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NASA NTRS2008

Rapid Biochemical Analysis on the International Space Station (ISS): Preparing for Human Exploration of the Moon and Mars

The Lab-on-a-Chip Application Development - Portable Test System, known as LOCAD-PTS, was launched to the International Space Station (ISS) aboard Space Shuttle Discovery (STS-116) on December 9th,2006. Since that time, it has remained onboard ISS and has been operated by the crew on 10 separate occasions LOCAD-PTS is a handheld device for rapid biochemical analysis; it consists of a spectrophotometer, a series of interchangeable cartridges, a pipette and several clean/sterilized swabbing kits to obtain samples from ISS surfaces. Sampling, quantitative analysis and data retrieval is performed onboard, therefore reducing the need to return samples to Earth. Less than 20 minutes are required from sampling to data, significantly faster than existing culture-based methods on ISS, which require 3-5 days. Different cartridges are available for the detection of different target molecules (simply by changing the formulation within each cartridge), thereby maximizing the benefit and applications addressed by a single instrument. Initial tests on ISS have focused on the detection of the bact.erial macromolecule endotoxin, a component of bacterial cell walls. LOCAD-PTS detects endotoxin with a cartridge that contains a formulation known as Limulus Amebocyte Lysate (LAL) assay. LAL is derived from blood of the horseshoe crab, Limulus polyphemus, and detects enodotoxin with an enzyme cascade that triggers generation Of a yellow colored dye, p-nitroanaline. The more p-nitroanaline product, the more endotoxin is in the original sample. To enable quantitative analysis, the absorbance of this color is measured by LOCAD-PTS through a 395 nm filter and compared with an internal calibration curve, to provide a reading on the LED display that ranges from 0.05 Endotoxin Units (EU)/ml to 5 EU/ml. Several surface sites were analyzed within ISS between March 2007 and February 2008, including multiple locations in the US Laboratory Destiny, Node 1 Unity, AMock, and Service Module Zvezda. The goals of this initial study were to i) test the cleanliness of reagents/supplies on orbit, ii) test the crew's ability to collect and process a sample in microgravity without contamination, iii) demonstrate nominal function of the LOCAD-PTS, and iv) provide a general survey of endotoxin within the ISS. The surface sites varied greatly in terms of their frequency-of-use and material texture/composition; from relatively smooth aluminum, to fabric, to the room temperature vulcanizing (RTV) rubber of a Extravehicular Mobility Unit (EMU) spacesuit. Results showed that: i) the swabbing kits and reagents remained clean on orbit, ii) the crew could collect and process a sample without contamination, and iii) the LOCAD-PTS functioned nominally in > 99% of the 55 tests completed. We will present detailed results of the survey of endotoxin on ISS surfaces. These results and technology are important in the near-term - by providing an extra tool in the toolbox for ISS microbial monitoring. They are also important in the longer term as valuable preparation for human exploration of the Moon and Mars. One of the proposed science goals for the human exploration of Mars will be to detect and characterize any indigenous biological molecules that may exist on the Martian surface. To achieve that goal, the crew must have the technology available onboard to differentiate indigenous biology from any terrestrial biological material brought to Mars by the spacecraft and crew (termed 'forward contamination'). The LAL assay is already one of the official methods used by NASA's planetary protection program to certify cleanliness of interplanetary robotic spacecraft prior to launch; and therefore endotoxin is a good marker of forward contamination (as well as other microbial molecules detectable with LOCAD-PTS e.g. box-1, 3-glucan and lipoteichoic acid). Furthermore, the distribution and abundance of these molecules on the ISS provides a good indicator of what to expect on the Crew Exploratioehicle Orion, the lunar lander Antares, and future crewed spacecraft destined for Mars. In addition, technology such as LOCAD-PTS has been proposed to help evaluate forward contamination during lunar surface operations by the crew, as preparation for the human exploration of Mars.

