Showing papers on "Fresnel zone published in 2004"

The Fresnel volume and transmitted waves

Abstract: In seismic imaging experiments, it is common to use a geometric ray theory that is an asymptotic solution of the wave equation in the high-frequency limit. Consequently, it is assumed that waves propagate along infinitely narrow lines through space, called rays, that join the source and receiver. In reality, recorded waves have a finite-frequency content. The band limitation of waves implies that the propagation of waves is extended to a finite volume of space around the geometrical ray path. This volume is called the Fresnel volume. In this tutorial, we introduce the physics of the Fresnel volume and we present a solution of the wave equation that accounts for the band limitation of waves. The finite-frequency wave theory specifies sensitivity kernels that linearly relate the traveltime and amplitude of band-limited transmitted and reflected waves to slowness variations in the earth. The Fresnel zone and the finite-frequency sensitivity kernels are closely connected through the concept of constructive interference of waves. The finite-frequency wave theory leads to the counterintuitive result that a pointlike velocity perturbation placed on the geometric ray in three dimensions does not cause a perturbation of the phase of the wavefield. Also, it turns out that Fermat’s theorem in the context of geometric ray theory is a special case of the finite-frequency wave theory in the limit of infinite frequency. Last, we address the misconception that the width of the Fresnel volume limits the resolution in imaging experiments.

Fresnel lens spotlight with coupled variation of the spacing of lighting elements

Abstract: A Fresnel lens spotlight whose emitted light beam has a variable aperture angle, having a reflector, a lamp and at least one Fresnel lens is provided. The at least one Fresnel lens has a negative focal length and a virtual focal point.

Multilayer Laue lenses as high-resolution x-ray optics

Abstract: Using Fresnel zone plates, a spatial resolution between 20 nm for soft x-rays and 70 nm for hard x-rays has been achieved. Improvement of the spatial resolution without loss of efficiency is difficult and incremental due to the fabrication challenges posed by the combination of small outermost zone width and high aspect ratios. We describe a novel approach for high-resolution x-ray focusing, a multilayer Laue lens (MLL). The MLL concept is a system of two crossed linear zone plates, manufactured by deposition techniques. The approach involves deposition of a multilayer with a graded period, sectioning it to the appropriate thickness, assembling the sections at the optimum angle, and using it in Laue geometry for focusing. The approach is particularly well suited for high-resolution focusing optics for use at high photon energy. We present a theory of the MLL using dynamic diffraction theory and Fourier optics.

Shear wave splitting in three-dimensional anisotropic media

Abstract: SUMMARY Splitting intensity, a new seismic observable that characterizes seismic anisotropy, can be ex- pressed as linear combinations of elastic perturbations involving 3-D sensitivity (or Frechet) kernels. We conduct a numerical study of elastic wave propagation in weakly anisotropic het- erogeneous media in order to investigate the validity of the different assumptions made in the derivation of these kernels. For characteristic periods larger than 6 s, the splitting parame- ters obtained from the analysis of synthetic seismograms calculated using a spectral-element method (SEM) are in excellent agreement with predictions based upon the 3-D kernels. This suggests that the kernels fully capture the complexity of shear wave splitting in heterogeneous anisotropic media and can be used for tomography. In addition, they can be used to calculate synthetic splitting parameters in 3-D anisotropic media, which represents a very small amount of computation compared with finite-difference or finite-element modelling. 3-D kernels dis- tribute sensitivity off of the reference ray given by the laws of geometrical optics. This has important consequences for the interpretation of apparent splitting parameters, which usually relies on ray theory. Apparent splitting parameters estimated at the surface can differ signif- icantly from the anisotropic properties in the underlying medium wherever heterogeneities occur with a characteristic wavelength smaller than approximately 0.75 times the width of the first Fresnel zone √ λz, with λ the wavelength and z the depth.

