Showing papers on "Reflection (physics) published in 1973"

Unified theory of Rayleigh-angle phenomena for acoustic beams at liquid-solid interfaces

Abstract: Various phenomena have been observed when a bounded acoustic beam is incident from a liquid onto the surface of a solid at or near the Rayleigh angle. These phenomena include: a shift of the reflected beam from the position predicted by geometrical acoustics, a null or minimum of intensity within the reflected beam, a 180° phase reversal of the field on either side of the null, a weak trailing field on only one side of the reflected beam and a frequency of least reflection when the solid is lossy. By carefully examining the reflection coefficient for angles in the vicinity of the Rayleight angle, and by taking into account the angular spectrum of plane waves that comprise a bounded beam, a model of the reflection process is developed that explains all of the observed phenomena. This model shows that the various critical-reflection effects result from the interference between a geometrically reflected field and the field of a leaky Rayleigh wave, which is excited by the incident beam. Moreover, this model resolves the conflict between various explanations made for these phenomena in the past; in particular, it is found that Schoch's classical description of a laterally displaced reflected beam is valid only for beams having a large width.

Matrix operator theory of radiative transfer. 1: rayleigh scattering.

Abstract: An entirely rigorous method for the solution of the equations for radiative transfer based on the matrix operator theory is reviewed. The advantages of the present method are: (1) all orders of the reflection and transmission matrices are calculated at once; (2) layers of any thickness may be combined, so that a realistic model of the atmosphere can be developed from any arbitrary number of layers, each with different properties and thicknesses; (3) calculations can readily be made for large optical depths and with highly anisotropic phase functions; (4) results are obtained for any desired value of the surface albedo including the value unity and for a large number of polar and azimuthal angles; (5) all fundamental equations can be interpreted immediately in terms of the physical interactions appropriate to the problem; and (6) both upward and downward radiance can be calculated at interior points from relatively simple expressions.

Direct estimation of the vocal tract shape by inverse filtering of acoustic speech waveforms

Abstract: This paper describes a new method for estimating the vocal tract area function directly from the acoustic speech waveform. Dynamic changes of the area functions and formants in voiced speech sounds are obtainable. The filtering processes of the inverse filter model and an acoustic tube model of speech are analyzed and they are shown to be identical, with the reflection coefficients in the acoustic tube model as a common factor, thus making possible the extraction of the reflection coefficients by the inverse filter processing of the speech signal. The discrete area function can easily be obtained from the set of reflection coefficients. Analysis examples for vowels, diphthongs, and consonants in vowel-consonant-vowel utterances are given.

Analysis and measurement of ultrasound backscattering from an ensemble of scatterers excited by sine‐wave bursts

Abstract: This paper develops a practical approximation for the backscattering of periodic bursts of sine waves by a volume of randomly distributed scatterers. The approximation is applied to the measurement of a “volumetric backscattering cross section,” using a substitution method in which the rms value of the gated backscattered signal is compared with the rms value of a wave reflected from a target of known coefficient of reflection. It is shown that the signal backscattered from the ensemble depends on the attenuation of the wave in the volume and upon the burst and gate lengths. An equation to obtain the volumetric backscattering cross section from experimental data is derived.

Reflection and Transmission of Beams at a Dielectric Interface

Abstract: When complex values are assigned to the source coordinates in the expressions for the fields radiated by a line or point source in a homogeneous medium, the resulting fields have the form of a two- or three-dimensional Gaussian beam. This fact may be utilized to develop results for beam propagation and scattering in inhomogeneous regions from corresponding results for point or line source fields. After justifying the analytic continuation procedure to derive rigorous integral solutions for the (two-dimensional) beam fields reflected by and transmitted through a plane dielectric interface, asymptotic results are obtained by the saddle point method; it is found that the analytic continuation to complex source coordinates can be performed directly on the asymptotic expressions for reflected, refracted and lateral wave constituents of ordinary line source fields. Interpretation of the reflected fields reveals that they incorporate directly the lateral beam shift, a phenomenon usually regarded as a diffraction...

Amplification of waves reflected from a rotating "black hole".

Abstract: The effect whereby waves are amplified during reflection from a rotating "black hole" is investigated. This process is connected with the extraction of energy and momentum from a "black hole." The conditions for the existence of the effect are found. The amplification factor is computed for the model case of scalar waves. For waves with frequencies which do not satisfy the conditions for the existence of the effect, partial cross sections for their capture by the "black hole" are computed.