Maule, J.↗

NASA NTRS1991

Effect of leading-edge geometry on boundary-layer receptivity to freestream sound

The receptivity to freestream sound of the laminar boundary layer over a semi-infinite flat plate with an elliptic leading edge is simulated numerically. The incompressible flow past the flat plate is computed by solving the full Navier-Stokes equations in general curvilinear coordinates. A finite-difference method which is second-order accurate in space and time is used. Spatial and temporal developments of the Tollmien-Schlichting wave in the boundary layer, due to small-amplitude time-harmonic oscillations of the freestream velocity that closely simulate a sound wave travelling parallel to the plate, are observed. The effect of leading-edge curvature is studied by varying the aspect ratio of the ellipse. The boundary layer over the flat plate with a sharper leading edge is found to be less receptive. The relative contribution of the discontinuity in curvature at the ellipse-flat-plate juncture to receptivity is investigated by smoothing the juncture with a polynomial. Continuous curvature leads to less receptivity. A new geometry of the leading edge, a modified super ellipse, which provides continuous curvature at the juncture with the flat plate, is used to study the effect of continuous curvature and inherent pressure gradient on receptivity.

Lin, Nay↗

NASA NTRS1975

Sasaki's variational optimization analysis of temperature and moisture advection in a severe storm environment

Temperature and moisture advection patterns of dry air intrusion were analyzed by a variational optimization method to relate mesoscale advection to a severe thunderstorm environment. The analysis results presented here were obtained from a case study, May 26, 1973, when a tornado squall line developed in Oklahoma in conjunction with a clearly delineated dry air intrusion. Observations from the synoptic upper air network were used for inputs of horizontal wind components, potential temperature, and mixing ratio at each 50 mb increment from 950 to 100 mb. An objective analysis was performed to assign values of the variables to grid points of a 15 x 14 horizontal grid with approximate 125 km grid spacing at each pressure level. After the analysis the data fields were smoothed using a variational formalism.

Mcfarland, M. J.↗

NASA NTRS1983

Effect of limb darkening functions variations on deconvolution of wide-field-of-view measurements of earth emitted radiation

A solution is presented to the problem of deconvolving wide field of view measurements of earth-emitted radiation for the case of limb-darkening functions which are geographically dependent. The method of linear perturbations is used and the effects of limb-darkening function variations at various scales are evaluated. A simple model for the geographical variation of the limb-darkening function based on the radiant exitance is introduced. It is shown that the effect of these variations on the global average radiant exitance vanishes identically, and is insignificant for large spatial scales. For wave numbers six through twelve, the limb-darkening effects are small but possibly significant. At wave numbers greater than twelve, the noise due to meteorological variability dominates for an orbit altitude of 1100 km. The smallness of these effects is due to the smoothness of the monthly averaged radiant exitance field.

Smith, G. L.↗

NASA NTRS2009

Structural Design Considerations for an 8-m Space Telescope

NASA's upcoming ARES V launch vehicle, with its' immerse payload capacities (both volume and mass) has opened the possibilities for a whole new paradigm of space observatories. It becomes practical to consider a monolith mirror of sufficient size to permit significant scientific advantages, both in collection area and smoothness or figure at a reasonable price. The technologies and engineering to manufacture and test 8 meter class monoliths is mature, with nearly a dozen of such mirrors already in operation around the world. This paper will discuss the design requirements to adapt an 8m meniscus mirror into a Space Telescope System, both launch and operational considerations are included. With objects this massive and structurally sensitive, the mirror design must include all stages of the process. Based upon the experiences of the Hubble Space Telescope, testing and verification at both component and integrated system levels are considered vital to mission success. To this end, two different component level test methods for gravity sag (the so call zero- gravity simulation or test mount) are proposed, with one of these methods suitable for the full up system level testing as well.

Arnold, William R. Sr.↗

NASA NTRSDate not supplied

Development of a C-ELS Specimen-Based Numerical Benchmark for Mode II Delamination and Assessment of Two VCCT-Based Propagation Strategies

