Showing papers on "Fresnel zone published in 2001"

Sharper images by focusing soft X-rays with photon sieves

Abstract: Fresnel zone plates consisting of alternating transmissive and opaque circular rings can be used to focus X-rays1. The spatial resolution that can be achieved with these devices is of the order of the width of the outermost zone and is therefore limited by the smallest structure (20–40 nm) that can be fabricated by lithography today2. Here we show that a large number of pinholes distributed appropriately over the Fresnel zones make it possible to focus soft X-rays to spot sizes smaller than the diameter of the smallest pinhole. In addition, higher orders of diffraction and secondary maxima can be suppressed by several orders of magnitude. In combination with the next generation of synchrotron light sources (free-electron lasers) these ‘photon sieves’ offer new opportunities for high-resolution X-ray microscopy and spectroscopy in physical and life sciences.

The effect of small-scale heterogeneity on the arrival time of waves

Abstract: SUMMARY Small-scale heterogeneity alters the arrival times of waves in a way that cannot by explained by ray theory. This is because ray theory is a high-frequency approximation that does not take the finite frequency of wavefields into account. We present a theory based on the first-order Rytov approximation that predicts well the arrival times of waves propagating in media with small-scale inhomogeneity with a length scale smaller than the width of Fresnel zones. In the regime for which scattering theory is relevant we find that caustics are easily generated in wavefields, but this does not influence the good prediction of finite frequency arrival times of waves by scattering theory. The regime of scattering theory is relevant when the characteristic length of heterogeneity is smaller than the width of Fresnel zones. The regime of triplications is independent of frequency but it is more significant the greater the magnitude of slowness fluctuations.

Diffractive/refractive optics for high energy astronomy - I. Gamma-ray phase Fresnel lenses

Abstract: Diffractive optics components such as Fresnel Zone Plates and their derivatives potentially form the basis for telescope systems for X-ray and gamma-ray astronomy with high sensitivity and superb angular resolution. The main problem is that systems with convenient design parameters involve very long focal lengths. The design considerations and performance of telescopes using a simple Phase Fresnel Lens on one spacecraft and a detector assembly on another are considered. Such systems are shown to have the potential to provide orders of magnitude improvement on currently available sensitivity. At the same time the angular resolution can be at the micro arcsecond level or better -sufficient to resolve the structure surrounding the event horizon of black holes in nearby galaxies.

The Accuracy of the Born and Ray Approximations in Time-Distance Helioseismology

Abstract: Time-distance helioseismology measures the time for acoustic wave packets to travel, through the solar interior, from one location on the solar surface to another. Interpretation of travel times requires an understanding of their dependence on subsurface inhomogeneities. Traditionally, time-distance measurements have been modeled in the ray approximation. Recent efforts have focused on the Born approximation, which includes finite-wavelength effects. In order to understand the limitations and ranges of validity of the ray and Born approximations, we apply them to a simple problem—adiabatic acoustic waves in a uniform medium with a spherical inclusion—for which a numerical solution to the wave equation is computationally feasible. We show that, for perturbations with length scales large compared to the size of the first Fresnel zone, both the Born and first-order ray approximations yield the same result and that the fractional error in the travel time shift, computed by either approximation, is proportional to the fractional strength of the sound speed perturbation. Furthermore, we demonstrate that for perturbations with length scales smaller than the first Fresnel zone the ray approximation can substantially overestimate travel time perturbations while the Born approximation gives the correct order of magnitude. The main cause of the inaccuracy of the Born approximation travel times is the appearance of a diffracted wave. This wave, however, has not yet been observed in the solar data.

High-efficiency nickel phase zone plates with 20 nm minimum outermost zone width

Abstract: Fresnel zone plates for high-resolution imaging in the soft x-ray regime were fabricated in nickel by a trilevel process, which makes use of electron-beam lithography, reactive-ion etching, and electrodeposition. In order to improve the zone plate’s resolution, which is determined by its outermost zone width, ZEP-7000 electron-beam resist was employed. Residues, which arose during pattern transfer by reactive-ion etching, and which hindered etching in small structures, were suppressed by a cleaning procedure. For improved electrodeposition process control, a nickel electroplating bath was optimized. Zone plates with minimum outermost zone widths of 20, 25 and 30 nm were fabricated, yielding 9.2%, 16.2% and 18.0% first-order diffraction efficiency, respectively, at λ=2.4 nm.

