Showing papers on "Fresnel zone published in 1995"

Beyond ray tomography: Wavepaths and Fresnel volumes

Abstract: Two techniques that account for the band-limited nature of seismic data are incorporated into tomographic traveltime inversion schemes. The first technique, the wavepath algorithm, is based upon the wave equation, the Born approximation, and an adjoint method for computing Frechet derivatives. Computation of a single wavepath requires the forward propagation of the seismic wavefield, as well as the reverse propagation of a residual wavefield. The second technique, the Fresnel volume approach, is based upon the paraxial ray approximation. The Fresnel volume algorithm requires little more computation than does conventional ray tracing and an order of magnitude less computer time than our calculation of wavepaths. When the Fresnel volume sensitivity functions are normalized by the area of the Fresnel ellipse perpendicular to the ray, the sensitivity estimates are very similar to the wavepaths. In particular, there is heightened sensitivity to velocity structure near the source and receiver locations. The normalization by the Fresnel ellipse area is necessary to ensure ray theoretical results in the limit of infinite frequency. Tomographic inversion based upon wavepaths or Fresnel volumes is more appropriate when considering the arrival time of the peak of the initial pulse rather than the first-arrival time. Furthermore, using the traveltime of the peak instead of the first-arrival time reduces the bias of tomograms to high velocity anomalies. The raypath, wavepath, and Fresnel volume techniques were applied to a set of cross-borehole traveltime observations gathered at the Grimsel Rock Laboratory. All methods imaged a low velocity fracture zone in the granitic site, in agreement with independent well information. Estimates of model parameter resolution are similar for the wavepath and Fresnel volume schemes. The source-receiver regions are the most well resolved areas. However, the model parameter resolution computed using a conventional ray-based formalism is more evenly distributed over the cross-borehole area.

Quarter-wave Fresnel zone planar lens and antenna

Abstract: A new variety of the Fresnel zone planar lens with enhanced focusing quality is proposed. Each full-wave zone is divided into four quarter-wave subzones, which are covered by dielectric rings having equal thickness but different permittivities. Based on this planar lens configuration, a transmissive-type Fresnel-zone antenna for DBS-reception with more than 50% aperture efficiency is developed and examined theoretically. >

Binary phase zone-plate arrays for laser-beam spatial-intensity distribution conversion

Abstract: We report on the theory and development of a diffractive element composed of a binary phase zone-plate array. This component conditions the intensity distribution in the focal plane of a conventional refractive lens to generate efficiently (82%) a flattop intensity envelope on target. Analysis of the design indicates that manufacturing tolerances are not critical. Experimental performances on target from x-ray emission and shock-breakout measurements are also presented.

Phase correcting zonal reflector incorporating rings

Abstract: An array of conducting elements printed on a grounded dielectric substrate functions as an electromagnetic phase shifter. With a fixed substrate and a given operating frequency, the phase shift is determined by the array parameters. In the paper, the spectral domain moment method model for analyzing homogeneous reflective phase shifters with conducting rings as elements is presented, and numerical and experimental results are given. A novel phase correcting Fresnel zonal reflector based on this model is reported. A 43% maximum antenna efficiency and -22 dB sidelobe level were measured in X-band. The bandwidth of the reflector is estimated to be greater than 10%. >

Single-pass and double-pass propagation through complex paraxial optical systems

Abstract: A generalized form of spectral representation theory is developed and used with the ABCD formulation of the Huygens–Fresnel integral for studying optical wave propagation through a random medium in the presence of any complex paraxial optical system that can be characterized by an ABCD ray matrix. Formal expressions are developed for the basic optical field moments and various related second-order statistical quantities in terms of three fundamental moments of the first- and second-order complex phase perturbations. Special propagation environments include line-of-sight propagation, single-pass propagation through arbitrary ABCD optical systems, and double-pass propagation through the same random medium in the presence of an ABCD optical system. For illustrative purposes the method is used in the development of expressions for the mean and the normalized variance of the irradiance associated with the Fourier-transform-plane geometry of a lens and the enhanced backscatter effect (EBS) associated with irradiance and phase fluctuations of a reflected Gaussian-beam wave from a Gaussian mirror. The EBS analysis accounts for both finite size and finite focal length of the mirror.

