Search NASASearch

SEARCH · Search NASA

Results for “spherical coordinates”

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

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10

Tunable-Bandwidth Filter System

A tunable-bandwidth filter system (TBFS), now undergoing development, is intended to be part of a remote-sensing multispectral imaging system that will operate in the visible and near infrared spectral region (wavelengths from 400 to 900 nm). Attributes of the TBFS include rapid tunability of the pass band over a wide wavelength range and high transmission efficiency. The TBFS is based on a unique integration of two pairs of broadband Raman reflection holographic filters with two rotating spherical lenses. In experiments, a prototype of the TBFS was shown to be capable of spectral sampling of images in the visible range over a 200-nm spectral range with a spectral resolution of .30 nm. The figure depicts the optical layout of a prototype of the TBFS as part of a laboratory multispectral imaging system for the spectral sampling of color test images in two orthogonal polarizations. Each pair of broadband Raman reflection holographic filters is mounted at an equatorial plane between two halves of a spherical lens. The two filters in each pair are characterized by steep spectral slopes (equivalently, narrow spectral edges), no ripple or side lobes in their pass bands, and a few nanometers of non-overlapping wavelength range between their pass bands. Each spherical lens and thus the filter pair within it is rotated in order to rapidly tune its pass band. The rotations of the lenses are effected by electronically controlled, programmable, high-precision rotation stages. The rotations are coordinated by electronic circuits operating under overall supervision of a personal computer in order to obtain the desired variation of the overall pass bands with time. Embedding the filters inside the spherical lenses increases the range of the hologram incidence angles, making it possible to continuously tune the pass and stop bands of the filters over a wider wavelength range. In addition, each spherical lens also serves as part of the imaging optics: The telephoto lens focuses incoming light to a field stop that is also a focal point of each spherical lens. A correcting lens in front of the field stop compensates for the spherical aberration of the spherical lenses. The front surface of each spherical lens collimates the light coming from the field stop. After the collimated light passes through the filter in the spherical lens, the rear surface of the lens focuses the light onto a charge-coupled-device image detector.

Aye, Tin

Application of a numerically generated orthogonal coordinate system to the solution of inviscid axisymmetric supersonic flow over blunt bodies

A numerically generated orthogonal coordinate system (with the body surface and shock wave as opposite boundaries) was applied with a time asymptotic method to obtain steady flow solutions for axisymmetric inviscid flow over several blunt bodies including spheres, paraboloids, ellipsoids, hyperboloids, hemisphere cylinders, spherically blunted cones, and a body with a concavity in the stagnation region. Comparisons with experimental data and with the results of other computational methods are discussed. The numerically generated orthogonal coordinate system is described and applications of the method to complex body shapes, particularly those with concave regions, are discussed.

Hamilton, H. H., II

SHarmonic: A fast and accurate implementation of spherical harmonics for electronic-structure calculations

The authors present SHarmonic, a new implementation of the spherical harmonics targeted for electronic-structure calculations. Their approach is to use explicit formulas for the harmonics written in terms of normalized Cartesian coordinates. This approach results in a code that is as precise as other implementations while being at least one order of magnitude more computationally efficient. The library can run on graphics processing units as well, achieving an additional order of magnitude in execution speed. This new implementation is simple to use and is provided under an open-source license; it can be readily used by other codes to avoid the error-prone and cumbersome implementation of the spherical harmonics.

Mathematics and Computing

A Voice and Mouse Input Interface for 3D Virtual Environments

There have been many successful stories on how 3D input devices can be fully integrated into an immersive virtual environment. Electromagnetic trackers, optical trackers, gloves, and flying mice are just some of these input devices. Though we can use existing 3D input devices that are commonly used for VR applications, there are several factors that prevent us from choosing these input devices for our applications. One main factor is that most of these tracking devices are not suitable for prolonged use due to human fatigue associated with using them. A second factor is that many of them would occupy additional office space. Another factor is that many of the 3D input devices are expensive due to the unusual hardware that are required. For our VR applications, we want a user interface that would work naturally with standard equipment. In this paper, we demonstrate applications or our proposed muitimodal interface using a 3D dome display. We also show that effective data analysis can be achieved while the scientists view their data rendered inside the dome display and perform user interactions simply using the mouse and voice input. Though the sphere coordinate grid seems to be ideal for interaction using a 3D dome display, we can also use other non-spherical grids as well.

