness of the Radon transform as a reliable extraction tool for damage-scattered waves in a stiffened aluminum plate and also suggest the possibility of generalizing this technique for application to a wide variety of complex, large-area structures.

He, Jiaze↗

NASA NTRS2011

Sky and Elemental Planetary Mapping Via Gamma Ray Emissions

Low-energy gamma ray emissions ((is) approximately 30keV to (is) approximately 30MeV) are significant to astrophysics because many interesting objects emit their primary energy in this regime. As such, there has been increasing demand for a complete map of the gamma ray sky, but many experiments to do so have encountered obstacles. Using an innovative method of applying the Radon Transform to data from BATSE (the Burst And Transient Source Experiment) on NASA's CGRO (Compton Gamma-Ray Observatory) mission, we have circumvented many of these issues and successfully localized many known sources to 0.5 - 1 deg accuracy. Our method, which is based on a simple 2-dimensional planar back-projection approximation of the inverse Radon transform (familiar from medical CAT-scan technology), can thus be used to image the entire sky and locate new gamma ray sources, specifically in energy bands between 200keV and 2MeV which have not been well surveyed to date. Samples of these results will be presented. This same technique can also be applied to elemental planetary surface mapping via gamma ray spectroscopy. Due to our method's simplicity and power, it could potentially improve a current map's resolution by a significant factor.

BATSE (the Burst and Transient Source Experiment)↗

NASA NTRS1993

A Novel Optical/digital Processing System for Pattern Recognition

This paper describes two processing algorithms that can be implemented optically: the Radon transform and angular correlation. These two algorithms can be combined in one optical processor to extract all the basic geometric and amplitude features from objects embedded in video imagery. We show that the internal amplitude structure of objects is recovered by the Radon transform, which is a well-known result, but, in addition, we show simulation results that calculate angular correlation, a simple but unique algorithm that extracts object boundaries from suitably threshold images from which length, width, area, aspect ratio, and orientation can be derived. In addition to circumventing scale and rotation distortions, these simulations indicate that the features derived from the angular correlation algorithm are relatively insensitive to tracking shifts and image noise. Some optical architecture concepts, including one based on micro-optical lenslet arrays, have been developed to implement these algorithms. Simulation test and evaluation using simple synthetic object data will be described, including results of a study that uses object boundaries (derivable from angular correlation) to classify simple objects using a neural network.

Boone, Bradley G.↗

NASA NTRS1983

Reconstruction of the mutual coherence function for a moving source

The acoustic radiation of a randomly fluctuating source in motion is characterized analytically to determine the mutual coherence function (MCF). A far-field relation is derived via a series of invertible transformations, and a higher-dimension Radon transformation is performed to reconstruct the MCF; explicit formulas for computing the MCF from the transformed radiation data are provided. The technique is applied to the cases of an axisymmetric line source of finite extent moving at constant velocity along a line and a spatially incoherent line source. Applications to X-ray tomography and analysis of the noise emitted by a moving jet aircraft are suggested.

Chow, P. L.↗

NASA NTRS2009

Detection of Rossby Waves in Multi-Parameters in Multi-Mission Satellite Observations and HYCOM Simulations in the Indian Ocean

Rossby waves are difficult to detect with in situ methods. However, as we show in this paper, they can be clearly identified in multi-parameters in multi-mission satellite observations of sea surface height (SSH), sea surface temperature (SST) and ocean color observations of chlorophyll-a (chl-a), as well as 1/12-deg global HYbrid Coordinate Ocean Model (HYCOM) simulations of SSH, SST and sea surface salinity (SSS) in the Indian Ocean. While the surface structure of Rossby waves can be elucidated from comparisons of the signal in different sea surface parameters, models are needed to gain direct information about how these waves affect the ocean at depth. The first three baroclinic modes of the Rossby waves are inferred from the Fast Fourier Transform (FFT), and two-dimensional Radon Transform (2D RT). At many latitudes the first and second baroclinic mode Rossby wave phase speeds from satellite observations and model parameters are identified.

