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All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Three-dimensional tomographic reconstruction of the flow around a revolving helicopter rotorblade - A numerical simulation

This paper discusses tomographic data acquisition and reconstruction procedures for determining the flow around a revolving helicopter rotor blade. The data acquisition procedure is simulated using, as a testbed, a numerical representation of the flow and projections through this known field are computed. An investigation has been made of: (1) the effect of the number of projections on the accuracy of the reconstruction and (2) the fidelity of the reconstruction when the region of intersection of all projections is smaller than the spatial extent of the flow.

Hesselink, L.↗
NASA NTRS2014

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↗
NASA NTRS2011

Tomographic Reconstruction of Mercury's Exosphere from MESSENGER Flyby Data

The exosphere of Mercury is among the best-studied examples of a common type of atmosphere, a surface-bounded exosphere. Mercury's exosphere was probed in 2008-2009 with Ultraviolet and Visible Spectrometer (UVVS) measurements obtained during three planetary flybys by the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft [1-3]. The measurements detailed the distribution of two previously known metallic constituents of Mercury's exosphere, Na and Ca, and indicated the presence in the gas phase of yet another metallic species, Mg. Such measurements can answer fundamental scientific questions regarding the relative importance of possible source and loss processes for exospheric species ejected from a surface boundary [4]. The trajectory of MESSENGER during the last of its three flybys provided the best spatial coverage prior to orbit insertion. The measurements by MESSENGER of Na, Ca, and Mg during the third flyby have been analyzed with a novel tomographic method. This approach maximizes the amount of information that can be extracted from line-of-sight measurements because it yields three-dimensional distributions of neutrals consistent with the data.

Killen, Rosemary M.↗
NASA NTRS2012

Longitudinal Differences of Ionospheric Vertical Density Distribution and Equatorial Electrodynamics

Accurate estimation of global vertical distribution of ionospheric and plasmaspheric density as a function of local time, season, and magnetic activity is required to improve the operation of space-based navigation and communication systems. The vertical density distribution, especially at low and equatorial latitudes, is governed by the equatorial electrodynamics that produces a vertical driving force. The vertical structure of the equatorial density distribution can be observed by using tomographic reconstruction techniques on ground-based global positioning system (GPS) total electron content (TEC). Similarly, the vertical drift, which is one of the driving mechanisms that govern equatorial electrodynamics and strongly affect the structure and dynamics of the ionosphere in the low/midlatitude region, can be estimated using ground magnetometer observations. We present tomographically reconstructed density distribution and the corresponding vertical drifts at two different longitudes: the East African and west South American sectors. Chains of GPS stations in the east African and west South American longitudinal sectors, covering the equatorial anomaly region of meridian approx. 37 deg and 290 deg E, respectively, are used to reconstruct the vertical density distribution. Similarly, magnetometer sites of African Meridian B-field Education and Research (AMBER) and INTERMAGNET for the east African sector and South American Meridional B-field Array (SAMBA) and Low Latitude Ionospheric Sensor Network (LISN) are used to estimate the vertical drift velocity at two distinct longitudes. The comparison between the reconstructed and Jicamarca Incoherent Scatter Radar (ISR) measured density profiles shows excellent agreement, demonstrating the usefulness of tomographic reconstruction technique in providing the vertical density distribution at different longitudes. Similarly, the comparison between magnetometer estimated vertical drift and other independent drift observation, such as from VEFI onboard Communication/Navigation Outage Forecasting System (C/NOFS) satellite and JULIA radar, is equally promising. The observations at different longitudes suggest that the vertical drift velocities and the vertical density distribution have significant longitudinal differences; especially the equatorial anomaly peaks expand to higher latitudes more in American sector than the African sector, indicating that the vertical drift in the American sector is stronger than the African sector.

total electron content↗
NASA NTRS1999

Experimental Investigation of Pool Boiling Heat Transfer Enhancement in Microgravity in the Presence of Electric Fields