In-depth resolution for a strip source in the Fresnel zone

Abstract: The problem of determining the achievable resolution limits in the reconstruction of a current distribution is considered. The analysis refers to the one-dimensional, scalar case of a rectilinear, bounded electric current distribution when data are collected by measurement of the radiated field over a finite rectilinear observation domain located in the Fresnel zone, orthogonal and centered with respect to the source. The investigation is carried out by means of analytical singular-value decomposition of the radiation operator connecting data and unknown, which is made possible by the introduction of suitable scalar products in both the unknown and data spaces. This strategy permits the use of the results concerning prolate spheroidal wave functions described by B. R. Frieden [Progress in Optics Vol. IX, WolfE., ed. (North-Holland, Amsterdam1971), p. 311.] For values of the space–bandwidth product much larger than 1, the steplike behavior of the singular values reveals that the inverse problem is severely ill posed. This, in turn, makes it mandatory to use regularization to obtain a stable solution and suggests a regularization scheme based on a truncated singular-value decomposition. The task of determining the depth-resolving power is accomplished with resort to Rayleigh’s criterion, and the effect of the geometrical parameters of the measurement configuration is also discussed.

High gain beam compression in new-generation thin-film x-ray waveguides

Abstract: X-ray waveguides can compress an incident beam for microscopy applications above 8 keV photon energy to sizes smaller than 100 nm in one dimension, a range which is not routinely accessed with other x-ray optics (e.g., Fresnel zone plates). Beryllium, because of its low absorption, is expected to provide the highest intensity gain. Measured gains for a beryllium waveguide of 74 nm thickness exceed values of 100 at 13 and 20 keV photon energy, which is an improvement by an order of magnitude compared to previously reported performances. The same object works also at 8 keV with gain 43.

Radio detection of high energy particles: Coherence versus multiple scales

Abstract: Radio Cherenkov emission underlies the detection of high energy particles via a signal growing like the particle energy squared. Cosmic-ray-induced electromagnetic showers are a primary application. While many studies have treated the phenomenon approximately, none have attempted to incorporate all the physical scales involved in problems with time- or spatially evolving charges. We find it is possible to decompose the calculated fields into the product of a form factor, characterizing a moving charge distribution, multiplying a general integral which depends on the charge evolution. In circumstances of interest for cosmic ray physics, the resulting expressions can be evaluated explicitly in terms of a few parameters obtainable from shower codes. The classic issues of Fraunhofer and Fresnel zones play a crucial role in the coherence.

Wavelength tunable diffractive transmission lens for hard x rays

Abstract: We report on the fabrication and testing of linear transmission Fresnel zone plates for hard x rays. The diffractive elements are generated by electron beam lithography and chemical wet etching of 〈110〉 oriented silicon substrates. By tilting the cylindrical lenses with respect to the x-ray beam, the effective path through the phase shifting zones can be varied. This makes it possible to optimize the diffraction efficiency over a wide range of photon energies, and to obtain effective aspect ratios not accessible with untilted optics. The diffraction efficiency of such a lens was measured as a function of the tilt angles for various energies between 8 and 29 keV. Values close to the theoretical limit were obtained for all energies. Because of the coherence preserving properties of diffractive optics, the method opens up opportunities for experiments using coherent hard x rays.

Maskless stereo lithography method and apparatus for freeform fabrication of 3-D objects

Abstract: A maskless stereo lithography method and apparatus for forming a three-dimensional object from a plurality of adhered laminae by exposing successive layers of a photo-curable material to a micro-focused energy beam generated by an array of Fresnel zone plates. The method includes the steps of (A) providing a controllable array of Fresnel zone plates; (B) forming a layer of material adjacent to any last formed layer of material in preparation for forming a subsequent lamina of the object; (C) exposing the material to the micro-focused energy beam to form the subsequent lamina of the object; and (D) repeating the steps of forming and exposing a plurality of times in order to form the object from a plurality of adhered laminae, wherein the array of Fresnel zone plates are employed to focus parallel beamlets of energy beam from a source so that the beamlets converge to an array of focal points at predetermined positions of a lamina in accordance with a computer-aided design file of the object.

