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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Panel-Segmentation [SWR-21-18]

Panel-Segmentation contains the scripts for automated metadata extraction of solar PV installations, using satellite imagery coupled with computer vision techniques. In this package, the user can perform the following actions: *Automatically generate a satellite image using a set of lat-long coordinates, and a Google Maps API key. Users would need to set up a Google Cloud account and get a Maps Static API key. Please refer to Setting Up Google Maps Static API Key section for this process. *Perform image segmentation on the satellite image, to locate the solar array(s) in the image on a pixel-by-pixel basis, using an image segmentation model (panel_detection_model.pth). Get classification of the installation (rooftop, ground mounted fixed-tilt or tracking, carport, etc). *Perform azimuth estimation on each solar array cluster in the masked image. *Detect solar panels and get its latitude, longitude, and address within a geographic bounding box through the SOL-Searcher Pipeline. *Detect and calculate hurricane damage on solar installations given pre-hurricane and post-hurricane satellite imagery through the Hurricane Detection Pipeline. *Detect and calculate hail damage on solar installations given satellite imagery through the Hail Detection pipeline. *Convert NOAA MESH (Maximum Estimated Size of Hail) grib2 files into kml or geojson files. *Estimate tilt and azimuth of a solar array by processing USGS LiDAR data for the array’s location.

Edun, Ayobami↗
DOE OSTI2016

Synthesis and characterization of α-NaYF{sub 4}: Yb, Er nanoparticles by reverse microemulsion method

A simple and cost effective reverse microemulsion system was newly designed to synthesis NaYF{sub 4}:20%Yb,2%Er upconverting luminescent nanoparticles. XRD results confirms the cubic structure of NaYF{sub 4} nanophosphor in the as prepared condition without any other impurity phases. The as-prepared sample itself having highly crystalline nanoparticle with well dispersed uniform morphology is the advantage of this reverse microemulsion process. HRTEM images of as prepared and calcined samples revealed spherical nanoclusters morphology with size of ~210 nm and ~245 nm respectively. The characteristic absorption wavelength that occurs at 980 nm due to transition of energy levels {sup 2}F{sub 5/2} to {sup 2}F{sub 7/2} for Yb{sup 3+} rare earth ion in as prepared and calcined upconversion nanoparticle confirms the presence of Yb{sup 3+} by UV-Visible spectroscopy which can act as a sensitizer for photonic upconversion. Therefore the absorption at NIR region and emission spectrum at visible region suggests that NaYF{sub 4}:20%Yb,2%Er is suitable for upcoversion process, due to its optical property and chemical stability this material also be useful for bio imaging applications.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Toward the fabrication of a 5- μm -resolution Wolter microscope for the National Ignition Facility (invited)

Advancements in computer-controlled polishing, metrology, and replication have led to an x-ray mirror fabrication process that is capable of producing high-resolution Wolter microscopes. Here, we present the fabrication and test of a nickel–cobalt replicated full-shell x-ray mirror that was electroformed from a finely figured and polished mandrel. This mandrel was designed for an 8-m source-to-detector-distance microscope, with 10× magnification, and was optimized to reduce shell distortions that occur within 20 mm of the shell ends. This, in combination with an improved replication tooling design and refined bath parameters informed by a detailed COMSOL Multiphysics® model, has led to reductions in replication errors in the mirrors. Mandrel surface fabrication was improved by implementing a computer-controlled polishing process that corrected the low-frequency mandrel figure error and achieved <2.0 nm RMS convergence error. X-ray tests performed on a pair of mirror shells replicated from the mandrel have demonstrated <10 μm full-width at half-maximum (FWHM) spatial resolution. Here, we discuss the development process, highlight results from metrology and x-ray testing, and define a path for achieving a program goal of 5 μm FWHM resolution.