In boiling high heat fluxes are possible driven by relatively small temperature differences, which make its use increasingly attractive in aerospace applications. The objective of the research is to develop ways to overcome specific problems associated with boiling in the low gravity environment by substituting the buoyancy force with the electric force to enhance bubble removal from the heated surface. Previous studies indicate that in terrestrial applications nucleate boiling heat transfer can be increased by a factor of 50, as compared to values obtained for the same system without electric fields. The goal of our research is to experimentally explore the mechanisms responsible for EHD heat transfer enhancement in boiling in low gravity conditions, by visualizing the temperature distributions in the vicinity of the heated surface and around the bubble during boiling using real-time holographic interferometry (HI) combined with high-speed cinematography. In the first phase of the project the influence of the electric field on a single bubble is investigated. Pool boiling is simulated by injecting a single bubble through a nozzle into the subcooled liquid or into the thermal boundary layer developed along the flat heater surface. Since the exact location of bubble formation is known, the optical equipment can be aligned and focused accurately, which is an essential requirement for precision measurements of bubble shape, size and deformation, as well as the visualization of temperature fields by HI. The size of the bubble and the frequency of bubble departure can be controlled by suitable selection of nozzle diameter and mass flow rate of vapor. In this approach effects due to the presence of the electric field can be separated from effects caused by the temperature gradients in the thermal boundary layer. The influence of the thermal boundary layer can be investigated after activating the heater at a later stage of the research. For the visualization experiments a test cell was developed. All four vertical walls of the test cell are transparent, and they allow transillumination with laser light for visualization experiments by HI. The bottom electrode is a copper cylinder, which is electrically grounded. The copper block is heated with a resistive heater and it is equipped with 6 thermocouples that provide reference temperatures for the measurements with HI. The top electrode is a mesh electrode. Bubbles are injected with a syringe into the test cell through the bottom electrode. The working fluids presently used in the interferometric visualization experiments, water and PF 5052, satisfy requirements regarding thermophysical, optical and electrical properties. A 30kV power supply equipped with a voltmeter allows to apply the electric field to the electrodes during the experiments. The magnitude of the applied voltage can be adjusted either manually or through the LabVIEW data acquisition and control system connected to a PC. Temperatures of the heated block are recorded using type-T thermocouples, whose output is read by a data acquisition system. Images of the bubbles are recorded with 35mm photographic and 16mm high-speed cameras, scanned and analyzed using various software packages. Visualized temperature fields HI allows the visualization of temperature fields in the vicinity of bubbles during boiling in the form of fringes. Typical visualized temperature distributions around the air bubbles injected into the thermal boundary layer in PF5052 are shown. The temperature of the heated surface is 35 C. The temperature difference for a pair of fringes is approximately 0.05 C. The heat flux applied to the bottom surface is moderate, and the fringe patterns are regular. In the image a bubble penetrating the thermal boundary layer is visible. Because of the axial symmetry of the problem, simplified reconstruction techniques can be applied to recover the temperature field. The thermal plume developing above the heated surface for more intensive heating is shown. The temperature distribution in the liquid is clearly 3D, and tomographic techniques have to be applied to recover the temperature distribution in such a physical situation. A sequence of interferometric images showing the temperature distribution around the rising bubble, recorded with a high-speed camera is shown. Again, the temperature distribution is 3D, and a more complex approach to the evaluation, the tomographic reconstruction has to be taken. Measurement of the temperature distribution from the fringe pattern temperature distributions that yield important information regarding heat transfer are determined. Two algorithms that allow the quantitative evaluation of interferometric fringe patterns and the reconstruction of temperature fields during boiling have been developed at the Heat Transfer Laboratory of the Johns Hopkins University. In the first algorithm the bubble is assumed to be axially symmetrical, which significantly reduces the computational effort for quantifying the temperature distribution around the bubble. For this purpose the thermal boundary layer around the bubble is divided into equidistant concentric shells, and the refractive index is assumed to be constant in each of the shells. Since large temperature gradients are expected in the vicinity of the bubble during boiling, the deflection of the light beam cannot be neglected in boiling experiments. Since the exit angle of the light beam is known, this allows to account for the deflections and phase shifts outside the boundary layer (in the bulk fluid and in the windows of the test cell). Three dimensional temperature distributions in the vicinity of the bubble are reconstructed using tomographic techniques. In tomography, the measurement volume is sliced into 2D planes. In the present study these planes are parallel to the heated surface. The objective is to determine the values of the field parameter of interest in form of the field function in these 2D planes. The field parameter is the change of the refractive index of the liquid in the measurement volume caused by temperature changes. By superimposing data for many 2D planes recorded at the same time instant, the 3D temperature distribution in the measurement volume is recovered.

