Showing papers on "Diffraction published in 1995"

Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings

Abstract: The rigorous coupled-wave analysis technique for describing the diffraction of electromagnetic waves by periodic grating structures is reviewed. Formulations for a stable and efficient numerical implementation of the analysis technique are presented for one-dimensional binary gratings for both TE and TM polarization and for the general case of conical diffraction. It is shown that by exploitation of the symmetry of the diffraction problem a very efficient formulation, with up to an order-of-magnitude improvement in the numerical efficiency, is produced. The rigorous coupled-wave analysis is shown to be inherently stable. The sources of potential numerical problems associated with underflow and overflow, inherent in digital calculations, are presented. A formulation that anticipates and preempts these instability problems is presented. The calculated diffraction efficiencies for dielectric gratings are shown to converge to the correct value with an increasing number of space harmonics over a wide range of parameters, including very deep gratings. The effect of the number of harmonics on the convergence of the diffraction efficiencies is investigated. More field harmonics are shown to be required for the convergence of gratings with larger grating periods, deeper gratings, TM polarization, and conical diffraction.

Extended depth of field through wave-front coding

Abstract: We designed an optical‐digital system that delivers near-diffraction-limited imaging performance with a large depth of field. This system is the standard incoherent optical system modified by a phase mask with digital processing of the resulting intermediate image. The phase mask alters or codes the received incoherent wave front in such a way that the point-spread function and the optical transfer function do not change appreciably as a function of misfocus. Focus-independent digital filtering of the intermediate image is used to produce a combined optical‐digital system that has a nearly diffraction limited point-spread function. This high-resolution extended depth of field is obtained through the expense of an increased dynamic range of the incoherent system. We use both the ambiguity function and the stationary-phase method to design these phase masks.

Phase-contrast imaging of weakly absorbing materials using hard X-rays

Abstract: IMAGING with hard X-rays is an important diagnostic tool in medicine, biology and materials science. Contact radiography and tomography using hard X-rays provide information on internal structures that cannot be obtained using other non-destructive methods. The image contrast results from variations in the X-ray absorption arising from density differences and variations in composition and thickness of the object. But although X-rays penetrate deeply into carbon-based compounds, such as soft biological tissue, polymers and carbon-fibre composites, there is little absorption and therefore poor image contrast. Here we describe a method for enhancing the contrast in hard X-ray images of weakly absorbing materials by resolving phase variations across the X-ray beam1–4. The phase gradients are detected using diffraction from perfect silicon crystals. The diffraction properties of the crystal determine the ultimate spatial resolution in the image; we can readily obtain a resolution of a fraction of a millimetre. Our method shows dramatic contrast enhancement for weakly absorbing biological and inorganic materials, compared with conventional radiography using the same X-ray energy. We present both bright-field and dark-field phase-contrast images, and show evidence of contrast reversal. The method should have the clinical advantage of good contrast for low absorbed X-ray dose.

Observation of two-photon "ghost" interference and diffraction.

Abstract: Observations of unusual diffraction and interference by two-photon correlation measurements are reported. The signal and idler beams produced by spontaneous parametric down-conversion are sent in different directions, and detected by two distant pointlike photon counting detectors. A double slit or a single slit is inserted into the signal beam. Interference-diffraction patterns are observed in coincidences by scanning the detector in the idler beam.

Observation of two-dimensional spatial solitary waves in a quadratic medium.

Abstract: We report the first experimental demonstration of two-dimensional spatial solitary waves in second-order nonlinear optical material When an intense optical beam is focused into a phase-matchable second-order nonlinear material, the fundamental and generated second-harmonic fields are mutually trapped as a result of the strong nonlinear coupling which counteracts both diffraction and beam walkoff

Optical Methods of Engineering Analysis

Abstract: Introduction 1. Light and interference 2. Classical interferometry 3. Photoelasticity theory 4. Basic applied photoelasticity 5. Photoelasticity methods and applications 6. Geometrical moire theory 7. In-plane motion and strain measurement 8. Moire mapping of slope, contour and displacement 9. Diffraction and Fourier optics 10. Moire with diffraction and Fourier optical processing 11. Procedures of moire analysis with optical processing 12. Principles of moire interferometry 13. A moire interferometer 14. Experimental methods in moire interferometry 15. Holographic interferometry theory 16. Holographic interferometry methods 17. Laser speckle and combinations of speckle fields 18. Speckle photography 19. Speckle correlation interferometry 20. Electronic speckle pattern interferometry 21. Phase shifting to improve interferometry.