Multipath tolerant cellular communication system and method

Abstract: A method for deploying a PCS system wherein radio transceivers are deployed at spacings which correspond to a diameter of a first Fresnel zone and set output powers of the transceivers to define cells which correspond to the first Fresnel zone of the transceivers. A PCS system having radio transceivers deployed at spacings corresponding to a diameter of a first Fresnel zone and operating at output powers which define cells corresponding to the first Fresnel zones of the transceivers. A handoff area surrounds the first Fresnel zone breakpoint.

The mutual coherence function and the backscatter amplification effect for a reflected Gaussian-beam wave in atmospheric turbulence

Abstract: The influence of a modified spectrum of refractive-index fluctuations (that includes a high wavenumber rise as well as inner- and outer-scale parameters) on the backscatter amplification effect, arising from double passage of an optical wave through statistically dependent inhomogeneities of a random medium, is studied here for the case of a Gaussian-beam wave reflected by a mirror of finite size. A formal expression is first developed for the mutual coherence function, which subsequently leads to tractable analytic models for the mean irradiance in the strictly backward direction. When the inner scale and Fresnel zone are of comparable size, the modified spectrum predicts significantly larger values of the enhancement factor than predicted by the Kolmogorov power-law spectrum. It is also shown in this analysis that by varying the focal length of the mirror the enhancement effects can be greater or less than those of a plane mirror, depending on focus adjustment. All calculations are based on weak irradiance fluctuations using complex ABCD ray-matrix representations for the propagation channel and a generalized spectral representation theory for the complex phase perturbations

Electromagnetic theory of Bragg-Fresnel linear zone plates

Abstract: An electromagnetic analysis of diffraction by Fresnel linear zone plates ruled into a homogeneous or a stratified media is developed. It takes advantage of the new possibilities brought by the introduction of the R-matrix propagation algorithm into the theory of lamellar gratings, namely, the large increase of the stability domain of the numerical results. Thus a linear Fresnel zone plate can be delt with as a period of such a grating, and the diffracted field can be computed for both TE and TM polarizations. Numerical examples show the convergence of the method and study the focusing properties of positive and negative zone plates. The influence of different parameters such as incidence or number of lines is pointed out.

Geometrical-spreading and ray-caustic decomposition of elementary seismic waves

Abstract: The computation of the geometrical-spreading factor and the number of caustics is often considered to be the most fundamental step in computing zero-order ray solutions for elementary-wave Green`s functions along a ray that originates at a point source and passes through a 3-D laterally inhomogeneous isotropic medium. Here, a new factorization method is described that establishes both quantities recursively along the ray segments into which the total ray can be subdivided. As a consequence of the proposed method, the point-source geometrical-spreading factor and the number of ray caustics along the total ray can be decomposed into (1) point-source spreading factors of the ray segments and (2) certain Fresnel zone contributions at the ray-segment connection points. In a so-called ``3-D simple medium,`` by which any 3-D laterally inhomogeneous medium can be approximated, the new factorization approach permits a simple computation of both quantities. It thus simplifies and provides new insights into the computation of ray-theoretical Green`s functions.

Fresnel zone lenses for an electro-optical 2 x 2 switch

Abstract: An optical two by two exchange bypass module formed by a combination of static and dynamic Fresnel zone lenses is proposed. The basic concept of this switching element is to cascade pairs of dynamic Fresnel zone lenses and pairs of static Fresnel zone lenses, located on each side of a 1.5 mm thick quartz-glass substrate. Two types of elements were designed, to operate at wavelengths of 1.52 micrometers and 0.633 micrometers . The dynamic Fresnel zone lenses on the frontside of the substrate are off-axis lenses which are made switchable by filling them with a liquid crystal after covering the Fresnel structure with a transparent electrode. The second electrode is deposited on a face down mounted cover-glass. The static lenses on the backside of the substrate are conventional on-axis Fresnel zone lenses. The dynamic and the static Fresnel zone lenses, whose blazed profiles have been approximated by multi-levels, have been fabricated by means of micro-structuring techniques. Static and dynamic, on-axis and off-axis Fresnel zone lenses with different focal lengths and of different circular diameters ranging from 0.2 mm to 2.0 mm have been realized. The measured spot-sizes of the Fresnel zone lenses were close to eighth diffraction limited values and the diffraction efficiency of the eight-level lenses was higher than 80%. The switching times of the dynamic lenses were in the range of several milli-seconds and the switching contrast was about 1:10.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Binary-phase Fresnel zone plate arrays for high-power laser beam smoothing