A method and an apparatus for generating a phase-modulated wave front of electromagnetic radiation

Abstract: The present invention provides a method and a system for generating a phase-modulated wave front. According to the present invention, the spatial phase-modulation is not performed on the different parts of the wave front individually as in known POSLMs. Rather, the spatial phase-modulation of the present invention is performed by generating an amplitude modulation in the wave front, Fourier or Fresnel transforming the amplitude modulated wave front, filtering Fourier or Fresnel components of the Fourier or Fresnel distribution with a spatial filter such as a phase contrast filter, and regenerating the wave front whereby the initial amplitude modulation has transformed into a phase-modulation.

A Hybrid Model for Propagation Loss Prediction in Tunnels

Abstract: The Fresnel zone theory is employed to determine the boundary to distinguish propagation regions for line-of sight topographies in tunnels. The formula for calculationg the break point distance is obtained. A hybrid propagation model combining the free space propagation model and the modified waveguide propagation model is proposed. The hybrid model and the break point distance formula are validated with our own and other published experimental data in various tunnels and at different frequencies. It is shown that the free space propagation model can be used to predict propagation loss in region prior to the break point , while the modified waveguide propagation model offers excellent prediction of propagation loss after break point.

Three-dimensional remote sensing by optical scanning holography

Abstract: A technique is presented by which holograms can be recorded when an object or scene is scanned with an optically heterodyned Fresnel zone pattern. The experimental setup, based on optical scanning holography, is described and experimental results are presented. We apply the scanning holography technique to three-dimensional reflective objects for the first time to our knowledge and address the unique requirements for such a system. We discuss holographic recording and numerical image reconstruction using a system point-spread function (PSF) approach. We demonstrate numerical image reconstruction of experimentally recorded holograms by two techniques: deconvolution with a simulated PSF and an experimentally acquired PSF.

Precise and simple optical alignment method for double-sided lithography.

Abstract: A method for aligning a photolithographic mask at the top of a transparent wafer that has a pattern on its bottom side is presented. The method is based on optical self-imaging of special alignment marks and provides submicrometer accuracy. The method is simple and robust and can conveniently be implemented on laboratory mask aligners for contact or proximity printing.

Wet-etched diffractive lenses for hard X-rays

Abstract: A method for the fabrication of linear transmission Fresnel zone plates for X-rays in the 8–15 keV photon energy range is presented. The diffractive elements are generated by electron-beam lithography and chemical wet etching of 〈110〉-oriented silicon membrane substrates. Diffractive structures with aspect ratios of more than 30 for 300 nm-wide structures were obtained. The diffraction efficiency of such a lens was measured for 13.3 keV radiation to be 20%.

X-ray imaging of acoustic wave interaction with dislocations

Abstract: We used stroboscopic X-ray topography to visualize the propagation of high-frequency (580 MHz), short wavelength (6 μm) surface acoustic waves in LiNbO 3 crystals. The images showed well-resolved individual acoustic wave fronts as well as their distortions caused by scattering on linear dislocations. The observed wave front shapes indicate that a considerable portion of acoustic energy flows along a dislocation line, providing forced vibration of the dislocation string and re-emission of the secondary elastic waves. We also found that the linear dislocations, situated perpendicular to the crystal surface, produce characteristic Fresnel zone contrast in the X-ray images due to an interference of the secondary elastic waves re-emitted by the vibrating dislocations.

Fresnel image floater

Abstract: An image projection device includes a Fresnel lens (11) positioned in an optical path of an illuminated image (10) in such a way that light from the image passes twice through the Fresnel lens (11). A first optical element may be a planar mirror (13) arranged to reflect light transmitted by said Fresnel lens (11) in a first direction back through the Fresnel lens (11) in a second direction. A second optical element may be provided for changing a path of light exiting said Fresnel lens in the second direction so that the projected image appears at a location away from the path of light from the image source to the Fresnel lens.

Theoretical and experimental investigations of the effect of diffractive multifocal focusing of radiation.

Abstract: The new optical effect of diffractive multifocal focusing of radiation, predicted earlier by theory, on a bicomponent diffraction system with small Fresnel numbers that consists of two plane screens with circular apertures on given optical axes, is confirmed experimentally. It is shown that the diffraction picture in the focal planes of such a system represents the circular nonlocal bands of the Fresnel zones with a bright narrow peak at the center, whose intensity in the experiment can exceed by six to ten times the value of the incident plane-wave intensity. Experimentally it is established that the diffractive multifocal focusing of radiation on real screens with axial circular apertures, whose diameters exceed the radiation wavelength, is insensitive to the rough external conditions: thickness of the screens, irregularities of the edges and nonideal form of the apertures, heterogeneity of the initial distribution of the incident-wave intensity, and changes in the medium of the wave propagation.

