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Showing papers on "Fresnel zone published in 1997"


Journal ArticleDOI
01 Feb 1997
TL;DR: In this article, the authors show that the size of the aperture has an important influence on the results of (Kirchhoff-type) migration and demigration, and that it is crucial not to have apertures below a certain size.
Abstract: The size of the aperture has an important influence on the results of (Kirchhoff-type) migration and demigration. For true-amplitude imaging, it is crucial not to have apertures below a certain size. For both the minimum migration and demigration apertures, theoretical expressions are established. Both minimum apertures depend on each other and, although a time-domain concept, are closely related to the frequency-dependent Fresnel zone on the searched-for subsurface reflector. This relationship sheds new light on the role of Fresnel zones in the seismic imaging of subsurface reflectors by showing that Fresnel zones are not only important in resolution studies but also for the correct determination of migration amplitudes. It further helps to better understand the intrinsic interconnection between prestack migration and demigration as inverse procedures of the same type. In contrast to the common opinion that it is always the greatest possible aperture that yields the best signal-to-noise enhancement, it is in fact the selection of a minimum aperture that should be desired in order to (a) enhance the computational efficiency and reduce the cost of the summation, (b) improve the image quality by minimizing the noise on account of summing the smallest number of traces, and (c) to have a better control over boundary effects. This paper demonstrates these features rather than addressing the question of how to achieve them technically.

119 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that large-scale downwarping of the 670-km discontinuity near subduction zones derived from underside reflection data can be explained as the long-wavelength manifestation of a single, small-scale (wavelengths of several hundreds of kilometres) deflection of the discontinuity inside and near subducting slabs.
Abstract: SUMMARY Currnet models of upper-mantle discontinuity topography derived from traveltime variations of long-period underside reflections (PdP or SdS waves) may contain gross errors due to the use of geometrical optics in relating observed traveltimes to depth variations of the discontinuity near the reflection point. The use of geometrical optics is not valid if variations in the depth of the discontinuities exist on a lateral scale smaller than the size of the Fresnel zone in the data. Geometrical optics does not take into account the large size and the complex structure of the traveltime surface of underside reflections and may introduce spurious structure when used in inversions. Examples of synthetic long-period PdP waveforms for reflections near subducting lithosphere show that scattering from expected small-scale depth variations of the discontinuities inside slabs causes complex waveform variations. For a 15–20s PdP wave these small-scale depth variations (with a scale-length of 4) are smaller than the Fresnel zone (roughly 20°) but larger than the PdP wavelength at 420 km depth (about 150–200 km). The synthetic waveforms are processed to obtain PdP traveltimes, which are in turn converted to apparent discontinuity depth at the reflection point using geometrical optics. The apparent discontinuity-depth variations are not only of the same order of magnitude as those obtained from real data but also exhibit artefacts that closely resemble features observed in current models. It is shown that large-scale (wavelengths of the order of 1000 km) downwarping of the 670-km discontinuity near subduction zones derived from underside reflection data can be explained as the long-wavelength manifestation of a single, small-scale (wavelengths of several hundreds of kilometres) deflection of the discontinuity inside and near subducting slabs.

81 citations


Patent
30 May 1997
TL;DR: In this article, an array of Fresnel zone plates is illuminated by parallel beamlets of narrow-band electromagnetic radiation, focusing a significant fraction of the incident radiation to foci on a substrate located at least several micrometers distant.
Abstract: An array of Fresnel zone plates is illuminated by parallel beamlets of narrow-band electromagnetic radiation. The individual zone plates focus a significant fraction of the incident radiation to foci on a substrate located at least several micrometers distant. The beamlets are capable of being individually turned on or off by shutters, or by deflecting small mirrors that would otherwise direct a beamlet to its Fresnel zone plate. Pattern generation is accomplished by moving the substrate while multiplexing the individual beamlets on or off.