Abstract: Binary-phase optics have been used by a number of high-power laser laboratories in order to achieve relatively smooth focal spots. However, the intensity envelopes have in general been of a sinc form rather than `top-hat.' This paper presents work on the production of uniform `top-hat' intensity focal spot profiles obtained from Fresnel binary phase zone plate (PZP) arrays of various designs. Phase plates are used to generate large area smooth focal spots and both theoretical and experimental focal spots are presented. These demonstrate the flexibility of this technique which provides a simple method of generating both uniform `top-hat' intensity profiles and spatially shaped foci, for use with high-power lasers.

The elliptical Fresnel-zone plate antenna

Abstract: The growing number of direct broadcast satellites (DBS) asks for simple, low-cost home receiving systems. The use of the Fresnel-zone plate antenna (FZPA), which is related to the optical lens, is also promising for this application. The aperture of the FZPA is plane and its structure is determined by the well-known Fresnel ellipsoids. In a practical situation the Fresnel zones are often attached to a window of a building. Then, the line between satellite and receiver is not perpendicular to the aperture and, consequently, the rings become elliptical. In the paper this elliptical FZPA is analysed for both linear and circular polarization. The latter is included because most of the future DBS will transmit circularly polarized waves. For this particular polarization a squint of the antenna beam is expected, because of the asymmetric antenna geometry. Kirchhoff's diffraction theory is used to calculate the mainlobe, the first sidelobe and the corresponding crosspolar lobes of elliptical FZPAs with absorbing rings.

Fresnel reflection termination system for high powered laser systems

Abstract: A fresnel reflection termination system includes a laser source, a folding mirror to reflect a laser beam, a focusing lens to focus the laser beam on the folding mirror, and a laser beam dump. The laser beam dump has an outer absorption surface for absorbing fresnel reflections, an inner termination area for capturing fresnel reflections, and a cooling mechanism within the inner termination area for dissipating heat generated by the captured fresnel reflections. The system terminates fresnel reflections to prevent costly damage to the environment or hardware surrounding the system.

X-ray focusing optics using flat or bent crystals with two-dimensionally modulated surfaces

Abstract: Calculations of focus characteristics for x‐ray focusing systems using either flat or bent crystals with two‐dimensional modulated surfaces are presented. Based on the wave‐optics approach, the analytical formulas are derived for elliptical Fresnel zone structures (flat crystals) and linear Bragg zone structures (toroidally bent crystals). It is shown that for a given Si(111) reflection and Ti Kα radiation, a micron‐size focal spot can be achieved by using only one flat crystal with a modulated surface. The peak intensity is then nearly 100 times higher than that of the flat crystal without modulations. However, for a toroidally bent crystal with both Fresnel and Bragg diffraction amplitudes, the latter becomes dominant, since, due to the bending, the rapid oscillations of the Fresnel diffraction amplitude vanish. It is also shown that a focal spot of 0.3 μm for a bent crystal with linear Bragg zone structures is approximately four times narrower than that of an unmodulated surface. From the analysis, the modulated surfaces for cylindrically and spherically bent crystals are deduced to be a combination of Bragg and Fresnel zones.

A three ray propagation model for PCS and micro-cellular services

Abstract: This paper presents a three ray propagation model for PCS and /spl mu/-cellular services. The salient concept of the proposed model is to maintain cell radii within the Fresnel zone break point. In this region, the path loss slope is similar to free space loss, irrespective of the propagation medium. This analogy is then used to predict cell radii for indoor and outdoor deployment of PCS; requiring virtually no computer aided prediction tools. It is further shown that the ceiling height plays an important role in antenna placement. The proposed method is appropriate for low power PCS and micro-cellular services, offering a greatly simplified and cost-effective deployment process.

