Showing papers on "Diffraction published in 1970"

Lens-System Diffraction Integral Written in Terms of Matrix Optics

Abstract: This paper deals with the propagation of coherent light through lens systems; it relates diffraction theory to ray optics. A diffraction integral is derived which relates the electromagnetic fields on the input plane of a lens system to those on its output plane. The kernel of the diffraction integral is written in terms of the elements of the ray matrix that describes the complete lens system; that kernel indicates a connection between ray optics and diffraction theory. It also provides a simple method for writing the diffraction integral for a lens system. The results are limited to the paraxial-ray approximation, but apply to symmetric and asymmetric lens systems. In the case of asymmetric systems, i.e., those containing rotated elliptical or cylindrical lenses, the ray-matrix formalism is extended so as to use a single fourth-order matrix. The diffraction integrals derived are applied to optical spatial filtering, optical-beam waveguides, optical resonators, and holography.

X-ray Photographic Studies of Liquid Crystals I. A Cybotactic Nematic Phase

Abstract: The X-ray diffraction patterns of the nematic phase of bis-(4′-n-octyloxybenzal)-2-chloro-1, 4-phenylenediamine show major maxima at two diffraction angles. The ones at the larger angle are due to the interaction of neighboring, parallel molecules and the average distance between the long axes of the molecules can be calculated using the formula 2d sin θ = 1.117γ. The maxima at the smaller diffraction angle are related to the length of the molecule; the observed diffraction pattern is explained by assuming that a part of the molecules are organized in groups (cybotactic groups) in such a way that the ends of the molecules lie in fairly well defined planes making an angle of about 45° with the direction of the long axis of the molecules. At lower temperatures the large majority of the molecules are arranged in these groups, and the groups appear to be fairly rigid. At higher temperatures the groups become less prominent, but they do not completely disappear.

A simple theory for seismic diffractions

Abstract: Existing diffraction theory is often cast in such a way as to preclude a ready qualitative understanding of diffraction phenomena. This difficulty can be overcome by making simplifying but realistic approximations which permit the diffractive response of an arbitrary subsurface with point‐source excitation to be obtained in a simple closed form. The main approximations are that the subsurface behaves as an acoustic medium, that its average velocity is constant, and that its reflectivity is low. An objective of this paper is to provide the field interpreter with a practical understanding of diffraction behavior.

Characteristics of a propagating Gaussian beam

Abstract: From diffraction theory, an expression is derived for the radius of a gaussian beam, in an output plane of a single lens, on-axis optical system, as a function of input waist radius, lens focal length, input waist to lens spacing, and lens to output plane spacing. Several special cases are discussed and plots of the important cases are included. The choice of the plots, and their scaling, was made on the basis of providing useful information to those people involved with typical problems in laser scanning systems, such as the location and size of the focused spot. The derivation includes a discussion of truncation effects.

III Light Beating Spectroscopy

Abstract: Publisher Summary This chapter discusses light beating spectroscopy, which is a direct analog of the familiar mixing of a.c. electrical signals in nonlinear circuit elements. The aspect of light beating spectroscopy, the mixing of two narrowband optical components which produces an a.c. component in the photocurrent at the optical difference frequency, is extensively employed in the analysis of the mode structure of lasers. When light is diffracted by ultrasonic waves in a fluid, the diffraction maxima contain components whose frequency is shifted from that of the incident light by integral multiples of the ultrasonic frequency. The shifts are measured by mixing the diffracted light with the incident laser light. The light, which is scattered from a fluid, has spectral components which are shifted in frequency from the incident light by inelastic photon-phonon scattering. Light, which is scattered by small impurities in a moving fluid, will be Doppler shifted by an amount proportional to the local fluid velocity.

