Showing papers on "Point source published in 1995"

The finite-element method for the propagation of light in scattering media - boundary and source conditions

Abstract: This paper extends our work on applying the Finite Element Method (FEM) to the propagation of light in tissue. We address herein the topics of boundary conditions and source specification for this method. We demonstrate that a variety of boundary conditions stipulated on the Radiative Transfer Equation can be implemented in a FEM approach, as well as the specification of a light source by a Neumann condition rather than an isotropic point source. We compare results for a number of different combinations of boundary and source conditions under FEM, as well as the corresponding cases in a Monte Carlo model.

Robust acoustic time reversal with high-order multiple scattering

Abstract: We report the first experiments showing the reversibility of transient acoustic waves through high-order multiple scattering by means of an acoustic time-reversal mirror. A point source generates a pulse which scatters through 2000 steel rods immersed in water. The time-reversed waves are found to converge to their source and recover their original wave form, despite the high order of multiple scattering involved and the usual sensitivity to initial conditions of time-reversal processes. Surprisingly, the observed resolution was one-sixth of the theoretical limit for the mirror's aperture.

Parametric localization of distributed sources

Abstract: Most array processing algorithms are based on the assumption that the signals are generated by point sources. This is a mathematical constraint that is not satisfied in many applications. In this paper, we consider situations where the sources are distributed in space with a parametric angular cross-correlation kernel. We propose an algorithm that estimates the parameters of this model using a generalization of the MUSIC algorithm. The method involves maximizing a cost function that depends on a matrix array manifold and the noise eigenvectors. We study two particular cases: coherent and incoherent spatial source distributions. The spatial correlation function for a uniformly distributed signal is derived. From this, we find the array gain and show that (in contrast to point sources) it does not increase linearly with the number of sources. We compare our method to the conventional (point source) MUSIC algorithm. The simulation studies show that the new method outperforms the MUSIC algorithm by reducing the estimation bias and the standard deviation for scenarios with distributed sources. It is also shown that the threshold signal-to-noise ratio required for resolving two closely spaced distributed sources is considerably smaller for the new method. >

A scheme of random summation of an empirical Green's function to estimate ground motions from future large earthquakes

Abstract: We present a scheme for random summation of an empirical Green9s function to synthesize ground motions from future large events. This scheme obeys the ω 2 scaling law at all frequencies and produces time histories whose envelopes are realistic. Assuming that the source parameters of the empirical Green9s function are known, one needs only to specify the stress parameter of the target event. In the method, the extended target area is approximated by a point source, whose rupture duration, however, is in accordance with its dimension. Although the method does not account for directivity of the source, tests with Mexican data show a good agreement between observed and synthesized motions. We use this approach to compute expected ground motions in the Valley of Mexico from a hypothetical M 8.2 event in the Guerrero gap.

Modeling and parameterization of near-source diffusion in weak winds

Abstract: A critical assessment is made of several different approaches that can be used for modeling near-source diffusion in weak winds, including the calm condition. For the convective boundary layer, the statistical theory approach is used in conjunction with the mixed-layer similarity scaling to compute mean concentrations in the near field. The maximum ground-level concentration and its location relative to a continuous point source are given as functions of the source height and wind speed, all made dimensionless through the use of the mixed-layer similarity scaling. The modal and the suggested parameterizations for turbulence and diffusion are only valid for the convective boundary layer over a flat and homogeneous terrain. For near-neutral and stable conditions, the gradient-transport approach is used. Some analytical models for the near-field concentration under the calm condition are discussed. Recommendations are made for the formulation of more sophisticated numerical models of near-source dif...

Analytical calculation of scatter distributions in SPECT projections

Abstract: In this paper the authors present a method for analytically calculating the distribution of photons detected in single photon emission computed tomography (SPECT) projections. The technique is applicable to sources in homogeneous and nonhomogeneous media. The photon distribution (primary, first-, and second-order Compton scatter) is computed using a precalculated camera-dependent look-up table in conjunction with an attenuation map of the scattering object and a map of the activity distribution. The speed and accuracy of this technique is compared to that of Monte Carlo simulations. The cases considered are a point source in a homogeneous and also in a nonhomogeneous scattering medium, an extended source in a nonhomogeneous medium, and a homogeneous cylinder filled uniformly with activity. The method is quantitatively accurate and faithfully reproduces the spatial distribution of the unscattered and scattered photons. For comparable statistical precision in the peak of the calculated distribution, their approach can result in a gain in calculation time over Monte Carlo simulators. For point sources, the computation times are improved by a factor of 20-150. However, this gain depends on the source configuration, and calculation times become comparable for an 800 voxel source and are five times slower for a 55000 voxel source. The method also offers an increase in the speed of computation of higher order Compton scatter events over a similar analytical technique.