A finite element (FE) benchmark example inspired by the calibrated end-loaded split (C-ELS) specimen is developed and used to assess the performance of delamination propagation capabilities based on linear elastic fracture mechanics (LEFM). The C-ELS specimen has the advantage of a longer region of stable delamination propagation compared to the existing mode II benchmark case. The new benchmark example may therefore provide a better assessment tool by enabling more stable crack growth in regions further away from the boundary conditions or load application. First, a benchmark result is created manually using two-dimensional finite element models of the C-ELS specimen with different delamination lengths. Second, the performance of the virtual crack closure technique (VCCT) delamination propagation capabilities in the Abaqus/Standard®1 FE code and the recently developed Progressive Release eXplicit-VCCT (PRX-VCCT) method are assessed by comparing the results to the benchmark case. Two examples with different starter delamination lengths are studied. A shorter starter length is chosen to create a scenario with unstable delamination propagation. A longer delamination encourages stable delamination propagation. Detailed results from three-dimensional analyses with aligned and misaligned meshes and two levels of mesh refinement are provided. In general, good agreement can be achieved between the results obtained from the quasi-static propagation analysis and the benchmark analysis. Numerical artifacts including anomalous unreleased nodes in the crack wake and zig-zag crack fronts occur for propagation analyses using Abaqus/Standard VCCT. In comparison, continuous, smooth, delamination fronts are observed for PRX-VCCT. The use of the benchmark case to assess different VCCT-based propagation strategies illustrates the value of establishing benchmark cases.

Composite Materials↗

NASA NTRS1996

Wavelet Sparse Approximate Inverse Preconditioners

There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.

Chan, Tony F.↗

NASA NTRS2024

Oculometric Biomarkers of Visuomotor Deficits in Clinically Asymptomatic Patients With Systemic Lupus Erythematosus Undergoing Long-Term Hydroxychloroquine Treatment

Introduction: This study examines a set of oculomotor measurements, or “oculometric” biomarkers, as potential early indicators of visual and visuomotor deficits due to retinal toxicity in asymptomatic Systemic Lupus Erythematosus (SLE) patients on long-term hydroxychloroquine (HCQ) treatment. The aim is to identify subclinical functional impairments that are otherwise undetectable by standard clinical tests and to link them to structural retinal changes. Methods: We measured oculomotor responses in a cohort of SLE patients on chronic HCQ therapy using a previously established behavioral task and analysis technique. We also examined the relationship between oculometrics, OCT measures of retinal thickness, and standard clinical perimetry measures of visual function in our patient group using Bivariate Pearson Correlation and a Linear Mixed-Effects Model (LMM). Results: Significant visual and visuomotor deficits were found in 12 asymptomatic SLE patients on long-term HCQ therapy compared to a cohort of 17 age-matched healthy controls. Notably, six oculometrics were significantly different. The median initial pursuit acceleration was 22%, steady-state pursuit gain 16%, proportion smooth 7%, and target speed responsiveness 31% lower, while catch-up saccade amplitude was 46% and fixation error 46% larger. Excluding the two patients with diagnosed mild toxicity, four oculometrics, all but fixation error and proportion smooth, remained significantly impaired compared to controls. Across our population of 12 patients (24 retinae), we found that pursuit latency, initial acceleration, steady-state gain, and fixation error were linearly related to retinal thickness even when age was accounted for, while standard measures of clinical function (Mean Deviation and Pattern Standard Deviation) were not. Discussion: Our data show that specific oculometrics are sensitive early biomarkers of functional deficits in SLE patients on HCQ that could be harnessed to assist in the early detection of HCQ-induced retinal toxicity and other visual pathologies, potentially providing early diagnostic value beyond standard visual field and OCT evaluations.

eye movements↗

NASA NTRS1980

Cyclic plasticity and failure of structural components

An analytical approach for low-cycle fatigue prediction is presented. The approach combines a cyclic plasticity model with the finite element method and a damage accumulation criterion for ductile metals. The cyclic plasticity model is based on the concept of the combination of several yield surfaces. The surfaces are related to the material uniaxial stress-strain curve idealized by piecewise linear segments. The damage criterion is based on the Coffin-Manson formulae modified for the mean stress variation effect. It is extended to the multiaxial varying stress-strain field and applied for both the crack initiation and the crack growth processes. The stable slow crack growth rate is approximated by the damage accumulation gradient computed from the cracked finite element models. This procedure requires fatigue testing data of only smooth specimens under constant strain amplitudes. The present approach is illustrated by numerical examples of an aircraft wing stiffened panel subjected to compression, which causes material yielding and residual tension.