SSH (SEA SURFACE HEIGHT)↗

NASA NTRS2014

A Semiautomated Multilayer Picking Algorithm for Ice-sheet Radar Echograms Applied to Ground-Based Near-Surface Data

Snow accumulation over an ice sheet is the sole mass input, making it a primary measurement for understanding the past, present, and future mass balance. Near-surface frequency-modulated continuous-wave (FMCW) radars image isochronous firn layers recording accumulation histories. The Semiautomated Multilayer Picking Algorithm (SAMPA) was designed and developed to trace annual accumulation layers in polar firn from both airborne and ground-based radars. The SAMPA algorithm is based on the Radon transform (RT) computed by blocks and angular orientations over a radar echogram. For each echogram's block, the RT maps firn segmented-layer features into peaks, which are picked using amplitude and width threshold parameters of peaks. A backward RT is then computed for each corresponding block, mapping the peaks back into picked segmented-layers. The segmented layers are then connected and smoothed to achieve a final layer pick across the echogram. Once input parameters are trained, SAMPA operates autonomously and can process hundreds of kilometers of radar data picking more than 40 layers. SAMPA final pick results and layer numbering still require a cursory manual adjustment to correct noncontinuous picks, which are likely not annual, and to correct for inconsistency in layer numbering. Despite the manual effort to train and check SAMPA results, it is an efficient tool for picking multiple accumulation layers in polar firn, reducing time over manual digitizing efforts. The trackability of good detected layers is greater than 90%.

Antarctic Ice-Sheet↗

NASA NTRS2013

Measuring Temperature-Dependent Propagating Disturbances in Coronal Fan Loops Using Multiple SDO-AIA Channels and Surfing Transform Technique

A set of co-aligned high resolution images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) is used to investigate propagating disturbances (PDs) in warm fan loops at the periphery of a non-flaring active region NOAA AR 11082. To measure PD speeds at multiple coronal temperatures, a new data analysis methodology is proposed enabling quantitative description of sub visual coronal motions with low signal-to-noise ratios of the order of 0.1. The technique operates with a set of one-dimensional surfing signals extracted from position-timeplots of several AIA channels through a modified version of Radon transform. The signals are used to evaluate a two-dimensional power spectral density distribution in the frequency - velocity space which exhibits a resonance in the presence of quasi-periodic PDs. By applying this analysis to the same fan loop structures observed in several AIA channels, we found that the traveling velocity of PDs increases with the temperature of the coronal plasma following the square root dependence predicted for the slow mode magneto-acoustic wave which seems to be the dominating wave mode in the studied loop structures. This result extends recent observations by Kiddie et al. (2012) to a more general class of fan loop systems not associated with sunspots and demonstrating consistent slow mode activity in up to four AIA channels.

Solar Corona↗

NASA NTRS1998

Phase Inversion: Inferring Solar Subphotospheric Flow and Other Asphericity from the Distortion of Acoustic Waves

A method is proposed for analyzing an almost monochromatic train of waves propagating in a single direction in an inhomogeneous medium that is not otherwise changing in time. An effective phase is defined in terms of the Hilbert transform of the wave function, which is related, via the JWKB approximation, to the spatial variation of the background state against which the wave is propagating. The contaminating effect of interference between the truly monochromatic components of the train is eliminated using its propagation properties. Measurement errors, provided they are uncorrelated, are manifest as rapidly varying noise; although that noise can dominate the raw phase-processed signal, it can largely be removed by low-pass filtering. The intended purpose of the analysis is to determine the distortion of solar oscillations induced by horizontal structural variation and material flow. It should be possible to apply the method directly to sectoral modes. The horizontal phase distortion provides a measure of longitudinally averaged properties of the Sun in the vicinity of the equator, averaged also in radius down to the depth to which the modes penetrate. By combining such averages from different modes, the two-dimensional variation can be inferred by standard inversion techniques. After taking due account of horizontal refraction, it should be possible to apply the technique also to locally sectoral modes that propagate obliquely to the equator and thereby build a network of lateral averages at each radius, from which the full three-dimensional structure of the Sun can, in principle, be determined as an inverse Radon transform.

Gough, Douglas↗

NASA NTRS1984

Neutrino tomography - Tevatron mapping versus the neutrino sky

The feasibility of neutrino tomography of the earth's interior is discussed, taking the 80-GeV W-boson mass determined by Arnison (1983) and Banner (1983) into account. The opacity of earth zones is calculated on the basis of the preliminary reference earth model of Dziewonski and Anderson (1981), and the results are presented in tables and graphs. Proposed tomography schemes are evaluated in terms of the well-posedness of the inverse-Radon-transform problems involved, the neutrino generators and detectors required, and practical and economic factors. The ill-posed schemes are shown to be infeasible; the well-posed schemes (using Tevatrons or the neutrino sky as sources) are considered feasible but impractical.

