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NASA NTRS2013

Science Opportunity Analyzer (SOA) Version 8

SOA allows scientists to plan spacecraft observations. It facilitates the identification of geometrically interesting times in a spacecraft s orbit that a user can use to plan observations or instrument-driven spacecraft maneuvers. These observations can then be visualized multiple ways in both two- and three-dimensional views. When observations have been optimized within a spacecraft's flight rules, the resulting plans can be output for use by other JPL uplink tools. Now in its eighth major version, SOA improves on these capabilities in a modern and integrated fashion. SOA consists of five major functions: Opportunity Search, Visualization, Observation Design, Constraint Checking, and Data Output. Opportunity Search is a GUI-driven interface to existing search engines that can be used to identify times when a spacecraft is in a specific geometrical relationship with other bodies in the solar system. This function can be used for advanced mission planning as well as for making last-minute adjustments to mission sequences in response to trajectory modifications. Visualization is a key aspect of SOA. The user can view observation opportunities in either a 3D representation or as a 2D map projection. Observation Design allows the user to orient the spacecraft and visualize the projection of the instrument field of view for that orientation using the same views as Opportunity Search. Constraint Checking is provided to validate various geometrical and physical aspects of an observation design. The user has the ability to easily create custom rules or to use official project-generated flight rules. This capability may also allow scientists to easily assess the cost to science if flight rule changes occur. Data Output allows the user to compute ancillary data related to an observation or to a given position of the spacecraft along its trajectory. The data can be saved as a tab-delimited text file or viewed as a graph. SOA combines science planning functionality unique to both JPL and the sponsoring spacecraft. SOA is able to ingest JPL SPICE Kernels that are used to drive the tool and its computations. A Percy search engine is then included that identifies interesting time periods for the user to build observations. When observations are then built, flight-like orientation algorithms replicate spacecraft dynamics to closely simulate the flight spacecraft s dynamics. SOA v8 represents large steps forward from SOA v7 in terms of quality, reliability, maintainability, efficiency, and user experience. A tailored agile development environment has been built around SOA that provides automated unit testing, continuous build and integration, a consolidated Web-based code and documentation storage environment, modern Java enhancements, and a focus on usability

Witoff, Robert J.↗
NASA NTRS2012

Rainbow Fourier Transform

We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).

Alexandrov, Mikhail D.↗
NASA NTRS2012

Linear Estimation of Particle Bulk Parameters from Multi-Wavelength Lidar Measurements

An algorithm for linear estimation of aerosol bulk properties such as particle volume, effective radius and complex refractive index from multiwavelength lidar measurements is presented. The approach uses the fact that the total aerosol concentration can well be approximated as a linear combination of aerosol characteristics measured by multiwavelength lidar. Therefore, the aerosol concentration can be estimated from lidar measurements without the need to derive the size distribution, which entails more sophisticated procedures. The definition of the coefficients required for the linear estimates is based on an expansion of the particle size distribution in terms of the measurement kernels. Once the coefficients are established, the approach permits fast retrieval of aerosol bulk properties when compared with the full regularization technique. In addition, the straightforward estimation of bulk properties stabilizes the inversion making it more resistant to noise in the optical data. Numerical tests demonstrate that for data sets containing three aerosol backscattering and two extinction coefficients (so called 3 + 2 ) the uncertainties in the retrieval of particle volume and surface area are below 45% when input data random uncertainties are below 20 %. Moreover, using linear estimates allows reliable retrievals even when the number of input data is reduced. To evaluate the approach, the results obtained using this technique are compared with those based on the previously developed full inversion scheme that relies on the regularization procedure. Both techniques were applied to the data measured by multiwavelength lidar at NASA/GSFC. The results obtained with both methods using the same observations are in good agreement. At the same time, the high speed of the retrieval using linear estimates makes the method preferable for generating aerosol information from extended lidar observations. To demonstrate the efficiency of the method, an extended time series of observations acquired in Turkey in May 2010 was processed using the linear estimates technique permitting, for what we believe to be the first time, temporal-height distributions of particle parameters.