The transient oxidation of alloys

Abstract: The pre-steady-state oxidation of a wide range of binary alloys of practical importance, in 1 atm oxygen at 600° C, is discussed in terms of the main determining parameters, namely the free energies of formation and growth rates of the component and complex oxides, the bulk alloy composition, the alloy interdiffusion coefficient, the oxygen solubility and diffusivity in the alloy, and effects such as epitaxy. Schematic diagrams are used to illustrate the morphology and structure of the films, as revealed by electron microscopy and diffraction. After tabulation of the sparse, and often apparently unreliable, fundamental parameters, a comparison is made within each of the following groups of alloys: (1) Fe-Cr, Ni-Cr, and Co-Cr alloys, in which the less noble metal is the same and the noble metal is varied, there being composition ranges in which noble metal oxide and less noble metal oxide respectively predominate but in which the oxides are partially miscible or react. (2) Ni-Al, Ni-Cr, Ni-Si, Ni-Mn, and Ni-Co alloys, in which the noble metal is the same, the less noble metals have a wide range of affinities for oxygen and oxidation rates, and the oxide phases produced include solid solutions, largely immiscible simple oxides, and complex oxides. (3) Cu-Ni, Cu-Zn, and Cu-Al alloys, in which the noble metal is the same and the less noble metal is varied, the oxides being largely immiscible.

X-ray and neutron diffraction study of tetragonal barium titanate

Abstract: An attempt is made to differentiate between the three previously proposed models of the structure of tetragonal BaTiO3. In the new model, the serious parameter-interaction problem was avoided by the use of both neutron and X-ray diffraction data collected from c-domain single crystals. The result of the refinement gave the displacement of the Ti atom from its cubic position as 0.0135 ± 0.0004 A; the R value was 0.027 and 0.024 for the neutron and X-ray data respectively. The analysis also showed that the temperature parameters, B33, along the c axis are approximately independent of mass; B33 = 0.32 ± 0.03 A2 from X-ray and 0.33 ± 0.04 A2 from neutron diffraction. The average value obtained for the B11 temperature parameters, B11 = 0.50 A2, is considerably higher than the B33 value, which thus clearly indicates the existence of low frequency optic modes at room temperature.

Three-dimensional Fourier synthesis of tosyl-elastase at 3.5 å resolution.

Abstract: X-ray diffraction data have been collected from four isomorphous crystalline derivatives of the proteolytic enzyme elastase, and a map of the three-dimensional electron density of the tosyl derivative has been calculated by Fourier synthesis of 2,750 independent terms. It shows clearly the conformation of the elastase polypeptide chain, the size and orientation of the amino-acid side-chains, and the position of the tosyl group which labels the active centre of the enzyme.

Variable Metal Mesh Coupler for Far Infrared Lasers

Abstract: In a far infrared molecular laser the traditional pierced output mirror has been replaced by an infrared interference filter, consisting of two metal mesh reflector grids. By adjusting the spacing between the two parallel grids, the reflectance of the filter can be varied. Theory and experiment of this variable reflector are presented. It allows convenient optimization of the coupling conditions of a laser for maximum power output. In contrast to hole coupling, the interference filter provides uniform coupling over the entire cross section of the reflector. This reduces the diffraction losses and improves the angular distribution of the output beam. The variable reflector has also been used to determine the linear gain of the laser.

Electric field-induced filament formation in AsTeGe glass

Abstract: The Ovshinsky memory effect (electrically reversible bistable resistivity) has been observed in AsTeGe glass (55%-35%-10% respectively by atomic percent). It is generally thought that an electrically induced conducting filament is responsible for the low resistance state. A cinematographic study of filament formation between two point contact probes on the surface of bulk samples of AsTeGe was made. To further characterize these filaments, electron microprobe analysis and X-ray diffraction were also employed. The cinematography results showed that the filament always grew out of the positive voltage terminal and that the formation of a continuous filament coincided with the establishment of a stable low resistance state. The electron microprobe analysis indicated that inside the filament there was a 37.6% (weight percent) increase in Te, a 40.8% decrease in As and a 47% decrease in Ge compared to the composition some distance away from the filament. X-ray diffraction patterns showed that the electric field-induced formation of filaments on the surface of amorphous AsTeGe introduced a definite crystallinity. It was not possible, however, to positively identify the crystalline structure.

