Showing papers on "Fresnel zone published in 1996"

Wavefield smoothing and the effect of rough velocity perturbations on arrival times and amplitudes

Abstract: Geometric ray theory is an extremely efficient tool for modelling wave propagation through heterogeneous media. Its use is, however, only justified when the inhomogeneity satisfies certain smoothness criteria. These criteria are often not satisfied, for example in wave propagation through turbulent media. In this paper, the effect of velocity perturbations on the phase and amplitude of transient wavefields is investigated for the situation that the velocity perturbation is not necessarily smooth enough to justify the use of ray theory. It is shown that the phase and amplitude perturbations of transient arrivals can to first order be written as weighted averages of the velocity perturbation over the first Fresnel zone. The resulting averaging integrals are derived for a homogeneous reference medium as well as for inhomogeneous reference media where the equations of dynamic ray tracing need to be invoked. The use of the averaging integrals is illustrated with a numerical example. This example also shows that the derived averaging integrals form a useful starting point for further approximations. The fact that the delay time due to the velocity perturbation can be expressed as a weighted average over the first Fresnel zone explains the success of tomographic inversions schemes that are based on ray theory in situations where ray theory is strictly not justified; in that situation one merely collapses the true sensitivity function over the first Fresnel zone to a line integral along a geometric ray.

A proposal for maskless, zone‐plate‐array nanolithography

Abstract: We propose a novel form of x‐ray projection lithography that: (1) requires no mask, and hence can be considered an x‐ray pattern generator; (2) is, in principle, capable of reaching the limits of the lithographic process. The new scheme utilizes an array of Fresnel zone plates, and matrix‐addressed micromechanical shutters to turn individual x‐ray beamlets on or off in response to commands from a control computer. Zone plate resolution is approximately equal to the minimum zone width, which can approach 10 nm. Zone plates are narrow‐band lensing elements: For a diffraction limited focus, the source bandwidth Δλ/λ should be less than or equal to the reciprocal of the number of zones N. An undulator having Nu magnetic sections emits collimated radiation in a bandwidth Δλ/λ=1/Nu. Nu is usually in the range 35–100. We present a system design based on 25 nm lithographic resolution using λ=4.5 nm. For N=100 the zone‐plate diameter is 10 μm. Each zone plate of the array would be responsible only for exposure wit...

Static and dynamic Fresnel zone lenses for optical interconnections

Abstract: Static and dynamic Fresnel zone lenses were fabricated in quartz glass by means of microstructuring techniques. Two types of on-axis and offaxis lenses with different focal lengths and of different apertures were designed to operate at wavelengths of 1·52 μm and 633 nm. The blazed profile of the onaxis and off-axis lenses was approximated by up to 16 and up to four discrete levels respectively. Dynamic, that is electrically switchable, lenses have been realized by filling the structured surface with liquid crystal. The optical properties of the lenses, such as the focal spot sizes and the diffraction efficiencies, were investigated. Further the switching behaviour of the dynamic lenses was studied. The design and fabrication of the static and dynamic, on-and off-axis Fresnel zone lenses as well as their optical and switching properties will be presented.

Focal switch: a new effect in low-Fresnel-number systems.

Abstract: It is shown for the first time we believe, that when a spherical wave illuminates a certain type of diffracting screen, in addition to the expected focal-shift effect, depending on the value of the Fresnel number of the focusing system, a focal switch effect can appear, i.e., an increase in the height of the lateral lobe of the axial-intensity distribution over that of the central lobe.