72 citations


Journal ArticleDOI
TL;DR: In this article, a new method is described that makes it feasible to include scattered and converted surface waves into waveform inversions for the three-dimensional (3-D) structure of the Earth.
Abstract: A new method is described that makes it feasible to include scattered and converted surface waves into waveform inversions for the three-dimensional (3-D) structure of the Earth. The single scattering (Born) approximation forms the basis of the method. In order to minimize the amplitude of the scattered wave field, the background model is first adapted to correct for nonconverted, forward-scattered wave energy. We then perform Born inversion of the difference between the measured and synthetic waveforms, including a suite of Love and Rayleigh modes. The Born approximation yields linear equations of the form Aδγ = δu Bor n, which allow the determination of the three-dimensional perturbations γ to the background model from the scattered wave field δu Born . This procedure is followed separately for each source-receiver pair to allow for optimized background models for each signal, as well as to minimize the computational burden. We winnow the data vector for each path by performing singular value decomposition using a diagonalization of AA T . In a realistic example we found that each vertical component seismogram yields 30-40 linear constraints on the 3-D Earth, significantly more than with conventional pure-path (WKBJ) inversions. In a synthetic test, one seismogram is shown to be able to image a simple model of a point scatterer off the great circle. As a spin-off of the formulation of the multimode inverse scattering problem, we not only obtain a series of eigenvectors that rank the sensitivity of a seismogram to Earth structure in a series of geometrical patterns, we also can compute the surface wave equivalent of a Fresnel zone.

61 citations


Journal ArticleDOI
Yajun Li1
TL;DR: In this article, the point of absolute maximum intensity switches from the former to the latter when the Fresnel number of the system decreases to a sufficiently low level, and both a mathematical formulation and a physical interpretation of this effect are presented.
Abstract: The system under consideration consists of a piece of thin diffractive element (the Fresnel zone plate) and a uniform, converging spherical wave that is incident on the diffractive element. The center of curvature of the incident spherical wave and the primary focus of the zone plate are the two foci of the system. The point of absolute maximum intensity switches from the former to the latter when the Fresnel number of the system decreases to a sufficiently low level. Both a mathematical formulation and a physical interpretation of this effect are presented.

44 citations


Journal ArticleDOI
TL;DR: In this paper, a local linear grating model was proposed to estimate the diffraction efficiency of high-numerical-aperture two-dimensional circular lenses with one-dimensional rigorous coupled-wave analysis.
Abstract: We describe a local linear grating model that permits estimation of the diffraction efficiency of high-numerical-aperture two-dimensional circular lenses with one-dimensional rigorous coupled-wave analysis. The model is self-consistent and is consistent with the scalar theory that results for low-numerical-aperture lenses. The accuracy of the model increases with the number of Fresnel zones of the lens. On the basis of this model we optimize the discrete phase profile of the lens for the maximum diffraction efficiency, using the random search method. The TE and the TM modes are optimized simultaneously. Their phase variations as functions of local grating periods are removed by cyclic shifts of the grating profiles, resulting in constructive summation at the focus and high diffraction efficiency.

43 citations


Journal ArticleDOI
TL;DR: In this article, high-resolution and large diameter condenser Fresnel zone plates were fabricated in a 0.35-μm-thick Ta layer on an SiN membrane, where sub-field length and position are randamized in order to supress the evolution of small figures at pattern divided parts such as subfield boundaries.

43 citations


Journal ArticleDOI
TL;DR: In this paper, the phase shift profile of a transparent object in a coherent wave is reconstructed from a set of two recorded intensity distributions, where the first Fresnel zone is much less than the characteristic size of the object's details.
Abstract: A novel algorithm for a reconstruction of the phase shift profile produced by a transparent object in a coherent wave, from a set of two recorded intensity distributions is presented. Contrary to well known algorithms of in-line holography, the method works under the near-field condition where the size of the first Fresnel zone is much less than the characteristic size of the object's details. Such a condition is typical for an in-line holography experimental setup with the use of coherent high energy x-rays (E > 20 keV) produced by synchrotron radiation sources of the third generation like ESRF. The novel algorithm is fast and insensitive to a partial loss of coherence or weak detector resolution. The method can be applied to x-ray refraction tomography.

20 citations


Journal ArticleDOI
TL;DR: In this paper, a backscatter radar echo from meteoric ionization is produced from the contributions from successive Fresnel zones as the meteor passes the specular condition, and the time variation of the reflection coefficient given in terms of the Fresnel Function is related to the creation rate of zones and hence to meteoroid atmospheric speed.