Comprehensive focusing analysis of various Fresnel zone plates

Abstract: A series-form expression for the individual diffracted field of a general annular ring is derived from the Rayleigh-Sommerfeld diffraction integral. It can be used for the accurate and fast simulation of any diffractive focusing element composed of concentric transparent rings. We present a comprehensive analysis, based on the leading term and the linear superposition principle, of the focusing performances of various Fresnel zone plates. Many problems, such as the equivalent aperture function, the diffraction efficiency, the focal spot pattern, the suppression of higher orders and the appearance of "fractional orders," and the explanation for the appearance of Fraunhofer diffraction patterns, are analytically investigated in detail. Because of the great similarity between Fresnel zone plates and multilevel diffractive lenses, most of the obtained results are also applicable to multilevel diffractive lenses.

Diffractional optics of millimetre waves

Abstract: Theory of diffraction. Short focusing Fresnel zone plates. Elements of diffraction quasioptics. Synthesis of diffractional elements. Diffractional antennae at millimetre wavelengths. The influence of surface form on the structure of Fresnel zones. Applications of diffractional optics and quasioptics. Diffractional antennae. Optical constants of materials at submillimetrics and millimetric wavelengths.

Infrared antennas coupled to lithographic Fresnel zone plate lenses

Abstract: Several designs for Fresnel zone plate lenses (FZPLs) to be used in conjunction with antenna-coupled infrared detectors have been fabricated and tested The designs comprise square and circular FZPLs with different numbers of Fresnel zones working in transmissive or reflective modes designed to focus infrared energy on a square-spiral antenna connected to a microbolometer A 163× maximum increase in response was obtained from a 15-zone circular FZPL in the transmissive mode Sensor measurements of normalized detectivity D* resulted in a 267× increase with FZPLs compared with measurements made of square-spiral antennas without FZPLs The experimental results are discussed and compared with values obtained from theoretical calculations

Fresnel aperture prestack depth migration

Abstract: We investigate possible improvements in seismic imaging. We discuss how the Fresnel zone relates to the migration aperture and introduce the concept of the Fresnel aperture, which is the direct time-domain equivalent, at the receivers’ surface, of the subsurface Fresnel zone. Through these concepts we propose a new and efficient method for optimal aperture selection and migration. For complex media, multipathing will occur and multiple Fresnel apertures can exist for a given image point. In practice, due to inaccuracies and smoothing of the background velocity macromodel, inaccuracies in the ray-tracing method used for Green’s function computations and possible noise corruption of the data, the true Fresnel apertures will, in many cases, be replaced by ‘false’ ones, with apparently new Fresnel apertures being added. Hence, contributions from these ‘false’ Fresnel apertures cause a noise-corrupted image of the subsurface. It is now assumed that the single scattered events are quite robust with respect to the above-mentioned distortions, and that their corresponding Fresnel apertures will remain essentially undistorted, with the strongest amplitudes. Based on this main assumption, we propose a method, analogous with velocity analysis, where the strong-amplitude Fresnel apertures can be picked interactively and at least semi-automatically. However, as in velocity analysis, a certain amount of user interaction has to be assumed. When this technique is combined with a prestack Kirchhoff-type depth-migration method, we call it Fresnel-aperture PSDM. This imaging method has been applied to data from both the Marmousi model and the North Sea. In both cases the improvements, when compared to conventional imaging, were considerable.

Diffraction-based solid immersion lens

Abstract: A solid immersion lens based on diffraction (dSIL) is proposed as an alternative to the conventional design based on refraction. A design analogous to a Fresnel zone plate is derived in accordance with the Huygens–Fresnel principle. Fabrication of a binary dSIL is achieved by electron-beam lithography and reactive-ion etching on LaSF35, with index n=2.014. Measurement of the point-spread function is performed with near-field optical microscopy. The results are in accord with the expected resolution enhancement of a factor n with respect to the diffraction limit.

Electrically controlled Fresnel zone plates made from ring-shaped 180 degrees domains.

Abstract: We present high efficiency, low noise electrically-controlled Fresnel phase zone plates that were made by creating ring-shaped 180° ferroelectric domains in a lithium niobate wafer. The primary focal lengths of these lenses ranged from 5 to 43 cm, and the light-gathering efficiency was over 37%, very close to the maximum theoretical value of 40.5%.