linear estimation↗
NASA NTRS2012

Helioseismology of a Realistic Magnetoconvective Sunspot Simulation

We compare helioseismic travel-time shifts measured from a realistic magnetoconvective sunspot simulation using both helioseismic holography and time-distance helioseismology, and measured from real sunspots observed with the Helioseismic and Magnetic Imager instrument on board the Solar Dynamics Observatory and the Michelson Doppler Imager instrument on board the Solar and Heliospheric Observatory. We find remarkable similarities in the travel-time shifts measured between the methodologies applied and between the simulated and real sunspots. Forward modeling of the travel-time shifts using either Born or ray approximation kernels and the sound-speed perturbations present in the simulation indicates major disagreements with the measured travel-time shifts. These findings do not substantially change with the application of a correction for the reduction of wave amplitudes in the simulated and real sunspots. Overall, our findings demonstrate the need for new methods for inferring the subsurface structure of sunspots through helioseismic inversions.

Sun-interior↗
NASA NTRS2013

Design of a Variational Multiscale Method for Turbulent Compressible Flows

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

Design↗
NASA NTRS2013

Evaluation of ACCMIP Outgoing Longwave Radiation from Tropospheric Ozone Using TES Satellite Observations.

We use simultaneous observations of tropospheric ozone and outgoing longwave radiation (OLR) sensitivity to tropospheric ozone from the Tropospheric Emission Spectrometer (TES) to evaluate model tropospheric ozone and its effect on OLR simulated by a suite of chemistry-climate models that participated in the Atmospheric Chemistry and Climate Model Intercomparison Project (ACCMIP). The ensemble mean of ACCMIP models show a persistent but modest tropospheric ozone low bias (5-20 ppb) in the Southern Hemisphere (SH) and modest high bias (5-10 ppb) in the Northern Hemisphere (NH) relative to TES ozone for 2005-2010. These ozone biases have a significant impact on the OLR. Using TES instantaneous radiative kernels (IRK), we show that the ACCMIP ensemble mean tropospheric ozone low bias leads up to 120mW/ sq. m OLR high bias locally but zonally compensating errors reduce the global OLR high bias to 39+/- 41mW/ sq. m relative to TES data. We show that there is a correlation (Sq. R = 0.59) between the magnitude of the ACCMIP OLR bias and the deviation of the ACCMIP preindustrial to present day (1750-2010) ozone radiative forcing (RF) from the ensemble ozone RF mean. However, this correlation is driven primarily by models whose absolute OLR bias from tropospheric ozone exceeds 100mW/ sq. m. Removing these models leads to a mean ozone radiative forcing of 394+/- 42mW/ sq. m. The mean is about the same and the standard deviation is about 30% lower than an ensemble ozone RF of 384 +/- 60mW/ sq. m derived from 14 of the 16 ACCMIP models reported in a companion ACCMIP study. These results point towards a profitable direction of combining satellite observations and chemistry-climate model simulations to reduce uncertainty in ozone radiative forcing.

troposphere↗
NASA NTRS2014

Space Radiation and the Challenges Towards Effective Shielding Solutions

The hazards of space radiation and their effective mitigation strategies continue to pose special science and technology challenges to NASA. It is widely accepted now that shielding space vehicles and structures will have to rely on new and innovative materials since aluminum, like all high Z materials, are poor shields against the particulate and highly ionizing nature of space radiation. Shielding solutions, motivated and constrained by power and mass limitations, couple this realization with "multifunctionality," both in design concept as well as in material function and composition. Materials endowed with effective shielding properties as well as with some degree of multi‐functionality may be the kernel of the so‐called "radiation‐smart" structures and designs. This talk will present some of the challenges and potential mitigation ideas towards the realization of such structures and designs.

