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At least 163 records · Page 9

A Tool for the Automated Collection of Space Utilization Data: Three Dimensional Space Utilization Monitor

Space Human Factors and Habitability (SHFH) Element within the Human Research Program (HRP) and the Behavioral Health and Performance (BHP) Element are conducting research regarding Net Habitable Volume (NHV), the internal volume within a spacecraft or habitat that is available to crew for required activities, as well as layout and accommodations within the volume. NASA needs methods to unobtrusively collect NHV data without impacting crew time. Data required includes metrics such as location and orientation of crew, volume used to complete tasks, internal translation paths, flow of work, and task completion times. In less constrained environments methods exist yet many are obtrusive and require significant post-processing. Examplesused in terrestrial settings include infrared (IR) retro-reflective marker based motion capture, GPS sensor tracking, inertial tracking, and multi-camera methods Due to constraints of space operations many such methods are infeasible. Inertial tracking systems typically rely upon a gravity vector to normalize sensor readings,and traditional IR systems are large and require extensive calibration. However, multiple technologies have not been applied to space operations for these purposes. Two of these include: 3D Radio Frequency Identification Real-Time Localization Systems (3D RFID-RTLS) Depth imaging systems which allow for 3D motion capture and volumetric scanning (such as those using IR-depth cameras like the Microsoft Kinect or Light Detection and Ranging / Light-Radar systems, referred to as LIDAR)

Vos, Gordon A.↗

Advances in LADAR Components and Subsystems at Raytheon

Raytheon is developing NIR sensor chip assemblies (SCAs) for scanning and staring 3D LADAR systems. High sensitivity is obtained by integrating high performance detectors with gain, i.e., APDs with very low noise Readout Integrated Circuits (ROICs). Unique aspects of these designs include: independent acquisition (non-gated) of pulse returns, multiple pulse returns with both time and intensity reported to enable full 3D reconstruction of the image. Recent breakthrough in device design has resulted in HgCdTe APDs operating at 300K with essentially no excess noise to gains in excess of 100, low NEP <1nW and GHz bandwidths and have demonstrated linear mode photon counting. SCAs utilizing these high performance APDs have been integrated and demonstrated excellent spatial and range resolution enabling detailed 3D imagery both at short range and long ranges. In the following we will review progress in real-time 3D LADAR imaging receiver products in three areas: (1) scanning 256 x 4 configuration for the Multi-Mode Sensor Seeker (MMSS) program and (2) staring 256 x 256 configuration for the Autonomous Landing and Hazard Avoidance Technology (ALHAT) lunar landing mission and (3) Photon-Counting SCAs which have demonstrated a dramatic reduction in dark count rate due to improved design, operation and processing.

Jack, Michael↗

Reconfigurable Hardware for Compressing Hyperspectral Image Data

High-speed, low-power, reconfigurable electronic hardware has been developed to implement ICER-3D, an algorithm for compressing hyperspectral-image data. The algorithm and parts thereof have been the topics of several NASA Tech Briefs articles, including Context Modeler for Wavelet Compression of Hyperspectral Images (NPO-43239) and ICER-3D Hyperspectral Image Compression Software (NPO-43238), which appear elsewhere in this issue of NASA Tech Briefs. As described in more detail in those articles, the algorithm includes three main subalgorithms: one for computing wavelet transforms, one for context modeling, and one for entropy encoding. For the purpose of designing the hardware, these subalgorithms are treated as modules to be implemented efficiently in field-programmable gate arrays (FPGAs). The design takes advantage of industry- standard, commercially available FPGAs. The implementation targets the Xilinx Virtex II pro architecture, which has embedded PowerPC processor cores with flexible on-chip bus architecture. It incorporates an efficient parallel and pipelined architecture to compress the three-dimensional image data. The design provides for internal buffering to minimize intensive input/output operations while making efficient use of offchip memory. The design is scalable in that the subalgorithms are implemented as independent hardware modules that can be combined in parallel to increase throughput. The on-chip processor manages the overall operation of the compression system, including execution of the top-level control functions as well as scheduling, initiating, and monitoring processes. The design prototype has been demonstrated to be capable of compressing hyperspectral data at a rate of 4.5 megasamples per second at a conservative clock frequency of 50 MHz, with a potential for substantially greater throughput at a higher clock frequency. The power consumption of the prototype is less than 6.5 W. The reconfigurability (by means of reprogramming) of the FPGAs makes it possible to effectively alter the design to some extent to satisfy different requirements without adding hardware. The implementation could be easily propagated to future FPGA generations and/or to custom application-specific integrated circuits.