Kalev, I.↗

NASA NTRS1996

Eye Movements Reveal Hierarchical Motion Processing

Purpose: In the analysis of visual motion, local features such as orientation are analyzed early in the cortical processing stream (V1), while integration across orientation and space is thought to occur in higher cortical areas such as MT, MST, etc. If all areas provide inputs to eye movement control centers, we would expect that local properties would drive eye movements with relatively short latencies, while global properties would require longer latencies. When such latencies are observed, they can provide information about when (and where?) various stimulus properties are analyzed. Methods: The stimulus employed was an elliptical Gabor patch with a drifting carrier, in which the orientations of the carrier grating and the contrast window were varied independently. We have previously demonstrated that the directional percepts evoked by this stimulus vary between the "grating direction" (the normal to the grating's orientation) and the "window direction", and that similar effects can be observed in reflexive eye movements. Subjects viewed such a stimulus while attempting to maintain steady fixation on the center of the pattern, and the small reflexive eye movements ("stare OKN") were recorded. In the middle of the trial, the orientation of either the grating or the window was rotated smoothly by 30 degrees. Results: Responses to the shift of both grating orientation and window orientation are seen in the average OKN slow phase velocity. Grating rotations produce a rapid OKN rotation to the grating direction (100 ms latency, 300 ms time constant), followed by a slower rebound to the steady state perceived direction midway between the grating and window directions. Window rotations, on the other hand, evoke a slower response (200 ms latency, 500 ms time constant). Conclusions: The results demonstrate multiple cortical inputs to eye movement control: a fast, early input driven by orientation, and a slower input from higher areas sensitive to global stimulus properties.

Mulligan, Jeffrey B.↗

NASA NTRS1974

A method for the measurement and the statistical analysis of atmospheric turbulence

The instantaneous values of output voltages representing the wind velocity vector and the temperature at different elevations of the 250-foot meteorological tower located at NASA Wallops Flight Center are provided with the three dimensional split-film TSI Model 1080 anemometer system. The output voltages are sampled at a rate of one every 5 milliseconds, digitized and stored on digital magnetic tapes for a time period of approximately 40 minutes, with the use of a specially designed data acqusition system. A new calibration procedure permits the conversion of the digital voltages to the respective values of the temperature and the velocity components in a Cartesian coordinate system connected with the TSI probe with considerable accuracy. Power, cross, coincidence and quadrature spectra of the wind components and the temperature are obtained with the use of the fast Fourier transform. The cosine taper data window and ensemble and frequency smoothing techniques are used to provide smooth estimates of the spectral functions.

Tieleman, H. W.↗

NASA NTRS1993

Models of Neptune's smooth recurrent radio emission

The quantitative response of the Planetary Radio Astronomy (PRA) instrument to a wave with polarization ellipse of arbitrary shape and orientation, arriving at the antennas from any direction, can be determined. This capability is used to model the time variation of intensity and circular polarization over a range of radio frequencies for proposed radio-source locations and emission characteristics at Neptune. At frequencies below 400 kHz the observed variation of intensity, polarization, and phase are closely simulated in an offset tilted dipole magnetic field by conjugate sources at midlatitude with filled emission cones. The phase of emission at higher frequencies is reproduced by sources at lower latitude. Modeled wide-cone emission does not reach the spacecraft at the observed phase nor have the polarization sense observed before closest approach. Source-surface maps of apparent polarization for the period before closest approach when instrumental response is especially sensitive to source location is presented. The method is capable of extension to more realistic models of the magnetic field.

Sawyer, Constance↗

NASA NTRS1997

Eddy Current Method for Fatigue Testing

Flux-focusing electromagnetic sensor using a ferromagnetic flux-focusing lens simplifies inspections and increases detectability of fatigue cracks and material loss in high conductivity material. A ferrous shield isolates a high-turn pick-up coil from an excitation coil. Use of the magnetic shield produces a null voltage output across the receiving coil in presence of an unflawed sample. Redistribution of the current flow in the sample caused by the presence of flaws. eliminates the shielding condition and a large output voltage is produced, yielding a clear unambiguous flaw signal. Maximum sensor output is obtained when positioned symmetrically above the crack. By obtaining position of maximum sensor output, it is possible to track the fault and locate the area surrounding its tip. Accuracy of tip location is enhanced by two unique features of the sensor; a very high signal-to-noise ratio of the probe's output resulting in an extremely smooth signal peak across the fault, and a rapidly decaying sensor output outside a small area surrounding the crack tip enabling the search region to be clearly defined. Under low frequency operation, material thinning due to corrosion causes incomplete shielding of the pick-up coil. Low frequency output voltage of the probe is therefore a direct indicator of thickness of the test sample. Fatigue testing a conductive material is accomplished by applying load to the material, applying current to the sensor, scanning the material with the sensor, monitoring the sensor output signal, adjusting material load based on the sensor output signal of the sensor, and adjusting position of the sensor based on its output signal.