ASCA and ROSAT observations of the QSF3 field: the X-ray background in the 0.1--7 keV band

Abstract: The X-ray background (XRB) from 0.1 to 7 keV has been studied using high spectral and spatial resolution data from the ASCA SIS and ROSAT PSPC. Analysing both the diffuse background radiation and resolved sources, we have carried out a series of joint spectral fits of the ASCA and ROSAT data. The spectrum of the XRB can be fit well by a single power-law from 1 to 7 keV; overall, the photon index of the power-law model ranges from 1.4 to 1.5, and no obvious excess is found between 1 and 3 keV. Below 1 keV, the models become more complicated and involve a mixture of extragalactic and Galactic sources. As some of the extragalactic contributions should be from point sources, we have examined the ASCA and ROSAT spectra of resolved sources individually: a stellar source having a well-fit thermal spectrum and two AGNs having a much steeper power-law spectrum (with photon index of about 3); the accumulated spectrum of other non-stellar sources resolved by ROSAT also has a steeper-than-average spectrum. Fitting the XRB spectrum observed by ASCA and the accumulated point source spectrum by ROSAT together by varying the contribution from steep spectrum sources, such as quasars, to the background, we find that they contribute less than 30 per cent in the 0.5--2 keV band and drop to below 10 per cent over 2--10 keV. This fraction is provided by sources brighter than a few times $10^{-15}$ \ergpercmpers (in the 0.5--2 keV band). Constrained by our spectral fitting results, the major contributor of the XRB must be a single population with similar flat spectra.

The x‐pinch as a point source of x rays for backlighting

Abstract: The fine metal wire x‐pinch is a compact source of soft‐x‐ray emission. Under certain conditions, x rays in the 3–7 keV range are emitted in <1 ns bursts from source regions that are <10 μm in size. The small size and high intensity of these 3–7 keV sources makes the x‐pinch useful as a point source for x‐ray backlighting. This capability has been demonstrated by using an x‐pinch to produce radiographic images of separate x‐pinches and z‐pinches.

Long‐period regional wave moment tensor inversion for earthquakes in the western United States

Abstract: Source parameters of moderate to large size (Mw > 4.5) earthquakes in the western United States from 1992 to 1994 are determined by point source moment tensor inversion of complete long-period (T > 35–50 s) ground motions recorded at regional distances (1°–12°). Stable long-period signals are obtained by low-pass filtering records from the very broadband seismometers recently deployed in several networks in the western United States. These signals are dominated by fundamental mode Rayleigh and Love waves, which have very simple waveforms due to the limited dispersion on the short paths to regional stations. Since long-period motions are relatively insensitive to the attenuation model and crustal structure used in the inversion, they provide robust constraints on the seismic moment and faulting geometry as long as adequate azimuthal coverage is available. Comparisons of solutions for 21 events with results of other regional and teleseismic wave inversions are made to assess the model dependence and uncertainties of our regional centroid moment tensor (RCMT) solutions. RCMT inversion has limited source depth resolution for shallow crustal events, but the focal mechanism and seismic moment determinations prove quite stable over a range of source depths in the crust, as well as over a range of crustal propagation models. Simultaneous waveform inversion of shorter-period body wave signals can improve the source depth resolution. By applying path corrections for heterogeneous crustal structure, shorter-period surface wave energy can also be inverted, allowing the methodology to be extended to lower-magnitude regional events as well. The RCMT procedure requires minimal signal processing, only a sparse broadband network, and a simple laterally homogeneous propagation model; thus it can readily be automated and applied in near real time to events in the magnitude range from 4.5 to 7.5 distributed over an area as large as the western United States.

