Showing papers on "Fresnel zone published in 2002"

Global surface wave diffraction tomography

Abstract: [1] We determine the effect of replacing geometrical ray theory in surface wave tomography with scattering theory. We describe a tomographic method based on a simplified version of the scattering sensitivity kernels that emerge from the Born or Rytov approximations in which surface wave travel times are a weighted average of phase or group slowness over the first Fresnel zone of the wave. We apply this “diffraction tomography” to Rayleigh and Love wave group velocity measurements to produce group velocity maps from 20 to 150 s period on a 2° × 2° grid globally. Using identical data and damping parameters, we also produce maps using “Gaussian tomography” which is based on ray theory with intuitive Gaussian smoothing constraints. Significant differences in the amplitude and geometry of the imaged features appear primarily at long periods but exist even in the short-period maps in regions where average path lengths are large. Diffraction tomography, therefore, is significant in most oceanic regions at all periods, but it is also important on continents at long periods at least. On average, diffraction tomography produces larger velocity anomalies in a period-dependent band of spherical harmonic degrees, and diffraction and Gaussian tomography maps decorrelate past a critical spherical harmonic degree that also depends on period. The widths of resolving kernels that emerge from diffraction tomography are systematically larger than those from Gaussian tomography. Finally, mantle features inferred from diffraction tomography tend to have larger amplitudes and extend deeper than those from Gaussian tomography.

Birefringent Fresnel zone plates in silica fabricated by femtosecond laser machining

Abstract: We demonstrate maskless, single-step fabrication of strongly birefringent Fresnel zone plates by focusing of femtosecond laser pulses deep within silica substrates. The process allows us to produce alternate zone rings directly by inducing a local refractive-index modification of the order of n~10-2 . The embedded zone plates shown in this Letter exhibit efficiencies that vary by as much as a factor of ~6 for orthogonal polarizations. Focal lengths of primary and secondary foci are shown to compare well with theory.

Determination of the influence zone for surface wave paths

Abstract: SUMMARY An approximate description of the zone of influence around the propagation path for a surface wave is provided by investigating the Fresnel zones for the frequency range of interest. The influence zone about surface wave paths, over which surface waves are coherent in phase, is identified as approximately one-third of the width of the first Fresnel zone. A technique called Fresnel-area ray tracing (FRT) for surface waves has been used to estimate this region around the ray path for each frequency. The FRT technique is developed by combining two standard ray tracing methods, i.e. kinematic ray tracing (KRT) and dynamic ray tracing (DRT). To obtain the exact Fresnel area in a laterally heterogeneous structure would require the solution of a large number of KRT equations. In contrast, the FRT approach requires just a few ray tracing calculations. In the first step, the trajectory of the surface wave is computed by solving the KRT system for the phase-velocity distribution at the required frequency. In the next step, the behaviour of rays in the zone surrounding the KRT path is calculated by solving the DRT system twice; once from the source to the receiver and once more from the receiver to the source along the same trajectory. Finally, combining the solutions of these ray tracing systems using paraxial ray theory, the Fresnel area around a central ray can be estimated. Using FRT, stationary-phase fields can be constructed around a central ray path in a laterally heterogeneous structure. The influence zone around the ray path is then estimated from the stationary-phase function with simple assumptions concerning the perturbed wavefield. The estimate of the influence zone can be efficiently calculated in laterally heterogeneous structure by using the FRT technique, and allows an extension of current methods of surface wave analysis, which have commonly been based on geometrical ray theory and on the approximation of great-circle propagation. This approach allows the treatment of finite-width rays as well as deviations in propagation from the great circle induced by moderate lateral heterogeneity as revealed by recent tomography models. Such finite-width rays should be of major benefit in enhancing ray-based surface wave tomography.

Fabrication of Fresnel zone plate embedded in silica glass by femtosecond laser pulses

Abstract: We fabricated the Fresnel zone plate by embedding voids in silica glass. We investigated the focusing properties by launching a He-Ne laser beam into the zone plate. The spot size of the primary focal point was 7.0 mum and agreed with the theoretical value of 6.1 mum. The diffraction efficiency was 2.0 %. This technique enables us to make alignment free micro-scale lenses inside bulk materials.

Focusing analysis of the pinhole photon sieve: individual far-field model

Abstract: Recently, a new class of diffractive optical element called a photon sieve, which consists of a great number of pinholes, was developed for the focusing and imaging of soft x rays. In terms of the closed-form formula for the far field of individual pinholes and the linear superposition principle, we present a simple yet accurate analytical model for the focusing of the pinhole photon sieve. This model is applicable to arbitrary paraxial illumination with arbitrary complex amplitude distribution at the photon sieve plane. We check the validity range of this model by comparing it with the exact Fresnel diffraction integral. Some special problems, such as the individual quasi-far-field correction for very large pinholes and the related phase shift induced by this correction, are also discussed.