Wilson, T. L.↗

NASA NTRS1984

Tomography by iterative convolution - Empirical study and application to interferometry

An algorithm for computer tomography has been developed that is applicable to reconstruction from data having incomplete projections because an opaque object blocks some of the probing radiation as it passes through the object field. The algorithm is based on iteration between the object domain and the projection (Radon transform) domain. Reconstructions are computed during each iteration by the well-known convolution method. Although it is demonstrated that this algorithm does not converge, an empirically justified criterion for terminating the iteration when the most accurate estimate has been computed is presented. The algorithm has been studied by using it to reconstruct several different object fields with several different opaque regions. It also has been used to reconstruct aerodynamic density fields from interferometric data recorded in wind tunnel tests.

Vest, C. M.↗

NASA NTRS1985

The observation of atmospheric structure with TOMS and some potential advancements

An overview is given of the Nimbus 7 Total Ozone Mapping Spectrometer (TOMS) which was designed to observe the spatial characteristics of total ozone that were not resolved by the nadir-viewing Nimbus BUV and SBUV instruments. At the wavelengths suitable for total ozone measurements, the radiance is large enough that the entire daytime atmosphere could be surveyed with about 50-km resolution from a polar orbiting satellite. The resulting high spatial resolution TOMS ozone images are found to reflect the internal dynamic structure of the lower atmosphere. Features which can be identified and tracked include: planetary wave scale troughs and ridges, mesoscale cutoff lows and rapidly moving troughs, jet stream confluence and difluence areas, hurricanes, and polar night lows. These features control the ozone above any given location and account for nearly all the variance in the total ozone. The instrument has been used to track the volcanic eruption clouds from El Chichon, Mount St. Helens, Alaid, and smaller eruptions such as Galunggung. It would be feasible to use a similar instrument on a geostationary platform to obtain half-hourly maps. Determination of the vertical ozone distribution in the lower stratosphere using Radon transform principles would be of importance in measuring jet stream folds and the related troposphere-stratosphere exchange.

Krueger, A. J.↗

NASA NTRS1997

Rapid Decimation for Direct Volume Rendering

An approach for eliminating unnecessary portions of a volume when producing a direct volume rendering is described. This reduction in volume size sacrifices some image quality in the interest of rendering speed. Since volume visualization is often used as an exploratory visualization technique, it is important to reduce rendering times, so the user can effectively explore the volume. The methods presented can speed up rendering by factors of 2 to 3 with minor image degradation. A family of decimation algorithms to reduce the number of primitives in the volume without altering the volume's grid in any way is introduced. This allows the decimation to be computed rapidly, making it easier to change decimation levels on the fly. Further, because very little extra space is required, this method is suitable for the very large volumes that are becoming common. The method is also grid-independent, so it is suitable for multiple overlapping curvilinear and unstructured, as well as regular, grids. The decimation process can proceed automatically, or can be guided by the user so that important regions of the volume are decimated less than unimportant regions. A formal error measure is described based on a three-dimensional analog of the Radon transform. Decimation methods are evaluated based on this metric and on direct comparison with reference images.

Gibbs, Jonathan↗

NASA NTRS1997

Near Real-Time Imaging of the Galactic Plane with BATSE

The discovery of new transient or persistent sources in the hard X-ray regime with the BATSE Earth occultation Technique has been limited previously to bright sources of about 200 mCrab or more. While monitoring known source locations is not a problem to a daily limiting sensitivity of about 75 mCrab, the lack of a reliable background model forces us to use more intensive computer techniques to find weak, previously unknown emission from hard X-ray/gamma sources. The combination of Radon transform imaging of the galactic plane in 10 by 10 degree fields and the Harvard/CFA-developed Image Search (CBIS) allows us to straightforwardly search the sky for candidate sources in a +/- 20 degree latitude band along the plane. This procedure has been operating routinely on a weekly basis since spring 1997. We briefly describe the procedure, then concentrate on the performance aspects of the technique and candidate source results from the search.

