Showing papers on "Fresnel zone published in 1993"

Radio propagation characteristics for line-of-sight microcellular and personal communications

Abstract: To acquire a knowledge of radio propagation characteristics in the microcellular environments for personal communications services (PCS), a comprehensive measurement program was conducted by Telesis Technologies Laboratory (TTL) in the San Francisco Bay area using three base station antenna heights of 3.2 m, 8.7 m, and 13.4 m and two frequencies at 900 MHz and 1900 MHz. Five test settings were chosen in urban, suburban, and rural areas in order to study propagation in a variety of environments. This paper reports the LOS measurements in different environments, all of which show variations of signal strength with distance that have distinct near and far regions separated by a break point. It was also found that the location of the break point for different frequencies and antenna heights can be calculated based on first Fresnel zone clearance. The regression analysis reveals a slope that is less than two before the break point, while it is greater than two after the break point. This break distance can be used to define the size of microcell and to design for fast hand-off. Beyond the first Fresnel zone break distance the base station antenna height gain was observed to approximately follow the square power law of antenna height. >

Resolution limits in ray tomography due to wave behavior: Numerical experiments

Abstract: Several factors limit the resolution obtained in ray tomography. Of these the least thoroughly discussed in the geophysical literature is the effect of the ray approximation itself; scattering is ignored and the information contained in a seismic trace is reduced to one traveltime pick. Frequency domain comparisons of ray tomography with diffraction tomography have suggested that the minimum feature size resolvable by ray tomography is of the order of the width of the first Fresnel zone. We investigate resolution in the spacetime domain with a numerical experiment. Four synthetic data sets were generated with a finite‐difference program corresponding to crosshole tomographic surveys at two hole separations and two frequencies. The scale of resolution achieved in tomograms derived from these is then assessed by calculating their semblance to filtered versions of the original model and reconstructions from data sets obtained by tracing rays through the original models. The results broadly confirm the relati...

Fresnel and refractive lenses for X-rays

Abstract: We present a Gaussian beam analysis of X-ray refractive and Fresnel lenses. The X-ray refractive lens is featured by an intrinsic soft (Gaussian) aperture due to strong absorption of X-rays by materials. We defined a parameter N0, the critical Fresnel number (CFN), to describe this optical property. The values of N0 for all practical materials are below 1000 for photon energies exceeding 30 eV, still lower for high-Z materials. The maximum effective Fresnel number of a lens is determined by its material to be 2N0 and its maximum enhancement of X-ray intensity is limited to (2πN0)2, independent of its shape. We found that the refractive lens is likely to be useful for manipulating nearly diffraction limited beam in the hard X-ray region and its application is severely restricted by available fabrication capabilities today. X-ray Fresnel lenses, both in cylindrical and linear forms, are proposed as superior focusing elements for hard X-rays. Their high efficiency, up to 100% in optimal construction, will enable us to manipulate beams with multiple lenses and obtain higher performance optics. Their design and fabrication are discussed in reference to those of X-ray Fresnel zone plates and micro Fresnel lenses for optoelectronics.

Determination of fresnel zones from traveltime measurements

Abstract: For a horizontally stratified (isotropic) earth, the rms‐velocity of a primary reflection is a key parameter for common‐midpoint (CMP) stacking, interval‐velocity computation (by the Dix formula) and true‐amplitude processing (geometrical‐spreading compensation). As shown here, it is also a very desirable parameter to determine the Fresnel zone on the reflector from which the primary zero‐offset reflection results. Hence, the rms‐velocity can contribute to evaluating the resolution of the primary reflection. The situation that applies to a horizontally stratified earth model can be generalized to three‐dimensional (3-D) layered laterally inhomogeneous media. The theory by which Fresnel zones for zero‐offset primary reflections can then be determined purely from a traveltime analysis—without knowing the overburden above the considered reflector—is presented. The concept of a projected Fresnel zone is introduced and a simple method of its construction for zero‐offset primary reflections is described. The pr...