Six-degrees-of-freedom alignment of two-dimensional array components by use of off-axis linear Fresnel zone plates

Abstract: A novel six-degrees-of-freedom (six-DOFs) alignment technique for assembling two-dimensional array components is presented. The technique uses off-axis linear Fresnel zone plates on one component that are combined with alignment targets on the other. The technique is compact and sensitive to all six DOFs; it was used to package an array of microlenses with a 32 x 32 array of GaAs multiple-quantum-well modulators flip-chip bonded to a 9 mm x 9 mm complementary-metal-oxide-semiconductor chip. By use of interference fringes to control the tilt misalignment, the worst-case misalignment of the microlenses relative to the chip is calculated to be as follows: lateral = 3.0 mum, rotational = 0.023 degrees , longitudinal = 13 mum, and tilt = 0.022 degrees . We also propose alternative implementations of the technique, including one that uses on-chip photodetectors to automate this six-DOF alignment technique.

X-ray zone plate fabrication using a focused ion beam

Abstract: An x-ray zone plate was fabricated using the novel approach of focused ion beam (FIB) milling. The FIB technique was developed in recent years, it has been successfully used for transmission electron microscopy (TEM) sample preparation, lithographic mask repair, and failure analysis of semiconductor devices. During FIB milling, material is removed by the physical sputtering action of ion bombardment. The sputter yield is high enough to remove a substantial amount of material, therefore FIB can perform a direct patterning with submicron accuracy. We succeeded in fabricating an x-ray phase zone plate using the Micrion 9500HT FIB station, which as a 50 kV Ga+ column. Circular Fresnel zones were milled in a 1.0-micrometer-thick TaSiN film deposited on a silicon wafer. The outermost zone width of the zone plate is 170 nm at a radius of 60 micrometer. An achieved aspect ratio was 6:1.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Methods of imaging, focusing and conditioning neutrons

Abstract: A compound refractive lens for neutrons is provided having a plurality of individual unit Fresnel lenses comprising a total of N in number. The unit lenses are aligned substantially along an axis, the i-th lens having a displacement t i orthogonal to the axis, with the axis located such that ∑ i = 1 N   t i = 0. Each of the unit lenses comprises a lens material having a refractive index decrement δ<1 at a wavelength λ<200 Angstroms. In a preferred mode, the lens above is configured such that the displacements t i are distributed and have a standard deviation σ t of the displacements t i about the axis, and wherein each of the unit lens has a smallest Fresnel zone width of s n −s n−1 , where s n and s n−1 are the zone radii of the n and n−1 zones and the standard deviation is σ t ≦[s n −s n−1 ]/4.

Modeling of radiative transfer in optical fiber drawing processes with fresnel interfaces

Abstract: Radiative heat transfer is the most dominant mode of heat transfer in an optical fiber drawing process, and its accurate prediction is the key to a realistic simulation of flow and heat transfer in the system. In this study, the finite-volume method (FVM) is developed to model radiative heat transfer in a gas enclosure as well as inside a glass preform with a Fresnel boundary at the gas-glass interface. Unlike diffuse boundaries, the reflections and transmissions at Fresnel boundaries are governed by Fresnel's relation and Snell's law, and they are strongly dependent on the angular direction. During the implementation of the FVM in semitransparent media, control-angle overlap may occur, and it is treated by assuming that the flux of radiant energy across a control angle is determined only by the discrete direction over this control angle and the corresponding radiative intensity. At the Fresnel boundary, a reflective or refractive intensity may not coincide with any discrete direction, and it is approximated by an intensity whose discrete direction makes the smallest angle with the corresponding reflective or refractive intensity. To validate the present FVM in semitransparent media with Fresnel boundaries, two benchmark problems are examined and the present solutions are found to be very accurate with a fine angular discretization. After that, the present model is applied to investigate an optical fiber drawing process with different boundary conditions and temperature distributions. For the diffuse boundary at the gas-preform interface, the results from the FVM are very close to those from the zonal method in each case. For the Fresnel boundary, the FVM provides a solution that tends to be higher in the upper neck-down region and lower in the low neck-down region than that from the same method with the diffuse boundary. The maximum difference between two solutions varies and may reach 10-15% at some cases.