Barghouty, Abdulnasser↗
NASA NTRS2014

Attendee Response to Guiding Questions of the September 2014 DOE Workshop on North Slope of Alaska Priorities

We advocate for several modeling approaches suitable to prove understanding of and capability to model aerosol behavior in nucleating droplets and ice and to model regional cloud systems at the mesoscale. The full complement of data that is ideal for particular study types is increasingly well understood; the ASR ISDAC Science Plan provides an excellent example of listing the data required for each study type targeted by that campaign. Whereas discussion here focused on the microscale and mesoscale, other studies should obviously focus on the regional, seasonal and global scale. When considering ice microphysics alone, laser focus on unconstrained model components could be usefully intensified (e.g., collision-coalescence kernels). Similarly, a focus on boundary layer structure would be deeply valuable to a wide range of model types. The expense of observations motivates efficient planning for observational data sets to support specific study approaches; the concept of closure is often useful (e.g., the surface energy budget).

nucleation↗
NASA NTRS2012

Iterative Atmospheric Correction Scheme and the Polarization Color of Alpine Snow

Characterization of the Earth's surface is crucial to remote sensing, both to map geomorphological features and because subtracting this signal is essential during retrievals of the atmospheric constituents located between the surface and the sensor. Current operational algorithms model the surface total reflectance through a weighted linear combination of a few geometry-dependent kernels, each devised to describe a particular scattering mechanism. The information content of these measurements is overwhelmed by that of instruments with polarization capabilities: proposed models in this case are based on the Fresnel reflectance of an isotropic distribution of facets. Because of its remarkable lack of spectral contrast, the polarized reflectance of land surfaces in the shortwave infrared spectral region, where atmospheric scattering is minimal, can be used to model the surface also at shorter wavelengths, where aerosol retrievals are attempted based on well-established scattering theories. In radiative transfer simulations, straightforward separation of the surface and atmospheric contributions is not possible without approximations because of the coupling introduced by multiple reflections. Within a general inversion framework, the problem can be eliminated by linearizing the radiative transfer calculation, and making the Jacobian (i.e., the derivative expressing the sensitivity of the reflectance with respect to model parameters) available at output. We present a general methodology based on a Gauss-Newton iterative search, which automates this procedure and eliminates de facto the need of an ad hoc atmospheric correction. In this case study we analyze the color variations in the polarized reflectance measured by the NASA Goddard Institute of Space Studies Research Scanning Polarimeter during a survey of late-season snowfields in the High Sierra. This insofar unique dataset presents challenges linked to the rugged topography associated with the alpine environment and a likely high water content due to melting. The analysis benefits from ancillary information provided by the NASA Langley High Spectral Resolution Lidar deployed on the same aircraft. The results obtained from the iterative scheme are contrasted against the surface polarized reflectance obtained ignoring multiple reflections, via the simplistic subtraction of the atmospheric scattering contribution. Finally, the retrieved reflectance is modeled after the scattering properties of a dense collection of ice crystals at the surface. Confirming that the polarized reflectance of snow is spectrally flat would allow to extend the techniques already in use for polarimetric retrievals of aerosol properties over land to the large portion of snow-covered pixels plaguing orbital and suborbital observations.

Polarized BRDF↗
NASA NTRS2013

File Specification for GEOS-5 FP (Forward Processing)