Discrete wavelength spectrometer

Abstract: A diffraction grating, diffraction structure or Fresnel zone device is formed on a first substrate for diffracting light components of different wavelengths An array of detectors is formed on a second substrate for detecting different wavelength components diffracted where the second substrate is spaced apart from the grating, structure or device to form a spectrometer Spectrometers sensitive to the particular spectral lines may be used for detecting the presence of substances The spectral resolution at such spectral lines may be increased relative to other regions to enhance the sensitivity of detection This is done by inverse Fourier transform of the desired discrete spectrum to obtain a desired transmission function and by half-toning the aperture function

On the effect of diffraction on traveltime measurements

Abstract: SUMMARY All observed waves are of finite frequency and are sensitive to a finite volume of the medium through which they pass. Diffraction causes a loss of information about time contained in the initial front of a wavefield (often referred to as wavefront healing). This effect depends upon frequency and propagation distance and imposes a low-pass filter on the spatial resolution of time measurements. A sequence of canonical, numerical experiments that simulate the diffraction of a perturbed plane wave at a fixed distance is described. Traveltimes are measured using a variety of techniques on a range of waveforms. It is empirically verified that a single Fresnel zone describes the spatial filtering effect of the propagation of a broad-band wavefield, even in the regime where the initial time perturbation cannot be represented by a linear perturbation term. For narrow-band wavefields, more Fresnel zones come into play as the bandwidth is reduced. Measurements of time include a component of signal-generated noise coherent over a small scale which scales with the Fresnel zone. It is found that, for traveltimes measured by automated picking, the width of the Fresnel zone is described by a time delay of (&I< T/4 (here T is one period). On the other hand, the width of the Fresnel zone for traveltimes measured by correlation is wider, characterized by a time delay of ldtl < T/4.

Fresnel zones for broadband data

Abstract: For monochromatic waves, the term “Fresnel zone” is well‐defined even though different authors use different terminology. Most authors use the definition originating from optics. There, the first Fresnel zone is defined as the area of a circular hole in a screen between a light source and an observation point that produces maximum light intensity in the observation point (Figure 1). If the radius of the hole is enlarged, minima and maxima in light intensity alternate. The first maximum is reached if the raypath difference between the direct ray and the ray traveling via the edge of the hole equals half a wavelength. The extension of the definition to energy reflected from a circular disk is straightforward (if we restrict ourselves to ray theory and neglect the angle dependency of the reflection coefficient) and is illustrated in Figure 2 (see also Sheriff, 1991).

Validity of the Fresnel approximation in the diffraction of collimated beams

Abstract: Most studies of the validity of the Fresnel approximation have relied principally on numerical results, because cancellation due to the oscillatory integrands suggests that the resulting field errors are difficult to analyze. A simple analysis is shown here, however, to give an excellent prediction of the associated errors in modeling the diffraction of a collimated beam. Further, the error estimates are presented as a universal contour map where only the contour labels depend on the aperture-size-to-wavelength ratio. The inaccuracy of the Kirchhoff boundary conditions effectively sets error bounds that are essential in deriving this universal map.

Uniformization of the axial intensity of diffraction axicons by polychromatic illumination.

Abstract: The axial intensity of axicons illuminated by a coherent wave usually exhibits rapid oscillations from diffraction on the sharp edges of the aperture of the element. These oscillations can be suppressed when the diffractive version of the axicon is illuminated from a polychromatic source. This possibility is examined based on the example of the annular-aperture logarithmic axicon. The estimate for the wavelength interval of the illuminating source required for uniformization is obtained with the help of the stationary-phase method. Furthermore the shape of the radial intensity distribution can be maintained almost unchanged. These findings are confirmed by numerical evaluation of the Fresnel diffraction integral.

Diffraction phenomena inside thick Fresnel zone plates

Abstract: The parabolic wave equation method is used to describe the complex wave field inside the body of a thick zone plate used to focus X ray radiation Two analytical approaches are applied: (1) Diffraction of a plane wave incident onto a separate interface between opaque and open zones is considered We construct an approximate analytical solution to the classical problem of diffraction by a dielectric wedge in terms of the Fresnel integral and a new special function (2) Coupled wave theory is used to describe collective effects of diffraction by many interfaces The zone plate is considered as thick diffraction grating with slowly varying period An analytical solution is found for three interacting modes A possibility to optimize the zone plate performance is shown Taken together, these results describe all the main features observed in the output field of realistic X ray zone plates

Diffractive beamshaping elements at the fabrication limit

Abstract: We treat the generation of flat-top intensity distributions, as required for laser applications at short wavelengths. To obtain high fill factors and almost arbitrary shapes, arrays of diffractive Fresnel zone plates at the fabrication limit are investigated. The angular power spectrum noise due to the binarization of the transmission phase function is smoothed using an incoherent source. The remaining zeroth order is ommited by the addition of a constant offset phase to the transmission phase function of the array. An analysis of etch-depth errors as well as an investigation of multilevel elements is appended. Simulation results, obtained by a 2-D analysis for radial symmetry, are compared to measurements. © 1996 Society of Photo-Optical Instrumentation Engineers.

