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All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Theoretical analysis of Wolter/LSM X-ray telescope systems

A ray tracing analysis has been performed for the spectral slicing zoom X-ray telescope for configurations in which a convex layered synthetic microstructure (LSM) optic is placed in front of the prime focus or a concave LSM optic is placed behind the prime focus. The analysis has considered the geometrical shape of the LSM optic to be either a hyperboloid, sphere, ellipsoid or constant optical path aspheric element for two configurations of the glancing incidence X-ray telescope: the ATM Experimental S-056 Wolter I system and the Stanford/MSFC Wolter-Schwarzchild nested system. For the different systems the RMS blur circle radii, the point spread function (PSF), the full width half maximum (FWHM) of the PSF have been evaluated as a function of field angle and magnification of the secondary to determine resolution of the system. The effects of decentration and tilt of the selected LSM element on the performance of the system have been studied to determine mounting and alignment tolerances.

Shealy, D. L.↗
NASA NTRS2010

A Review of Discrete Element Method (DEM) Particle Shapes and Size Distributions for Lunar Soil

As part of ongoing efforts to develop models of lunar soil mechanics, this report reviews two topics that are important to discrete element method (DEM) modeling the behavior of soils (such as lunar soils): (1) methods of modeling particle shapes and (2) analytical representations of particle size distribution. The choice of particle shape complexity is driven primarily by opposing tradeoffs with total number of particles, computer memory, and total simulation computer processing time. The choice is also dependent on available DEM software capabilities. For example, PFC2D/PFC3D and EDEM support clustering of spheres; MIMES incorporates superquadric particle shapes; and BLOKS3D provides polyhedra shapes. Most commercial and custom DEM software supports some type of complex particle shape beyond the standard sphere. Convex polyhedra, clusters of spheres and single parametric particle shapes such as the ellipsoid, polyellipsoid, and superquadric, are all motivated by the desire to introduce asymmetry into the particle shape, as well as edges and corners, in order to better simulate actual granular particle shapes and behavior. An empirical particle size distribution (PSD) formula is shown to fit desert sand data from Bagnold. Particle size data of JSC-1a obtained from a fine particle analyzer at the NASA Kennedy Space Center is also fitted to a similar empirical PSD function.

Lane, John E.↗
NASA NTRS1992

Wave diffraction in weak cosmic-ray-modified shocks

Weakly multidirectional, long-wavelength cosmic-ray-modified shocks are studied via multiple scale perturbation techniques. The effects of diffraction are discussed in terms of Green's function solutions of the linearized 1 + 3D Burgers and 1 + 3D KdVB equations, and also in terms of solutions with singular Dirac delta initial distributions. The solutions show a monotonic decrease of the wave-front curvature with increasing time owing to the effects of wave diffraction. The shape of the wave surface is discussed in terms of solutions S to the wave eikonal equation corresponding to singular initial conditions. For the fast magnetosonic wave propagating in the positive x-direction, the wave phase surface S = 0 has elliptic cross sections with the planes x = constant and has a convex paraboloidal shape. Plane-wave solutions of the 1 + 3D KdVB equation are discussed.