Aranki, Nazeeh↗

Utilizing 3D-DIC on Mars 2020 Rover Wheel Assembly: Test-Analysis Correlation

Following the successful implementation of full-field photogrammetry, more specifically three-dimensional Digital Image Correlation (3D-DIC), on the Mars 2020 Heat Shield Structural Failure Review assessment, 3D-DIC was selected as one of the primary measurement techniques for the Mars 2020 Rover wheel assembly qualification test at the NASA Jet Propulsion Laboratory (JPL). To validate the Rover wheel landing loads simulations, it was extremely important to have high confidence in the wheel models. Due to the large deformations and strains that the wheel would be subject to during landing, traditional instrumentation such as linear variable displacement transducers (LVDTs), electrical-resistance strain gages and string potentiometers, would not be sufficient on their own to provide all the necessary validation data. Therefore, the NASA Engineering and Safety Center (NESC) provided the 3D-DIC expertise and support to measure the high deformation and strain in the wheel flexures and qualify the overall structural response of the Mars 2020 rover wheel assembly. There were two key objectives for the photogrammetry technique: (1) monitor the wheel response in real-time, guarding against anomalous behavior and failure, and (2) provide test data for test-analysis correlation to validate and/or improve the high-fidelity computational model. The contents of this paper will focus on the challenges of applying 3D-DIC to the Mars 2020 Rover wheel assembly and how these challenges were overcome. Examples of test-analysis correlation during the stiffness characterization and structural qualification will be presented and discussed in detail. Experimental results were compared with the analysis and showed excellent agreement between the predicted behavior and helped validate the high-fidelity models.

Mars 2020 Rover Wheel↗

3D Cloud Tomography and Droplet Size Retrieval from Multi-Angle Polarimetric Imaging of Scattered Sunlight from Above

Tomography aims to recover a three-dimensional (3D) density map of a medium or an object. In medical imaging,it is extensively used for diagnostics via X-ray computed tomography (CT). We define and derive a tomographyof cloud droplet distributions via passive remote sensing. We use multi-view polarimetric images to fit a 3Dpolarized radiative transfer (RT) forward model. Our motivation is 3D volumetric probing of vertically-developedconvectively-driven clouds that are ill-served by current methods in operational passive remote sensing. Currenttechniques are indeed based on strictly 1D RT modeling and applied to a single cloudy pixel, where cloud geometrydefaults to that of a plane-parallel slab. Incident unpolarized sunlight, once scattered by cloud droplets, changesits polarization state according to droplet size. Therefore, polarimetric measurements in the rainbow and gloryangular regions can be used to infer the droplet size distribution. This work defines and derives a framework for afull 3D tomography of cloud droplets for both their mass concentration in space and their distribution across arange of sizes. This gridded 3D retrieval of key microphysical properties is made tractable by our novel approachthat involves a restructuring and partial linearization of an open-source polarized 3D RT code to accommodate aspecial two-step iterative optimization technique. Physically-realistic synthetic clouds are used to demonstrate themethodology with rigorous uncertainty quantification, while a real-world cloud imaged by AirMSPI is processedto illustrate the new remote sensing capability

Schechner, Yoav Y.↗

Application of Scanning-Imaging X-Ray Microscopy to Fluid Inclusion Candidates in Carbonates of Carbonaceous Chondrites