47 OTHER INSTRUMENTATION↗
DOE OSTI2014

WE-B-19A-01: SRT II: Uncertainties in SRT

SRS delivery has undergone major technical changes in the last decade, transitioning from predominantly frame-based treatment delivery to imageguided, frameless SRS. It is important for medical physicists working in SRS to understand the magnitude and sources of uncertainty involved in delivering SRS treatments for a multitude of technologies (Gamma Knife, CyberKnife, linac-based SRS and protons). Sources of SRS planning and delivery uncertainty include dose calculation, dose fusion, and intra- and inter-fraction motion. Dose calculations for small fields are particularly difficult because of the lack of electronic equilibrium and greater effect of inhomogeneities within and near the PTV. Going frameless introduces greater setup uncertainties that allows for potentially increased intra- and interfraction motion, The increased use of multiple imaging modalities to determine the tumor volume, necessitates (deformable) image and contour fusion, and the resulting uncertainties introduced in the image registration process further contribute to overall treatment planning uncertainties. Each of these uncertainties must be quantified and their impact on treatment delivery accuracy understood. If necessary, the uncertainties may then be accounted for during treatment planning either through techniques to make the uncertainty explicit, or by the appropriate addition of PTV margins. Further complicating matters, the statistics of 1-5 fraction SRS treatments differ from traditional margin recipes relying on Poisson statistics. In this session, we will discuss uncertainties introduced during each step of the SRS treatment planning and delivery process and present margin recipes to appropriately account for such uncertainties. Learning Objectives: To understand the major contributors to the total delivery uncertainty in SRS for Gamma Knife, CyberKnife, and linac-based SRS. Learn the various uncertainties introduced by image fusion, deformable image registration, and contouring variation. Learn a variety of strategies for dealing with uncertainty, including margin recipes and explicit visualization of uncertainty. Understand how the assessment of PTV margins differs from regular fractionation (van Herk recipe) for 1–5 fraction deliveries.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Dark Energy Survey Year 3 Results: Photometric Data Set for Cosmology

In this work, we describe the Dark Energy Survey (DES) photometric data set assembled from the first three years of science operations to support DES Year 3 cosmologic analyses, and provide usage notes aimed at the broad astrophysics community. Y3 GOLD improves on previous releases from DES, Y1 GOLD, and Data Release 1 (DES DR1), presenting an expanded and curated data set that incorporates algorithmic developments in image detrending and processing, photometric calibration, and object classification. Y3 GOLD comprises nearly 5000 deg 2 of grizY imaging in the south Galactic cap, including nearly 390 million objects, with depth reaching a signal-to-noise ratio ~10 for extended objects up to iAB ~ 23.0, and top-of-the-atmosphere photometric uniformity <3 mmag. Compared to DR1, photometric residuals with respect to Gaia are reduced by 50%, and per-object chromatic corrections are introduced. Y3 GOLD augments DES DR1 with simultaneous fits to multi-epoch photometry for more robust galactic color measurements and corresponding photometric redshift estimates. Y3 GOLD features improved morphological star–galaxy classification with efficiency >98% and purity >99% for galaxies with 19 < i AB < 22.5. Additionally, it includes per-object quality information, and accompanying maps of the footprint coverage, masked regions, imaging depth, survey conditions, and astrophysical foregrounds that are used to select the cosmologic analysis samples.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

SU-E-J-117: Verification Method for the Detection Accuracy of Automatic Winston Lutz Test

Purpose: Winston Lutz test (WLT) has been a standard QA procedure performed prior to SRS treatment, to verify the mechanical iso-center setup accuracy upon different Gantry/Couch movements. Several detection algorithms exist,for analyzing the ball-radiation field alignment automatically. However, the accuracy of these algorithms have not been fully addressed. Here, we reveal the possible errors arise from each step in WLT, and verify the software detection accuracy with the Rectilinear Phantom Pointer (RLPP), a tool commonly used for aligning treatment plan coordinate with mechanical iso-center. Methods: WLT was performed with the radio-opaque ball mounted on a MIS and irradiated onto EDR2 films. The films were scanned and processed with an in-house Matlab program for automatic iso-center detection. Tests were also performed to identify the errors arise from setup, film development and scanning process. The radioopaque ball was then mounted onto the RLPP, and offset laterally and longitudinally in 7 known positions ( 0, ±0.2, ±0.5, ±0.8 mm) manually for irradiations. The gantry and couch was set to zero degree for all irradiation. The same scanned images were processed repeatedly to check the repeatability of the software. Results: Miminal discrepancies (mean=0.05mm) were detected with 2 films overlapped and irradiated but developed separately. This reveals the error arise from film processor and scanner alone. Maximum setup errors were found to be around 0.2mm, by analyzing data collected from 10 irradiations over 2 months. For the known shift introduced using the RLPP, the results agree with the manual offset, and fit linearly (R{sup 2}>0.99) when plotted relative to the first ball with zero shift. Conclusion: We systematically reveal the possible errors arise from each step in WLT, and introduce a simple method to verify the detection accuracy of our in-house software using a clinically available tool.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Ultrafast self-gating Bragg diffraction of exploding nanocrystals in an X-ray laser