Webb, G. M.↗
NASA NTRS2005

Generic Sensor Modeling Using Pulse Method

Recent development of high spatial resolution satellites such as IKONOS, Quickbird and Orbview enable observation of the Earth's surface with sub-meter resolution. Compared to the 30 meter resolution of Landsat 5 TM, the amount of information in the output image was dramatically increased. In this era of high spatial resolution, the estimation of spatial quality of images is gaining attention. Historically, the Modulation Transfer Function (MTF) concept has been used to estimate an imaging system's spatial quality. Sometimes classified by target shapes, various methods were developed in laboratory environment utilizing sinusoidal inputs, periodic bar patterns and narrow slits. On-orbit sensor MTF estimation was performed on 30-meter GSD Landsat4 Thematic Mapper (TM) data from the bridge pulse target as a pulse input . Because of a high resolution sensor s small Ground Sampling Distance (GSD), reasonably sized man-made edge, pulse, and impulse targets can be deployed on a uniform grassy area with accurate control of ground targets using tarps and convex mirrors. All the previous work cited calculated MTF without testing the MTF estimator's performance. In previous report, a numerical generic sensor model had been developed to simulate and improve the performance of on-orbit MTF estimating techniques. Results from the previous sensor modeling report that have been incorporated into standard MTF estimation work include Fermi edge detection and the newly developed 4th order modified Savitzky-Golay (MSG) interpolation technique. Noise sensitivity had been studied by performing simulations on known noise sources and a sensor model. Extensive investigation was done to characterize multi-resolution ground noise. Finally, angle simulation was tested by using synthetic pulse targets with angles from 2 to 15 degrees, several brightness levels, and different noise levels from both ground targets and imaging system. As a continuing research activity using the developed sensor model, this report was dedicated to MTF estimation via pulse input method characterization using the Fermi edge detection and 4th order MSG interpolation method. The relationship between pulse width and MTF value at Nyquist was studied including error detection and correction schemes. Pulse target angle sensitivity was studied by using synthetic targets angled from 2 to 12 degrees. In this report, from the ground and system noise simulation, a minimum SNR value was suggested for a stable MTF value at Nyquist for the pulse method. Target width error detection and adjustment technique based on a smooth transition of MTF profile is presented, which is specifically applicable only to the pulse method with 3 pixel wide targets.

Helder, Dennis L.↗
NASA NTRS1994

Late Cenozoic flexural deformation of the middle U.S. Atlantic passive margin

Despite the century-long recognition of regional epeirogeny along the middle Atlantic passive margin, relatively few studies have focused on understanding postrift uplift mechanisms. Here, we demonstrate that epeirogenic uplift of the central Appalachian Piedmont and subsidence of the Salisbury Embayment represent first-order, flexural isostatic processes driven by continental denudation and offshore deposition. Our results show that regional epeirogenic processes, present on all Atlantic-type passive margins, are best resolved by specific stratigraphic and geomorphic relationships, rather than topography. A simple one-dimensional geodynamic model, constrained by well-dated Baltimore Canyon trough, Coastal Plain, and lower Susquehanna River (piedmont) stratigraphy, simulates flexural deforamtion of the U.S. Atlantic margin. The model represents the passive margin lithosphree as a uniformly thick elastic plate, without horizontal compressive stresses, that deforms flexurally under the stress of strike-averaged, vertically applied line loads. Model results illustrate a complex interaction among margin stratigraphy and geomorphology, the isostatic repsonse to denudational and depositional processes, and the modulating influence of exogenic forces such as eustasy. The current elevation, with respect to modern sea level, of fluvial terraces and correlateive Coastal Plain deposits or unconformities is successfully predicted through the synthesis of paleotopography, eustatic change, and margin flexure. Results suggest that the middle U.S. Atlantic margin landward of East Coast Magnetic Anomaly is underlain by lithoshpere with an average elastic thickness of 40 km (flexural rigidity, D = 4 X 10(exp 23) N m), the margin experience an average, long-term denudation rate of approximately 10m/m.y., and the Piedmont has been flexurally upwaped between 35 and 130 meters in the last 15 m.y. Long term isostatic continental uplift resulting rom denudation and basin subsidence resulting rom sediment loading are accomodated primately by a convex-up flexural hinge, physiographically represented by the Fall Zone. Our results elucidate an inherent danger in using topography alone to constrain late-stage passive margin deformation mechanisms. Only through careful synthesis of field stratigraphic and geomorphic elements such as fluvial terraces, Coastal Plain deposits, and offshore stratigraphy can age control be extended from the offshore depositional setting to the erosionally dominated continent. This sudy demonstrates that despite a relatively subdued topography, the middle U.S. Atlantic margin experiences progressive flexural isostatic deformation similar to that proposed for high-relief margins characterized by great escarpments. Thus margin topographic diversity remains a function of other factors, such as lithospheric composition and/or structure, supracrustal stratigraphy and structure, degree of drainage integration, drainage divide migration and climate.