In order to search for such fluid inclusions in carbonaceous chondrites, a nondestructive technique using x-ray micro-absorption tomography combined with FIB sampling was developed and applied to a carbonaceous chondrite. They found fluid inclusion candidates in calcite grains, which were formed by aqueous alteration. However, they could not determine whether they are really aqueous fluids or merely voids. Phase and absorption contrast images can be simultaneously obtained in 3D by using scanning-imaging x-ray microscopy (SIXM). In refractive index, n=1-sigma+i(beta), in the real part, 1-sigma is the refractive index with decrement, sigma, which is nearly proportional to the density, and the imaginary part, beta, is the extinction coefficient, which is related to the liner attenuation coefficient, mu. Many phases, including water and organic materials as well as minerals, can be identified by SIXM, and this technique has potential availability for Hayabusa-2 sample analysis too. In this study, we examined quantitative performance of d and m values and the spatial resolution in SIXM by using standard materials, and applied this technique to carbonaceous chondrite samples. We used POM ([CH2O]n), silicon, quartz, forsterite, corundum, magnetite and nickel as standard materials for examining the sigma and mu values. A fluid inclusion in terrestrial quartz and bi-valve shell (Atrina vexillum), which are composed of calcite and organic layers with different thickness, were also used for examining the spatial resolution. The Ivuna (CI) and Sutter's Mill (CM) meteorites were used as carbonaceous chondrite samples. Rod- or cube-shaped samples 20-30 micron in size were extracted by using FIB from cross-sectional surfaces of the standard materials or polished thin sections of the chondrites, which was previously observed with SEM. Then, the sample was attached to a thin W-needle and imaged by SIXM system at beamline BL47XU, SPring-8, Japan. The slice thickness was 109.3 nm and the pixel size was mostly 100 nm.

Tsuchiyama, Akira↗

Terrain tracking for lander guidance using binary phase-only spatial filters

We demonstrate the use of binary phase-only spatial filters (BPOFs) for tracking target sites through a sequence of gray-scale terrain images. The filters are demonstrated in a closed loop guidance system for a laboratory lander mockup. Images of a 3D terrain board taken by the lander's video camera are preprocessed to produce binary intensity contour maps of a simulated planetary surface. A BPOF is made from a section of the current preprocessed image centered on the exact desired landing site. After the lander has descended to a lower altitude, the BPOF is correlated with a new image. The position of the correlation peak is used in making the next filter and to guide the lander so as to recenter the landing site in the camera's view. We present testbed results of the accuracy with which a site may be tracted from orbit to landing, and the maximum scale, translation, and rotation which can be tolerated between subsequent images. Application of the results to NASA's proposed Mars Rover Sample Return (MRSR) and Mars Environmental Survey (MESUR) missions is discussed.

Reid, Max B.↗

First Flight of the Gamma-Ray Imager Polarimeter for Solar Flares (GRIPS) Instrument

The Gamma-Ray Imager/Polarimeter for Solar ares (GRIPS) instrument is a balloon-borne telescope designed to study solar-flare particle acceleration and transport. We describe GRIPS's first Antarctic long-duration flight in January 2016 and report preliminary calibration and science results. Electron and ion dynamics, particle abundances and the ambient plasma conditions in solar flares can be understood by examining hard X-ray (HXR) and gamma-ray emission (20 keV to 10 MeV). Enhanced imaging, spectroscopy and polarimetry of flare emissions in this energy range are needed to study particle acceleration and transport questions. The GRIPS instrument is specifically designed to answer questions including: What causes the spatial separation between energetic electrons producing hard X-rays and energetic ions producing gamma-ray lines? How anisotropic are the relativistic electrons, and why can they dominate in the corona? How do the compositions of accelerated and ambient material vary with space and time, and why? GRIPS's key technological improvements over the current solar state of the art at HXR/gamma-ray energies, the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI), include 3D position-sensitive germanium detectors (3D-GeDs) and a single-grid modulation collimator, the multi-pitch rotating modulator (MPRM). The 3D-GeDs have spectral FWHM resolution of a few hundred keV and spatial resolution less than 1cu mm. For photons that Compton scatter, usually greater or equal to 150 keV, the energy deposition sites can be tracked, providing polarization measurements as well as enhanced background reduction through Compton imaging. Each of GRIPS's detectors has 298 electrode strips read out with ASIC/FPGA electronics. In GRIPS's energy range, indirect imaging methods provide higher resolution than focusing optics or Compton imaging techniques. The MPRM grid-imaging system has a single-grid design which provides twice the throughput of a bi-grid imaging system like RHESSI. The grid is composed of 2.5 cm deep tungsten-copper slats, and quasi-continuous FWHM angular coverage from 12.5-162 arcsecs are achieved by varying the slit pitch between 1-13 mm. This angular resolution is capable of imaging the separate magnetic loop footpoint emissions in a variety of are sizes. In comparison, RHESSI's 35-arcsec resolution at similar energies makes the footpoints resolvable in only the largest ares.