The Use of Lagrangian Methods To Describe Turbulent Transport of Heat from a Wall

Abstract: Tracking of heat markers released instantaneously from a point source on a wall boundary in a numerically simulated turbulent channel flow is used to describe the transfer of heat. The trajectories of 16 129 heat markers are monitored in time and space. These results are used to calculate temperature fields generated by continuous line or planar sources and the temperature profile in a channel with a heated bottom wall and a cooled top wall. The good agreement between the calculated fully-developed profile and the profile generated by a direct numerical simulation illustrates the equivalence of the Lagrangian and Eulerian approaches. The main point to be made is that dispersion from an instantaneous point source is a basic element. Its understanding could provide a better foundation for establishing the physics of wall heat transfer than is supplied by Eulerian analyses.

Point source excitation in direct and inverse scattering: The soft and the hard small sphere

Abstract: A spherical wave emanating from a point source is scattered by either a soft or a hard body. The incident spherical wave has a wavelength which is much larger than the characteristic dimension of the scatterer and it is modified in such a way as to recover the plane wave incidence when the source point recedes to infinity. Using low frequency expansions the scattering problem is transformed to a sequence of exterior potential problems in the presence of a monopole singularity located at the source of the incident wave field. Complete expansions for the scattering amplitude are provided. The method is applied to the cases of'a soft and a hard sphere and the first three approximations for the near, as well as the far, field are evaluated. It is observed that every one, after the first, low frequency approximation of the far field, involves one spherical multipole more than the corresponding approximation for the case of an incident plane wave. As the point singularity tends to infinity, the relative results recover all the known expressions for plane incidence. It is shown that for point excitation the Rayleigh approximation of the scattering amplitude for a hard sphere is of the second order, in contrast to the case of plane excitation which is of the third order. Simple algorithms that specify the radius and the position of a soft and a hard sphere are proposed, which are based on the additional dependence of the scattering amplitude represented by the distance from the point source to the centre of the scatterer. The inversion algorithm is shown to be stable whenever the source point is not too far away from the target sphere. A simple way to decide whether the sphere is a soft or a hard body is also provided.

The vertical structure of concentration fluctuation statistics in plumes dispersing in the atmospheric surface layer

Abstract: This paper describes a study of the vertical structure of concentration fluctuations in a neutrally buoyant plume from an elevated point source in slightly convective to moderately stable meteorological conditions at ranges of between 12.5 and 100 m for a range of source heights between 1 and 5 m. Observations were made of concentration fluctuations in a dispersing plume using a vertical array of sixteen very fast-response photoionization detectors placed at heights between 0.5 and 16 m. Vertical profiles of a number of concentration statistics were extracted, namely, mean concentration, fluctuation intensity, intermittency factor, peak-to-mean concentration ratio, mean dissipation rate of concentration variance, and various concentration time and length scales of dominant motions in the plume (e.g., integral macro-scale, in-plume mid-scale and Taylor micro-scale). The profiles revealed a similarity to corresponding crosswind profiles for a fully elevated plume, but showed greater and greater departure from the latter shapes once the plume had grown in the vertical so that its lower dege began to interact progressively more strongly with the ground. The evolution of the concentration probability density function at a fixed range, but with decreasing height from the ground, is similar to that obtained at a fixed height but with increasing distance from the source. Concentration power spectra obtained at different heights all had an extensive inertial-convective subrange spanning at least two decades in frequency, but spectra measured near the ground had a greater proportion of the total concentration variance in the lower frequencies (energetic subrange), with a correspondingly smaller proportion in the higher frequencies (inertial-convective subrange). It is believed that these effects result from the increased mean shear near the surface, and blocking by the surface. The effect of enhanced shear-induced molecular diffusion on concentration fluctuations is examined.

Scattering of sound from a spatially distributed, spherically symmetric source by a sphere

Abstract: General expressions are derived for the scattering of sound from a spatially distributed, spherically symmetric source by rigid and nonrigid spheres. The incident field is determined using a Hankel transform for spherically symmetric variables. The scattered fields are determined by matching the total pressure and normal velocity at the surface of the sphere. Examples of the total and scattered fields are given for a ball source and a spherically symmetric source with a Gaussian spatial distribution. These solutions are compared with results for a point source.