Kao, David L.

Electromagnetic deep-probing (100-1000 kms) of the Earth's interior from artificial satellites: Constraints on the regional emplacement of crustal resources

A spherical harmonic analysis program is being tested which takes magnetic data in universal time from a set of arbitrarily space observatories and calculates a value for the instantaneous magnetic field at any point on the globe. The calculation is done as a least mean-squares value fit to a set of spherical harmonics up to any desired order. The program accepts as a set of input the orbit position of a satellite coordinates it with ground-based magnetic data for a given time. The output is a predicted time series for the magnetic field on the Earth's surface at the (r, theta) position directly under the hypothetically orbiting satellite for the duration of the time period of the input data set. By tracking the surface magnetic field beneath the satellite, narrow-band averages crosspowers between the spatially coordinated satellite and the ground-based data sets are computed. These crosspowers are used to calculate field transfer coefficients with minimum noise distortion. The application of this technique to calculating the vector response function W is discussed.

Hermance, J. F.

Numerical studies of major and minor stratospheric warmings caused by orographic forcing

A primitive equation spectral model using spherical harmonics is formulated to study dynamic interactions between the troposphere and stratosphere in association with sudden stratospheric warmings. Using sigma coordinates for five tropospheric layers and log-pressure coordinates for 26 stratospheric and mesospheric layers, separate model equations for each system are combined to form single matrix governing equations. The gradual introduction of large scale topography to balanced initial states representative of observed mean winter conditions in the Northern Hemisphere is used for the generation of planetary waves during 40-day time integrations. Results of these integrations indicate that stratospheric warmings can be simulated by this orographic forcing and that mean momentum flux divergence due to zonal mean motion appears to be an essential mechanism of these simulated sudden warmings. It was found that the strength of the polar night jet can be a determining factor whether a warming becomes 'major' or 'minor'.

Koermer, J. P.

An improved computational technique for calculating electromagnetic forces and power absorptions generated in spherical and deformed body in levitation melting devices

An improved computational technique for calculating the electromagnetic force field, the power absorption and the deformation of an electromagnetically levitated metal sample is described. The technique is based on the volume integral method, but represents a substantial refinement; the coordinate transformation employed allows the efficient treatment of a broad class of rotationally symmetrical bodies. Computed results are presented to represent the behavior of levitation melted metal samples in a multi-coil, multi-frequency levitation unit to be used in microgravity experiments. The theoretical predictions are compared with both analytical solutions and with the results of previous computational efforts for the spherical samples and the agreement has been very good. The treatment of problems involving deformed surfaces and actually predicting the deformed shape of the specimens breaks new ground and should be the major usefulness of the proposed method.

Zong, Jin-Ho

An Improved Computational Technique for Calculating Electromagnetic Forces and Power Absorptions Generated in Spherical and Deformed Body in Levitation Melting Devices

An improved computational technique for calculating the electromagnetic force field, the power absorption and the deformation of an electromagnetically levitated metal sample is described. The technique is based on the volume integral method, but represents a substantial refinement; the coordinate transformation employed allows the efficient treatment of a broad class of rotationally symmetrical bodies. Computed results are presented to represent the behavior of levitation melted metal samples in a multi-coil, multi-frequency levitation unit to be used in microgravity experiments. The theoretical predictions are compared with both analytical solutions and with the results or previous computational efforts for the spherical samples and the agreement has been very good. The treatment of problems involving deformed surfaces and actually predicting the deformed shape of the specimens breaks new ground and should be the major usefulness of the proposed method.