The Use of Surface-Elastic-Wave Reflection Gratings in Large Time-Bandwidth Pulse-Compression Filters

Abstract: A new type of surface-wave device has been developed which uses the reflection of surface elastic waves to achieve a desired transfer function. A series of experiments on the reflection of surface waves at normal and oblique incidence from periodic arrays of grooves and overlayer stripes provided guidelines for the choice of the type of reflector, the reflection angle, and the depth of grooves. A prototype pulse-compression filter with a time-bandwidth product of 1500 (T=30 /spl mu/S, /spl Delta/f=50 MHz) has been developed. The grooves were etched into LiNbO/sub 3/ by a neutralized argon ion beam in a manner which provided precise depth control and a desired amplitude response. This reflective-array compressor (RAC) has proved to be relatively free of spurious signals and second-order effects and, as a result, large capacities have been obtained. In the prototype device, rms phase errors were 3.5 deg or less and, as a result, the compressed-pulse sidelobe structure was near ideal. A compression ratio of 1500 was demonstrated. The same device, when operated over a wider bandwidth, yielded a compression ratio of about 4000 with only a modest sacrifice in the level of the time sidelobes.

Generalized radiation impedances and reflection coefficients of circular and annular ducts

Abstract: Morse's equation for the radiation impedance of a vibrating rigid piston is extended to give the generalized radiation impedances of all modes in circular and annular ducts which have arbitrary wall admittance and which terminate in an infinite baffle. The extended equation is reduced to a single infinite integral which is a function of the mode radiation directivity factors. An infinite matrix equation is derived which relates the generalized mode reflection coefficients to the radiation impedances. Results are presented which show that the duct-wall admittance is a significant parameter in the effect of duct-determination reflections and that mode-coupling reflection effects may be more important than direct-mode reflection effects.

Method of filtering modes in optical waveguides

Abstract: Modes are filtered in an optical waveguide by selecting and providing a periodic variation, such as a surface corrugation or a refractive index variation, in a filter region in the waveguide. The filter region diverts light in an unwanted mode from the propagation axis by scattering or reflection. Both planar waveguide filters and fiber-optic filters are disclosed.

Amplification of waves during reflection from a rotating "black hole"

Abstract: The effect whereby waves are amplified during reflection from a rotating "black hole" is investigated. This process is connected with the extraction of energy and momentum from a "black hole." The conditions for the existence of the effect are found. The amplification factor is computed for the model case of scalar waves. For waves with frequencies which do not satisfy the conditions for the existence of the effect, partial cross sections for their capture by the "black hole" are computed.

Ultrasonic reflection of a bounded beam at Rayleigh and critical angles for a plane liquid‐solid interface

Abstract: Limited beams of low MHz ultrasound are directed at plane interfaces between water and different solids. Reradiated energy is observed by means of schlieren visualization outside the region predicted by Schoch for incidence at the Rayleigh angle. Some of the solids have properties that would cause prediction of a beam displacement many times that for aluminum. Previous thoery would predict the reflected beam to emerge totally separated from the incident beam for several of the materials used, but no such separation is observed. It is concluded that the reradiated field is composed of specular reflection and Rayleigh‐wave radiation at and near the Rayleigh angle. These two radiations are out of phase at low MHz frequencies, and where they coexist and are of equal amplitude, which occurs within the specular region, a null strip occurs. This strip is sharply defined at exactly the Rayleigh angle. Surface waves (sometimes called pseudosurface waves) are also generated at the longitudinal and shear critical angles. These are also shown to radiate into the fluid but are generated to a much lesser degree and are difficult to demonstrate by schlieren visualization.

Determination of absorption and scattering coefficients for nonhomogeneous media. 1: theory.

Abstract: Equations are derived to determine the diffuse reflectance and transmittance of inhomogeneous materials. The equations are valid for collimated incident radiation for any angle of incidence. The effects of boundary reflectance and anisotropic scattering are included. The equations are derived from the equation of radiative transport, using the Schuster-Schwartzchild approximation. They are sufficiently simple to be used for spectroscopic determination of the absorption and scattering coefficients. Numerical comparison with more exact solutions of the equation of radiative transfer show very good agreement for all cases except for reflectance in the highly anisotropic case, where agreement is only fair.

Use Of Wavefront Curvature To Relate Seismic Data With Subsurface Parameters

Abstract: A Dix-type formula relating the normal moveout velocity (VNMO) to the parameters of a two-dimensional, dipping bed, multilayered model of the earth is discussed. The formula results from (1) showing that the VNMO is related to the radius of curvature of the wavefront emerging at the surface after reflection from some interior horizon, and (2) expressing this radius in terms of the parameters of the earth model. An example with severely dipping layers is used to compute the VNMO from the formula, which is then compared to the value of moveout velocity obtained from a synthetic velocity gather generated at the same point in the model.