Herman, Cila↗
NASA NTRS2024

A Feasibility Study of 4-D Tomography of Soft X-ray Magnetosheath Emissivities Using Multi-Spacecraft Measurements

Upcoming heliophysics missions utilize state-of-the-art wide field-of-view (FOV) imaging technology to measure and investigate the space plasma environment on a global scale. At Earth, remote sensing of soft X-ray emissions, which are generated via the charge exchange interaction between heavy solar wind ions and exospheric neutral atoms, is a promising means to investigate the global magnetosheath structure, its response to varying solar wind conditions, and the spatiotemporal properties of the dayside magnetic reconnection. Data analysis techniques such as optical tomography can provide additional structural and time-varying information from the observed target and thus enhance the mission’s scientific return. In this work, we simulate multiple and simultaneous observations of the dayside magnetosphere using soft X-ray imagers located at long-distance vantage points to reconstruct the time-dependent, three-dimensional (3-D) structure of the magnetosheath using a dynamic tomographic approach. The OpenGCCM MHD model is used to simulate the time-varying response of the magnetosheath to solar wind conditions and, subsequently, generate synthetic soft X-ray images from multiple spacecraft vantage points separated along a common orbit. A detailed analysis is then performed to identify the nominal set of spacecraft that produces the highest fidelity tomographic reconstruction of the magnetopause. This work aims to (i) demonstrate, for the first time, the use of dynamic tomography to retrieve the time-varying magnetosheath structure and (ii) identify a nominal mission design for multi-spacecraft configurations aiming for optical tomography.

3-D/4_d tomography↗
NASA NTRS1993

Tomographic decoding algorithm for a nonoverlapping redundant array

A tomographic reconstruction algorithm is developed for the nonoverlapping redundant array X-ray imaging system whereby the background contributions from out-of-focus planes can be eliminated. The algorithm makes use of two constraints derived from the physical characteristics of the nonoverlapping redundant array system in tandem with the correlation decoding process. It is simple, direct, and noniterative. Tomographic images of computer-generated planar and three-dimensional objects are provided to illustrate the effectiveness of the algorithm.

Yin, Lo I.↗
NASA NTRS2002

Hierarchies of Models: Toward Understanding Planetary Nebulae

Stars like our sun (initial masses between 0.8 to 8 solar masses) end their lives as swollen red giants surrounded by cool extended atmospheres. The nuclear reactions in their cores create carbon, nitrogen and oxygen, which are transported by convection to the outer envelope of the stellar atmosphere. As the star finally collapses to become a white dwarf, this envelope is expelled from the star to form a planetary nebula (PN) rich in organic molecules. The physics, dynamics, and chemistry of these nebulae are poorly understood and have implications not only for our understanding of the stellar life cycle but also for organic astrochemistry and the creation of prebiotic molecules in interstellar space. We are working toward generating three-dimensional models of planetary nebulae (PNe), which include the size, orientation, shape, expansion rate and mass distribution of the nebula. Such a reconstruction of a PN is a challenging problem for several reasons. First, the data consist of images obtained over time from the Hubble Space Telescope (HST) and spectra obtained from Kitt Peak National Observatory (KPNO) and Cerro Tololo Inter-American Observatory (CTIO). These images are of course taken from a single viewpoint in space, which amounts to a very challenging tomographic reconstruction. Second, the fact that we have two disparate and orthogonal data types requires that we utilize a method that allows these data to be used together to obtain a solution. To address these first two challenges we employ Bayesian model estimation using a parameterized physical model that incorporates much prior information about the known physics of the PN. In our previous works we have found that the forward problem of the comprehensive model is extremely time consuming. To address this challenge, we explore the use of a set of hierarchical models, which allow us to estimate increasingly more detailed sets of model parameters. These hierarchical models of increasing complexity are akin to scientific theories of increasing sophistication, with each new model/theory being a refinement of a previous one by either incorporating additional prior information or by introducing a new set of parameters to model an entirely new phenomenon. We apply these models to both a simulated and a real ellipsoidal PN to initially estimate the position, angular size, and orientation of the nebula as a two-dimensional object and use these estimates to later examine its three-dimensional properties. The efficiency/accuracy tradeoffs of the techniques are studied to determine the advantages and disadvantages of employing a set of hierarchical models over a single comprehensive model.