Zong, Jin-Ho

Application of spherical near-field measurements to microwave holographic diagnosis of antennas

Microwave diagnosis of antennas is considered as a viable tool for the determination of reflector surface distortions and location of defective radiating elements of array antennas. A hybrid technique based on the combination of the spherical near-field measurements and holographic metrology reconstruction is presented. The measured spherical near-field data are first used to construct the far-field amplitude and phase patterns of the antenna on specified regularized u-nu coordinates. These data are then utilized in the surface profile reconstruction of the holographic technique using a fast-Fourier-transform (FFT)/iterative approach. Results of an experiment using a 156-cm reflector antenna measured at 11.3 GHz are presented for both the original antenna and the antenna with four attached bumps. Several contour and gray-scaled plots are presented for the reconstructed surface profiles of the measured antennas. The recovery effectiveness of the attached bumps has been demonstrated. The hybrid procedure presented is used to assess the achieved accuracy of the holographic reconstruction technique because of its ability to determine very accurate far-field amplitude and phase data from the spherical near-field measurements.

Rahmat-Samii, Yahya

Corrections for atmospheric refractivity in satellite laser ranging

The effects of departures from the spherical symmetry assumption are investigated by describing the refractivity profile on the earth's surface as a generalized function of the surface coordinates. Aspects of satellite ranging geometry are considered and the representation of the true group refractivity of the atmosphere at any point on the earth's surface is discussed. Surface meteorological data obtained from a few east coast weather stations are analyzed to obtain typical values of the higher order bias terms.

Iyer, R. S.

Re-Entry Simulation and Landing Area for YES2

The REST simulator includes many parameters: a) Inertial <-> Fix to Earth reference system; b) Geodetic <-> Geocentric coordinates; c) Rotational velocity of the Atmosphere; d) Effect of the rotation of the Earth; e) Bulge effect of the Earth; f) Spherical harmonic expansion for the Earth s gravitational potential, J2 (zonal); g) Heat flux, temperature in the wall; h) Drag coefficient for different regimes; i) Flow regime status; j) Density model NRLMSISE-00; k) Wind model HWM-93; l) G2S atmospheric model with the latest meteorological conditions and m) Landing area (Monte Carlo Simulations)

Calzada, Silvia

The influence of orography on the transport of atmospheric constituents

Given the fact that martian orography varies over a range of two scale heights (cf., about one scale height on Earth), it is thought that on Mars some aspects of the circulation should be affected to a large degree by the presence of orography. Initial results from two numerical models are presented that illustrate the effect of orography on cross-equatorial transport on Mars. On Earth, western boundary currents are found not only in the oceans as one would expect, but also in the troposphere, the most notable example being the East African Jet, which has an important effect on the monsoon circulation of the Eastern Indian Ocean. Two models were used for this investigation: a simple GCM (hereafter referred to as the SGCM); and a simple one-level barotropic model (BM). The SGCM solves the hydrostatic primitive equations on a sphere by representing model variables by spherical harmonics in the horizontal, with nonlinear terms being calculated in grid-point space. In the vertical, the model uses the sigma coordinate system in finite-difference form. The model represents the radiative processes in the atmosphere by a Newtonian relaxation to a specified zonal mean temperature state and surface drag by Rayleigh friction in the lowest model level.

Joshi, Manoj M.

Numerical check on the accuracy of spherical-wave expansions.

A simple and sensitive test for evaluating the numerical accuracy of a spherical-wave expansion is presented. The basic idea is to compare two different expansions of the same electromagnetic field, computed with respect to different coordinate origins. The use of the technique is illustrated by an example based on the experimental pattern of a horn antenna.

Ludwig, A. C.

Precision Effects for Solar Image Coordinates Within the FITS World Coordinate System

The FITS world coordinate system (WCS) provides a number of tools for precisely specifying the spatial coordinates of an image. Many of the finer details that the WCS addresses have not historically been taken into account in solar image processing. This paper examines various effects which can affect the expression of coordinates in FITS headers, to determine under what conditions such effects need to be taken into account in data analysis, and under what conditions they can be safely ignored. Effects which are examined include perspective, parallax, spherical projection, optical axis determination, speed-of-light effects, stellar aberration, gravitational deflection, and scattering and refraction at radio wavelengths. Purely instrumental effects, such as misalignment or untreated optical aberrations, are not considered. Since the value of the solar radius is an experimental quantity, the effect of adopting a specific radius value is also examined. These effects are examined in the context of a previous paper outlining a WCS standard for encoding solar coordinates in FITS files. Aspects of that previous paper are clarified and extended in the present work.