Realization of a time-domain Fresnel lens with coherent control

Abstract: Perturbative chirped pulse excitation leads to oscillations of the excited state amplitude These coherent transients are governed by interferences between resonant and off-resonant contributions Control mechanisms in both frequency and time domain are used to modify these dynamics First, by applying a phase step in the spectrum, we manipulate the phase of the oscillations By direct analogy with Fresnel zone lenses, we then conceive highly phase-amplitude modulated pulse shapes that slice destructive interferences out of the excitation time structure and enhance the final population

Characterization of T-ray binary lenses.

Abstract: Multilevel phase-shift Fresnel diffractive zone plates fabricated on silicon wafers have been used as T-ray imaging lenses. The imaging results, including spatial and temporal distribution of T-rays measured at the focal planes in the frequency range from 0.5 to 1.5 THz, indicate that the performance of the diffractive terahertz (THz) lens is comparable with or better than that of conventional refractive THz lenses. The unique properties of the T-ray binary lens make it possible to fabricate excellent optics for narrow-band THz applications.

Diffractive-refractive optics for high energy astronomy - II. Variations on the theme

Abstract: In a companion paper diffractive-refractive optics components such as Fresnel Zone Plates and their derivatives have been proposed as a basis for telescope systems for X-ray and gamma-ray astronomy with high sensitivity and superb angular resolution. A wide family of configurations is possible and the first paper concentrated on simple systems for gamma-ray energies. The main problems arise from the very long focal lengths involved (~10 6 km) and from chromatic aberration in the focussing system. Ideas are presented here that could in some circumstances allow the focal length to be reduced by many orders of magnitude. In addition it is shown how lenses which are to first order achromatic might be constructed. Finally, the possibility of using similar optical components for X-ray and gamma-ray interferometry is discussed.

Fresnel Zone Antennas

Abstract: Acknowledgement. 1: Introduction. 2: Offset Fresnel Zoneplate. 3: Phase Correcting Zoneplates. 4: Zonal Reflectors. 5: Single Printed Flat Reflector. 6: Reflective Array Antenna. 7: Other Fresnel Zone Antennas. Bibliography. Index.

Simulation of high-resolution x-ray zone plates.

Abstract: A full-wave approach to quantitative characterization of x-ray zone plate lenses is proposed. Distributed focusing efficiency η(z) of a multifocus optical element is defined as the energy flux through the Airy disk of a reference perfect lens with variable focal length z. Maxima of this function characterize diffraction efficiencies and spatial resolution of the zone plate foci. The parabolic wave equation is used to take into account diffraction effects inside the optical element. Rough and fuzzy interface models are introduced to describe realistic zone profiles. Numerical simulation reveals the limited capability of zone width reduction to improve the zone plate imaging performance. The possibilities of second-order focus enhancement by optimization of the zone plate thickness, line-to-space ratio, and zone tilt are studied numerically.

Defining the Fresnel zone for broadband radiation

Abstract: The concept of the Fresnel zone is central to many areas of imaging. In tomographic imaging, the transverse spatial resolution can be limited by the size of the first Fresnel zone, usually defined only for monochromatic radiation. With the increasing prevalence of broadband tomographic imaging systems, a generalization of this concept is required. Here, a proposed generalization is described in the context of femtosecond optics, and experimentally verified using terahertz time-domain spectroscopy. Based on this definition, a simple zone plate design is demonstrated.

Achromatic fresnel optics based lithography for short wavelength electromagnetic radiations

Abstract: A lithography apparatus having achromatic Fresnel objective (AFO) that combines a Fresnel zone plate and a refractive Fresnel lens. The zone plate provides high resolution for imaging and focusing, while the refractive lens takes advantage of the refraction index change properties of appropriate elements near absorption edges to recombine the electromagnetic radiation of different energies dispersed by the zone plate. This compound lens effectively solves the high chromatic aberration problem of zone plates. The lithography apparatus allows the use of short wavelength radiation in the 1-15 nm spectral range to print high resolution features as small as 20 nm.

Parallel maskless optical lithography for prototyping, low-volume production, and research

Abstract: Earlier we reported on a proof-of-concept maskless-lithography system that used an array of Fresnel zone plates to focus multiple beams of 442 nm light onto a substrate, and micromechanics for multiplexing light to the several zone plates, enabling patterns of arbitrary geometry, at 350 nm linewidth, to be written. We referred to the technique as zone-plate-array lithography (ZPAL). We also demonstrated zone-plate-array microscopy. Here, we report on a “preprototype” ZPAL system operating at an exposure wavelength of 400 nm, capable of quick-turn-around, maskless lithography. We describe the lithography results with this system as well the development of high-speed data delivery systems, high-numerical-aperture zone plates (up to 0.95), and a multiplexing scheme that will enable us to move to a “full-prototype” system capable of 210 nm feature sizes at a moderate but useful throughput of ∼0.25 cm2 in 20 min.