Log-amplitude variance and wave structure function: a new perspective for Gaussian beams

Abstract: Two naturally linked pairs of nondimensional parameters are identified such that either pair, together with wavelength and path length, completely specifies the diffractive propagation environment for a lowest-order paraxial Gaussian beam. Both parameter pairs are intuitive, and within the context of locally homogeneous and isotropic turbulence they reflect the long-recognized importance of the Fresnel zone size in the behavior of Rytov propagation statistics. These parameter pairs, called, respectively, the transmitter and receiver parameters, also provide a change in perspective in the analysis of optical turbulence effects on Gaussian beams by unifying a number of behavioral traits previously observed or predicted, and they create an environment in which the determination of limiting interrelationships between beam forms is especially simple. The fundamental nature of the parameter pairs becomes apparent in the derived analytical expressions for the log-amplitude variance and the wave structure function. These expressions verify general optical turbulence-related characteristics predicted for Gaussian beams, provide additional insights into beam-wave behavior, and are convenient tools for beam-wave analysis.

Multilayer gratings efficiency: numerical and physical experiments

Abstract: Recently the possibility of focusing, imaging and spectroscopy with Fresnel zones etched on a flat multilayer substrate instead of a curved substrate has been shown. This is now known as Bragg-Fresnel Multilayer lenses (BFML). Lamellar gratings etched in a multilayer (LMG) are the basic type of Bragg-Fresnel optics. In this paper we describe important points in the fabrication, computer simulation, and testing of the LMs. They can be very interesting as a spectroscopic device with a relatively high dispersion and efficiency. We develop a rigorous theory of diffraction combined with the layer-by-layer differential integration numerical method. The agreement with experimentals results obtained for a lamellar grating with several period and various etched depths in a W/Si multilayer is very good. The main result is an increase of the effective extinction depth ( t ext ) in short-period gratings which gives a possibility to increase the absolute diffraction efficiency of the LGM practically from 30% to 60% in the first order with a totally suppressed zero order.

Examples of Fresnel diffraction using Gaussian modes

Abstract: Gaussian beam modes, which are normally associated with laser cavities and quasi-optical propagation, can be used to solve some classic problems in Fresnel diffraction. A particular advantage of the technique is that, for the cases of the uniformly illuminated circular aperture, narrow slit and straight edge, it is possible to derive analytical recursive relationships for the mode amplitude coefficients, which allow for speedy computation of the diffraction patterns.

Design procedure for a Fresnel-zone plate antenna

Abstract: A design procedure for two types of Fresnel-zone plate antennas is presented: viz. antennas with absorbing/transparent zones and phase-correcting zones. Design objectives are the optimization of the gain of the lens of the antenna and the side-lobe envelope of its radiation pattern. The design rules are derived from numerical simulations.

Fresnel zone plate reflector incorporating rings

Abstract: A novel high-efficiency Fresnel zone plate reflector antenna is presented. The reflector consists of an inhomogeneous array of circular conducting rings printed on a grounded substrate. By adjusting the geometrical parameters of the rings and the distances between them, the reflector provides a space-varying phase correction required for focusing an incoming plane wave. Compared with a phase reversal zone plate, an average of 3-dB gain improvement and significant sidelobe reduction have been obtained. >

Dynamical theory of stratified Fresnel linear zone plates

Abstract: A dynamical theory is given for calculating the performances of stratified Fresnel linear zone plates (SFLZP’s). The Born expansion extended to the Fresnel diffraction is used to prove a fundamental theorem giving the diffraction efficiency and the diffraction pattern of transmission or reflection SFLZP’s. The method is valuable as long as the wavelength is smaller than the characteristic parameter of the zone plate. It allows us to evaluate the performances of reflection multilayer SFLZP’s, i.e., the so-called Bragg–Fresnel optics recently developed for x-ray optics.