System for reading two-dimensional images using ambient and/or projected light

Abstract: A system for reading a two-dimensional image, and for comparing the two-dimensional image to stored data representative of a known image. The optical scanning device comprises a sensor for capturing the two-dimensional image, which sensor includes a light source for projecting an emitted light towards the two-dimensional image and an optical assembly for focussing light, which may be ambient and or emitted light from the light source, reflected from the framed two-dimensional image onto a CMOS or CCD detector for detecting the focussed light, the detector including a photodiode array for sensing the focussed light and generating a signal therefrom. Aiming of the sensor to read the two-dimensional image is facilitated by a frame locator consisting of a laser diode which emits a beam that is modified by optics, including diffractive optics, to divide the beam into beamlets which having a spacing therebetween that expands to match the dimensions of the field of view of the sensor, forming points of light at the target to define the edges of the field of view.

Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation

Abstract: The diffraction of electromagnetic waves for light focused by a high numerical aperture lens from a first material into a second material is treated. The second material has a different refractive index from that of the first material and introduces spherical aberration. We solve the diffraction problem for the case of a planar interface between two isotropic and homogeneous materials with this interface perpendicular to the optical axis. The solution is obtained in a rigorous mathematical manner, and it satisfies the homogeneous wave equation. The electric and magnetic strength vectors are determined in the second material. The solution is in a simple form that can be readily used for numerical computation. A physical interpretation of the results is given, and the paraxial approximation of the solution is derived.

Structural and optical properties of poly lactic acids

Abstract: Fibrous and crystal structures of a helical polymer, poly‐L‐lactic acid (PLLA), were analyzed by using x‐ray diffraction experiments. It was confirmed that the molecular residues were arranged on a nonintegral 10/3 helix as De Santis and Kovacs [Biopolymers 6, 299 (1968)] reported. The atomic positions in a monomeric unit, which were proposed by Hoogsteen, Postema, Pennings, ten Brinke, and Zugenmaier [Macromolecules 23, 634 (1990)], were validated. However, the previous reports on the positions of the two helical chains were found to be in error. The correct positions were determined. The second helical chain shifts from the base center by 0.45, 0.25, and 0.61 A along a, b, and c axes. Besides, the second chain rotates by 2.46° with respect to the first. Distribution function of the crystallites in various drawn fibers were determined as a function of spiral angle. Optical gyrations of PLLA and poly‐D‐lactic acid fibers were successfully measured by using high accuracy universal polarimeter, as functions of temperature and drawing ratio. By using x‐ray data of the change of the fibrous structure by drawing treatments, the gyration tensor components of PLLA could be calculated. It is of great interest that gyration tensor component g33 along the helical axis is extremely large, ∼(3.85±0.69)×10−2, which corresponds to a rotatory power of (9.2±1.7)×103°/mm, about two orders of magnitude larger than those of ordinary crystals. This is the first experimental evidence that helical polymers will produce enormous optical activity in the solid state. Helical polymers will be important for the elucidation of gyro‐optical properties of solids and promising for new optical applications utilizing their large optical activity.

Diffraction of Water Waves by Porous Breakwaters

Abstract: Diffraction of water waves by porous breakwaters is studied based on the linear potential wave theory. The formulation of the problem includes a newly derived relation for the fluid motion through thin porous structures in addition to the conventional governing equation and boundary conditions for small-amplitude waves in ideal fluids. The porous boundary condition, indirectly verified by collected experimental data, is obtained by assuming that the flow within the porous medium is governed by a convection-neglected and porous-effect-modeled Euler equation. A vertically two-dimensional problem with long-crested waves propagating in the normal direction of an infinite porous wall is first solved and the solution is compared with available experimental data. The wave diffraction by a semiinfinite porous wall is then studied by the boundary-layer method, in which the outer approximation is formulated by virtue of the reduced two-dimensional solution. It is demonstrated that neglect of the inertial effect of the porous medium leads to an overestimate of the functional performance of a porous breakwater.

On diffraction by aperiodic structures

Abstract: This paper gives a rigorous treatment of some aspects of diffraction by aperiodic structures such as quasicrystals. It analyses diffraction in the limit of the infinite system, through an appropriately defined autocorrelation. The main results are a justification of the standard way of calculating the diffraction spectrum of tilings obtained by the projection method and a proof of a variation on a conjecture by Bombieri and Taylor.