In structural determination of crystalline proteins using intense femtosecond X-ray lasers, damage processes lead to loss of structural coherence during the exposure. We use a nonthermal description for the damage dynamics to calculate the ultrafast ionization and the subsequent atomic displacement. These effects degrade the Bragg diffraction on femtosecond time scales and gate the ultrafast imaging. This process is intensity and resolution dependent. At high intensities the signal is gated by the ionization affecting low resolution information first. At lower intensities, atomic displacement dominates the loss of coherence affecting high-resolution information. We find that pulse length is not a limiting factor as long as there is a high enough X-ray flux to measure a diffracted signal.

47 OTHER INSTRUMENTATION↗
DOE OSTI2018

Water Film Structure during Rupture as Revealed by MDS Image Analysis

The structure of thin water films during the rupture process was investigated by a new approach, which combines molecular dynamics simulation (MDS) with image processing analysis. The analysis procedure was developed to convert MDS trajectories to readable 3D images. The water films were studied at different thicknesses by MDS to determine the critical thickness at which the film ruptures. The potential energy of each specific film thickness during the simulation time was analyzed, and the results showed that the potential energy of stable films remained unchanged while the potential energy kept decreasing for films which ruptured during the simulation time. By applying the new procedure, the molecular porosity, which is defined as the void fraction between the volume of molecular pores in the water film and the total volume of the water film, was calculated. The results of molecular porosity for different film thicknesses during the simulation time suggested a critical molecular porosity as 49%. In other words, stable films have a molecular porosity of less than 49%. If a water film has a molecular porosity greater than 49%, rupture occurs during the simulation. This research was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences.

molecular dynamics simulation, film stability, ima↗
DOE OSTI2014

Automatic tracking of arbitrarily shaped implanted markers in kilovoltage projection images: A feasibility study

Purpose: Certain types of commonly used fiducial markers take on irregular shapes upon implantation in soft tissue. This poses a challenge for methods that assume a predefined shape of markers when automatically tracking such markers in kilovoltage (kV) radiographs. The authors have developed a method of automatically tracking regularly and irregularly shaped markers using kV projection images and assessed its potential for detecting intrafractional target motion during rotational treatment. Methods: Template-based matching used a normalized cross-correlation with simplex minimization. Templates were created from computed tomography (CT) images for phantom studies and from end-expiration breath-hold planning CT for patient studies. The kV images were processed using a Sobel filter to enhance marker visibility. To correct for changes in intermarker relative positions between simulation and treatment that can introduce errors in automatic matching, marker offsets in three dimensions were manually determined from an approximately orthogonal pair of kV images. Two studies in anthropomorphic phantom were carried out, one using a gold cylindrical marker representing regular shape, another using a Visicoil marker representing irregular shape. Automatic matching of templates to cone beam CT (CBCT) projection images was performed to known marker positions in phantom. In patient data, automatic matching was compared to manual matching as an approximate ground truth. Positional discrepancy between automatic and manual matching of less than 2 mm was assumed as the criterion for successful tracking. Tracking success rates were examined in kV projection images from 22 CBCT scans of four pancreas, six gastroesophageal junction, and one lung cancer patients. Each patient had at least one irregularly shaped radiopaque marker implanted in or near the tumor. In addition, automatic tracking was tested in intrafraction kV images of three lung cancer patients with irregularly shaped markers during 11 volumetric modulated arc treatments. Purpose-built software developed at our institution was used to create marker templates and track the markers embedded in kV images. Results: Phantom studies showed mean ± standard deviation measurement uncertainty of automatic registration to be 0.14 ± 0.07 mm and 0.17 ± 0.08 mm for Visicoil and gold cylindrical markers, respectively. The mean success rate of automatic tracking with CBCT projections (11 frames per second, fps) of pancreas, gastroesophageal junction, and lung cancer patients was 100%, 99.1% (range 98%–100%), and 100%, respectively. With intrafraction images (approx. 0.2 fps) of lung cancer patients, the success rate was 98.2% (range 97%–100%), and 94.3% (range 93%–97%) using templates from 1.25 mm and 2.5 mm slice spacing CT scans, respectively. Correction of intermarker relative position was found to improve the success rate in two out of eight patients analyzed. Conclusions: The proposed method can track arbitrary marker shapes in kV images using templates generated from a breath-hold CT acquired at simulation. The studies indicate its feasibility for tracking tumor motion during rotational treatment. Investigation of the causes of misregistration suggests that its rate of incidence can be reduced with higher frequency of image acquisition, templates made from smaller CT slice spacing, and correction of changes in intermarker relative positions when they occur.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2011