Fresnel optical element and projection display device

Abstract: Each of a plurality of Fresnel prisms 12 is formed so that a refractive surface 12 thereof includes a non-light incidence surface 12 c upon which any light ray emitted from a projector 1 is not directly incident because it is intercepted by another Fresnel prism 12, the non-light incidence surface having an angle τ′ with a reflective surface 12 b which is different from the prism apex angle τ of each of the plurality of Fresnel prisms. As a result, a light ray reflected by the refractive surface 12 a of each of the plurality of Fresnel prisms without passing through the refractive surface can be preventing from emerging, as unnecessary light, toward the viewer's line of sight.

Role of diffractive and refractive optics in x-ray astronomy

Abstract: No future X-ray telescope is likely ever to have angular resolution significantly superior to the Chandra X-Ray Observatory without adopting a new technology. We consider focusing systems based upon diffraction and refraction rather than grazing incidence reflection. The elements are Fresnel zone plates and refractive lenses in configurations where chromatic aberration is corrected over a finite bandwidth. This technique is likely to be especially effective in the intermediate regime between the 0.5 arcsec capability of the Chandra telescope and the one-tenth microarcsec resolution required for the NASA "Vision Mission" entitled the "Black Hole Imager." Diffractive/refractive systems can also be configured as high throughput flux concentrators for third generation X-ray timing studies and non-dispersive spectroscopy. They may also have an important role in very high resolution spectroscopy. Because these elements focus by transmitting X-rays at normal incidence they can be extremely lightweight compared to grazing incidence telescopes. Furthermore the figure accuracy and surface smoothness are much less critical. On the other hand diffractive/refractive optics are characterized by chromatic aberration, which can be corrected only in small wavelength bands. Focal lengths range up to 105 km making the application of diffractive/refractive X-ray optics to astronomy dependent upon the development of technology for formation flying of very widely separated spacecraft.

Method for reduction of background artifacts of images in scanning holography with a Fresnel-zone-plate coded aperture.

Abstract: Near-infrared scanning holography with a Fresnel zone plate (FZP) coded aperture has potential applications in imaging through turbid media. However, the nonnegative intensity-distribution function of the FZP coded aperture introduces the background artifacts into the reconstructed images, reducing the contrast and the signal-to-noise ratio (SNR) of the images. A novel method termed as the composite hologram is proposed to reduce the artifacts. The computer simulations showed that the contrast and the SNR of the reconstructed images had improvements of at least 50.2% and 5.58-dB, respectively, compared with the conventional method. The composite hologram of a metal ring with a 6.0-mm diameter made by a wire with a 0.4-mm diameter immersing in 1% intralipid solution was recorded, and the reconstruction was performed numerically. The experimental results demonstrated that the contrast and the SNR of the reconstructed image had improvements of at least 32.3% and 2.51-dB, respectively.

Fresnel diffraction supercontinuum generation

Abstract: White supercontinuum (SC) produced from Fresnel diffraction was demonstrated in BK7 glasses using femtosecond laser pulses. For input pulse energy below the threshold for the onset of self-focusing and SC generation, an aperture was placed into the beam before the BK7 glass to redistribute the intensity by diffraction along the propagation axis to produce a stable SC. The SC occurred at various distances from the aperture containing odd number of Fresnel zones, mainly the first. This result plays an important role in studying the properties of SC sources as well as the diffraction field distribution. A distinct and stable interference ring pattern inside the conical four-photon emission is observed and attributed to the spatial arrangement of small-scale filaments at different distances in the glass.