Harmon, B. A.↗

NASA NTRS2012

Validation of Atmosphere/Ionosphere Signals Associated with Major Earthquakes by Multi-Instrument Space-Borne and Ground Observations

The latest catastrophic earthquake in Japan (March 2011) has renewed interest in the important question of the existence of pre-earthquake anomalous signals related to strong earthquakes. Recent studies have shown that there were precursory atmospheric/ionospheric signals observed in space associated with major earthquakes. The critical question, still widely debated in the scientific community, is whether such ionospheric/atmospheric signals systematically precede large earthquakes. To address this problem we have started to investigate anomalous ionospheric / atmospheric signals occurring prior to large earthquakes. We are studying the Earth's atmospheric electromagnetic environment by developing a multisensor model for monitoring the signals related to active tectonic faulting and earthquake processes. The integrated satellite and terrestrial framework (ISTF) is our method for validation and is based on a joint analysis of several physical and environmental parameters (thermal infrared radiation, electron concentration in the ionosphere, lineament analysis, radon/ion activities, air temperature and seismicity) that were found to be associated with earthquakes. A physical link between these parameters and earthquake processes has been provided by the recent version of Lithosphere-Atmosphere-Ionosphere Coupling (LAIC) model. Our experimental measurements have supported the new theoretical estimates of LAIC hypothesis for an increase in the surface latent heat flux, integrated variability of outgoing long wave radiation (OLR) and anomalous variations of the total electron content (TEC) registered over the epicenters. Some of the major earthquakes are accompanied by an intensification of gas migration to the surface, thermodynamic and hydrodynamic processes of transformation of latent heat into thermal energy and with vertical transport of charged aerosols in the lower atmosphere. These processes lead to the generation of external electric currents in specific regions of the atmosphere and the modifications, by dc electric fields, in the ionosphere-atmosphere electric circuit. We retrospectively analyzed temporal and spatial variations of four different physical parameters (gas/radon counting rate, lineaments change, long-wave radiation transitions and ionospheric electron density/plasma variations) characterizing the state of the lithosphere/atmosphere coupling several days before the onset of the earthquakes. Validation processes consist in two phases: A. Case studies for seven recent major earthquakes: Japan (M9.0, 2011), China (M7.9, 2008), Italy (M6.3, 2009), Samoa (M7, 2009), Haiti (M7.0, 2010) and, Chile (M8.8, 2010) and B. A continuous retrospective analysis was preformed over two different regions with high seismicity- Taiwan and Japan for 2003-2009. Satellite, ground surface, and troposphere data were obtained from Terra/ASTER, Aqua/AIRS, POES and ionospheric variations from DEMETER and COSMIC-I data. Radon and GPS/TEC were obtaining from monitoring sites in Taiwan, Japan and Italy and from global ionosphere maps (GIM) respectively. Our analysis of ground and satellite data during the occurrence of 7 global earthquakes has shown the presence of anomalies in the atmosphere. Our results for Tohoku M9.0 earthquake show that on March 7th, 2011 (4 days before the main shock and 1 day before the M7.2 foreshock of March 8, 2011) a rapid increase of emitted infrared radiation was observed by the satellite data and an anomaly was developed near the epicenter. The GPS/TEC data indicate an increase and variation in electron density reaching a maximum value on March 8. From March 3 to 11 a large increase in electron concentration was recorded at all four Japanese ground-based ionosondes, which returned to normal after the main earthquake. Similar approach for analyzing atmospheric and ionospheric parameters has been applied for China (M7.9, 2008), Italy (M6.3, 2009), Samoa (M7, 2009), Haiti (M7.0, 2010) and Chile (M8.8, 2010) eahquakes. Results have revealed the presence of related variations of these parameters implying their connection with the earthquake process. The second phase (B) of this validation included 102 major earthquakes (M>5.9) in Taiwan and Japan. We have found anomalous behavior before all of these events with no false negatives. False alarm ratio for false positives is less then 10% and has been calculated for the same month of the earthquake occurrence for the entire period of analysis (2003-2009). The commonalities for detecting atmospheric/ionospheric anomalies are: i.) Regularly appearance over regions of maximum stress (i.e., along plate boundaries); ii.) Anomaly existence over land and sea; and iii) association with M>5.9 earthquakes not deeper than 100km. Due to their long duration over the same region these anomalies are not consistent with a meteorological origin. Our initial results from the ISTF validation of multi-instrument space-borne and ground observations show a systematic appearance of atmospheric anomalies near the epicentral area, one to seven (average) days prior to the largest earthquakes, and suggest that it could be explained by a coupling process between the observed physical parameters and the pre-earthquake preparation processes.

Ouzounov, Dimitar↗