Comparative sensitivity of human and rat neural cultures to chemical-induced inhibition of neurite outgrowth

There is a need for rapid, efficient and cost-effective alternatives to traditional in vivo developmental neurotoxicity testing. In vitro cell culture models can recapitulate many of the key cellular processes of nervous system development, including neurite outgrowth, and may be used as screening tools to identify potential developmental neurotoxicants. The present study compared primary rat cortical cultures and human embryonic stem cell-derived neural cultures in terms of: 1) reproducibility of high content image analysis based neurite outgrowth measurements, 2) dynamic range of neurite outgrowth measurements and 3) sensitivity to chemicals which have been shown to inhibit neurite outgrowth. There was a large increase in neurite outgrowth between 2 and 24 h in both rat and human cultures. Image analysis data collected across multiple cultures demonstrated that neurite outgrowth measurements in rat cortical cultures were more reproducible and had higher dynamic range as compared to human neural cultures. Human neural cultures were more sensitive than rat cortical cultures to chemicals previously shown to inhibit neurite outgrowth. Parallel analysis of morphological (neurite count, neurite length) and cytotoxicity (neurons per field) measurements were used to detect selective effects on neurite outgrowth. All chemicals which inhibited neurite outgrowth in rat cortical cultures did so at concentrations which did not concurrently affect the number of neurons per field, indicating selective effects on neurite outgrowth. In contrast, more than half the chemicals which inhibited neurite outgrowth in human neural cultures did so at concentrations which concurrently decreased the number of neurons per field, indicating that effects on neurite outgrowth were secondary to cytotoxicity. Overall, these data demonstrate that the culture models performed differently in terms of reproducibility, dynamic range and sensitivity to neurite outgrowth inhibitors. While human neural cultures were more sensitive to neurite outgrowth inhibitors, they also had a lower dynamic range for detecting chemical-induced neurite outgrowth inhibition and greater variability from culture-to-culture as compared to rat primary cortical cultures.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

SU-E-T-141: Automated Dose Point Placement for Cervical Cancer Brachytherapy Using Tandem and Ovoid Applicators

Purpose: To develop a standalone application, which automatically and consistently calculates the coordinates of points A and H based solely on the implanted applicator geometry for cervical cancer HDR brachytherapy. Methods: Manchester point A and ABS point H are both located 2cm lateral from the central tandem plane. While both points are located 2cm above the cervical os, surrogates for the os differ. Point A is defined relative to the anatomical cervical os. Point H is defined relative to the intersection of the tandem with the superior aspects of the ovoids. The application takes an input text file generated by the treatment planning system (TPS, BrachyVision, Varian) that specifies the source geometries. It then outputs the 3D coordinates of points A and H in both the left and right directions. The algorithm was implemented and tested on 34 CT scans of 7 patients treated with HDR brachytherapy delivered using tandem and ovoids. A single experienced user retrospectively and manually placed points A and H on the CT scans, whose coordinates were used as the gold standard for the comparison to the automatically calculated points. Results: The automatically calculated coordinates of points A and H agree within 0.7mm with the gold standard. The averages and standard deviations of the 3D coordinate difference between points placed by the two methods are 0.3±0.1 and 0.4±0.1mm for points A and H, respectively. The maximum difference in 3D magnitude is 0.7mm. Conclusion: The algorithm consistently calculates dose point coordinates independently of the planner for cervical cancer brachytherapy treated with tandem and ovoids. Automated point placement based on the geometry of the implanted applicators agrees in sub-millimeter with careful manual placements by an experienced user. This algorithm expedites the planning process and eliminates dependencies on either user input or TPS visualization tools.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Optimization of oncological {sup 18}F-FDG PET/CT imaging based on a multiparameter analysis