Duncan, Nicole↗

Exocentric judgements in real environments and stereoscopic displays

Spatial direction errors during interpretation of perspective images, such as 3D map displays, may originate from misjudgment of the orientation of the viewing direction used to make the display. One source of these errors could be perceptual evidence of the display surface. Two experiments are reported in which the same judgment exocentric task was presented, but the cues to the picture surface were reduced or eliminated by presenting the task as a stereoscopic, virtual image or by a geometrically matched physical model. A theory developed to model exocentric direction errors on perspective displays has been fitted to the data from these two experiments. The parameters estimated from the fit in both experiments indicate that the subjects may be more correctly estimating the viewing direction than in ordinary perspective displays. Consequently, in some real world or stereo viewing conditions, errors in estimating the viewing direction are not likely to dominate exocentric direction errors.

Ellis, Stephen R.↗

Validation of Spherically Symmetric Inversion by Use of a Tomographically Reconstructed Three-Dimensional Electron Density of the Solar Corona

Determining the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (spherically symmetric inversion, SSI) was developed in the 1950s and has been widely applied to interpret various observations. However, to date there is no study of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 solar radius as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066).We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally smaller than about a factor of two; the former has the lower peak but extends more in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50 deg. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt), as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with the reconstruction by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.

corona↗

Image processing methods in two and three dimensions used to animate remotely sensed data

Image processing methods and software used to animate nonimaging remotely sensed data on cloud cover are described. Three FORTRAN programs were written in the VICAR2/TAE image processing domain to perform 3D perspective rendering, to interactively select parameters controlling the projection, and to interpolate parameter sets for animation images between key frames. Operation of the 3D programs and transferring the images to film is automated using executive control language and custom hardware to link the computer and camera.

Hussey, K. J.↗

Upcoming Lunar Mission Landing Sites: Viewing and Analysis with Celestial Mapping System

The Celestial Mapping System (CMS) is a powerful software platform designed to create virtual 3D globes for celestial bodies within our solar system, with a specific focus on lunar mapping. CMS offers a rich array of functionalities, including high-resolution imagery visualization, precise measurement tools, and analytical capabilities that cater to the needs of planetary scientists and mission planners. This abstract explores how CMS has been leveraged to conduct in-depth analyses of 12 lunar missions to the South Pole, including missions like Chandraayan 3, Russian Space Agency's Luna 25, Xelene 1, and Intuitive Machines Nova-C lander I. Moreover, the integration of HORUS (Hyper-effective nOise Removal Unit Software) into CMS enhances its capabilities, allowing for the rendering of images in a 3D globe format and providing visibility into permanently shadowed regions. CMS represents a cutting-edge tool for lunar surface awareness, equipment placement planning, and traverse path optimization

Moon↗

Effect of Clouds on Optical Imaging of the Space Shuttle During the Ascent Phase: A Statistical Analysis Based on a 3D Model

Clouds are highly effective in obscuring optical images of the Space Shuttle taken during its ascent by ground-based and airborne tracking cameras. Because the imagery is used for quick-look and post-flight engineering analysis, the Columbia Accident Investigation Board (CAIB) recommended the return-to-flight effort include an upgrade of the imaging system to enable it to obtain at least three useful views of the Shuttle from lift-off to at least solid rocket booster (SRB) separation (NASA 2003). The lifetimes of individual cloud elements capable of obscuring optical views of the Shuttle are typically 20 minutes or less. Therefore, accurately observing and forecasting cloud obscuration over an extended network of cameras poses an unprecedented challenge for the current state of observational and modeling techniques. In addition, even the best numerical simulations based on real observations will never reach "truth." In order to quantify the risk that clouds would obscure optical imagery of the Shuttle, a 3D model to calculate probabilistic risk was developed. The model was used to estimate the ability of a network of optical imaging cameras to obtain at least N simultaneous views of the Shuttle from lift-off to SRB separation in the presence of an idealized, randomized cloud field.