Fabrication of high-resolution zone plates with wideband extreme-ultraviolet holography

Abstract: We report an achromatic holographic method to fabricate high-resolution x-ray optics using coherent extreme-ultraviolet radiation from an undulator source. The interference pattern between two spherical beams, which are created using Fresnel zone plates, is recorded to produce a higher-resolution zone plate. Analytical and simulation results showing the formation of the zone plate pattern was confirmed experimentally with the production and testing of a lens with 60-nm outermost zone width. The combination of extreme-ultraviolet light, which exposes photoresists with practically no proximity effect, and holography, which guarantees the accurate placement of zones, addresses the main difficulties faced in the improvement of the resolution of x-ray lenses. Holography with extreme-ultraviolet light has the potential to produce lenses with sub-10-nm resolution.

Resolution in two-dimensional tomographic reconstructions in the Fresnel zone from Born scattered fields

Abstract: The problem of determining the achievable resolution in the reconstruction of a dielectric object from the knowledge of its scattered field is dealt with. We face such problem for a two-dimensional and scalar geometry and assume the scattered field collected over a bounded and rectilinear domain located in the Fresnel zone with respect to the unknown object. The analysis is performed by casting the problem as the inversion of the linear operator arising from the Born approximation and by means of the singular value decomposition (SVD) of the relevant operator. The role of the parameters of the measurement configuration, as the sensing geometry and the adopted frequencies, is highlighted by using as guidelines results concerning the case of strip objects.

94 GHz zonal ring reflector for helicopter collision avoidance

Abstract: A single-layer reflector antenna combining eight and four correcting Fresnel zones is presented. The progressive phase shift is achieved by circular and annular patches. The choice of a quarter-wavelength thickness substrate provides naturally 0 and 180° correcting zones that simplify the reflector design. A prototype of reflector antenna working at 94 GHz has been designed, built and measured. Measurement results show 70% improvement of antenna aperture efficiency compared to the half-wave Fresnel zone plate reflector .

Effects of localization of the areas of sound scattering by surface wind waves

Abstract: Experimental studies of the scattering of a monochromatic sound signal by a rough sea surface are carried out. The signal is produced by a point source in a shallow-water basin. The measurements are performed with the use of horizontal and vertical linear receiving arrays. The experimental data are compared with the estimates obtained on the basis of the model developed by the authors for resonant sound scattering by surface roughness. A satisfactory agreement between the experiments and the calculations is achieved. It is shown that the scattered signal is formed within small surface areas, whose sizes have the same order of magnitude as the first Fresnel zone with respect to the source and the receiving system.

Effects of ionospheric scintillation on Transit satellite measurement of total electron content

Abstract: [1] Ionospheric scintillation can affect not only satellite communications but also satellite measurements of the ionosphere, such as the measurements of total electron content (TEC) made using Transit-like signal transmissions. In this work a numerical phase-screen propagation simulation is applied to study the accuracy of the measurement of TEC made with Transit-like signals. To measure TEC, the phase from coherently related 150 and 400 MHz tones is combined to obtain an estimate of the phase imparted to a propagating signal by transmission through the ionosphere. This phase is processed to remove ambiguities of 2π and converted to a relative value of TEC. However, scattering caused by ionospheric irregularities produces amplitude fading and phase variations that degrade the TEC measurement in several ways. Rapid phase variations that may be associated with deep fades can degrade the phase-ambiguity removal process. Fresnel filtering causes scintillation when intrinsic ionospheric variations are of the size of the Fresnel zone and smaller. Receiver noise also acts to degrade the phase measurements and is especially important during the deepest fades. This paper considers the effects of all these processes and develops rule-of-thumb qualifiers to assure the accuracy of Transit-like measurements of TEC.

Optical implementation of real-time incoherent 3D imaging and display system using modified triangular interferometer

Abstract: In this paper, a real-time incoherent 3D imaging and display system using the modified triangular interferometer is optically implemented The incoherent holographic system based-on this modified triangular interferometer employs the superposition of Fresnel zone patterns, in which the respective positions and intensities of the 3D object points are uniquely encoded and from this system the complex holograms without bias and conjugate images for the 3D object can be obtained In addition, the real and imaginary parts of a complex hologram are obtained by subtracting and adding two hologram patterns Then, illuminating them coherently and recombining the light passing through the transparencies by the use of the beam splitter allows the complex addition to be performed Then, the desired 3D image is reconstructed through Fresnel diffraction From some experiments with a 3D object of "dies", it is found that the incoherent 3D imaging and display system without the bias and conjugate image can be optically implemented in real-time by using a modified triangular interferometer© (2004) COPYRIGHT SPIE--The International Society for Optical Engineering Downloading of the abstract is permitted for personal use only