Millimeter-wave specular and diffuse multipath components of terrain

Abstract: Multipath interference data were obtained at a frequency of 95 GHz over pathlengths of 100-250 m by measuring height-gain interference patterns over various types of terrain. Data were collected over grass, lake, ice, snow, concrete, asphalt, and gravel surfaces. The transmit antenna was kept fixed, while the receive antenna translated vertically resulting in grazing angles between approximately 0.5-2.0°. Full illumination of the Fresnel zones was accomplished by broad-beamwidth horn antennas at both ends. Measured interference patterns indicate the presence of both specular and diffuse multipath components. A technique was developed to separate these components by filtering in the spatial Fourier-transform domain by appropriate choice of the notch frequency for the specular component and the bandpass-filter bandwidth for the diffuse components. The notch frequency is chosen according to system geometry considerations. Using this unique separation technique, specular and diffuse reflection coefficients were deduced for various terrain types. The separation technique developed in this paper can be readily applied to existing height-gain data if the system geometry is known.

Analytical expressions for Fresnel volumes and interface fresnel zones of seismic body waves. Part 2: Transmitted and converted waves. Head waves

Abstract: Fresnel volumes and interface Fresnel zones of transmitted and head waves are studied. The relation derived for transmitted waves may also be used for converted reflected waves. Considerable attention is devoted to the penetration of Fresnel volumes across structural interfaces, particularly for head waves.

Analytical expression for fresnel volumes and interface fresnel zones of seismic body waves. Part 1: Direct and unconverted reflected waves

Abstract: Fresnel volumes, plane-sectional Fresnel zones and interface Fresnel zones of direct and unconverted reflected waves are studied. Exact analytical expressions for various parameters of Fresnel volumes and Fresnel zones are derived and discussed. Among others, these expressions are related to semi-axes of Fresnel zones, to overshooting and penetration distances, and to the off-ray shifts of Fresnel zones.

Steeply reflected ScSH precursors from the D″ region

Abstract: We present evidence for precursors to the ScS and SScS (SDS and sSDS) phases observed at epicentral distances smaller than 30°. These precursors are intermittently observed in broadband recordings from the six Incorporated Research Institutions for Seismology stations used (western Pacific region and South America). They appear approximately 35–50 s ahead of the ScS arrival on the transverse component and are independent of hypocentral depth. The observed precursors are characterized by relatively large amplitudes in the frequency band from 0.05 to 0.2 Hz. A more detailed analysis is restricted to a subsidiary data set from station SNZO (New Zealand). The coherency, frequency dependence, slowness, polarity, and polarization of the precursors are discussed. Many explanations for SDS can be rejected, and we conclude that a reflector 180 km above the core-mantle boundary causes these occasionally strong precursors. The large SDS/ScS amplitudes at low frequencies require an unrealistically large impedance contrast for a one-dimensional model. We test the possibility of focusing the SDS phase by a discontinuity with topography and show that structure with scale lengths of ∼l9°–25° (1200–1600 km, i.e., larger than the Fresnel zone) can account for large intermittently observed SDS amplitudes with their geometrical reflection points within the same Fresnel zone. This is surprising, since it is often assumed that scale lengths smaller than the Fresnel zone must be responsible for variations within a Fresnel zone. The limited data set permits no conclusions about the global properties of this phase or its implied reflector.