Wavelength Dependent Leakage in a Fresnel-based Air-silica

Abstract: An air-silica structured fibre is designed with air holes placed in circular rings marking the effective Fresnel zones of the waveguide. By educing the holes to six in each ring and pulling the fibre to appropriate dimensions, light at 633nm leaks out between the holes and is unable to propagate along the fibre. On the other hand confinement and propagation is achieved at 1550nm despite a large hole separation.

A test of ray theory and scattering theory based on a laboratory experiment using ultrasonic waves and numerical simulation by finite-difference method

Abstract: SUMMARY The structure of the Earth is represented by a wide spectrum of small- and large-scale structures. However, tomographic imaging techniques based on ray theory are often applied inappropriately in models with a characteristic length of heterogeneity smaller than the wavelength and width of the Fresnel zone. In other words, the conditions for ray theory are not satisfied in such models. It is therefore necessary to apply the diffraction theory of waves in tomographic reconstruction techniques in order to retrieve images of the Earth with a more general theory for wave propagation than ray theory. Physically speaking, scattering theory takes the finite-frequency effect of waves into account. We performed a test of ray theory and scattering theory in an ultrasonic wave experiment and in a numerical finite-difference experiment using random media with correlation lengths smaller than the width of the Fresnel zone. We used a stochastic approach to compute the mean squared value of time-shift variations calculated from ray theory and diffraction theory. The theoretical results were compared with the experimental values obtained in the laboratory experiment using rock samples with different length-scales of heterogeneity and from numerical experiments on wave propagation in quasi-random media. We observed that ray theory systematically overestimates the mean squared value of time-shift variations, while the observed statistical values from the laboratory experiments are well predicted by scattering theory. This means that tomographic imaging techniques based on ray theory suffer from a loss of resolution when the reconstructing models have a characteristic length of heterogeneity smaller than the width of the Fresnel zone.

Near-field stacking of zone plates in the x-ray range.

Abstract: We use Fresnel zone plates as focusing optics in hard x-ray microprobes at energies typically between 6 and 30 keV While a spatial resolution close to 01 {micro}m can currently be achieved, highest spatial resolution is obtained only at reduced diffraction efficiency due to manufacturing limitations with respect to the aspect ratios of zone plates To increase the effective thickness of zone plates, we are stacking several identical zone plates on-axis in close proximity If the zone plates are aligned laterally to within better than an outermost zone width and longitudinally within the optical near-field, they form a single optical element of larger effective thickness and improved efficiency and reduced background from undiffracted radiation This allows us both to use zone plates of moderate outermost zone width at energies of 30 keV and above, as well as to increase the efficiency of zone plates with small outermost zone widths particularly for the energy range of 6-15 keV

In-depth resolution from multifrequency Born fields scattered by a dielectric strip in the Fresnel zone.

Abstract: The achievable depth resolution in reconstructing the permittivity profile of a dielectric strip under the Born approximation when data are collected in the Fresnel zone is studied. We consider a rectilinear measurement aperture and an orthogonal and centered rectilinear investigation domain. The roles of the aperture extent and frequency diversity are highlighted.

Optical system for a fresnel lens light, especially for a spotlight or floodlight

Abstract: The optical system for the Fresnel lens light has an ellipsoidal reflector ( 1 ), a light source ( 2 ) and a Fresnel lens ( 3 ). The distance (a) between the Fresnel lens ( 3 ) and the reflector ( 1 ) is related to the distance (b) between the light source ( 2 ) and the reflector ( 1 ) and is determined by the selected aperture angle for the propagated light beam, e.g. to provide spotlight or floodlight. The distance (b) is adjusted by moving the light source ( 2 ) from a first focal point (F 1 ) in a direction toward or away from the vertex (V) of the reflector ( 1 ). The ellipsoidal reflector ( 1 ) is made of a metallic material or a transparent material. At least one of the respective surfaces on opposite sides of the reflector has a number of thin layers. Surfaces of the at least one Fresnel lens and/or the reflector can be structured to provide more uniform illumination of a given area. The optical system is useful for lights for film, stage, studio and photography.

Achromatic fresnel optics for ultraviolet and x-ray radiation

Abstract: An achromatic Fresnel optic that combines a Fresnel zone plate and a refractive Fresnel lens. The zone plate provides high resolution for imaging and focusing, while the refractive lens takes advantage of the refraction index change properties of appropriate elements near absorption edges to recombine the electromagnetic radiation of different energies dispersed by the zone plate. This compound lens effectively solves the high chromatic aberration problem of zone plates. The AFO has a wide range of potential applications in lithography, microimaging with various contrast mechanisms and measurement techniques.