Pazzaglia, Frank J.↗
NASA NTRS1985

A Natural Bias Approach to Cardinal Spline Curves

The cardinal spline approach to defining interpolatory curves is of interest in the application of computer graphics to modelling and animation problems. The formulation of this interpolation problem (C) a vector valued function V is obtained which forms a C1 map from 0,n into the plane in such a way that V(i) and V prime (i) attain prespecified (vector) values P sub i and T sub i for the integers i=0, 1,...n. The intent is that the planar curves V(s) pass through each point P sub i in the direction corresponding to T sub i. In actual practice it is common for only the interpolation points P sub i to be user specified. Suitable tangents T sub i are then provided by some heuristic to complete the specification of (C). A convex control polygon yields a convex interpolant. Examples exist where the interpolant fails to be convex if the tangents are left unbiased.

Fletcher, G. Y.↗
NASA NTRS2003

Imparting Desired Attributes by Optimization in Structural Design

Commonly available optimization methods typically produce a single optimal design as a Constrained minimum of a particular objective function. However, in engineering design practice it is quite often important to explore as much of the design space as possible with respect to many attributes to find out what behaviors are possible and not possible within the initially adopted design concept. The paper shows that the very simple method of the sum of objectives is useful for such exploration. By geometrical argument it is demonstrated that if every weighting coefficient is allowed to change its magnitude and its sign then the method returns a set of designs that are all feasible, diverse in their attributes, and include the Pareto and non-Pareto solutions, at least for convex cases. Numerical examples in the paper include a case of an aircraft wing structural box with thousands of degrees of freedom and constraints, and over 100 design variables, whose attributes are structural mass, volume, displacement, and frequency. The method is inherently suitable for parallel, coarse-grained implementation that enables exploration of the design space in the elapsed time of a single structural optimization.

Sobieszczanski-Sobieski, Jaroslaw↗
NASA NTRS2017

Coronagraph Design Optimization for Segmented Aperture Telescopes

The goal of directly imaging Earth-like planets in the habitable zone of other stars has motivated the design of coronagraphs for use with large segmented aperture space telescopes. In order to achieve an optimal trade-o between planet light throughput and di racted starlight suppression, we consider coronagraphs comprised of a stage of phase control implemented with deformable mirrors (or other optical elements), pupil plane apodization masks (gray scale or complex valued), and focal plane masks (either amplitude only or complex-valued, including phase only such as the vector vortex coronagraph). The optimization of these optical elements, with the goal of achieving 10 or more orders of magnitude in the suppression of on-axis (starlight) di racted light, represents a challenging non-convex optimization problem with a nonlinear dependence on control degrees of freedom. We develop a new algorithmic approach to the design optimization problem, which we call the "Auxiliary Field Optimization" (AFO) algorithm. The central idea of the algorithm is to embed the original optimization problem, for either phase or amplitude (apodization) in various planes of the coronagraph, into a problem containing additional degrees of freedom, speci cally ctitious "auxiliary" electric elds which serve as targets to inform the variation of our phase or amplitude parameters leading to good feasible designs. We present the algorithm, discuss details of its numerical implementation, and prove convergence to local minima of the objective function (here taken to be the intensity of the on-axis source in a "dark hole" region in the science focal plane). Finally, we present results showing application of the algorithm to both unobscured o -axis and obscured on-axis segmented telescope aperture designs. The application of the AFO algorithm to the coronagraph design problem has produced solutions which are capable of directly imaging planets in the habitable zone, provided end-to-end telescope system stability requirements can be met. Ongoing work includes advances of the AFO algorithm reported here to design in additional robustness to a resolved star, and other phase or amplitude aberrations to be encountered in a real segmented aperture space telescope.