FROM↗

3D GeoWall Analysis System for Shuttle External Tank Foreign Object Debris Events

An analytical, advanced imaging method has been developed for the initial monitoring and identification of foam debris and similar anomalies that occur post-launch in reference to the space shuttle s external tank (ET). Remote sensing technologies have been used to perform image enhancement and analysis on high-resolution, true-color images collected with the DCS 760 Kodak digital camera located in the right umbilical well of the space shuttle. Improvements to the camera, using filters, have added sharpness/definition to the image sets; however, image review/analysis of the ET has been limited by the fact that the images acquired by umbilical cameras during launch are two-dimensional, and are usually nonreferenceable between frames due to rotation translation of the ET as it falls away from the space shuttle. Use of stereo pairs of these images can enable strong visual indicators that can immediately portray depth perception of damaged areas or movement of fragments between frames is not perceivable in two-dimensional images. A stereoscopic image visualization system has been developed to allow 3D depth perception of stereo-aligned image pairs taken from in-flight umbilical and handheld digital shuttle cameras. This new system has been developed to augment and optimize existing 2D monitoring capabilities. Using this system, candidate sequential image pairs are identified for transformation into stereo viewing pairs. Image orientation is corrected using control points (similar points) between frames to place the two images in proper X-Y viewing perspective. The images are then imported into the WallView stereo viewing software package. The collected control points are used to generate a transformation equation that is used to re-project one image and effectively co-register it to the other image. The co-registered, oriented image pairs are imported into a WallView image set and are used as a 3D stereo analysis slide show. Multiple sequential image pairs can be used to allow forensic review of temporal phenomena between pairs. The observer, while wearing linear polarized glasses, is able to review image pairs in passive 3D stereo.

Brown, Richard↗

Results from Two Full-Scale Hawker 4000 Fuselage Drop Tests

In the spring of 2022, NASA Langley Research Center (LaRC) conducted two full-scale drop tests on a Hawker 4000 partial fuselage structure for the evaluation of composite material response under dynamic impact loading conditions. The specific objectives of the tests were to induce dynamic composite damage initiation and progression and in primary structure and to understand the nature of the failure modes. The tests were conducted via dividing the fuselage hardware into three smaller sections. Dynamic drop tests were conducted on the forward and aft portions of the fuselage under different dynamic loading conditions, while the middle section was reserved for materials testing. Both tests were conducted by dropping the test articles from a height of 14 feet with significant amounts of pitch, which was added to initiate damage in specific regions of the structure. The test articles were ballasted then instrumented with accelerometers at various locations and speckle-coated on both exterior sides with a black and white stochastic pattern for use with three-dimensional digital image correlation (3D-DIC). In addition, the interior belly portion of the forward section test article was also speckle-coated, which was intended to capture deformations on the belly of the test article from the interior at impact. The interior of the aft section test article was not speckle-coated. Prior to testing, bow-tie markers were applied at various locations for use in marker tracking, to measure impact conditions such as vertical impact velocity and pitch. In this report, a partial summary of the data collected from the tests is presented. The data was primarily in the form of accelerometers to measure impact acceleration and 3D-DIC to measure deformation and failure onset and propagation. Post-test inspections revealed the primary damage mechanism was fiber cracking and delamination primarily in and around the area that contacted the impact surface. Acceleration pulse shapesin the ballast locations were trapezoidal in nature and ranged between 10 g and 40 g, depending on the location and test.