Purpose: This paper describes a method to achieve consistent clinical image quality in {sup 18}F-FDG scans accounting for patient habitus, dose regimen, image acquisition, and processing techniques. Methods: Oncological PET/CT scan data for 58 subjects were evaluated retrospectively to derive analytical curves that predict image quality. Patient noise equivalent count rate and coefficient of variation (CV) were used as metrics in their analysis. Optimized acquisition protocols were identified and prospectively applied to 179 subjects. Results: The adoption of different schemes for three body mass ranges (<60 kg, 60–90 kg, >90 kg) allows improved image quality with both point spread function and ordered-subsets expectation maximization-3D reconstruction methods. The application of this methodology showed that CV improved significantly (p < 0.0001) in clinical practice. Conclusions: Consistent oncological PET/CT image quality on a high-performance scanner was achieved from an analysis of the relations existing between dose regimen, patient habitus, acquisition, and processing techniques. The proposed methodology may be used by PET/CT centers to develop protocols to standardize PET/CT imaging procedures and achieve better patient management and cost-effective operations.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2024

Divide and conquer: using RhizoVision Explorer to aggregate data from multiple root scans using image concatenation and statistical methods

Roots are important in agricultural and natural systems for determining plant productivity and soil carbon inputs. Sometimes, the amount of roots in a sample is too much to fit into a single scanned image, so the sample is divided among several scans, and there is no standard method to aggregate the data. Here, we describe and validate two methods for standardizing measurements across multiple scans: image concatenation and statistical aggregation. We developed a Python script that identifies which images belong to the same sample and returns a single, larger concatenated image. These concatenated images and the original images were processed with RhizoVision Explorer, a free and open-source software. An R script was developed, which identifies rows of data belonging to the same sample and applies correct statistical methods to return a single data row for each sample. These two methods were compared using example images from switchgrass, poplar, and various tree and ericaceous shrub species from a northern peatland and the Arctic. Most root measurements were nearly identical between the two methods except median diameter, which cannot be accurately computed by statistical aggregation. We believe the availability of these methods will be useful to the root biology community.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

Bayesian Abel Inversion in Quantitative X-Ray Radiography

A common image formation process in high-energy X-ray radiography is to have a pulsed power source that emits X-rays through a scene, a scintillator that absorbs X-rays and uoresces in the visible spectrum in response to the absorbed photons, and a CCD camera that images the visible light emitted from the scintillator. The intensity image is related to areal density, and, for an object that is radially symmetric about a central axis, the Abel transform then gives the object's volumetric density. Two of the primary drawbacks to classical variational methods for Abel inversion are their sensitivity to the type and scale of regularization chosen and the lack of natural methods for quantifying the uncertainties associated with the reconstructions. In this work we cast the Abel inversion problem within a statistical framework in order to compute volumetric object densities from X-ray radiographs and to quantify uncertainties in the reconstruction. A hierarchical Bayesian model is developed with a likelihood based on a Gaussian noise model and with priors placed on the unknown density pro le, the data precision matrix, and two scale parameters. This allows the data to drive the localization of features in the reconstruction and results in a joint posterior distribution for the unknown density pro le, the prior parameters, and the spatial structure of the precision matrix. Results of the density reconstructions and pointwise uncertainty estimates are presented for both synthetic signals and real data from a U.S. Department of Energy X-ray imaging facility.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Automatic microseismic event picking via unsupervised machine learning