Redding, Dave↗
NASA NTRS1993

Two generalizations of Kohonen clustering

The relationship between the sequential hard c-means (SHCM), learning vector quantization (LVQ), and fuzzy c-means (FCM) clustering algorithms is discussed. LVQ and SHCM suffer from several major problems. For example, they depend heavily on initialization. If the initial values of the cluster centers are outside the convex hull of the input data, such algorithms, even if they terminate, may not produce meaningful results in terms of prototypes for cluster representation. This is due in part to the fact that they update only the winning prototype for every input vector. The impact and interaction of these two families with Kohonen's self-organizing feature mapping (SOFM), which is not a clustering method, but which often leads ideas to clustering algorithms is discussed. Then two generalizations of LVQ that are explicitly designed as clustering algorithms are presented; these algorithms are referred to as generalized LVQ = GLVQ; and fuzzy LVQ = FLVQ. Learning rules are derived to optimize an objective function whose goal is to produce 'good clusters'. GLVQ/FLVQ (may) update every node in the clustering net for each input vector. Neither GLVQ nor FLVQ depends upon a choice for the update neighborhood or learning rate distribution - these are taken care of automatically. Segmentation of a gray tone image is used as a typical application of these algorithms to illustrate the performance of GLVQ/FLVQ.

Bezdek, James C.↗
NASA NTRS2016

Using Tabulated Experimental Data to Drive an Orthotropic Elasto-Plastic Three-Dimensional Model for Impact Analysis

An orthotropic elasto-plastic-damage three-dimensional model with tabulated input has been developed to analyze the impact response of composite materials. The theory has been implemented as MAT 213 into a tailored version of LS-DYNA being developed under a joint effort of the FAA and NASA and has the following features: (a) the theory addresses any composite architecture that can be experimentally characterized as an orthotropic material and includes rate and temperature sensitivities, (b) the formulation is applicable for solid as well as shell element implementations and utilizes input data in a tabulated form directly from processed experimental data, (c) deformation and damage mechanics are both accounted for within the material model, (d) failure criteria are established that are functions of strain and damage parameters, and mesh size dependence is included, and (e) the theory can be efficiently implemented into a commercial code for both sequential and parallel executions. The salient features of the theory as implemented in LS-DYNA are illustrated using a widely used composite - the T800S/3900-2B[P2352W-19] BMS8-276 Rev-H-Unitape fiber/resin unidirectional composite. First, the experimental tests to characterize the deformation, damage and failure parameters in the material behavior are discussed. Second, the MAT213 input model and implementation details are presented with particular attention given to procedures that have been incorporated to ensure that the yield surfaces in the rate and temperature dependent plasticity model are convex. Finally, the paper concludes with a validation test designed to test the stability, accuracy and efficiency of the implemented model.

Polymer Matrix Composites↗
NASA NTRS1985

Taylor-Goertler instabilities of Tollmien-Schlichting waves and other flows governed by the interactive boundary layer equations

The Taylor-Gortler vortex instability equations are formulated for steady and unsteady interacting boundary layer flows of the type which arise in triple-deck theory. The effective Gortler number is shown to be a function of the all shape in the boundary layer and the possibility of both steady and unsteady Taylor-Gortler modes exists. As an example the steady flow in a symmetrically constricted channel is considered and it is shown that unstable Gortler vortices exist before the boundary layers at the wall develop the Goldstein singularity. As an example of an unsteady spatially varying basic state the instability of high frequency large amplitude Tollmien-Schlichting waves in a curved channel were considered. It is shown that they are unstable in the first Stokes layer stage of the hierarchy of nonlinear states. The Tollmien-Schlichting waves are shown to be unstable in the presence of both convex and concave curvature.

Hall, P.↗
NASA NTRS2016

Design and Calibration of a Raman Spectrometer for use in a Laser Spectroscopy Instrument Intended to Analyze Martian Surface and Atmospheric Characteristics for NASA