The GEOS-5 FP Atmospheric Data Assimilation System (GEOS-5 ADAS) uses an analysis developed jointly with NOAA's National Centers for Environmental Prediction (NCEP), which allows the Global Modeling and Assimilation Office (GMAO) to take advantage of the developments at NCEP and the Joint Center for Satellite Data Assimilation (JCSDA). The GEOS-5 AGCM uses the finite-volume dynamics (Lin, 2004) integrated with various physics packages (e.g, Bacmeister et al., 2006), under the Earth System Modeling Framework (ESMF) including the Catchment Land Surface Model (CLSM) (e.g., Koster et al., 2000). The GSI analysis is a three-dimensional variational (3DVar) analysis applied in grid-point space to facilitate the implementation of anisotropic, inhomogeneous covariances (e.g., Wu et al., 2002; Derber et al., 2003). The GSI implementation for GEOS-5 FP incorporates a set of recursive filters that produce approximately Gaussian smoothing kernels and isotropic correlation functions. The GEOS-5 ADAS is documented in Rienecker et al. (2008). More recent updates to the model are presented in Molod et al. (2011). The GEOS-5 system actively assimilates roughly 2 × 10(exp 6) observations for each analysis, including about 7.5 × 10(exp 5) AIRS radiance data. The input stream is roughly twice this volume, but because of the large volume, the data are thinned commensurate with the analysis grid to reduce the computational burden. Data are also rejected from the analysis through quality control procedures designed to detect, for example, the presence of cloud. To minimize the spurious periodic perturbations of the analysis, GEOS-5 FP uses the Incremental Analysis Update (IAU) technique developed by Bloom et al. (1996). More details of this procedure are given in Appendix A. The assimilation is performed at a horizontal resolution of 0.3125-degree longitude by 0.25- degree latitude and at 72 levels, extending to 0.01 hPa. All products are generated at the native resolution of the horizontal grid. The majority of data products are time-averaged, but four instantaneous products are also available. Hourly data intervals are used for two-dimensional products, while 3-hourly intervals are used for three-dimensional products. These may be on the model's native 72-layer vertical grid or at 42 pressure surfaces extending to 0.1 hPa. This document describes the gridded output files produced by the GMAO near real-time operational FP, using the most recent version of the GEOS-5 assimilation system. Additional details about variables listed in this file specification can be found in a separate document, the GEOS-5 File Specification Variable Definition Glossary. Documentation about the current access methods for products described in this document can be found on the GMAO products page: http://gmao.gsfc.nasa.gov/products/.

GSI↗
NASA NTRS2013

File Specification for GEOS-5 FP-IT (Forward Processing for Instrument Teams)

The GEOS-5 FP-IT Atmospheric Data Assimilation System (GEOS-5 ADAS) uses an analysis developed jointly with NOAA's National Centers for Environmental Prediction (NCEP), which allows the Global Modeling and Assimilation Office (GMAO) to take advantage of the developments at NCEP and the Joint Center for Satellite Data Assimilation (JCSDA). The GEOS-5 AGCM uses the finite-volume dynamics (Lin, 2004) integrated with various physics packages (e.g, Bacmeister et al., 2006), under the Earth System Modeling Framework (ESMF) including the Catchment Land Surface Model (CLSM) (e.g., Koster et al., 2000). The GSI analysis is a three-dimensional variational (3DVar) analysis applied in grid-point space to facilitate the implementation of anisotropic, inhomogeneous covariances (e.g., Wu et al., 2002; Derber et al., 2003). The GSI implementation for GEOS-5 FP-IT incorporates a set of recursive filters that produce approximately Gaussian smoothing kernels and isotropic correlation functions. The GEOS-5 ADAS is documented in Rienecker et al. (2008). More recent updates to the model are presented in Molod et al. (2011). The GEOS-5 system actively assimilates roughly 2 × 10(exp 6) observations for each analysis, including about 7.5 × 10(exp 5) AIRS radiance data. The input stream is roughly twice this volume, but because of the large volume, the data are thinned commensurate with the analysis grid to reduce the computational burden. Data are also rejected from the analysis through quality control procedures designed to detect, for example, the presence of cloud. To minimize the spurious periodic perturbations of the analysis, GEOS-5 FP-IT uses the Incremental Analysis Update (IAU) technique developed by Bloom et al. (1996). More details of this procedure are given in Appendix A. The analysis is performed at a horizontal resolution of 0.625-degree longitude by 0.5-degree latitude and at 72 levels, extending to 0.01 hPa. All products are generated at the native resolution of the horizontal grid. The majority of data products are time-averaged, but four instantaneous products are also available. Hourly data intervals are used for two-dimensional products, while 3-hourly intervals are used for three-dimensional products. These may be on the model's native 72-layer vertical grid or at 42 pressure surfaces extending to 0.1 hPa. This document describes the gridded output files produced by the GMAO near real-time operational GEOS-5 FP-IT processing in support of the EOS instrument teams. Additional details about variables listed in this file specification can be found in a separate document, the GEOS-5 File Specification Variable Definition Glossary.