Characterization of a Fresnel zone plate using higher-order diffraction

Abstract: The performance of a Fresnel zone plate has been tested by observing the focusing property of higher-order diffraction. The Fresnel zone plate was fabricated by the electron-beam lithography technique. The zone material was made from 1 µm-thick tantalum and the outermost zone width was 0.25 µm. The third-order focused spot size measured by the knife-edge scan method was 0.1 µm full width at half-maximum at an X-ray energy of 8 keV, which is exactly equal to one-third of the first-order focal spot size.

Hard X-ray microbeam experiments with a sputtered-sliced Fresnel zone plate and its applications.

Abstract: Hard X-ray microbeam experiments with sputtered-sliced Fresnel zone plates have been performed. Zone plates with an outermost zone width of 0.25 µm (#FZP1) and 0.1 µm (#FZP2) were fabricated and evaluated. In a scanning X-ray microscopy experiment, a line-and-space pattern with structure as fine as 0.1 µm was resolved using #FZP2 at an X-ray wavelength of 1 A. As an application of the microbeam technique, a two-dimensional distribution of constituent elements in forensic samples has been obtained (e.g. section view of human and elephant hairs) using fluorescent scanning microscopy.

Axial irradiance distribution throughout the whole space behind an annular aperture

Abstract: In many photonics and fiber-optics applications, the irradiance distribution in the very near field (z/ D < 0.25) behind a circular or annular aperture is of interest. We present the results of detailed calculations of the irradiance distribution throughout the entire space behind an annular aperture. Included as a special case of the annular aperture is the circular aperture and the opaque circular disk. A log–log plot over many orders of magnitude in axial distance provides particular insight. The behavior throughout the Fresnel and Fraunhofer region is well known; however, we pay particular attention to the behavior in the near field. A variety of subtle effects in the near field are presented and discussed.

The limits and complementary nature of traveltime and waveform tomography

Abstract: Introduction Seismic traveltime tomography has proven to be an effective imaging tool in many applications. More recently, the technique of waveform tomography has emerged, in which we use wave-theoretical methods and the direct arrival waveform. Traveltime methods, while reasonably robust, are known to have a reduced resolution that scales with the Fresnel zone, while the superior resolution of waveform methods scales with the wavelength (Williamson, 1991; Schuster, 1996). Waveform methods, however, are far more likely to fail due to a lack of robustness. Resolution is usually estimated by examining the “impulse response” of a given algorithm: This procedure can be carried out analytically; numerical studies generally confirm the predictions (Williamson and Worthington, 1993). However, studies based on spatial delta functions fail to account for non-linear effects created by distortions of the wavefield, or by high order scattering. In this paper we show that nonlinear effects can dramatically affect the performance of high resolution of waveform tomography. We use “chequerboard” models in which the anomaly sizes vary from the dominant wavelength to the approximate size of the first Fresnel zone.

Fresnel lens sheet and transmission screen using the same

Abstract: PROBLEM TO BE SOLVED: To provide a Fresnel lens sheet without causing stray light itself. SOLUTION: The Fresnel lens sheet is formed with a number of prism groups extending on a straight line or to an arcuate form on its light incident surface, in which total reflecting surfaces for totally reflecting incident light and emitting the light to an observer side are formed on the individual prisms constituting the prism groups. The heights of the prisms in the respective regions of the light incident surfaces of the Fresnel lens sheet are made higher than the heights of the prisms in the other regions. COPYRIGHT: (C)2004,JPO

Wavelength-compensated Fourier and Fresnel transformers: a unified approach.

Abstract: We recognize that one can adapt any dispersion-compensated broadband optical Fourier transformer to achieve wavelength compensation in the Fresnel diffraction region just by inserting a diffractive lens at the input plane and vice versa. This unification procedure is employed in a second stage in the design of a novel hybrid (diffractive–refractive) optical setup that provides, in a sequential way, nearly wavelength-independent Fresnel diffraction patterns in the irradiance of the object transmittance.

An analysis of DTV propagation into and within a room in a domestic environment

Abstract: A window in a room within a domestic environment in a structure with aluminum siding is analyzed with respect to its radiating properties. The window is modeled as a rectangular aperture, which diffracts the distant horizontally polarized signal from a DTV transmitting antenna into the environment of the room. The diffraction signal, also horizontally-polarized, is combined with the distant signal, which penetrates the aluminum siding at some loss, and thereby a field distribution within the room is created. The window-diffracted signal is almost entirely a near field (Fresnel zone) within the room while the distant field is a far field (Fraunhofer zone) within the room. Various locations within the room are examined with respect to echoes, with and without scattering (human) bodies. A receiving antenna is positioned at the locations examined.