Coherence properties of a reflected optical wave in atmospheric turbulence

Abstract: The transverse spatial coherence radius is studied for both the monostatic and bistatic laser radar problems involving an optical wave propagating through atmospheric turbulence in the weak-fluctuation regime over a path of length L and then reflected in the reverse direction from a finite mirror with finite focal length FR. Formal expressions are developed for the wave structure function and the modulus of the complex degree of coherence in the general Gaussian-beam wave case, and tractable analytic results are derived for the special case of a diverging (or spherical) wave at the transmitter and observation points in the beam symmetrically located with respect to the beam centerline. By varying the focal length of the mirror, one minimizes the spatial coherence radius of a reflected spherical wave when the receiver is located near the plane defined by the radius of curvature of the mirror (i.e., L/FR ~ 2) and maximizes it when L/FR is approximately 6–7. Effects of inner scale, outer scale, and the high wave-number deviation from pure power-law behavior are taken into account in the assumed spectral models for refractive-index fluctuations. Analogous to line-of-sight propagation, the spatial coherence radius based on a modified spectrum is generally less than that based on the von Karman spectrum, particularly when the coherence radius is of the order of the inner scale of turbulence.

The relationship between the first Fresnel zone and the normalized geometrical spreading factor1

Abstract: Conventionally, the Fresnel zone and the geometrical spreading factor are investigated separately, because they belong to different theories of wave propagation. However, if the paraxial ray method is used for establishing the Fresnel–Kirchhoff diffraction formula for a laterally inhomogeneous multilayered medium, it can be shown that the normalized geometrical spreading factor is inversely proportional to the area of the first Fresnel zone associated with the reflection point. Therefore, if no diffracting edge cuts the first Fresnel zone, the geometrical optics approximation represents the principal part of the wavefield obtained by Fresnel–Kirchhoff diffraction theory. Otherwise, the geometrical optics approximation has to be corrected by adding edge diffractions. It is also shown that Kirchhoff-type migration and geometrical spreading factor correction both reduce the first Fresnel zone to a zone with unit area.

Zone plates for x-ray optics at grazing incidence angles

Abstract: The results of calculations on the optical properties of zone plates at grazing incidence angles are presented. In terms of the diffraction theory, the diffraction integrals for the Fresnel zone geometries are shown to be similar at normal and grazing incidence angles in the Fresnel approximation. One-dimensional and two-dimensional cases are discussed.

Characterization of thermal distortion effects on beamline optics for EUV interferometry and soft x‐ray microscopy

Abstract: This study analyzes synchrotron radiation heat loading effects on optical components of beamline BL12.0 for EUV interferometry and soft x‐ray microscopy at the Advanced Light Source (ALS). Newly developed indirect side‐cooled beamline optics were considered, and the resulting surface distortion of mirrors and grating indicates that there is no significant degradation of beamline performance in spectral resolution or throughput. Also analyzed are the effects of heat loading on end‐station components, such as Fresnel zone plates, transmission gratings, masks and membranes. Experimental results of heat loaded membranes are presented as well in this writing.

Method for removing non-geologic amplitude variations from seismic data

Abstract: A method for removing non-geologic amplitude variations from seismic data. The method is based on the premise that lateral amplitude variations with spatial wavelengths shorter than the width of the Fresnel zone, a known wave propagation effect, for the target cannot be caused by changes in the reflectivity of the target and must, therefore, be due to non-geologic causes. The method permits these non-geologic amplitude effects to be identified and removed from the seismic data. The method may be implemented either manually or automatically by a computer.

Electromagnetic study of a photolithography setup for periodic masks and application to nonperiodic masks

Abstract: We develop a rigorous electromagnetic analysis to study the field diffracted by a metallic or dielectric grating made of rectangular rods, lying over a stratified media. The analysis generalizes the modal theory of perfectly conducting lamellar gratings combined with the R-matrix propagation algorithm in order to avoid numerical instabilities, thus allowing treatment of layers and gratings of arbitrary thickness. We then study the field map obtained under the conditions stated in a previous patent that described a process for casting on a support the faithful reproduction of a mask pierced with periodically distributed slits. We make a systematic study of the influence of the various parameters (incidence, mark–space ratio, groove spacing, groove depth, polarization, conductivity of the metal) on the field map below the mask. We discover a large tolerance over the parameters, close to the values stated in the patent. The result is that the setup described in the patent valid for periodic maps can be used for duplicating nonperiodic masks (e.g., linear Fresnel zone plates) as well as chirped gratings or gratings with nonrectilinear grooves.

