The three-dimensional distribution of scattered energy from a point unidirectional source
Three-dimensional distribution of scattered gamma radiation from point unidirectional source
RADIATION DISTRIBUTION↗
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Electromagnetic inverse scattering
A three-dimensional electromagnetic inverse scattering identity, based on the physical optics approximation, is developed for the monostatic scattered far field cross section of perfect conductors. Uniqueness of this inverse identity is proven. This identity requires complete scattering information for all frequencies and aspect angles. A nonsingular integral equation is developed for the arbitrary case of incomplete frequence and/or aspect angle scattering information. A general closed-form solution to this integral equation is developed, which yields the shape of the scatterer from such incomplete information. A specific practical radar solution is presented. The resolution of this solution is developed, yielding short-pulse target resolution radar system parameter equations. The special cases of two- and one-dimensional inverse scattering and the special case of a priori knowledge of scatterer symmetry are treated in some detail. The merits of this solution over the conventional radar imaging technique are discussed.
Bojarski, N. N.↗
Photoelastic Analysis of Three-dimensional Stress Systems Using Scattered Light
A method has been developed for making photoelastic analyses of three-dimensional stress systems by utilizing the polarization phenomena associated with the scattering of light. By this method, the maximum shear and the directions of the three principal stresses at any point within a model can be determined, and the two principal stresses at a free-bounding surface can be separately evaluated. Polarized light is projected into the model through a slit so that it illuminates a plane section. The light is continuously analyzed along its path by scattering and the state of stress in the illuminated section is obtained. By means of a series of such sections, the entire stress field may be explored. The method was used to analyze the stress system of a simple beam in bending. The results were found to be in good agreement with those expected from elementary theory.
Weller, R↗
The k-space formulation of the n-dimensional scattering problem
The n-dimensional scattering problem is solved by means of a k-space formulation of the field equations, thereby replacing the conventional integral equation formulation by a set of two algebraic equations in two unknowns in two spaces (the constitutive equation being an algebraic equation in x-space). These equations are solved by an iterative method with the aid of the fast Fourier transform (FFT) algorithm connecting the two spaces, requiring very simple initial approximations. Since algebraic and FFT equations are used, the number of arithmetic multiple-add operations and storage allocations required for a numerical solution are reduced from the order of N sq (for solving the matrix equations resulting from the conventional integral equations) to the order of N(log base 2 of N) and N, respectively (where N is the number of data points required for the specification of the problem). The advantage gained in speed and storage is thus of the order of N/log base 2 of N and N, respectively. This method is thus considerably more efficient than the conventional matrix method, and permits exact numerical solutions for much larger problems. Arguments are presented toward the view that the field equations are more fundamental in k-space. The details and some numerical results of the application of this method to the three-dimensional electromagnetic scattering problems are presented as an example.
Bojarski, N. N.↗
A three-dimensional hard spheres theory of scattering of gas atoms from a solid surface
Three dimensional model of monatomic gases interacting with solid surfaces represented by similar, noninteracting hard spheres
Goodman, F. O.↗
Satellite observations of snow and ice with an imaging passive microwave spectrometer
The scanning microwave spectrometer (SCAMS) on the Nimbus-6 satellite continuously maps the terrestrial surface with a resolution of about 150 km at 22.235 and 31.400 GHz. SCAMS observes at six angles besides nadir, yielding brightness temperatures which are a function of the distribution and character of various types of snow and ice, including microstructure and subsurface profiles in refractive index, loss (moisture or salinity), and temperature. Spectral signatures exhibiting interesting topographical structure have been observed. To aid in the interpretation of these data, a model was developed to describe the propagation of microwave intensity in a scattering medium characterized by three-dimensional random fluctuations of refractive index in addition to nonrandom variations in permittivity, temperature, and loss. The model combines Maxwell's equations in the Born approximation with radiative-transfer theory; this approach yields the variation of intensity with polarization, direction, and position.
Fisher, A. D.↗
Measurement capabilities of a one-dimensional LDV system
The capability is investigated of a single component laser Doppler velocimeter (LDV) system for the measurement of three dimensional mean and turbulent flow statistics. Sets of general equations defining the parameters measured by a single component LDV system are derived. Solutions to the equations for different configurations of a single forward scatter LDV system show that three-dimensional mean velocity measurements can be made with a minimum restriction on the precision for detecting the Doppler frequency. Measurements of the three-dimensional cross products and correlation parameters are shown to require a significantly higher precision in the Doppler frequency detection.
Cliff, W. C.↗
Semiclassical theory of the three-turning- point-problem.
Phase shift from scattering by atoms with attractive potentials, predicting virtual energy states for incident energies in three-turning point range
ENERGY SPECTRUM↗
Effects of multiple scattering on light pulses reflected by turbid atmospheres
Multiple scattering contributions to lidar returns from turbid atmospheres are derived by means of an analytical theory. It is assumed that scattering takes place mainly at small angles except for one event that scatters the light backward. The phase functions are approximated by the sum of Gaussian functions of the scattering angle in both the forward and backward directions. The three-dimensional radiative transfer equation is transformed to a one-dimensional problem by means of Fourier transforms. Neumann solutions to the transformed equation of radiative transfer are then found. A number of examples are presented for cloud, fog and haze models. The results are found to be in satisfactory agreement with results obtained from the Monte Carlo analysis of Kunkel (1974) and the theory of light pulses doubly scattered by turbid atmospheres which was developed by Eloranta (1972).