Simpson, John W.↗

NASA NTRS1999

The Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

The Kalman filter is the optimal filter in the presence of known Gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions (e.g., Miller 1994). Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz (1963) model as well as more realistic models of the oceans (Evensen and van Leeuwen 1996) and atmosphere (Houtekamer and Mitchell 1998). A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter equations to allow for correct update of the ensemble members (Burgers 1998). The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to quite puzzling in that results of state estimate are worse than for their filter analogue (Evensen 1997). In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use Lorenz (1963) model to test and compare the behavior of a variety implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

Zhu, Yanqiu↗

NASA NTRS2003

Long-Range Solar Activity Predictions: A Reprieve from Cycle #24's Activity

We discuss the field of long-range solar activity predictions and provide an outlook into future solar activity. Orbital predictions for satellites in Low Earth Orbit (LEO) depend strongly on exospheric densities. Solar activity forecasting is important in this regard, as the solar ultra-violet (UV) and extreme ultraviolet (EUV) radiations inflate the upper atmospheric layers of the Earth, forming the exosphere in which satellites orbit. Rather than concentrate on statistical, or numerical methods, we utilize a class of techniques (precursor methods) which is founded in physical theory. The geomagnetic precursor method was originally developed by the Russian geophysicist, Ohl, using geomagnetic observations to predict future solar activity. It was later extended to solar observations, and placed within the context of physical theory, namely the workings of the Sun s Babcock dynamo. We later expanded the prediction methods with a SOlar Dynamo Amplitude (SODA) index. The SODA index is a measure of the buried solar magnetic flux, using toroidal and poloidal field components. It allows one to predict future solar activity during any phase of the solar cycle, whereas previously, one was restricted to making predictions only at solar minimum. We are encouraged that solar cycle #23's behavior fell closely along our predicted curve, peaking near 192, comparable to the Schatten, Myers and Sofia (1996) forecast of 182+/-30. Cycle #23 extends from 1996 through approximately 2006 or 2007, with cycle #24 starting thereafter. We discuss the current forecast of solar cycle #24, (2006-2016), with a predicted smoothed F10.7 radio flux of 142+/-28 (1-sigma errors). This, we believe, represents a reprieve, in terms of reduced fuel costs, etc., for new satellites to be launched or old satellites (requiring reboosting) which have been placed in LEO. By monitoring the Sun s most deeply rooted magnetic fields; long-range solar activity can be predicted. Although a degree of uncertainty in the long-range predictions remains, requiring future monitoring, we do not expect the next cycle's + 2-sigma value will rise significantly above solar cycle #23's activity level.

Richon, K.↗

NASA NTRS1997

A Numerical Method for Calculating Stellar Occultation Light Curves from an Arbitrary Atmospheric Model

We present a method for speeding up numerical calculations of a light curve for a stellar occultation by a planetary atmosphere with an arbitrary atmospheric model that has spherical symmetry. This improved speed makes least-squares fitting for model parameters practical. Our method takes as input several sets of values for the first two radial derivatives of the refractivity at different values of model parameters, and interpolates to obtain the light curve at intermediate values of one or more model parameters. It was developed for small occulting bodies such as Pluto and Triton, but is applicable to planets of all sizes. We also present the results of a series of tests showing that our method calculates light curves that are correct to an accuracy of 10(exp -4) of the unocculted stellar flux. The test benchmarks are (i) an atmosphere with a l/r dependence of temperature, which yields an analytic solution for the light curve, (ii) an atmosphere that produces an exponential refraction angle, and (iii) a small-planet isothermal model. With our method, least-squares fits to noiseless data also converge to values of parameters with fractional errors of no more than 10(exp -4), with the largest errors occurring in small planets. These errors are well below the precision of the best stellar occultation data available. Fits to noisy data had formal errors consistent with the level of synthetic noise added to the light curve. We conclude: (i) one should interpolate refractivity derivatives and then form light curves from the interpolated values, rather than interpolating the light curves themselves; (ii) for the most accuracy, one must specify the atmospheric model for radii many scale heights above half light; and (iii) for atmospheres with smoothly varying refractivity with altitude, light curves can be sampled as coarsely as two points per scale height.