17 citations


Patent
TL;DR: In this article, an acoustic transducer is coupled with a phase fresnel zone in a section of the acoustic carrier to constructively interfere at the location in the prostate by moving the carrier along at least a portion of the urethra surrounded by the prostate.
Abstract: A system for treating a prostate includes an acoustic carrier, a phase fresnel zone in a section of the acoustic carrier, and an acoustic transducer. The phase fresnel zone is formed in the acoustic carrier adjacent a first end of the acoustic carrier and extends at least partially around the outer surface of the acoustic carrier. An acoustic transducer is coupled to a second end of the acoustic carrier. In treating the prostate, which surrounds a urethra, the acoustic carrier is inserted into the urethra and positioned so that the phase fresnel zone is situated in a region of the urethra surrounded by the prostate. Acoustic waves are transmitted into the second end of the acoustic carrier and the phase fresnel zone focuses the acoustic waves to constructively interfere at the location in the prostate. By moving the acoustic carrier, the phase fresnel zone may be moved along at least a portion of the region of the urethra surrounded by the prostate while the acoustic waves are being transmitted.

16 citations


Journal ArticleDOI
TL;DR: In this paper, the authors describe an FZP with a focal length of f = 3 m for 8 keV and a number of zones of varying sizes and diameters.
Abstract: The advent of high-brightness x-ray sources in the 10–40 keV region opens new possibilities of experiments with microbeams. Techniques to form these focused beams may be based on glancing mirrors, phase elements, or diffractive optics, in particular Fresnel zone plates (FZPs). Because of the long focal length and large acceptance, FZPs designed to work in the hard x-ray region tend to have quite large diameters and large numbers of zones. For instance, the zone plate described in this article has a 1860 μm diam, a focal length of f=3 m (for 8 keV), and 1860 zones. On a standard pattern generator, circular shapes are always approximated as simpler structures. The tolerance requirement for shape and positions of zones depends on the number of zones, and it is necessary to guarantee that the circular structures are approximated to the required degree of accuracy while keeping the size of the data structure to a reasonable size for processing by the exposure system. For instance, if polygons are used to appro...

Journal ArticleDOI
TL;DR: In this paper, the authors proposed the use of Fresnel zones for modes to simplify the analysis of mode scattering at large-scale inhomogeneities in multimode waveguides.
Abstract: The notion of Fresnel zones for modes is introduced which is analogous to the usual Fresnel zones introduced for rays. It is shown that by using Fresnel zones for modes one can simplify the analysis of mode scattering at large-scale inhomogeneities in multimode waveguides. The mode amplitude variations due to scattering by an opaque screen and by refractive index inhomogeneities are considered. In the latter case the formulas obtained in the scope of this approach are statistical averaging suited and similar to those of geometrical optics and the Rytov method widely used to calculate fluctuations of ray complex amplitudes. The results of a tank experiment carried out to test the predictions concerning the mode scattering by an opaque screen are presented.

Journal ArticleDOI
TL;DR: In this article, the scaling factor between the input pattern and the filter can be adjusted at will with the help of converging beam illumination and using an adjusting device consisting of a combination of Fresnel zone plates.

Journal ArticleDOI
TL;DR: In this paper, a qualitative picture based on Fourier optics is given to explain these markedly relaxed tolerances with respect to depth errors for planar optical elements and even for low Fresnel numbers.
Abstract: Numerical simulations have been performed to study the influence of resist-developing errors on continuous-relief microlenses. For very low Fresnel numbers (N 2), the focal length is essentially determined by the diffraction at the lateral pattern of the segments, and deviations from the ideal blaze influence only the efficiency. A qualitative picture based on Fourier optics is given to explain these markedly relaxed tolerances with respect to depth errors for planar optical elements and even for low Fresnel numbers.

Proceedings ArticleDOI
20 Jun 1997
TL;DR: In this paper, a method of phase-correcting Fresnel zone plate lens antennas for operation at two or more frequency bands is described, and a new analysis is derived for apportioning the amount of phase correction to give the desired performance at the chosen frequencies.
Abstract: A description is given of a method of designing phase- correcting Fresnel zone plate lens antennas for operation at two or more frequency bands. A new analysis is derived for apportioning the amount of phase correction to give the desired performance at the chosen frequencies. The result permits the development of narrow-beam, high-gain behavior at two or more bands, with reduced gain at other frequencies.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Journal ArticleDOI
TL;DR: In this article, the angular spectrum solution for diffraction is used to establish the validity of a standard, formal series for non-paraxial wave propagation, and a simple, generic algebraic corrections to the field estimates found by using the paraxial model is derived.
Abstract: Asymptotic analysis of the angular spectrum solution for diffraction is used to establish the validity of a standard, formal series for nonparaxial wave propagation. The lowest term corresponds to the field in the Fresnel approximation, and this derivation clarifies some of the remarkable aspects of Fresnel validity for both small and large propagation distances. This asymptotic approach is extended to derive simple, generic algebraic corrections to the field estimates found by using the paraxial model, i.e., the Fresnel approximation. Contour maps of the field errors associated with the diffraction of collimated beams—both uniform and Gaussian—in two and three dimensions demonstrate the effectiveness of these corrections.