X-ray focusing optics. I. Applications of wave optics to doubly curved crystals with a point x-ray source

Abstract: A wave optics approach to the calculations of the intensity distribution of an x‐ray point source image with a two‐dimensional (2D) focusing geometry is presented. Analytical formulas are derived to calculate the intensity distribution at the focal plane. This approach has taken into account the effects of x‐ray scattering within a 2D bent crystal, which includes the x‐ray refraction and absorption inside the crystal, and the effects of elastically deformed crystals described by the anisotropic elasticity theory. Based upon the elastic bending model, the modified Bragg law and 2D lens equations are discussed. In addition, the x‐ray extinction distance for curved crystals is found to be dependent on the size and the bending radius of bent crystals. For a monochromatic x‐ray point source, calculation of the intensity distribution with a 2D bent silicon crystal is given for both perfect and misaligned sources. The spatial resolution and the size of the image are determined.

Series expansion of electrostatic potential radiated by a point source in isotropic Maxwellian plasma

Abstract: A new algebraic approach is proposed to calculate the electrostatic potential distributed around a point source in isotropic Maxwellian plasma. The method derives a power series expansion of the radial distance from the source with frequency-dependent coefficients. Distance and frequency are normalized to the Debye length and to the plasma frequency, respectively, so that the expression keeps its entire generality whatever the experimental conditions might be. The proposed method is based upon the Mittag-Lefler expansion of the inverse of the plasma dispersion function for the infinite series of Landau poles. After mathematical clarification of the validity of this expansion, a significant correction of the previous works leads to a self-consistent interpretation of the true contribution of the higher-order poles at large distance from the source. The power series expansion is compared to the classical so-called “Landau wave approximation” which is proved to include in reality the contribution of higher-order poles independently from the plasma temperature. For practical use the power expansion is needed to obtain a precise result at distances from the source shorter than about 15 Debye lengths, while the Landau wave approximation gives correct results at larger distances. This work provides all necessary baselines for precise three-dimensional modeling of mutual impedance devices to be used in space plasma experiments where the Debye length is comparable to the spacecraft size.

The average cosine due to an isotropic light source in the ocean

Abstract: The average cosine of the light field created by an isotropic point source (IPS) embedded in a homogeneous ocean is investigated with a Monte Carlo model. Two volume scattering functions (VSFs) are used in the model, taken from Petzold (1972), to compute the radiance distributions at various distances from the source. The simulated radiance distributions are compared with measurements of the point spread function made at Lake Pend Oreille, Idaho, during the 1992 optical closure experiment. An analytic model is presented for which is valid to at least 15 optical lengths from the source. The model shows that the mean light path, derived from , is a strong function of the single scattering albedo and the VSF. We found that errors in estimating the absorption coefficient by neglecting the increase in the mean light path, which is due to scattering, vary between 5% and 12% for nearly all natural waters. A mathematical proof is given that as the distance to the IPS goes to zero. An analytic expression is derived for close to a finite diffuse-isotropic source which shows that approaches one as the distance decreases, but at extremely close distances, as the distance to the surface of the source goes to zero. At distances beyond one attenuation length, for finite sources small compared to an attenuation length, behaves essentially as it would for a point source. An asymptotic model for as a function of the single scattering albedo is given with coefficients that depend on the VSF. Model results and comparisons with measured PSFs reveal the surprising result that the light field from an embedded isotropic point source in the ocean does not exhibit asymptotic behavior as far as 15 attenuation lengths from the source.

Shear-wave focusing with a laser-ultrasound phased-array

Abstract: Pulsed laser arrays have been used to improve the beam parameters of laser generated ultrasound. The focusing and steering of shear-acoustic-wave beams generated by an array of thermoelastic sources has been investigated. A modeling of the impulse diffraction response of a single line source was derived from the point source model (Surface Center Of Expansion) of the thermoelastic source. The acoustic field launched by an array of point- or line-sources has been computed. Experimentally, the impulse response of a line source has been measured by using a heterodyne interferometer. It was shown with a 16-beam YAG laser, that shear-acoustic-wave beams can be focused and steered inside a duraluminum sample with a great efficiency.