The chemical bond and atomic displacements in SrTiO3 from X‐ray diffraction analysis

Abstract: The deformation electron-density (dynamic Fourier) maps and the anharmonicity of atomic displacements in strontium titanate, SrTiO 3 (Gram-Charlier model), were studied by high-precision single-crystal X-ray diffraction analysis at 145(1) and 296(2) K. Space group Pm3m, cubic, λ(Mo Kα) = 0.71069 A, Z = 1, F(000) = 84, T = 145 (1)K, a = 3.8996(5)A, V = 59.30(2)A 3 , D x = 5.138(2) g cm -3 , μ = 26.778 mm -1 , R = 0.0063, wR = 0.0040, S = 1.05 for 131 unique reflections and T = 296(2)K, a = 3.901(1)A, V = 59.36(5)A 3 , D x = 5.133(4) g cm -3 , μ = 26.700 mm -1 , R = 0.0071, wR = 0.0050, S = 1.40 for 109 unique reflections. Strong anharmonicity of the atomic displacements was observed for all atoms at 145 K and for Ti and O atoms at 296 K. These are explained by a model in which electronic instability in the TiO 6 octahedron leads to a displacement of the Ti atom from the center of the octahedron, and the lattice instability resulting from the consequent stretching of the Sr-O bonds leads to a rotation of the octahedra. Both distortions show only short-range order at the temperature studies, but show indications of freezing out as the temperature is lowered towards the rotational phase transition at 106 K. The experimental dynamic Fourier deformation electron-density maps and the Hirshfeld atomic charges were calculated

Amorphous silica studied by high energy X-ray diffraction

Abstract: The use of hard X-rays (60–300 keV) for diffraction studies of disordered materials has several advantages: higher resolution in direct space, smaller correction terms, removal of truncation effects, the possibility for operating in extreme environments and for direct comparison between X-ray and neutron data. A feasibility study of amorphous silica has been performed at 95 keV, using a wiggler synchrotron beam-line at HASYLAB and a cylindrical sample, 3 mm in diameter. The range of Q between 0.8 and 32 A−1 was covered. A thorough discussion of the experimental challenges is given. The resulting systematic error intrinsic to the scattering process (not including errors in the form-factors) is found to be of the order of 0.2%. The data have been analyzed in terms of a model of the short-range order. The OSiO bond angle distribution is found to be nearly Gaussian, centered around 109.3(3)° with a rms value of 4.2(3)°. For the SiOSi bond angle, several types of distribution V(α) = V1(α) sin(α) were investigated. Best fits were obtained for rather broad distributions with V having its maximum at 147° and V1 at 180°.

High-efficiency multilayer dielectric diffraction gratings.

Abstract: The design and performance of a new type of high-efficiency diffraction grating for use in either transmission or reflection are described. The gratings are produced in a multilayer dielectric coating deposited upon optically flat substrates. By proper design of the multilayer stack and grating structure, a diffraction efficiency in excess of 96% for polarized light in the m = -1 order in reflection has been achieved.

JCPDS--International Centre for Diffraction Data round robin study of silver behenate. A possible low-angle X-ray diffraction calibration standard

Abstract: A task group of the JCPDS—International Center for Diffraction Data (ICDD) was established with the charge of investigating the use of silver behenate, CH 3 (CH 2 ) 20 COO·Ag, as a possible low-angle calibration standard for powder diffraction applications. Utilizing several data collection and analysis techniques, long-period spacing ( d 001 ) values with a range of 58.219–58.480 A were obtained. Using the same collected data and one data analysis refinement calculation method resulted in dm values with a range of 58.303–58.425 A. Data collected using a silicon internal standard and the same singular data analysis calculation method provided d 001 values with a range of 58.363–58.381 A.