Finite Difference Analysis of Rayleigh Wave Scattering at Vertical Discontinuities

Abstract: The finite difference iterative method yields the full wave solution to problems without exact solution that involve the scattering of elastic surface waves at vertical discontinuities in homogeneous media. The technique successfully predicts the results for a problem for which an analytical solution does exist, that of a Rayleigh wavelet propagating on a homogeneous, isotropic, semi-infinite half space. For a Rayleigh wave of unit amplitude incident normally at a 90° corner in a homogeneous medium of Poisson's ratio σ = 0.245, the amplitude coefficients for transmission and reflection were found to be 0.64 ± 0.02 and 0.36 ± 0.02, respectively, whereas the corresponding phase shifts were −79 ± 5° and 38 ± 5°. About 45% of the incident energy is converted into body waves at the corner, and more than 90% of this energy is radiated back into a sector of the plane included between lines making angles of 15° with the two free surfaces. All these results, which are independent of wavelength, agree well with other published data. In the related problem of Rayleigh wave scattering at a downward step discontinuity, the dependence on step height of the transmission and reflection coefficients and of the phase shifts for a given wavelength component has also been investigated. Results show good agreement with both experimental curves and earlier theoretical work. This type of numerical simulation may be applied to other two-dimensional geometries, including layered media problems.

Reflection of light ions from solid surfaces

Abstract: The reflection of 20-50 keV7 Be from gold and silver targets has been studied experimentally and theoretically. The experiments were carried out using a radiotracer technique. Theoretical values of the reflection coefficients were derived from calculated range profiles. The study is an extension of earlier work and as found previously, agreement between theory and experiment is obtained. Reflection coefficients were also calculated for 1H, 2H, 3H and 4He incident on Nb. These calculations should apply to other heavy targets also.

Total Reflection Raman Spectra; Raman Scattering due to the Evanescent Wave in Total Reflection.

Abstract: Several methods of infrared spectra have been devised for surface chemistry, including the attenuated total re­ flection (ATR) method, which was developed by Fahrenfort and by Harrick. The former calculated the relation between the reflectivities and values of the absorption coefficient at angles of incidence above the critical angle. The latter calculated the penetration depth of incident light into the optically rare medium and suggested that this method is sensitive to molecular absorption on the surface. Some workers applied the ATR methods to studies of electrode reactions in situ and adsorptions. In the infrared region water has strong absorption which is apt to disturb studies of adsorbed species. Therefore we developed a Raman spectra method corresponding to the ATR method. It observes Raman scattering due to evanescent wave in total reflection, which may be called Total Reflection Raman Spectra. We measured the de­ pendence of this intensity on the angle of incidence, which agrees with the inclination of the calculation.

Instability-generated laser reflection in plasmas

Abstract: The decay of laser radiation into another electromagnetic wave plus either an ion acoustic wave (Brillouin) or an electron plasma wave (Raman) is studied. The nonlinear evolution of these instabilities was studied in electromagnetic, relativistic-particle simulations. Particular attention is focused on relativistic-particle production by the Raman instability and laser light reflection by the Brillouin instability. Several techniques to reduce these instability effects are also presented. (MOW)

Caustic surfaces and irradiance for reflection and refraction from an ellipsoid, elliptic paraboloid, and elliptic cone.

Abstract: General formulas are derived for the caustic surface and irradiance over an arbitrary receiver surface for point source radiation on collimated rays that are reflected or refracted by a curved surface. Specific formulas are obtained for light from a point source that is deflected by an ellipsoid, an elliptic paiaboloid, and an elliptic cone. As a numerical example caustic surfaces are calculated for a concave spherical surface and a concave paraboloid.

The mathematical problem of reflection solved by an extension of the WKB method

Abstract: Starting with two first order linear differential equations having slowly varying coefficients and mutually connected by the dependent variables, the reflection problem is solved approximately as in the cases of electromagnetic and acoustic waves. An extension of the WKB method is developed and applied to study this problem up to any higher order of accuracy one requires. The solution of the second order differential equation in normal form by the extended WKB method is used to find the characteristics of propagation at a point of discontinuity of higher order derivative of the parameter.

An application of one-dimensional inverse-scattering theory for inhomogeneous regions

Abstract: One-dimensional inverse-scattering theory is applied to the study of the reflection of electromagnetic waves from an inhomogeneous region having a refractive index n(x) = [1-(1/k^{2})q(x)]^{1/2} where k = 2\pi/\lambda , and \lambda is the free-space wavelength. The exact refractive index profile is obtained that will produce a reflection coefficient in which the frequency dependence is described by the Butterworth approximation.