Radar Tomography For Cavities Detection

Abstract: Preliminary tests on laboratory models have enabled us to provide some guidelines for traveltime ray tomography with GPR applied to civil engineering problems, specifically to find voids in pillars, walls and structures. The width of the Fresnel zone and the source and receiver locations are the limits to resolution capability. For crosshole geometry a criterion to know resolution capability, based on detectable wavenumbers, is analytically derived. Acquisition and reconstruction parameters (source and receiver location, operating frequency, measurement number, acquisition time, slowness grid) are discussed and optimized with tomographic experiments on some models drilled expressly to produce voids. Tomography is solved by SVD, experimenting both regular and irregular gridding. An iterative procedure for noise reduction is proposed to improve the solution. A sort of black and white tomography is also applied to explore the actual limits of straight ray approximation. For crosshole geometry a wavenumber decomposition of the problem is proposed and the benefits discussed.

Effects of the microstructuring process on diffraction properties of bragg-fresnel lenses.

Abstract: The effects appearing in a crystal microstructuring by reactive ion etching on diffraction properties of Bragg–Fresnel lenses were studied. Possible deviations of the real zone structures from ideal ones were considered. The influence of the Fresnel zone displacements due to sidewall undercutting effects and due to a mask erosion was analyzed. Technological tolerances for a different zone profile shape were defined.

Regular ArticleEffects of the Microstructuring Process on Diffraction Properties of Bragg–Fresnel Lenses

Abstract: The effects appearing in a crystal microstructuring by reactive ion etching on diffraction properties of Bragg–Fresnel lenses were studied. Possible deviations of the real zone structures from ideal ones were considered. The influence of the Fresnel zone displacements due to sidewall undercutting effects and due to a mask erosion was analyzed. Technological tolerances for a different zone profile shape were defined.

Processing of high-resolution, deep-tow marine seismic data

Abstract: Conventional near‐surface seismic systems provide limited resolution of ocean bottom sedimentary horizons. This problem is related to the size of the Fresnel zone and is particularly important in deep water or topographically rugged regions. The French Institute for Marine Research and Exploitation (IFREMER) has recently investigated methods to overcome this limitation.

Switchable Fresnel zone lenses for optical interconnections

Abstract: Various on-axis and off-axis Fresnel zone lenses with different focal lengths and of different apertures were fabricated in quartz glass by means of microstructuring techniques. The kinoform profile of the diffractive optical elements was approximated by a staircase-like profile having a number of discrete phase levels. Dynamic, that is electrically switchable, lenses have been realized by filling the structured surface with liquid crystal. By applying an AC-voltage the elements can be switched from the state of a `focusing lens' to that of a `transparent glass- plate'. The optical properties of the lenses as well as the switching behavior were studied. Experimental measurements will be compared with theoretical results.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Application of the edge wave superposition method

Abstract: Numerical examples of high-frequency synthetic seismograms of body waves in a 2-D layered medium with complex interfaces (faults, wedges, curvilinear, corrugated) are presented. The wave field modeling algorithm combines the possibilities of the ray method and the edge wave superposition method. This approach preserves all advantages of the ray method and eliminates restrictions related to diffraction by boundary edges and to caustic effects in singular regions. The method does not require two-point ray tracing (source-to-receiver), and the position of the source, as well as the type of source, and the position of receivers can be chosen arbitrarily. The memory and the time required for synthetic seismogram computation are similar to ray synthetic seismograms. The computation of the volume of the medium (the Fresnel volume or Fresnel zones), which gives the essential contribution to the wave field, is included in the modeling program package. In the case of complicated irregular interface (or a layered medium with a regular ray field at the last interface), the method displays a high accuracy of wave field computation. Otherwise, the method can be considered a modification of the ray method with regularization by the superposition of edge waves.