Journal ArticleDOI
TL;DR: In this paper, the irradiance covariance and variance functions associated with a reflected Gaussian-beam wave from a glint target (retroreflector) are calculated and compared with similar results based on a specular target (smooth finite mirror).
Abstract: The irradiance (intensity) covariance and variance functions associated with a reflected Gaussian-beam wave from a glint target (retroreflector) are calculated and compared with similar results based on a specular target (smooth finite mirror). Detailed results are presented for the normalized irradiance variance, or scintillation index, of the reflected wave for both types of reflector in an improved model of atmospheric turbulence that incorporates a high-wave-number rise just before the dissipation range in addition to inner–outer-scale parameters. Numerical comparisons show that values of the normalized irradiance variance based on the improved model of refractive-index fluctuations (henceforth called the modified spectrum) can be up to 32% greater than those predicted by the Kolmogorov power-law spectrum when the inner scale is comparable in size with the first Fresnel zone. All analytic expressions derived here are based on weak-fluctuation theory using generalized spectral representations of the complex phase perturbations.

Journal ArticleDOI
TL;DR: In this article, the authors present two important issues often demanded when patterning DOEs using EBL: the first one is the attainment of accurate resist three-dimensional shaping to increase DOE efficiency, this task is accomplished by developing a new proximity correction algorithm able to shape the resist in one shot of exposure.


Journal ArticleDOI
TL;DR: In this article, the authors deal with the synthesis of diffractive optical elements for the generation of confined beams in free-space propagation, and the main objective concerns the optimization of the trade-off among beam confinement, diffraction efficiency, and technical feasibility.
Abstract: We deal with the synthesis of diffractive optical elements for the generation of confined beams in free-space propagation. Our main objective concerns the optimization of the trade-off among beam confinement, diffraction efficiency, and technical feasibility. Solutions are derived from a purely theoretical analysis, and they are then tested experimentally.

Journal ArticleDOI
TL;DR: In this article, a linear zone plate surface structure was created on the surface of mica crystal and used for obtaining spectrally resolved images of 120 fs laser-produced plasma.
Abstract: A linear zone plate surface structure was created on the surface of mica crystal and used for obtaining spectrally resolved images of 120 fs laser-produced plasma. A linear Fresnel zone structure was optimized on a wavelength λ = 9.16 A and has a focal length of f = 5 cm, minimum zone width Δzn = 300 nm, total length l = 10 cm, total width of zone plate 2rn = 122.6 μm. Images of laser-produced plasma in the spectral range 9.12−9.31 A were obtained. For high Z (Lanthanum) element target the size of the x-ray radiation spot was not more than 20 μm.

Journal Article
01 Jan 1997-Optik
TL;DR: In this paper, the Fourier transform of Schell-model beam is also a Schell model beam, which is proportional to a triple correlation, and each Schellmodel beam can be considered as the bispectrum of the another.

Proceedings ArticleDOI
02 Dec 1997
TL;DR: In this paper, a new kind of Fresnel zone plate antenna with a continuous phase structure is designed, and the authors call it a diffraction antenna, which can increase the diffraction efficiency.
Abstract: The phase Fresnel zone plate, whose diffraction efficiency is up 97%, has been made. Because of the advantages of thinner thickness, lighter weight and design flexibility, the phase Fresnel zone plate has been considered for use as a MM-wave antenna so as to increase the diffraction efficiency. However, zone plates with only four phase steps are generally made up to now, so the diffraction efficiency is only about 80%, and the highest gain is no more than 35 dB. To overcome this weakness, a new kind of Fresnel zone plate antenna with a continuous phase structure is designed, and the authors call it a diffraction antenna.