The as-quenched form of the omega phase in Zr-Nb alloys

Abstract: The as-quenched Ω phase was examined in the Zr-Nb system using high resolution dark field electron microscopy and selected area diffraction The morphology of the Ω phase was shown to be based upon (111) tl(0001) rows of particles 10 to 15A in diameter with an interparticle spacing of 15 to 25A The row morphology is in agreement with previous observations on a Zr-Ti alloy In the Zr-8 wt pct Nb alloy, clusters made up of many rows were observed and, as the solute content increased up to 15 wt pct Nb, the clusters became smaller and the length of the individual rows decreased Sharp ω reflections and {111} planes of intensity in reciprocal space were observed in the 8 wt pct Nb alloy As the niobium content increased, the ω reflections broadened and became more diffuse, while the thickness of the {111} planes of intensity increased It was suggested that the sharp ω reflections result from scattering by the clusters while the {111} planes of intensity result from scattering by isolated rows of particles Comparison of the ω morphology with the diffraction effects showed good agreement with these suggestions In alloys with 15 wt pct and higher Nb content, the 0001 and 0002 broadened ω reflections were observed to be displaced toward each other alongω phase It was suggested that these displacements are related to the mechanism of the transformation, which is thought to involve instability of the bcc structure relative to atomic displacement waves The electron diffraction patterns were in agreement with predictions concerning this mechanism

Diffraction-Limited Scalar Image Formation with Holograms of Arbitrary Shape

Abstract: A theory of image formation is presented for a large-angle, point reference hologram, whose recording arrangement consists of a surface of arbitrary shape, a point reference source, and the object. The hologram is illuminated by a spherical wave during reconstruction. The resulting image field is similar to that of a Fourier-transform hologram. An exact, integral formulation of monochromatic, scalar diffraction theory is used to find the image field. The hologram is modeled by surface sources determined from the irradiance of the recorded field. The image field produced by the holographic system approximates the field produced by the ideal system, which forms the image of a point object by launching a converging, spherical wave.

Optically Induced Refractive Index Changes in BaTiO3

Abstract: The phenomenon of ``optical damage,'' that is, optically induced changes in the index of refraction, can be used as a form of holographic storage in transparent ferroelectric crystals. In this paper we describe a series of experiments which characterize the optical damage in ferroelectric BaTiO3. This is done by recording in a single crystal of the material a plane wave hologram, i.e., a diffraction grating, with a laser at one wavelength and reconstructing the hologram with a laser at another wavelength. The time‐dependence and steady‐state value of the diffracted light is studied with respect to variations in incident light intensity, temperature, writing wavelength, and grating spacing. A model describing the optical damage, based on the work of Chen [F. S. Chen, J. Appl. Phys. 40, 3389 (1969)] and Johnston [W. D. Johnston, Jr., J. Appl. Phys. 41, 3279 (1970)] is presented and the results explained in terms of this model.

X-Ray Photographic Studies of Liquid Crystals: II. Apparent Molecular Length and Thickness in Three Phases of Ethyl-p-ethoxybenzal-p-aminobenzoate

Abstract: A general theory is developed for the relation between the molecular length and the position of a diffraction maximum found at diffraction angles of the order of 4°, for nematic and isotropic phases containing elongated molecules. Using this theory and a previously developed one for the relation between the intermolecular distance and the position of the major diffraction maximum at larger diffraction angles, molecular parameters are determined for three phases of ethyl-p-sthoxybenzal-p-aminobenzoate. These parameters are: the thickness of the smectic layers (19.941 A), the length of the molecules in the isotropic phase (21.4 A), and the intermolecular distances in the smectic (4.894 A), nematic (4.932–4.950 A), and isotropic phases (4.950–5.182 A), all as a function of temperature. From these data, densities and volume expansion coefficients are calculated which agree very well with literature data on similar compounds. There appears to be no room for rotation of the molecules around their long ...