Seismic Refraction and Reflection Measurements at “Byrd” Station, Antarctica *

Abstract: Seismic refraction and reflection shooting was carried out along three profiles about 10 km long, angled 60° to one another, near “Byrd” station, Antarctica, during the 1970–71 field season. No dependence of velocity upon azimuth was found, but velocities at 200 or 300 m depth were slightly greater than at a site 30 km away where measurements were made in 1958. The difference can probably be attributed to different ice fabrics arising from a 50% difference in snow accumulation rates at the two sites. The velocity depth and density–velocity functions at the two sites are also significantly different, but close agreement was found at each site between the depths to significant changes in the velocity gradient and the depths of fundamental change in the densification process. Such agreement may permit density–depth curves, and consequently accumulation rates, to be measured by seismic refraction shooting alone. The reflection shooting on a common reflection-point profile led to a good determination of mean velocity through the ice as a function of angle of incidence. The results agree closely with similar measurements at the 1958 site, and with an anisotropic model based on glaciological and sonic logging observations in the deep drill hole. The mean vertical velocity of 3.90–3.93 km/s through the solid ice is about 2% higher than has commonly been used for determinations of ice thickness from seismic reflection shooting.

Strain-Wave Reflections During Ballistic Impact of Fabric Panels

Abstract: A numerical model is presented which describes the strain level build-up in yarns due to multiple strain wave reflections from yarn crossover intersections in a woven fabric subject to ballistic impact. Crossing yarns present barriers from which strain waves are partially reflected. The maximum yarn strain occurs at the point of impact and decays with distance along the yarn away from this point. The rapidity of decay is governed by the crossover reflection coefficient. Using observations of the deformation cone size of ballistically impacted fabric panels, it is concluded that the reflection coef ficient is small (approximately 0.01). The strain increases with time at different rates for different reflection coefficients until failure at the impact point. Extensions of this model to other fibrous structures are discussed.

Apparatus for measuring surface flatness

Abstract: The flatness of a surface is measured using a scanning beam of light. For scanning the surface, a light beam is periodically deflected by a rotating polygonal mirror. The periodic displacement of the scanning beam reflected on the surface is fully compensated by its reflection on the same face of the polygonal mirror. As a consequence, a beam leaves the polygonal mirror substantially on the same path and in the opposite direction as the beam exiting from a light source such as a laser. If the scanning beam reflected from the surface impinges on an embossment or recess the reflected beam is displaced perpendicularly to the scan direction, this displacement not being compensated by its reflection on the polygonal mirror. This displacement, which is a function of the distance of the scanned point from a perfectly plane surface, is sensed by a linear array of photodetectors.

Measurement of thin films by optical waveguiding technique

Abstract: In order to measure the thickness and refractive index of a transparent thin film on a substrate of higher refractive index, such as a film of silicon oxide on a substrate of silicon, an optical wave is coupled into and guided through the film. The guided wave is coupled into the film by means of the phenomenon of the tunneling into the film of an evanescent wave from a beam of light incident on the surface of an adjacent coupling medium at an angle greater than the critical angle for total internal reflection in the medium. The intensity minima of the optical radiation which can be coupled out of the film back into the coupling medium (overall reflection), as a function of angle, yields data from which the desired thickness and refractive index can be determined.

Body waves in a “real Earth”. Part I

Abstract: A theoretical analysis of body waves in a “real Earth” is presented. The earth model consists of an arbitrary number of spherical liquid and solid layers. The algebraic part of the analysis deals with the way to obtain generalized rays out of the exact solution. It is shown that the Rayleigh matrix, and not the Rayleigh determinant, should be used to expand the solution into a power series of modified reflection and transmission coefficients in order to obtain rays.

Semiclassical Theory of Saturated Absorption in Gases

Abstract: A three-dimensional theory for the resonant interaction of electromagnetic waves with a gas of two-level atoms is formulated in terms of macroscopic variables. The theory is utilized to find the steady-state attenuation of a plane wave in the presence of another plane wave running in the opposite direction with different amplitude. Contributions are included from the reflection of the oppositely running wave by an induced standing-wave inhomogeneity in the population inversion of the medium. The resulting attenuation and reflection coefficients are expressed as velocity integrals of continued fractions. Correspondence is made with existing gas-laser theories, yielding the formulation of a high-intensity ring-laser theory. Analytic approximations for the coefficients are presented for the Doppler-limit cases of both waves weak, one wave weak, and negligible reflection (rate-equation approximation). More-general cases have been calculated numerically. The attenuation coefficients exhibit a Lamb-dip feature. The relative depth of the dip increases rapidly with power at low saturation levels, slowly at high saturation, and is greater in the attenuation of the weaker wave. The width of the dip is nonlinearly power broadened. The shape of the dip is very nearly Lorentzian, except for one special case at high power in which the line splits. The propagation equations for the two waves are integrated over long absorption paths. A large resulting attenuation increases the relative size of the dip while decreasing the power broadening.