Weinman, J. A.↗
Three-dimensional gas turbulence measurement with a laser-Doppler velocimeter system
Laser-Doppler system records gas-velocity data over wide dynamic range in three-dimensional space without physical probe. System detects shift in laser beam scattered by flowing particles and uses this frequency to calculate particle velocities. Technique is based on principle that laser beam scattered by flowing particles is shifted in frequency by amount proportional to laser frequency.
Fuller, C. E.↗
Emissivity of half-space random media
Scattering of electromagnetic waves by a half-space random medium with three-dimensional correlation functions is studied with the Born approximation. The emissivity is calculated from a simple integral and is illustrated for various cases. The results are valid over a wavelength range smaller or larger than the correlation lengths.
Tsang, L.↗
Raman scattering applied to hypersonic air flow
The Raman scattering technique was applied to measure the local static temperature and gas number density over a sharp-edge flat-plate model in a Mach 5 nozzle of the Langley nozzle test chamber with air as the test gas. The angle of attack varied from -5 to 15 deg, and the stagnation temperature varied from 317 to 442 K, with stagnation pressures ranging from 170 kN to 2.8 MN/sq m. The measured values of static temperature and density ranged from 60 to 100 K and from 0.03 to 0.8 kg/cu m, respectively. A comparison with calculated values based on static pressure measurements along the model shows that the Raman scattering technique is a viable measurement method in applications to high-speed three-dimensional flows.
Hillard, M. E., Jr.↗
Application of DOT-MORSE coupling to the analysis of three-dimensional SNAP shielding problems
The use of discrete ordinates and Monte Carlo techniques to solve radiation transport problems is discussed. A general discussion of two possible coupling schemes is given for the two methods. The calculation of the reactor radiation scattered from a docked service and command module is used as an example of coupling discrete ordinates (DOT) and Monte Carlo (MORSE) calculations.
Straker, E. A.↗
A laser Doppler system for the remote sensing of boundary layer winds in clear air conditions
The system discussed uses a laser Doppler radar in combination with a velocity azimuth display mode of scanning to determine the three-dimensional wind field in the atmospheric boundary layer. An attractive feature of this CW monostatic system is that the ambient aerosol provides a 'sufficient' scattering target to permit operation under clear air conditions. Spatial resolution is achieved by focusing.
Lawrence, T. R.↗
Application of holography to flow visualization within rotating compressor blade row
Two holographic interblade row flow visualization systems were designed to determine the three-dimensional shock patterns and velocity distributions within the rotating blade row of a transonic fan rotor, utilizing the techniques of pulsed laser transmission holography. Both single- and double-exposure bright field holograms and dark field scattered-light holograms were successfully recorded. Two plastic windows were installed in the rotor tip casing and outer casing forward of the rotor to view the rotor blade passage. The viewing angle allowed detailed investigation of the leading edge shocks and shocks in the midspan damper area; limited details of the trailing edge shocks also were visible. A technique was devised for interpreting the reconstructed holograms by constructing three dimensional models that allowed identification of the major shock systems. The models compared favorably with theoretical predictions and results of the overall and blade element data. Most of the holograms were made using the rapid double-pulse technique.
Wuerker, R. F.↗
Laser Doppler anemometer for water tunnel applications.
A laser Doppler anemometer for three-dimensional velocity measurement in liquids and gases under a wide range of laboratory conditions has been developed. The instrument is particularly well suited for water tunnel applications. It is portable, easily aligned, and inexpensive (excluding electronic units). It operates in backscatter or forward scatter mode. In both cases all optical components, including laser and photomultiplier, remain on a common base. The system has built-in traversing capability and an aiming device for visualizing the focal (test) point. Design details and representative velocity measurements are given.
Bossel, H. H.↗
A symmetrical laser Doppler velocity meter and its application to turbulence characterization
A symmetrical method of optical heterodyning of the Doppler shifted scattered laser radiation developed for velocity measurements with a minimal instrumental spectral broadening and a high signal-to-noise ratio. The method employs two laser beams incident on the moving scatterer and does not use any reference beam for heterodyning. The Doppler signal frequency is independent of the scattering angle and the signal possesses no receiving aperture broadening. Optical alignment is simple. Typical values of the instrumental spectral broadening were approximately 0.8 percent of the center frequency of the Doppler signal, and the signal-to-noise ratio was approximately 25 dB, obtained from an air flow system using submicron dioctylphthalate scattering aerosol. Experimental and theoretical studies were made on the characteristics of the Doppler signal and the effect of system parameters in turbulent flow measurement. The optimization process involved in the beam optics and in the use of a spatial filter is described. For localized flow measurement in any direction of the three-dimensional orthogonal coordinates, the system, using uncorrected optical components, had a sensing volume which can be described by a sensitive length of 600 microns and a diameter of 100 microns.
Mazumder, M. K.↗
Particle and flow field measurements by laser holography
Holograms make transmission recordings of aerodynamic events which are real-illuminated with ground-glass light diffusers and with no requirements for precision. The three-dimensional interferograms can be recorded by stored-beam, double-exposure, and double-plate techniques. Weak traveling shock waves, generated by rotating blade rows of an aircraft fan compressor, can be visualized by rapid double-exposure holograms recorded with a ruby laser. The same laser technique can also determine flow velocities from holograms of small flow-entrained particles. Particles larger than one-quarter millimeter are recorded under rear diffuse illumination conditions. Smaller particles can be recorded by their own forward scattering of laser light through the sensitivity of the holographic process for weak signals. Since the holographic apparatus can be path-matched, both particle and flow interferograms can be recorded with lasers of short coherence length.
Wuerker, R. F.↗