3D Var↗
NASA NTRS2014

A Numerical Testbed for Remote Sensing of Aerosols, and its Demonstration for Evaluating Retrieval Synergy from a Geostationary Satellite Constellation of GEO-CAPE and GOES-R

We present a numerical testbed for remote sensing of aerosols, together with a demonstration for evaluating retrieval synergy from a geostationary satellite constellation. The testbed combines inverse (optimal-estimation) software with a forward model containing linearized code for computing particle scattering (for both spherical and non-spherical particles), a kernel-based (land and ocean) surface bi-directional reflectance facility, and a linearized radiative transfer model for polarized radiance. Calculation of gas absorption spectra uses the HITRAN (HIgh-resolution TRANsmission molecular absorption) database of spectroscopic line parameters and other trace species cross-sections. The outputs of the testbed include not only the Stokes 4-vector elements and their sensitivities (Jacobians) with respect to the aerosol single scattering and physical parameters (such as size and shape parameters, refractive index, and plume height), but also DFS (Degree of Freedom for Signal) values for retrieval of these parameters. This testbed can be used as a tool to provide an objective assessment of aerosol information content that can be retrieved for any constellation of (planned or real) satellite sensors and for any combination of algorithm design factors (in terms of wavelengths, viewing angles, radiance and/or polarization to be measured or used). We summarize the components of the testbed, including the derivation and validation of analytical formulae for Jacobian calculations. Benchmark calculations from the forward model are documented. In the context of NASA's Decadal Survey Mission GEOCAPE (GEOstationary Coastal and Air Pollution Events), we demonstrate the use of the testbed to conduct a feasibility study of using polarization measurements in and around the O2 A band for the retrieval of aerosol height information from space, as well as an to assess potential improvement in the retrieval of aerosol fine and coarse mode aerosol optical depth (AOD) through the synergic use of two future geostationary satellites, GOES-R (Geostationary Operational Environmental Satellite R-series) and TEMPO (Tropospheric Emissions: Monitoring of Pollution). Strong synergy between GEOS-R and TEMPO are found especially in their characterization of surface bi-directional reflectance, and thereby, can potentially improve the AOD retrieval to the accuracy required by GEO-CAPE.

Aerosols↗
NASA NTRS2014

Visible Motion Blur

A method of measuring motion blur is disclosed comprising obtaining a moving edge temporal profile r(sub 1)(k) of an image of a high-contrast moving edge, calculating the masked local contrast m(sub1)(k) for r(sub 1)(k) and the masked local contrast m(sub 2)(k) for an ideal step edge waveform r(sub 2)(k) with the same amplitude as r(sub 1)(k), and calculating the measure or motion blur Psi as a difference function, The masked local contrasts are calculated using a set of convolution kernels scaled to simulate the performance of the human visual system, and Psi is measured in units of just-noticeable differences.

Watson, Andrew B.↗
NASA NTRS2011

Testing of the Support Vector Machine for Binary-Class Classification

The Support Vector Machine is a powerful algorithm, useful in classifying data in to species. The Support Vector Machines implemented in this research were used as classifiers for the final stage in a Multistage Autonomous Target Recognition system. A single kernel SVM known as SVMlight, and a modified version known as a Support Vector Machine with K-Means Clustering were used. These SVM algorithms were tested as classifiers under varying conditions. Image noise levels varied, and the orientation of the targets changed. The classifiers were then optimized to demonstrate their maximum potential as classifiers. Results demonstrate the reliability of SMV as a method for classification. From trial to trial, SVM produces consistent results

autonomous target recognition systemr↗
NASA NTRS2009

Simulating and Detecting Radiation-Induced Errors for Onboard Machine Learning

Spacecraft processors and memory are subjected to high radiation doses and therefore employ radiation-hardened components. However, these components are orders of magnitude more expensive than typical desktop components, and they lag years behind in terms of speed and size. We have integrated algorithm-based fault tolerance (ABFT) methods into onboard data analysis algorithms to detect radiation-induced errors, which ultimately may permit the use of spacecraft memory that need not be fully hardened, reducing cost and increasing capability at the same time. We have also developed a lightweight software radiation simulator, BITFLIPS, that permits evaluation of error detection strategies in a controlled fashion, including the specification of the radiation rate and selective exposure of individual data structures. Using BITFLIPS, we evaluated our error detection methods when using a support vector machine to analyze data collected by the Mars Odyssey spacecraft. We found ABFT error detection for matrix multiplication is very successful, while error detection for Gaussian kernel computation still has room for improvement.