Knuth, Kevin H.↗
NASA NTRS2003

Hierarchies of Models: Toward Understanding Planetary Nebulae

Stars like our sun (initial masses between 0.8 to 8 solar masses) end their lives as swollen red giants surrounded by cool extended atmospheres. The nuclear reactions in their cores create carbon, nitrogen and oxygen, which are transported by convection to the outer envelope of the stellar atmosphere. As the star finally collapses to become a white dwarf, this envelope is expelled from the star to form a planetary nebula (PN) rich in organic molecules. The physics, dynamics, and chemistry of these nebulae are poorly understood and have implications not only for our understanding of the stellar life cycle but also for organic astrochemistry and the creation of prebiotic molecules in interstellar space. We are working toward generating three-dimensional models of planetary nebulae (PNe), which include the size, orientation, shape, expansion rate and mass distribution of the nebula. Such a reconstruction of a PN is a challenging problem for several reasons. First, the data consist of images obtained over time from the Hubble Space Telescope (HST) and spectra obtained from Kitt Peak National Observatory (KPNO) and Cerro Tololo Inter-American Observatory (CTIO). These images are of course taken from a single viewpoint in space, which amounts to a very challenging tomographic reconstruction. Second, the fact that we have two disparate and orthogonal data types requires that we utilize a method that allows these data to be used together to obtain a solution. To address these first two challenges we employ Bayesian model estimation using a parameterized physical model that incorporates much prior information about the known physics of the PN. In our previous works we have found that the forward problem of the comprehensive model is extremely time consuming. To address this challenge, we explore the use of a set of hierarchical models, which allow us to estimate increasingly more detailed sets of model parameters. These hierarchical models of increasing complexity are akin to scientific theories of increasing sophistication, with each new model/theory being a refinement of a previous one by either incorporating additional prior information or by introducing a new set of parameters to model an entirely new phenomenon. We apply these models to both a simulated and a real ellipsoidal PN to initially estimate the position, angular size, and orientation of the nebula as a two-dimensional object and use these estimates to later examine its three-dimensional properties. The efficiency/accuracy tradeoffs of the techniques are studied to determine the advantages and disadvantages of employing a set of hierarchical models over a single comprehensive model.

Knuth, Kevin H.↗
NASA NTRS2003

Three-Dimensional Morphological Analysis of ALH84001 Magnetite Using Electron Tomography

We report here the crystal morphologies of MV-1 and ALH84001 magnetites as calculated by back-projection using electron tomography. In the present study, we used a 300 keV TEM with a field emission gun (Tecnai F-30 from FEI Inc.), equipped with a 2048 x 2048 pixel CCD camera from Gatan Inc. to image magnetite crystals over tilt ranges of approx. +/- 72 deg in 2 deg tilt intervals. The images were aligned for back-projection, either manually, or through the use of fiducial 5 nm Au spheres affixed to the specimen prior to microscopy. Three-dimensional (3-D) reconstructions were computed using weighted back-projection of the tilted views. The tomograms were viewed and analyzed as a series of slices 1.0 nm thick, taken parallel to the specimen-supporting grid, using the IMOD software package. The shape of each magnetite crystal was determined by defining the external contour of a given magnetite in each slice and assembling a stack of these contours in 3-D. To aid in visualization, the stacked contour array was reduced to an optimal mesh by Delaunay triangulation. The surface normal to each of the triangles in the mesh was calculated and the triangle faces colored according to the orientation of that surface normal relative to the principal crystallographic axis of magnetite. Green surfaces correspond to {111} orientations, blue surfaces to {100} orientations, and red surfaces to {110} orientations. Triangles whose surface normal did not correspond to one of the principal axes were colored gray. Within the experimental and numerical uncertainties of the deconvolution, the tomographic reconstruction of both MV-1 and ALH84001 magnetites are equivalent and correspond to a truncated hexa-octahedral morphology.