This project's goal is the design of a Raman spectroscopy instrument to be utilized by NASA in an integrated spectroscopy strategy that will include Laser-Induced Breakdown Spectroscopy (LIBS) and Laser-Induced Florescence Spectroscopy (LIFS) for molecule and element identification on Mars Europa, and various asteroids. The instrument is to be down scaled from a dedicated rover mounted instrument into a compact unit with the same capabilities and accuracy as the larger instrument. The focus for this design is a spectrometer that utilizes Raman spectroscopy. The spectrometer has a calculated range of 218 nm wavelength spectrum with a resolution of 1.23 nm. To filter out the laser source wavelength of 532 nm the spectrometer design utilizes a 532 nm wavelength dichroic mirror and a 532 nm wavelength notch filter. The remaining scatter signal is concentrated by a 20 x microscopic objective through a 25-micron vertical slit into a 5mm diameter, 1cm focal length double concave focusing lens. The light is then diffracted by a 1600 Lines per Millimeter (L/mm) dual holographic transmission grating. This spectrum signal is captured by a 1-inch diameter double convex 3 cm focal length capture lens. An Intensified Charge Couple Device (ICCD) is placed within the initial focal cone of the capture lens and the Raman signal captured is to be analyzed through spectroscopy imaging software. This combination allows for accurate Raman spectroscopy to be achieved. The components for the spectrometer have been bench tested in a series of prototype developments based on theoretical calculations, alignment, and scaling strategies. The mounting platform is 2.5 cm wide by 8.8 cm long by 7 cm height. This platform has been tested and calibrated with various sources such as a neon light source and ruby crystal. This platform is intended to be enclosed in a ruggedized enclosure for mounting on a rover platform. The size and functionality of the Raman spectrometer allows for the rover to carry other mission critical devices. This project will be continued at NASA until the requirements are met for the expected initial 2020 launch date.

Lucas, John F.↗
NASA NTRS2014

Interval Predictor Models with a Formal Characterization of Uncertainty and Reliability

This paper develops techniques for constructing empirical predictor models based on observations. By contrast to standard models, which yield a single predicted output at each value of the model's inputs, Interval Predictors Models (IPM) yield an interval into which the unobserved output is predicted to fall. The IPMs proposed prescribe the output as an interval valued function of the model's inputs, render a formal description of both the uncertainty in the model's parameters and of the spread in the predicted output. Uncertainty is prescribed as a hyper-rectangular set in the space of model's parameters. The propagation of this set through the empirical model yields a range of outputs of minimal spread containing all (or, depending on the formulation, most) of the observations. Optimization-based strategies for calculating IPMs and eliminating the effects of outliers are proposed. Outliers are identified by evaluating the extent by which they degrade the tightness of the prediction. This evaluation can be carried out while the IPM is calculated. When the data satisfies mild stochastic assumptions, and the optimization program used for calculating the IPM is convex (or, when its solution coincides with the solution to an auxiliary convex program), the model's reliability (that is, the probability that a future observation would be within the predicted range of outputs) can be bounded rigorously by a non-asymptotic formula.

Crespo, Luis G.↗
NASA NTRS2004

Measurement of an Evaporating Drop on a Reflective Substrate

A figure depicts an apparatus that simultaneously records magnified ordinary top-view video images and laser shadowgraph video images of a sessile drop on a flat, horizontal substrate that can be opaque or translucent and is at least partially specularly reflective. The diameter, contact angle, and rate of evaporation of the drop as functions of time can be calculated from the apparent diameters of the drop in sequences of the images acquired at known time intervals, and the shadowgrams that contain flow patterns indicative of thermocapillary convection (if any) within the drop. These time-dependent parameters and flow patterns are important for understanding the physical processes involved in the spreading and evaporation of drops. The apparatus includes a source of white light and a laser (both omitted from the figure), which are used to form the ordinary image and the shadowgram, respectively. Charge-coupled-device (CCD) camera 1 (with zoom) acquires the ordinary video images, while CCD camera 2 acquires the shadowgrams. With respect to the portion of laser light specularly reflected from the substrate, the drop acts as a plano-convex lens, focusing the laser beam to a shadowgram on the projection screen in front of CCD camera 2. The equations for calculating the diameter, contact angle, and rate of evaporation of the drop are readily derived on the basis of Snell s law of refraction and the geometry of the optics.