Patent
19 Mar 1997
TL;DR: In this paper, the authors propose to obtain a spatial intensity distribution of laser light which has been converged weakly at its center part and intensely at its peripheral part by arranging a specific composite Fresnel zone plate right before or behind a condenser lens.
Abstract: PROBLEM TO BE SOLVED: To obtain a spatial intensity distribution of laser light which has been converged weakly at its center part and intensely at its peripheral part by arranging a specific composite Fresnel zone plate right before or behind a condenser lens. SOLUTION: The composite Fresnel zone plate 1 has a unit cell obtained by providing a Fresnel zone plate, which is optically different in pitch, concentrically in a Fresnel zone plate together. Then this unit cell and a complementary unit cell which is opposite in phase difference of 0 and π radian from the unit cell are arranged in quantities at random on the same plate so that they are in half-and-half proportion. The obtained composite Fresnel zone plate 1 is arranged right before or behind the condenser lens. For example, the laser light L outputted from a large-output laser after passing through the composite Fresnel zone plate 1 is converged by the condenser lens 2. An object 3 is placed almost at a distance of the focal length (f) of the condenser lens 2.

Journal Article
01 Jan 1997-Optik
TL;DR: Fresnel diffraction patterns by a circular plane wave with phase singularities of charge one and charge two are calculated in this article, where a dark circular spot is found at the centre in the transverse plane and its size increases approximately linearly with the propagation distance when the Fresnel number is small.

Journal ArticleDOI
TL;DR: In this paper, a lensless joint transform correlator is used to determine the relative x -y position of two pinholes placed in parallel arms of a Mach-Zehnder interferometer.
Abstract: The lensless joint transform correlator optically determines the relative x -y position of two pinholes. The pinholes are placed in parallel arms of a Mach-Zehnder interferometer. The Fraunhaufer diffraction patterns combine to form a joint transform plane. Because of the interference of the two signals, a Fresnel zone is formed in the joint Fraunhaufer diffraction pattern. This is captured and used in a second stage, just as the joint power spectrum is in a joint transform correlator. The joint transform is illuminated with a plane wave, and the output taken in the focal plane of the Fresnel zone. As with the single-lens joint transform correlator, the lensless joint transform correlator exhibits magnification between the input displacement and the output peak displacement. By using the third or fifth order focus of the Fresnel zone, the output resolution can be improved by a factor of three or five in both the x and y dimensions. The output has very good peak-to-noise ratio and position resolution. A peak-to-noise ratio of 106 dB with a resolution of 1.4 µm are observed when using the fifth order focus of the Fresnel zone.

01 Jan 1997
TL;DR: In this paper, a software tool for the analysis and evaluation of a single microwave relay link has been developed, and a cost optimization method for a microwave radio network involving more than two antennas is developed.
Abstract: This paper deals with wave propagation calculation and cost optimization software development for microwave radio. The software presents a design tool for line of sight link planning. The main cost factor in a microwave network depends on tower structure and antenna heights. Antenna heights are normally chosen to overcome the first Fresnel zone obstruction. A software tool for the analysis and evaluation of a single microwave relay link has been developed. In addition, cost optimization method for a microwave radio network involving more than two antennas has been developed. This paper includes calculations and analysis of the geographical data in the chosen area in order to determine the effective earth's radius to achieve better optimization. In addition, terrain profile generation and microwave point-to-point link calculation was considered

Patent
28 Aug 1997
TL;DR: In this article, a lensless joint transform correlator optically determines the relative position of two pinholes placed in parallel arms of a Mach-Zehnder interferometer.
Abstract: A lensless joint transform correlator optically determines the relative position of two pinholes placed in parallel arms of a Mach-Zehnder interferometer. The Fraunhaufer diffraction patterns combine to form a joint power spectrum signal in the joint transform plane. Because of the interference of the two pinhole signals, an encoded lens comprising a Fresnel zone is formed in the joint Fraunhaufer diffraction pattern which is illuminated with a plane wave, and the output signal is taken in the focal plane of the Fresnel zone and magnifies the input pinhole displacement by a factor of ten, enhancing its use in precision positioning servo systems for mask alignment.

01 Jul 1997
TL;DR: In this article, the Fresnel coefficients have been applied to the reflection of unpolarized monochromatic radiation by a sea water capillary wave facet, and the result for a single tilted facet has been integrated over all possible tilts and wave numbers to predict the horizontal, vertical, and unpolarised infrared radiance arising from the windruffled ocean surface.
Abstract: : The Fresnel coefficients have been applied to the reflection of unpolarized monochromatic radiation by a sea water capillary wave facet. The result for a single tilted facet has been integrated over all possible tilts and wave numbers to predict the horizontal, vertical, and unpolarized infrared radiance arising from the wind-ruffled ocean surface.