How much does the migration aperture actually contribute to the migration result

Abstract: Reflection energy from a linear reflector comes from the integrant over an aperture, often described by the Fresnel zone. Within the Fresnel zone, the diffraction energy constructively builds the reflection energy. To get true reflection amplitude, a migration aperture that is twice the Fresnel zone size must be considered. This paper derives the size of the prestack Fresnel zone as a function of half the source-receiver offset. It evaluates how the size of the migration aperture affects the migration result, then establishes an acceptable minimum migration aperture for horizontal reflectors. For both zero-offset and offset data, twice the Fresnel zone size is the minimum migration aperture to preserve true amplitude. A migration aperture that is larger does not improve the migration result.

Flatland optics. II. Basic experiments.

Abstract: In "Flatland optics: fundamentals" [J. Opt. Soc. Am. A 17, 1755 (2000)] we described the basic principles of two-dimensional (2D) optics and showed that a wavelength lambda in three-dimensional (3D) space (x,y,z) may appear in Flatland (x,z) as a wave with another wavelength, lambda = lambda/cosalpha. The tilt angle alpha can be modified by a 3D (Spaceland) individual who then is able to influence the 2D optics in a way that must appear to be magical to 2D Flatland individuals-in the spirit of E. A. Abbott's science fiction story [Flatland, a Romance of Many Dimensions, 6th ed. (Dover, New York, 1952)] of 1884. We now want to establish the reality or objectivity of the 2D wavelength lambda by some basic experiments similar to those that demonstrated roughly 200 years ago the wave nature of light. Specifically, we describe how to measure the 2D wavelength lambda by mean of five different arrangements that involve Young's biprism configuration, Talbot's self-imaging effect, measuring the focal length of a Fresnel zone plate, and letting light be diffracted by a double slit and by a grating. We also performed experiments with most of these arrangements. The results reveal that the theoretical wavelength, as predicted by our Flatland optics theory, does indeed coincide with the wavelength lambda as measured by Flatland experiments. Finally, we present an alternative way to understand Flatland optics in the spatial frequency domains of Flatland and Spaceland.

Observation of diffraction multifocal radiation focusing

Abstract: It is shown experimentally that by placing a flat screen with an axial hole in a diffraction field formed by the first open Fresnel zone upon diffraction of a plane electromagnetic wave from a parallel screen with a hole of a larger diameter, one can observe diffraction multifocal focusing of radiation in the near-field zone of the first screen. The diffraction pattern in the near-field zone of the first screen in focal planes represents circular nonlocalised Fresnel bands with a bright narrow peak at the centre, whose intensity is 6 — 10 greater than that of the incident wave.

High Resolution Imaging of Magnetic Domains with Magnetic Soft X-ray Microscopy

Abstract: X-ray magnetic circular dichroism (X-MCD), i.e. the dependence of the absorption coefficient of circularly polarized X-rays on the projection of the magnetization in a ferromagnetic system onto the photon propagation direction, yields e. g. at L2,3 edges in transition metals large values up to 50%. In combination with a soft x-ray microscope where Fresnel zone plates as optical elements provide a lateral resolution down at 25nm, X-MCD can be used to image magnetic microstructures. This photon based technique allows for recording images in varying external magnetic fields, it exhibits inherent chemical specificity, a high sensitivity due to the large contrast and allows to distinguish between in-plane and out-of plane contributions. In this report the basic features of this novel technique will be outlined and results obtained with the XM-1 microscope at the ALS (Berkeley/CA) with thermomagnetically written bits in magneto-optical storage systems demonstrate the applicability of this new experimental technique to technological relevant issues.

Atom gratings produced by large-angle atom beam splitters

Abstract: An asymptotic theory of atom scattering by large amplitude periodic potentials is developed in the Raman-Nath approximation. The atom grating profile resulting from the scattering is evaluated in the Fresnel zone for triangular, sinusoidal, magneto-optical, and bichromatic field potentials. Analytic asymptotic expressions are obtained for the Fourier components of the atomic wave function following scattering. It is shown that, owing to the scattering into two groups of momentum states rather than two distinct momentum components, the corresponding spatial density profiles differ significantly from pure sinusoids.