Thomas-Keprta, Kathie L.↗
NASA NTRS1996

Structural relations between collagen and mineral in bone as determined by high voltage electron microscopic tomography

Aspects of the ultrastructural interaction between collagen and mineral crystals in embryonic chick bone have been examined by the novel technique of high voltage electron microscopic tomography to obtain three-dimensional information concerning extracellular calcification in this tissue. Newly mineralizing osteoid along periosteal surfaces of mid-diaphyseal regions from normal chick tibiae was embedded, cut into 0.25 microns thick sections, and documented at 1.0 MV in the Albany AEI-EM7 high voltage electron microscope. The areas of the tissue studied contained electron dense mineral crystals associated with collagen fibrils, some marked by crystals disposed along their cylindrically shaped lengths. Tomographic reconstructions of one site with two mineralizing fibrils were computed from a 5 degrees tilt series of micrographs over a +/- 60 degrees range. Reconstructions showed that the mineral crystals were platelets of irregular shape. Their sizes were variable, measured here up to 80 x 30 x 8 nm in length, width, and thickness, respectively. The longest crystal dimension, corresponding to the c-axis crystallographically, was generally parallel to the collagen fibril long axis. Individual crystals were oriented parallel to one another in each fibril examined. They were also parallel in the neighboring but apparently spatially separate fibrils. Crystals were periodically (approximately 67 nm repeat distance) arranged along the fibrils and their location appeared to correspond to collagen hole and overlap zones defined by geometrical imaging techniques. The crystals appeared to be continuously distributed along a fibril, their size and number increasing in a tapered fashion from a relatively narrow tip containing smaller and infrequent crystals to wider regions having more densely packed and larger crystals. Defined for the first time by direct visual 3D imaging, these data describe the size, shape, location, orientation, and development of early crystals in normal bone collagen. The results suggest that platelet-shaped crystals are arranged in channels or grooves which are formed by collagen hole zones in register and that crystal sizes may exceed the dimensions of hole zones. Such data agree with those from mineral-matrix interaction in normally calcifying avian tendon obtained by similar high voltage tomographic means, but in addition they indicate a possible gradual and continuous deposition of crystals in collagen of bone unlike tendon and imply that individual collagen fibrils in local regions of osteoid are organized such that they all may be aligned in a coherent manner.

NASA Discipline Number 40-40↗
NASA NTRS2000

Coronal Reconstruction using LASCO and UVCS Observations

The main goal of the research described in the original proposal was to develop methods to quantify coronal and inner-heliospheric velocity fields of the 'quiet' solar wind. For this we planned to use several sources of observations:(1) SOHO/UVCS velocity information in the range 1.5-3 Solar Radii obtained from Doppler dimming observations; (2) projected solar wind velocities (into the plane of the sky) obtained from SOHO/ LASCO images (1.1-30 Solar Radii), primarily derived from two-dimensional correlation tracking techniques; (3) Interplanetary scintillation observations of the heliospheric (> 26 Solar Radii) solar wind velocity from the Solar-Terrestrial Environment Laboratory (STELab) in Nagoya, Japan; (4) Ecliptic in situ observations: data for the ecliptic solar wind are available from the MIT and Los Alamos plasma experiments on the Earth-orbiting IMP-8 spacecraft, from the Cellas instrument on SOHO near the LI Lagrange point, and from the WIND spacecraft; (5) Out-of-ecliptic in situ observations: these data are available primarily from the Los Alamos SWOOPS instrument on Ulysses, which passed over the solar north pole in August 1995, about one year prior to the Whole Sun Month period. Where ever possible we planned to use the first Whole Sun Month as the main time period for the analysis, since we expected that for this period it would be easiest to obtain adequate coverage over the extended period of time required to analyze 'quiet' solar wind patterns. Beyond the observations mentioned above (primarily SOHO data) we extended our selection of data to several events identified in the Yohkoh/SXT data base which directly promised to provide us with clues about the connection between the slow solar wind observed by IPS in the inner heliosphere and their sources in the low corona, in particular active regions. We also obtained valuable results using SWOOPS ill situ observations from the pole-to-pole passage of Ulysses in a comparison with solar wind velocities derived from a tomographic reconstruction of Nagoya IPS observations.