The Computation of Diffraction Patterns in the Presence of Aberrations

Abstract: The diffraction integral for the disturbance produced in the image plane normal to the optical axis by an extra-axial pencil has been shown to lead to a Fourier transform provided the exit pupil surface is taken to be that of the reference sphere. It has been shown also that, except for small aperture and field sizes, the effect on the wave-front aberration of a shift of the image plane is not represented with sufficient accuracy merely by a term proportional to the aperture squared. Both of these results have been respected in formulating a numerical technique for the calculation of point spread functions. The diffraction integral is evaluated in polar coordinates, and is such that no error is made in approximating the domain of the exit pupil in cases where this may be represented by an ellipse. A study of the accuracy obtained has shown that, if each quadrant of the pupil is divided into a 20 × 20 mesh of elementary areas, the error in the intensity is not expected to exceed 0·8 per cent of the intensi...

Microwave Frequency Acoustic Surface‐Wave Loss Mechanisms on LiNbO3

Abstract: The temperature and frequency dependence of the attenuation of 0.5–5‐GHz acoustic surface waves on LiNbO3 has been measured. For propagation in vacuum a frequency‐squared dependence of the total attenuation is obtained with a value at 1 GHz of 0.9 dB/μsec. Temperature‐dependence measurements using a novel three‐transducer technique show the dominant loss (0.7 dB/μsec at 1 GHz) mechanism to be the interaction with thermally excited elastic waves. Propagation in air results in an additional loss linearly proportional to frequency with a value of 0.2 dB/μsec at 1 GHz. The effects of beam steering and diffraction losses are also investigated both theoretically and experimentally. Both misalignment of transducers with respect to pure mode propagation axes and misalignment of the propagation‐plane perpendicular can add significantly to delay line insertion loss. This beam steering loss on Y‐cut Z‐propagating LiNbO3 is considerably higher than on the 41.5° rotated‐cut X‐propagating orientation. The loss mechanis...

The dyadic diffraction coefficient for a perfectly conducting wedge

Abstract: : A ray-fixed coordinate system is introduced and used to derive a new, compact form of the dyadic diffraction coefficient for an electromagnetic wave incident on a perfectly-conducting wedge. This diffraction coefficient is merely the sum of two dyads; furthermore, with the use of simple correction factors which have the same form for plane, cylindrical, conical or spherical waves incident on the edge, the dyadic diffraction coefficient is valid in the transition regions of the shadow and reflection boundaries.

Survey of Literature on Reflection and Scattering of Sound Waves at the Sea Surface

Abstract: The problem of diffraction of waves at uneven surfaces has received increasing attention in the past 15–20 years. This has resulted in a large number of reports and papers in the open literature. In this review article most of the publications dealing with sound waves and pressure release surfaces (both theoretical and experimental) that appeared up to the beginning of 1969 are mentioned as references. They are classified by subject, and the main currents in the literature (Rayleigh and Uretsky method for sinusoidal boundaries, Eckart theory with Kirchhoff approximation for random surfaces, experiments at sea) are analyzed and discussed. General trends, relations between studies, agreements, and contradictions are mentioned. It is found that nearly all of the publications cover only part of the problem: although the wave diffraction at rough surfaces is a function of three basic quantities simultaneously (i.e. time, frequency of incident wave, and geometry), most of the papers deal with only one or anothe...

A New Method of Preparing θ-Alumina and the Interpretation of Its X-Ray-powder Diffraction Pattern and Electron Diffraction Pattern

Abstract: Highly crystallized θ-alumina was obtained by a two-step treatment, by hydrothermal and thermal treatment, of η-alumina. Its X-ray-powder diffraction pattern was interpreted based on the structure of θ-gallia, and least-squares refinements were carried out. The electron diffraction pattern of θ-alumina from boehmite was also interpreted, and the directional relations between the phases were established.

An alternative integral equation for propagation over irregular terrain, 2

Abstract: An integral equation for cauculating the attenuation of radio waves propagating over irregular terrain is rederived. The integral equation is applied to three terrain profiles, and the solutions are compared with solutions obtained by using classical methods such as the residue series and diffraction theory.