SUMMARY Effective and efficient arrival picking plays an important role in microseismic and earthquake data processing and imaging. Widely used short-term-average long-term-average ratio (STA/LTA) based arrival picking algorithms suffer from the sensitivity to moderate-to-strong random ambient noise. To make the state-of-the-art arrival picking approaches effective, microseismic data need to be first pre-processed, for example, removing sufficient amount of noise, and second analysed by arrival pickers. To conquer the noise issue in arrival picking for weak microseismic or earthquake event, I leverage the machine learning techniques to help recognizing seismic waveforms in microseismic or earthquake data. Because of the dependency of supervised machine learning algorithm on large volume of well-designed training data, I utilize an unsupervised machine learning algorithm to help cluster the time samples into two groups, that is, waveform points and non-waveform points. The fuzzy clustering algorithm has been demonstrated to be effective for such purpose. A group of synthetic, real microseismic and earthquake data sets with different levels of complexity show that the proposed method is much more robust than the state-of-the-art STA/LTA method in picking microseismic events, even in the case of moderately strong background noise.

Chen, Yangkang↗
DOE OSTI2019

High-Resolution Electron Microscopy and Kinetic Studies of Precipitation Hardening Reactions in Cast Al-5.8Zn-2.2Mg-2.5Cu

Precipitation age hardening (T6) response of Al-5.8Zn-2.2Mg-2.5Cu alloy in near-net-shaped cast condition was investigated. Cast samples were manufactured using the controlled diffusion solidification (CDS) technology combined with a metallic mold tilt pour gravity casting process. This study was conducted using (1) non-isothermal aging during differential scanning calorimetry (DSC) experiments and (2) isothermal aging during which transient bulk and micro-hardness measurements taken at four aging temperatures of 343, 393, 433 and 473 K. A detailed microstructural investigation combined with a quantitative image analysis was carried out on both DSC and hardness specimens using high-resolution electron microscopy (HREM) and energy-dispersive spectroscopy (EDS) elemental mappings. Hardness measurements were analyzed using a kinetic modeling approach (single state variable combined with a kinetic equation that is valid for the Al-Zn-Mg-Cu alloys). The results confirm the formation of hardening phases of GP zone, intermediate hardening metastable phase η′ and equilibrium phase η. The results of calorimetric measurements, electron microscopy and selected area diffraction patterns are in good agreement and confirm transient precipitation/dissolution sequences. A mean value of activation energy Q{sub A} of 75 kJ/mol was evaluated for combined bulk diffusion rate of alloying elements during precipitation of strengthening phases within Al matrix.

36 MATERIALS SCIENCE↗
DOE OSTI2014

HiRes deconvolved Spitzer images of 89 protostellar jets and outflows: New data on the evolution of the outflow morphology

To study the role of protosellar jets and outflows in the time evolution of the parent cores and the protostars, the astronomical community needs a large enough database of infrared images of protostars at the highest spatial resolution possible to reveal the details of their morphology. Spitzer provides unprecedented sensitivity in the infrared to study both the jet and outflow features, however, its spatial resolution is limited by its 0.85 m mirror. Here, we use a high-resolution deconvolution algorithm, 'HiRes,' to improve the visualization of spatial morphology by enhancing resolution (to subarcsecond levels in the IRAC bands) and removing the contaminating side lobes from bright sources in a sample of 89 protostellar objects. These reprocessed images are useful for detecting (1) wide-angle outflows seen in scattered light, (2) morphological details of H{sub 2} emission in jets and bow shocks, and (3) compact features in MIPS 24 μm images as protostar/disk and atomic/ionic line emission associated with the jets. The HiRes FITS image data of such a large homogeneous sample presented here will be useful to the community in studying these protostellar objects. To illustrate the utility of this HiRes sample, we show how the opening angle of the wide-angle outflows in 31 sources, all observed in the HiRes-processed Spitzer images, correlates with age. Our data suggest a power-law fit to opening angle versus age with an exponent of ∼0.32 and 0.02, respectively, for ages ≤8000 yr and ≥8000 yr.

79 ASTRONOMY AND ASTROPHYSICS↗