Chamberlain, D. M.↗

NASA NTRS2001

Cloud Spatial Structure and 3D Radiative Transfer

Cloud radiative properties are sensitive to drop size and other parameters of cloud micro-structure, but also to cloud shape, spacing, and other parameters of cloud macro-structure, including internal fractal structure. New information on cloud structure is being derived from a variety of cloud radars and lidars. Ongoing field programs such as DoE/ARM are improving the measurement and modelling of physical and radiative properties of clouds. A parallel effort is underway to improve cloud remote sensing, especially from the new suite of EOS (Earth Observing System) instruments which are beginning to provide higher spectral, spatial resolution, and/or angular resolution. Key parameters for improving pixel-scale retrievals are cloud thickness and photon mean-free-path, which together determine the scale of "radiative smoothing" of cloud fluxes and radiances. This scale has been observed as a change in the spatial spectrum of Landsat cloud radiances, and was also recently found with the Goddard micropulse lidar, by searching for returns from directions nonparallel to the incident beam. "Offbeam" Lidar returns are now being used to estimate the cloud "radiative Green's function", (G). G depends on cloud thickness and may be used to retrieve that important quantity. G is also being applied to improving simple estimates of cloud radiative properties that are based on the "Independent Pixel Approximation" or IPA. This and other measurements of 3D transfer in clouds, coupled with Monte Carlo and other 3D transfer methods, are beginning to provide a better understanding of the dependence of radiation on cloud inhomogeneity, and to suggest new retrieval and parameterization algorithms which take account of cloud inhomogeneity. An international "Intercomparison of 3D Radiation Codes" or I3RC, program is underway to coordinate and evaluate the variety of 3D radiative transfer methods now available, and to make them more widely available. Information is on the Web at: http://climate.gsfc.nasa.gov/I3RC. Input consists of selected cloud fields derived from data sources such as radar, microwave and satellite, and from models involved in the GEWEX Cloud Systems Studies. Output is selected radiative quantities that characterize the large-scale properties of the fields of radiative fluxes and heating. Several example cloud fields will be used to illustrate the effects of cloud inhomogeneity and 3D radiation.

Cahalan, Robert F.↗

NASA NTRS1987

New main reflector, subreflector and dual chamber concepts for compact range applications

A compact range is a facility used for the measurement of antenna radiation and target scattering problems. Most presently available parabolic reflectors do not produce ideal uniform plane waves in the target zone. Design improvements are suggested to reduce the amplitude taper, ripple and cross polarization errors. The ripple caused by diffractions from the reflector edges can be reduced by adding blended rolled edges and shaping the edge contour. Since the reflected edge continues smoothly from the parabola onto the rolled surface, rather than being abruptly terminated, the discontinuity in the reflected field is reduced which results in weaker diffracted fields. This is done by blending the rolled edges from the parabola into an ellipse. An algorithm which enables one to design optimum blended rolled edges was developed that is based on an analysis of the continuity of the surface radius of curvature and its derivatives across the junction. Futhermore, a concave edge contour results in a divergent diffracted ray pattern and hence less stray energy in the target zone. Design equations for three-dimensional reflectors are given. Various examples were analyzed using a new physical optics method which eliminates the effects of the false scattering centers on the incident shadow boundaries. A Gregorian subreflector system, in which both the subreflector and feed axes are tilted, results in a substantial reduction in the amplitude taper and cross polarization errors. A dual chamber configuration is proposed to eliminate the effects of diffraction from the subreflector and spillover from the feed. A computationally efficient technique, based on ray tracing and aperture integration, was developed to analyze the scattering from a lossy dielectric slab with a wedge termination.

Pistorius, C. W. I.↗