The fractional Fresnel transform

Abstract: We show how Fresnel transform computations can be simplified by using the diffraction properties of periodic objects. Such a simplification occurs at locations along the propagation axis which are defined by the fractional Talbot order. An extension to non periodic objects can be obtained by approximations compatible with those defining the domain of the Fresnel diffraction. Such considerations determine the theoretical framework for the fractional Fresnel transform, the main practical advantage of which is the existence of fast algorithms for computing the diffracted fields at given locations along the propagation axis.

Wave-front analysis using Fresnel lens arrays.

Abstract: A compact wave-front sensor is implemented by an array of two-beam common path inversion interferometers. Each element of the array consists of two Fresnel lenses in a confocal configuration. The wave-front data can be extracted from a superposition of the zero-order undiffracted wave and the twice-diffracted first-order wave. The result is a high-sensitivity, compact, and stable interferometric wave-front sensor.

A Compendium of Coded Mask Designs

Abstract: Many different patterns have been proposed for coded masks, from Fresnel zone plates, through scatter-hole designs, to various patterns which are ‘optimal’ in different senses. We present a compendium of such patterns, with examples and their autocorrelation functions, together with a bibliography of associated literature.

3-D crosswell transmissions; paraxial ray solutions and reciprocity paradox

Abstract: Transmission of seismic waves through a 3-D earth model is of fundamental importance in seismology. If the model consists of many layers separated by curved interfaces, the only feasible solution to the transmitted waves is the one given by the geometrical optics approximation. Transmitted rays, transmitted wavefield, and the first Fresnel zone associated with a transmission point can be expressed by four 2 x 2 constant matrices constituting the 4 x 4 linearized ray transformation matrix. Generally, the ray transformation matrix can be constructed by dynamic ray tracing. However, if the layers are homogeneous, it can be formulated in closed form by using elementary vector calculus and coordinate transformations. Using the symplecticity of the ray transformation matrix, transmissions in opposite directions can be formulated by the ray transformation matrix for only one direction, and a reciprocity relation can be established. After the decomposition theorem for the ray transformation matrix, the transmitted wavefield in a model with many curved interfaces can be computed in a cascaded way. Using the B-matrix decomposition theorem, the normalized geometrical spreading factor can be expressed by means of the area of the first Fresnel zone of a transmission point. If seismic waves propagate through a locally spherical interface, the reciprocity relation may not hold. Using ray theory, this fact is shown by formulating the transmitted wavefield with the two principal radii of curvature of the transmitted wavefront at the transmission point under consideration. Using wave theory, this fact is shown by analyzing the Debye integral with the method of stationary phase.

Flat printed lens and reflector antennas

Abstract: The performance of the printed single and double layer phase correcting arrays is theoretically analysed. Then, the latest development of the single printed reflector is reported. The successful design of a practical size single printed reflector for the reception of direct broadcasting by satellite (DBS) is described. The reflector covers three full Fresnel zones and a quarter wave zone, and has a 59.4 cm diameter and 0.8 focal length to diameter ratio. A 43% maximum antenna efficiency and a bandwidth of greater than 10% were measured. The close-in sidelobes of the antenna are about -22 dB and the far-out sidelobes are below -30 dB. >

Spectrum Invariance for a Particular Class of Optical Fields Propagated in Far Zone

Abstract: This paper describes invariance of the normalized optical spectrum for a particular class of optical fields propagated in the far zone from a secondary, spatially, partially coherent source The optical field across the secondary planar source is inhomogeneous to give the complex degree of spectral coherence such that μ = h(αω(ρ1–ρ2))exp(iɛω(ρ12–ρ22)), where α, ɛ are constants, ω is optical frequency, and ρ1, ρ2 denote two points in the secondary source This expression for μ is the same as obtained in the Fresnel zone from a primary, spatially incoherent source The invariance law does not hold for the spectrum of the light propagated from the primary source