full scale testing↗

Results from Two Full-Scale Hawker 4000 Fuselage Drop Tests

In the spring of 2022, NASA Langley Research Center (LaRC) conducted two full-scale drop tests on a Hawker 4000 partial fuselage structure for the evaluation of composite material response under dynamic impact loading conditions. The specific objectives of the tests were to induce dynamic composite damage initiation and progression and in primary structure and to understand the nature of the failure modes. The tests were conducted via dividing the fuselage hardware into three smaller sections. Dynamic drop tests were conducted on the forward and aft portions of the fuselage under different dynamic loading conditions, while the middle section was reserved for materials testing. Both tests were conducted by dropping the test articles from a height of 14 feet with significant amounts of pitch, which was added to initiate damage in specific regions of the structure. The test articles were ballasted then instrumented with accelerometers at various locations and speckle-coated on both exterior sides with a black and white stochastic pattern for use with three-dimensional digital image correlation (3D-DIC). In addition, the interior belly portion of the forward section test article was also speckle-coated, which was intended to capture deformations on the belly of the test article from the interior at impact. The interior of the aft section test article was not speckle-coated. Prior to testing, bow-tie markers were applied at various locations for use in marker tracking, to measure impact conditions such as vertical impact velocity and pitch. In this report, a partial summary of the data collected from the tests is presented. The data was primarily in the form of accelerometers to measure impact acceleration and 3D-DIC to measure deformation and failure onset and propagation. Post-test inspections revealed the primary damage mechanism was fiber cracking and delamination primarily in and around the area that contacted the impact surface. Acceleration pulse shapesin the ballast locations were trapezoidal in nature and ranged between 10 g and 40 g, depending on the location and test.

full scale testing↗

Using DIC for Long Slender Structures

High-strain composite deployable structures have been developed for systems such as solar arrays, camera masts or solar sailing propulsion elements. Composite booms in such applications are often flattened and then rolled into a small footprint for low-packaged volume and are then deployed in space. There is a need to obtain deformation for long, slender composite booms on earth through gravity offloading by suspending them vertically and applying distal end (tip) loads. Three-dimensional digital image correlation (3D-DIC), along with other measurement techniques, were used to obtain strain and displacement along the length of a 7.5 m subscale composite Triangular, Rollable, and Collapsible (TRAC) boom in preparation for full scale testing of a 30 m boom. However, incorporating 3D-DIC as a primary measurement tool on long, slender, high-aspect-ratio boom structures presents significant challenges. Challenges include small correlated area due to high aspect ratio, limited standoff distance due to size of test area, coordinate system alignment of multiple camera systems along the length of the boom, nodal mesh extraction for adequate test/analysis correlation, as well as measurement comparison between DIC and other instrumentation used such as fiber optic strain sensing (FOSS) and laser displacement tracking. The contents of the proposed paper will focus on techniques and methods for overcoming the previously mentioned challenges associated with applying 3D-DIC to long, slender boom structures. Results from subscale test along with lessons learned will be discussed.

Deployable Boom↗

Average Cross-Sectional Area of DebriSat Fragments Using Volumetrically Constructed 3D Representations

Debris fragments from the hypervelocity impact testing of DebriSat are being collected and characterized for use in updating existing satellite breakup models. One of the key parameters utilized in these models is the ballistic coefficient of the fragment which is directly related to its area‐to‐mass ratio. However, since the attitude of fragments varies during their orbital lifetime, it is customary to use the average cross‐sectional area in the calculation of the area‐to‐mass ratio. The average cross‐sectional area is defined as the average of the projected surface areas perpendicular to the direction of motion and has been shown to be equal to one‐fourth of the total surface area of a convex object. Unfortunately, numerous fragments obtained from the DebriSat experiment show significant concavity (i.e., shadowing) and thus we have explored alternate methods for computing the average cross‐sectional area of the fragments. An imaging system based on the volumetric reconstruction of a 3D object from multiple 2D photographs of the object was developed for use in determining the size characteristic (i.e., characteristics length) of the DebriSat fragments. For each fragment, the imaging system generates N number of images from varied azimuth and elevation angles and processes them using a space‐carving algorithm to construct a 3D point cloud of the fragment. This paper describes two approaches for calculating the average cross‐sectional area of debris fragments based on the 3D imager. Approach A utilizes the constructed 3D object to generate equally distributed cross‐sectional area projections and then averages them to determine the average cross‐sectional area. Approach B utilizes a weighted average of the area of the 2D photographs to directly compute the average cross‐sectional area. A comparison of the accuracy and computational needs of each approach is described as well as preliminary results of an analysis to determine the "optimal" number of images needed for the 3D imager to accurately measure the average cross sectional area of objects with known dimensions.

Scruggs, T.↗