Incoherent imaging of crystals using thermally scattered electrons

Abstract: Thermal diffuse scattering of electrons through large angles by a simple low-index crystal projection is examined in the context of a phonon model, based on the Warren approximation of X-ray diffraction The scattering from an individual atomic column is visualized in terms of an assembly of independent `packets' of atoms Within a packet, the scattering is partially coherent, causing the columnar intensity to deviate from that calculated with an Einstein independent oscillator model For typical atomic spacings, this deviation is limited to within 20%

Nonlinear wave loads on a slender vertical cylinder

Abstract: The diffraction of water waves by a vertical circular cylinder is considered in the regime where the wave amplitude A and cylinder radius a are of the same order, and both are small compared to the wavelength. The wave slope is small, and a conventional linear analysis applies in the outer domain far from the cylinder. Significant nonlinear effects exist in the complementary inner domain close to the cylinder, associated with the free-surface boundary condition. Using inner coordinates scaled with respect to a, it is shown that the leading-order nonlinear contribution to the velocity potential includes terms proportional to both A2a and A3. The wave load which acts on the cylinder near the free surface includes second- and third-harmonic components which are proportional respectively to A2a2 and A3a. In a conventional perturbation analysis, where A [Lt ] a, these components would be ordered in magnitude corresponding to the different powers of A, but here they are of the same order. The second- and third-order components of the total force are of comparable magnitude for practical values of the wave slope.

Seismic response of three-dimensional alluvial valleys for incident P, S, and Rayleigh waves

Abstract: A simplified indirect boundary-element method (BEM) is presented. It is used to compute the seismic response of three-dimensional alluvial valleys under incident P, S , and Rayleigh waves. The method is based on the integral representations for scattered elastic waves using single-layer boundary sources. This approach is called indirect BEM in the literature as the sources strengths should be obtained as an intermediate step. Scattered waves are constructed at the boundaries from which they radiate. Therefore, this method can be regarded as a numerical realization of Huygens' principle. Boundary conditions lead to a system of integral equations for boundary sources. A simplified discretization scheme is used. It is based on the approximate rectification of the surfaces involved using circles for the numerical and analytical integration of the exact Green's function for the unbounded elastic space. Various examples are given for three-dimensional problems of scattering and diffraction of elastic waves by soft elastic inclusion models of alluvial deposits in an elastic half-space. Results are displayed in both frequency and time domains. These results show the significant influence of locally generated surface waves in seismic response, and they evince three-dimensional effects.

A generalized diffraction synthesis technique for high performance reflector antennas

Abstract: Stringent requirements on reflector antenna performances in modern applications such as direct broadcast satellite (DBS) communications, radar systems, and radio astronomy have demanded the development of sophisticated synthesis techniques. Presented in the paper is a generalized diffraction synthesis technique for single- and dual-reflector antennas fed by either a single feed or an array feed. High versatility and accuracy are achieved by combining optimization procedures and diffraction analysis such as physical optics (PO) and physical theory of diffraction (PTD). With this technique, one may simultaneously shape the reflector surfaces and adjust the positions, orientations, and excitations of an arbitrarily configured array feed to produce the specified radiation characteristics such as high directivity, contoured patterns, and low sidelobe levels, etc. The shaped reflectors are represented by a set of orthogonal global expansion functions (the Jacobi-Fourier expansion), and are characterized by smooth surfaces, well-defined (superquadric) circumferences, and continuous surface derivatives. The sample applications of contoured beam antenna designs and reflector surface distortion compensation are given to illustrate the effectiveness of this diffraction synthesis technique. >

Atom wave interferometry with diffraction gratings of light.

Abstract: We have developed a novel interferometer for atom de Broglie waves, where amplitude division and recombination is achieved by diffraction at standing light waves operating as phase gratings. Our new atom interferometer is the exact mirror image of interferometers for light, with the roles of atoms and photons interchanged, and it directly demonstrates coherence of the diffraction of atomic waves at standing light waves. Easy manipulation of the phase, intensity, and polarization of the standing light wave permits novel studies of atomic coherence properties.

Near-field optical microscope based on local perturbation of a diffraction spot.

Abstract: Using a vibrating opaque metallic tip, which periodically and locally modifies the electromagnetic field distribution of a diffraction spot focused onto a sample surface through a microscope objective lens, we have observed optical resolution better than the diffraction limit both with topographical features and with purely optical ones. This procedure simultaneously generates a reflection-mode near-field optical signal and a tapping-mode atomic force microscope signal and can therefore map independently the topography and the optical properties of a specimen.

Incommensurate crystal structures

Abstract: An overview is given of the crystallography of aperiodic crystals, in particular of incommensurately modulated structures and incommensurate intergrowth compounds. The symmetry, the description of the structure and diffraction are described. An extensive discussion is given of crystallographic methods for determination of incommensurate crystal structures. A series of specific compounds is discussed in detail, covering the various ways of incommensurateness. Special attention is given to the commensurate approximation and to the superspace description of superstructures. An historical introduction and a section on the relation between physical properties and incommensurate structure are included.