Acoustic scattering by an air-bubble near the sea surfaceacoustic scattering by an air-bubble near the sea surface

Abstract: Sound scattering by and air bubble in a boundless fluid is an old classical problem (19). If the air bubble is near and strongly interacting with the (flat) surface of a liquid half-space, then the scattering cross section (SCS) of the bubble differs substantially from its value far-away from the interface. We present the exact solution for this scattering problem which is valid for any incidence direction of the (plane) sound waves, and for any bubble depth, obtained by the general method of images. The bubble is no longer assumed to be a point simple, harmonic, radially pulsating oscillator, but is described as a continuous, spatially extended body, having an infinity of modes and resonances. The interaction with the boundary, or the image is not treated by means of the simple Lloy's mirror formula for point source ( or scatterers), but by a general extended continuum approach, This benchmark solution makes use of the addition theorems for the spherical wavefunctions. The resulting SCS contains contributions from the bubble, its image, the invident wave, and the reflected wave from the boundary. It is expressed in terms of coupling coefficients, bmn, products of Wigner-3j simbols. The formulations in illustrated with many computed plots for bubbles at various depths, and the results compare favorably with earlier experimental observations. The approach also serves to describe scattering by fish near the sea surface, in an exact fashion. Acoustic scattering by near-surface bubbles also has many other applications such as in the improvement of the performance of sensor that must operate through hubby media, and in the understanding of its connection with approaches to model oceanic fluxes.

Mechanisms of local earthquakes in 3-D inhomogeneous media determined by waveform inversion

Abstract: SUMMARY A method of waveform inversion for determination of a point source mechanism and its time function is developed. It allows the use of amplitudes for relocalization of the event and in a simplistic way the optimization of the structural model as well. This is accomplished by minimization of the residual norm during modelling of the data in a phase space comprising both hypocentral coordinates and structural interpolation parameters. The ray method, used to solve the forward problem, allows consideration of generally 3-D inhomogeneous isotropic media with arbitrarily curved interfaces. Seismograms generated by sources buried in such media can be inverted provided that identification of individual body-wave phases in the observed records can be made. The point source approximation restricts application of the method to weak events only. The moment tensor description advantageously allows us to investigate local seismicity, for which it is reasonable to suppose that the foci in general have a non-DC mechanism. The method includes an error analysis consisting of transformation of the data noise variance into confidence regions for volumetric, DC and CLVD parts of the retrieved moment tensor and for its principal axes (T, N and P) as well. Tests of the method were first performed on synthetic data generated for a configuration of a local seismic network near Dobra Voda, Slovakia. In the next step, the real data from the region were inverted to obtain the mechanism of a small earthquake of local magnitude of about 2.

An infrared embedded source in the l1251 molecular cloud

Abstract: Using the Dominion Astrophysical Observatory's 1.8 m telescope and infrared array detector, we have detected a near-infrared extended source embedded in the dark molecular cloud L1251. We measure the mean surface brightnesses in J, H and K to be 16.5, 14.1, and 14.1 magnitudes per square arcsecond, respectively. The central object is associated with the IRAS point source 22343+7501, and is composed of more than one source. Millimetre observations using the James Clerk Maxwell telescope yield integrated fluxes ranging from 0.23 (at 1.3 mm) to 0.71 (at 0.8 mm) Jy. Deep J and K' images taken with the Redeye detector on the Canada-France-Hawaii telescope show the source near the extended nebulosity to be multiple. The nebulosity contains a great deal of chaotic structure, and extends more than 30 arcseconds in J and over 20 arcseconds in K'. The line-of-sight absorption to IRAS 22343+7501 is estimated to be 32± 5 magnitudes, which is comparable to values found for similar objects. The spectral energy distribution is characteristic of an embedded source, and the range of fluxes at the different wavelengths imply that a single temperature for the cloud is not valid. The near-IR, far-IR and mm observations are consistent with the objects in this cloud being just past the protostar stage of evolution.

Determination of full energy peak efficiency for cylindrical volume sources by the use of a point source standard in gamma-spectrometry

Abstract: A new method has been developed for calculating the full energy peak efficiency of gamma-spectrometry measurement systems. The technique uses the relationship between total- and full energy efficiency of a Ge-detector. First, the full energy peak efficiency of a closed point source standard centred at the face of the detector is measured at different energies with known activities of nuclides. As this calibration records all the required characteristics of the detector, other experimental or theoretical views are not necessary. The experimental part is therefore complete and all other factors are calculated from the efficiency calibration of the point source and detector with a recently developed Monte Carlo simulation [G. Haase et al., Nucl. Instr. and Meth. A 329 (1993) 483, and Nucl. Instr. and Meth. A 336 (1993) 206] for determining the total efficiency. This MC-simulation calculates all the other factors required, namely: the sum of the path lengths of the photons in the volume source and the detector, the sum of the path lengths of the photons in the detector for the point source, the value of the self-attenuation of the photons in the volume source and the total efficiency of the point and volume sources.