Thompson, W. T.

Optical Testing Using Portable Laser Coordinate Measuring Instruments

High precision, portable coordinate measuring instruments (CMI) such as laser radars (LR) and laser trackers (LT) have been used for optical system alignment and integration. The LRs ability to perform a non-contact scan of surfaces was previously utilized to characterize large spherical and aspheric mirrors. In this paper, we explore the use of a CMI as an accurate, fast, robust, and non-contact tool for prescription characterization of powered optical surfaces. Using Nikons MV-224350 LR and Leicas Absolute Tracker AT401402 instruments, proof of concept measurements were performed to characterize a variety of optical components by measuring the actual and apparent, or equivalently the direct and through (DT), coordinates of calibrated metrology targets. Custom macros in metrology software and other data reduction code were developed to compute surface-ray intercepts and surface slopes from the DT shots. The calculated data is fit to an aspheric surface formula to obtain the optimum prescription. The results were compared to the nominal parameters and were crosschecked using LR scans or other approaches. We discuss potential applications across the fields of optical component fabrication and system alignment and testing.

Khreishi, M.

Nanocrystalline Chalcopyrite Materials (CuInS2 and CuInSe2) via Low-Temperature Pyrolysis of Molecular Single-Source Precursors

Nanometer sized particles of the chalcopyrite compounds CuInS2 and CuInSe2 were synthesized by thermal decomposition of molecular single-source precursors (PPh3)2CuIn(SEt)4 and (PPh3)2CuIn(SePh)4, respectively, in the non-coordinating solvent dioctyl phthalate at temperatures between 200 and 300 C. The nanoparticles range in size from 3 - 30 nm and are aggregated to form roughly spherical clusters of about 500 nm in diameter. X-ray diffraction of the nanoparticle powders shows greatly broadened lines indicative of very small particle sizes, which is confirmed by TEM. Peaks present in the XRD can be indexed to reference patterns for the respective chalcopyrite compounds. Optical spectroscopy and elemental analysis by energy dispersive spectroscopy support the identification of the nanoparticles as chalcopyrites.

Castro, Stephanie L.

Optical Testing Using Portable Laser Coordinate Measuring Instruments

High precision, portable coordinate measuring instruments (CMI) such as laser radars (LR) and laser trackers (LT) have been used for optical system alignment and integration. The LR's ability to perform a non-contact scan of surfaces was previously utilized to characterize large spherical and aspheric mirrors. In this paper, we explore the use of a CMI as an accurate, fast, robust, and non-contact tool for prescription characterization of powered optical surfaces. Using Nikon's MV-224/350 LR and Leica's Absolute Tracker AT401/402 instruments, proof of concept measurements were performed to characterize a variety of optical components by measuring the actual and apparent, or equivalently the "direct and through" (D&T), coordinates of calibrated metrology targets. Custom macros in metrology software and other data reduction code were developed to compute surface-ray intercepts and surface slopes from the D&T shots. The calculated data is fit to an aspheric surface formula to obtain the optimum prescription. The results were compared to the nominal parameters and were crosschecked using LR scans or other approaches. We discuss potential applications across the fields of optical component fabrication and system alignment and testing.

Khreishi, Manal

A spherical harmonics method for asteroid pole determination

A new and general method is presented for determining pole orientations of unresolved solar system bodies that exhibit brightness variation with rotation. The accuracy of the method is limited only by the number of available apparitions, which imposes the degree where the Legendre expansion must be truncated. It is shown that power spectra of lightcurves provide enough information to extract pole coordinates from the data, independent of body shape and albedo variegation. The method has been tested using several computer-generated synthetic light-curves, and the accuracy is found to be about 5 deg in both the longitude and latitude of the pole, which is considerably better than that obtained from the standard triaxial ellipsoid model. Finally, the new spherical harmonics method has been applied to six well-observed asteroids: 16 Psyche, 22 Kalliope, 39 Laetitia, 44 Nysa, 45 Eugenia, and 349 Dembowska.

Lumme, K.