data analysis↗
NASA NTRS2010

A High-Throughput, Adaptive FFT Architecture for FPGA-Based Space-Borne Data Processors

Historically, computationally-intensive data processing for space-borne instruments has heavily relied on ground-based computing resources. But with recent advances in functional densities of Field-Programmable Gate-Arrays (FPGAs), there has been an increasing desire to shift more processing on-board; therefore relaxing the downlink data bandwidth requirements. Fast Fourier Transforms (FFTs) are commonly used building blocks for data processing applications, with a growing need to increase the FFT block size. Many existing FFT architectures have mainly emphasized on low power consumption or resource usage; but as the block size of the FFT grows, the throughput is often compromised first. In addition to power and resource constraints, space-borne digital systems are also limited to a small set of space-qualified memory elements, which typically lag behind the commercially available counterparts in capacity and bandwidth. The bandwidth limitation of the external memory creates a bottleneck for a large, high-throughput FFT design with large block size. In this paper, we present the Multi-Pass Wide Kernel FFT (MPWK-FFT) architecture for a moderately large block size (32K) with considerations to power consumption and resource usage, as well as throughput. We will also show that the architecture can be easily adapted for different FFT block sizes with different throughput and power requirements. The result is completely contained within an FPGA without relying on external memories. Implementation results are summarized.

Nguyen, Kayla↗
NASA NTRS2012

Determining Wheel-Soil Interaction Loads Using a Meshfree Finite Element Approach Assisting Future Missions with Rover Wheel Design

A wheel experiencing sinkage and slippage events poses a high risk to rover missions as evidenced by recent mobility challenges on the Mars Exploration Rover (MER) project. Because several factors contribute to wheel sinkage and slippage conditions such as soil composition, large deformation soil behavior, wheel geometry, nonlinear contact forces, terrain irregularity, etc., there are significant benefits to modeling these events to a sufficient degree of complexity. For the purposes of modeling wheel sinkage and slippage at an engineering scale, meshfree finite element approaches enable simulations that capture sufficient detail of wheel-soil interaction while remaining computationally feasible. This study demonstrates some of the large deformation modeling capability of meshfree methods and the realistic solutions obtained by accounting for the soil material properties. A benchmark wheel-soil interaction problem is developed and analyzed using a specific class of meshfree methods called Reproducing Kernel Particle Method (RKPM). The benchmark problem is also analyzed using a commercially available finite element approach with Lagrangian meshing for comparison. RKPM results are comparable to classical pressure-sinkage terramechanics relationships proposed by Bekker-Wong. Pending experimental calibration by future work, the meshfree modeling technique will be a viable simulation tool for trade studies assisting rover wheel design.

Contreras, Michael T.↗
NASA NTRS2015

Measurement of Flaw Size From Thermographic Data

Simple methods for reducing the pulsed thermographic responses of delaminations tend to overestimate the size of the delamination, since the heat diffuses in the plane parallel to the surface. The result is a temperature profile over the delamination which is larger than the delamination size. A variational approach is presented for reducing the thermographic data to produce an estimated size for a flaw that is much closer to the true size of the delamination. The method is based on an estimate for the thermal response that is a convolution of a Gaussian kernel with the shape of the flaw. The size is determined from both the temporal and spatial thermal response of the exterior surface above the delamination and constraints on the length of the contour surrounding the delamination. Examples of the application of the technique to simulation and experimental data are presented to investigate the limitations of the technique.

Winfree, William P.↗

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