Reflective fresnel lens for sub-millimeter wave power distribution

Abstract: A reflective Fresnel lens for shaping an incident wave for efficiently delivering the incident wave to an array of receivers, having a wavelength within a predetermined range. The Fresnel lens comprises a ground plate and a plurality of reflective elements formed at various levels of the ground plate. The predetermined range includes millimeter wavelength range, sub-millimeter wavelength range or microwave wavelength range.

Spectral anomalies in focused waves of different Fresnel numbers.

Abstract: Light propagation induces remarkable changes in the spectrum of focused diffracted beams. We show that spectral changes take place in the vicinity of phase singularities in the focal region of spatially coherent, polychromatic spherical waves of different Fresnel numbers. Instead of the Debye formulation, we use the Kirchhoff integral to evaluate the focal field accurately. We find that as a result of a decrease in the Fresnel number, some cylindrical spectral switches are geometrically transformed into conical spectral switches.

Multistatic–multiview resolution from Born fields for strips in Fresnel zone

Abstract: We address the inverse scattering problem of estimating the resolution limits achievable in the reconstruction of a dielectric strip object within a two-dimensional and scalar geometry. The scattered field is observed over a bounded rectilinear domain located in the Fresnel zone, and a single-frequency multistatic–multiview configuration is considered. The analysis is performed by casting the problem as the inversion of the linearized scattering operator arising from the Born approximation and by means of its singular-value decomposition. Finally, the role of the geometrical parameters of the measurement configuration is highlighted.

Chromatic compensation of broadband light diffraction: ABCD-matrix approach

Abstract: Compensation of chromatic dispersion for the optical implementation of mathematical transformations has proved to be an important tool in the design of new optical methods for full-color signal processing. A novel approach for designing dispersion-compensated, broadband optical transformers, both Fourier and Fresnel, based on the collimated Fresnel number is introduced. In a second stage, the above framework is fully exploited to achieve the optical implementation of the fractional Fourier transform (FRT) of any diffracting screen with broadband illumination. Moreover, we demonstrate that the amount of shift variance of the dispersion-compensated FRT can be tuned continuously from the spatial domain, which is totally space variant, to the spectral domain, which is totally space invariant, with the chromatic correction remaining unaltered.

X-ray imaging microscopy using Fresnel zone plate objective and quasimonochromatic undulator radiation

Abstract: An imaging microscopy experiment in a hard x-ray region has been performed at the undulator beamline 40XU of SPring-8. The helical undulator at the BL40XU provides quasimonochromatic radiation with a bandwidth of 1.2% at 8.34 keV. A Fresnel zone plate with an outermost zone width of 0.25 μm and a Fresnel zone number of 100 is used as an objective. The natural bandwidth of the undulator radiation of BL40XU is nearly equal to the monochromaticity required for the zone plate objective. Therefore, compared with conventional beamlines with a crystal monochromator, the available photon flux is higher by two orders. Fine structure of test patterns with 0.25 μm line and space was clearly observed at an x-ray energy of 8.34 keV within an exposure time of 1.5 ms.

Lensless imaging from diffraction intensity measurements by use of a noniterative phase-retrieval method.

Abstract: A method of reconstructing the complex amplitude of an object that is illuminated by a coherent wave from its Fresnel diffraction patterns is proposed for high-frequency wave phenomena such as x-rays and electron waves. A noniterative phase-retrieval method that uses a Gaussian filter is employed here, and it is shown that the object's illumination with amplitude distribution in the Fraunhofer diffraction pattern of a circular aperture can be used as a substitute for the Gaussian filter. This method has an advantage over other noniterative phase-retrieval methods in that it can retrieve phase vortices.