Structure and Density of FeS at High Pressure and High Temperature and the Internal Structure of Mars

Abstract: In situ x-ray diffraction measurements revealed that FeS, a possible core material for the terrestrial planets, transforms to a hexagonal NiAs superstructure with axial ratio (c/a) close to the ideal close-packing value of 1.63 at high pressure and high temperature. The high-pressure-temperature phase has shorter Fe-Fe distances than the low-pressure phase. Significant shortening of the Fe-Fe distance would lead to metallization of FeS, resulting in fundamental changes in physical properties of FeS at high pressure and temperature. Calculations using the density of the high-pressure-temperature FeS phase indicate that the martian core-mantle boundary occurs within the silicate perovskite stability field.

LEED and DLEED as modern tools for quantitative surface structure determination

Abstract: The last decade has seen remarkable new developments in the field of low energy electron diffraction (LEED) which are reviewed in the present paper. The arrival of sophisticated and fast techniques for the measurement of diffraction intensities in the early 1980s was a challenge to theory. Its answer was the development of tensor LEED (TLEED) in 1985. It allows the fast calculation of intensities for structures not too far from a certain reference. This made quantitative surface structure analysis approach new frontiers both with respect to structural complexity and-with the help of the routine use of reliability factors-to precision. Simultaneously, the new experimental techniques allowed access to two-dimensional intensity maps, i.e. the measurement of diffuse intensity distributions. Theory could be modified to calculate such distributions and so gave birth to the diffuse LEED technique (DLEED) which allows the retrieval of the local structure in case of disordered adsorption. The basics and the development of both TLEED and DLEED is reviewed. TLEED is the basis for direct methods and is used in effective search procedures for surface structures structurally close to a certain reference. It can also be used to simulate the substitution of surface atoms by different chemical species as well as to account for surface vibrations. In addition to carrying the information about the local structure, DLEED patterns very recently could be successfully interpreted in a holographic sense yielding real space images directly.

Third-harmonic wave diffraction by a vertical cylinder

Abstract: The diffraction of regular waves by a vertical circular cylinder in finite depth water is considered, within the frame of potential theory. The wave slope kA is assumed to be small so that successive boundary value problems at orders kA , k 2 A 2 , and k 3 A 3 can be formulated. Here we focus on the third-order ( k 3 A 3 ) problem but restrict ourselves to the triple-frequency component of the diffraction potential. The method of resolution is based on eigenfunction expansions and on the integral equation technique with the classical Green function expressed in cylindrical coordinates. Third-order (triple-frequency) loads are calculated and compared with experimental measurements and approximate methods based on long-wave theories.

Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field. I

Abstract: We consider the electromagnetic diffraction occurring when light is focused by a lens without spherical aberration through a planar interface between materials of mismatched refractive indices, which focusing produces spherical aberration. By means of a rigorous vectorial electromagnetic treatment developed previously for this problem by Torok et al. [ J. Opt. Soc. Am. A12, 325 ( 1995)], the time-averaged electric energy density distributions in the region of the focused probe are numerically evaluated for air–glass and air–silicon interfaces as functions of lens numerical aperture and probe depth. Strehl intensity, lateral and axial sizes, and axial location of the probe are shown to be regular functions for low numerical apertures and probe depths but irregular functions for high numerical apertures and probe depths. An explanation to account for these occurrences is presented that also explains some previous experimental results of confocal microscopy.

Effect of structural aluminium on the mesoporous structure of MCM-41

Abstract: X-ray diffraction (XRD), 27Al magic-angle-spinning (MAS) NMR, N2 adsorption measurements and transmission electron microscopy (TEM) show that the one-dimensional channels of the mesoporous aluminosilicate MCM-41 containing only structural (four-coordinate) aluminium are much shorter in the sample with an Si/Al ratio of 34.1 (ca. 160 A) than in purely siliceous MCM-41 (ca. 400 A). The quality of the XRD patterns rapidly deteriorates as the aluminium content of the solid increases. However, aluminosilicate MCM-41 still preserves a perfect mesoporous structure with an average pore diameter of ca. 30 A, a surface area of 990 m2 g–1 and a pore volume of 0.74 cm3 g–1. When the Na+ form of aluminosilicate MCM-41 is transformed into the Bronsted acidic H+ form, and some of the aluminium is removed from the structure, the uniform hexagonal mesopores partially collapse and macropores 200–2000 A in diameter are formed.