Hick, P. P.↗
NASA NTRS1982

Model studies of laser absorption computed tomography for remote air pollution measurement

Model studies of the potential of laser absorption-computed tomography are presented which demonstrate the possibility of sensitive remote atmospheric pollutant measurements, over kilometer-sized areas, with two-dimensional resolution, at modest laser source powers. An analysis of this tomographic reconstruction process as a function of measurement SNR, laser power, range, and system geometry, shows that the system is able to yield two-dimensional maps of pollutant concentrations at ranges and resolutions superior to those attainable with existing, direct-detection laser radars.

Wolfe, D. C., Jr.↗
NASA NTRS1982

Holographic interferometry of transparent media using light scattered by embedded test objects

Fringe formation and localization in holographic interferometry of transparent media are discussed for configurations in which light enters the medium and is scattered back through it by an embedded diffuse object. Fringe order numbers are doubled, and the fringe localization region is translated and compressed by a factor of two. The results are applicable to tomographic reconstruction of aerodynamic density fields around opaque test objects.

Prikryl, I.↗
NASA NTRS1992

Ultrasonic time-of-flight monitoring of the position of the liquid/solid interface during the Bridgman growth of germanium

Ultrasound has been used to track the movement of the solid/liquid interface during the vertical Bridgman growth of germanium. Digitally processed data representing the received ultrasonic signal indicated a time lag prior to crystal growth, and showed a growth rate close to the pulling rate of the furnace. No effect of the ultrasonic energy on the growth of the crystal or on the formation of defects was observed. The interface was located to within 0.3 mm in the presence of substantial temperature gradients. An extension of the work presented could lead to a tomographic reconstruction of the interface shape.

Carter, John N.↗
NASA NTRS1994

Tomographic separation of composite spectra. 2: The components of 29 UW Canis Majoris

We have analyzed the UV photospheric lines of 29 CMa, a 4.39 day period, double-lined O-type spectroscopic binary. Archival data from International Ultraviolet Explorer (IUE)(28 spectra well distributed in oribital phase) were analyzed with several techniques. We find that the mass ratio is q = 1.20 +/- 0.16 (secondary more massive) based on three independent arguments. A tomography algorithm was used to produce the separate spectra of the two stars in six UV spectral regions. The MK spectral classifications of the primary and secondary, O7.5-8 Iab and O9.7 Ib, respectively, were estimated through a comparison of UV line ratios with those in spectral standard stars. The flux ratio of the stars in the UV is 0.36 +/- 0.07 (primary brighter). The primary has a strong P Cygni NIV wavelength 1718 feature, indicating a strong stellar wind. We also present tomographic reconstructions of visual spectral data in the range 4300-4950 A, based on seven observations of differing orbital phases, which confirm the UV classifications, and show that the primary is an Of star. From the spectral classifications, we estimate the temperatures of the stars to be 33,750 K and 29,000 K for primary and secondary, respectively. We then fit visual and UV light curves and show that reasonably good fits can be obtained with these temperatures, a semicontact configuration, an inclination of 74 deg. +/- 2 deg., and an intensity ratio r is less than 0.5.

Bagnuolo, William G., Jr.↗