X-ray source system at the Marshall Space Flight Center X-ray calibration facility

Abstract: In preparation for calibrating the Advanced X-ray Astrophysics Facility, a multicomponent x- ray source system has been assembled for use at the x-ray calibration facility at MSFC. The system consists of an electron impact point source with filters, a penning gas discharge source, and two monochromators fed by rotating anode x-ray generator. The purpose and predicted performance characteristics of these elements are described as they apply to the AXAF calibration. The planned source characterizations, performed in June 1995 through June 1996 time period, are also described.

X-ray focusing optics. II. Properties of doubly bent crystals with an extended x-ray source

Abstract: Calculations and analysis of an extended x‐ray source image with a 2D focusing geometry are presented. Based upon the calculations for an x‐ray point source image (Paper Ia), theoretical expressions are derived which reveal the contributions from both the Bragg and the optical (Fresnel) diffractions to the intensity distribution of the image at the focal plane. That is, for a given focusing geometry, the intensity distribution of the image of an extended source consists not only of the crystal rocking curves for a bent crystal, due to the Bragg diffraction; but also of the optical diffraction, the Fresnel integral, due to the phase correlations of the thickness and the spatial extent of a doubly bent crystal. The contribution from the optical diffraction depends solely upon the bent crystal focusing geometry. The relationship between the source and the image at the focal plane is obtained, and the intensity distribution of an extended x‐ray source image with a 2D bent silicon crystal is given.

Ecological Niches in Infrared and Sub-Millimeter Space Astronomy: Expected Sensitivity as a Function of Observatory Parameters

Abstract: Using current estimates of the celestial and atmospheric background emission, infrared source crowding, and detector performance, we estimate expected point source sensitivities for possible future infrared and sub-millimeter observatories on the ground, in the air, and in space. Our goal is to evaluate the effects of variations in basic observatory system parameters for typical operation over the wavelength range labmda ~3 - 1000 microns. For the first time in a general astronomical journal, we evaluate mission design goals for the wavelength range identified as the premier for this decade. Here we emphasize the effects of telescope temperature, aperture, and emissivity upon detectable point source signal level using diffraction-limited instrumentation, along with approximations to improvements in sensitivities using the new generation of array detectors. We find that [1] for broadband imaging, a larger aperture is more important than extremely low optical system temperature in detecting weak sources in two situations: (1) at short wavelengths, where a telescope need only be cooled to several tens of kelvins for the optical system emission to fall below that of the celestial background, and (2) at far-infrared and sub-millimeter wavelengths, where interstellar "cirrus" and extragalactic confusion eventually determine the limits to sensitivity, which, below some critical temperature, can only be improved upon by increasing the effective angular resolution. [2] for moderate-resolution spectroscopy (lambda/delta-lambda ~30 - 2000), the faintest signal level is always achieved when the telescope temperature is low enough so that the optical system contributes less than the celestial background. This temperature declines as the wavelength increases, so, for example, T ~ 100 microns. However, for sub-millimeter wavelengths, on or near the Rayleigh-Jeans side of the optical system emission, sensitivity increases less strongly with declining temperature. Consequently, large, warm (ground-based and airborne) sub-millimeter telescopes compete favorably with small cold ones in space and those windows accessible from within the Earth's atmosphere. [3] for high-resolution spectroscopy {lambda/delta-lambda >~ 105+), the thermal background from sky and optical system can be low enough that detector noise limits achievable sensitivity. If so, the telescope temperature need not be extremely low and light-gathering aperature is relatively more important. However, to take full advantage of reduced thermal background via high spectral resolution, detector performance may need to be near optimum. [4] conversely, in many circumstances, current and near-future detectors are over-specified in key aspects of operation compared to the high background of the far-infrared. Under such circumstances, detectors may be operated in non-optimum conditions without significant adverse effects upon overall system sensitivity.