Chao, David F.↗
NASA NTRS1986

Taylor-Goertler instabilities of Tollmien-Schlichting waves and other flows governed by the interactive boundary-layer equations

The Taylor-Goertler vortex instability equations are formulated for steady and unsteady interacting boundary-layer flows. The effective Goertler number is shown to be a function of the wall shape in the boundary layer and the possibility of both steady and unsteady Taylor-Goertler modes exists. As an example the steady flow in a symmetrically constricted channel is considered and it is shown that unstable Goertler vortices exist before the boundary layers at the wall develop the Goldstein singularity discussed by Smith and Daniels (1981). As an example of an unsteady spatially varying basic state, it is considered the instability of high-frequency large-amplitude two- and three-dimensional Tollmien-Schlichting waves in a curved channel. It is shown that they are unstable in the first 'Stokes-layer stage' of the hierarchy of nonlinear states discussed by Smith and Burggraf (1985). This instability of Tollmien-Schlichting waves in an internal flow can occur in the presence of either convex or concave curvature. Some discussion of this instability in external flows is given.

Hall, Philip↗
NASA NTRS2008

Re-entry vehicle shape for enhanced performance

A convex shell structure for enhanced aerodynamic performance and/or reduced heat transfer requirements for a space vehicle that re-enters an atmosphere. The structure has a fore-body, an aft-body, a longitudinal axis and a transverse cross sectional shape, projected on a plane containing the longitudinal axis, that includes: first and second linear segments, smoothly joined at a first end of each the first and second linear segments to an end of a third linear segment by respective first and second curvilinear segments; and a fourth linear segment, joined to a second end of each of the first and second segments by curvilinear segments, including first and second ellipses having unequal ellipse parameters. The cross sectional shape is non-symmetric about the longitudinal axis. The fourth linear segment can be replaced by a sum of one or more polynomials, trigonometric functions or other functions satisfying certain constraints.

Brown, James L.↗
NASA NTRS1974

An analysis of the radiation from apertures in curved surfaces by the geometrical theory of diffraction

In this paper the geometrical theory of diffraction is extended to treat the radiation from apertures of slots in convex perfectly conducting surfaces. It is assumed that the tangential electric field in the aperture is known so that an equivalent infinitesimal source can be defined at each point in the aperture. Surface rays emanate from this source which is a caustic of the ray system. A launching coefficient is introduced to describe the excitation of the surface ray modes. If the field radiated from the surface is desired, the ordinary diffraction coefficients are used to determine the field of the rays shed tangentially from the surface rays. The field of the surface ray modes is not the field on the surface; hence if the mutual coupling between slots is of interest, a second coefficient related to the launching coefficient must be employed. In the region adjacent to the shadow boundary, the component of the field directly radiated from the source is represented by Fock-type functions. In the illuminated region the incident radiation from the source (this does not include the diffracted field components) is treated by geometrical optics. This extension of the geometrical theory of diffraction is applied to calculate the radiation from slots on elliptic cylinders, spheres, and spheroids.

Pathak, P. H.↗
NASA NTRS1973

The radiation from apertures in curved surfaces

The geometrical theory of diffraction is extended to treat the radiation from apertures or slots in convex, perfectly-conducting surfaces. It is assumed that the tangential electric field in the aperture is known so that an equivalent, infinitesimal source can be defined at each point in the aperture. Surface rays emanate from this source which is a caustic of the ray system. A launching coefficient is introduced to describe the excitation of the surface ray modes. If the field radiated from the surface is desired, the ordinary diffraction coefficients are used to determine the field of the rays shed tangentially from the surface rays. The field of the surface ray modes is not the field on the surface; hence if the mutual coupling between slots is of interest, a second coefficient related to the launching coefficient must be employed. In the region adjacent to the shadow boundary, the component of the field directly radiated from the source is presented by Fock-type functions. In the illuminated region the incident radiation from the source (this does not include the diffracted field components) is treated by geometrical optics. This extension of the geometrical theory of diffraction is applied to calculate the radiation from slots on elliptic cylinders, spheres and spheroids.

Pathak, P. H.↗