Pupil conjugation connecting device in projection optical system

Abstract: PURPOSE:To obtain a projection optical system in which a Fresnel fringes of Fresnel-elements having a prism operation and a positive power are not projected by arranging optical elements having a periodic construction by shifting toward an optical axis from an intermediate-image position. CONSTITUTION:A pupil conjugation connecting elements (device) 30 is constituted of eccentric Fresnel lenses 31, 32 divided into two sheets, correction lenses 33, 34 inserted between the Fresnel lenses 31 and 32. The center F1 of the eccentric Fresnel lenses 31 and 32 is made eccentric to the center F2 of correction lenses 33 and 34. When the eccentric Fresnel lenses 31 and 34 are arranged by shifting from an inter-mediate image 13 in this way, Fresnel fringes of eccentric Fresnel lenses 31 and 32 are made to be a defocus state to a projection lens 21 of a second projection lens system 20. Thus, the image of the fringes is never formed inside a projected image.

Multilayer phase correcting fresnel zone plate reflector antennas

Abstract: Owing to its flat nature and light weight etc., the Fresnel zone plate antenna is becoming very attractive for such applications as DBS reception and receive-only VSAT. The disadvantages of low efficiency and high sidelobes of the simple and the phase reversing zone plates can be improved by using phase correcting techniques. In this paper, a systematic investigation on the efficiency and sidelobe performance of subzone phase correcting zone plate antennas is presented. The design of a form of multilayer phase correcting zone plate reflector is described. A quarter-wave zone plate reflector constructed with three dielectric layers and metallized rings is reported, with measured peak efficiency of 55 per cent.

Diffraction of multilayer gratings and zone plates in the x-ray region using the Born approximation

Abstract: New devices combining the Bragg reflection from periodic multilayer structures with Fraunhofer or Fresnel diffraction arising from lateral patterning of the multilayer are now available for x-ray optics. Using the Green’s-function method, we establish an integral equation for the scattered amplitude that is valid in the framework of both Fraunhofer and Fresnel diffraction. The scattered amplitude is given in the first and the second Born approximations for multilayer mirrors, laminar and sawtooth-profile multilayer gratings, and linear multilayer zone plates. The main diffractive properties of these devices are deduced. The efficiencies are computed in the first and/or in the second Born approximation and are compared with efficiencies obtained from a rigorous electromagnetic theory when they are available.

Periodic orbits and molecular photoabsorption

Abstract: A method for the semiclassical evaluation of molecular photoabsorption rates in terms of contributions of periodic orbits is developed and applied to a collinear model of CO2. It is shown that for a satisfactory quantitative description effects have to be taken into account which originate from a finite extension of the Franck-Condon transition region in comparison with the extension of Fresnel zones of the contributing periodic orbits.

Three-dimensional primary zero-offset reflections

Abstract: Zero‐offset reflections resulting from point sources are often computed on a large scale in three‐dimensional (3-D) laterally inhomogeneous isotropic media with the help of ray theory. The geometrical‐spreading factor and the number of caustics that determine the shape of the reflected pulse are then generally obtained by integrating the so‐called dynamic ray‐tracing system down and up to the two‐way normal incidence ray. Assuming that this ray is already known, we show that one integration of the dynamic ray‐tracing system in a downward direction with only the initial condition of a point source at the earth’s surface is in fact sufficient to obtain both results. To establish the Fresnel zone of the zero‐offset reflection upon the reflector requires the same single downward integration. By performing a second downward integration (using the initial conditions of a plane wave at the earth’s surface) the complete Fresnel volume around the two‐way normal ray can be found. This should be known to ascertain t...

Hot Images from Obscurations

Abstract: Certain damage observed on the optics in NOVA is consistent with nonlinear holographic imaging. Our analysis shows how to circumvent this problem and leads to an explanation for a twenty year old puzzle.

Fresnel approximation for off-axis illumination of a circular aperture

Abstract: Various formulations have been proposed for the Fresnel approximation for diffraction by a circular aperture. These formulations can describe the effects of convergent illumination, finite value of Fresnel number, and off-axis illumination. The retention of a further term, which is dependent on the coordinates of the focus and the observation point, is proposed. This results in a redefined axial optical coordinate, giving improved prediction of the diffracted field for off-axis points.

Performance comparison of hard x-ray plates fabricated by two different methods

Abstract: Two types of fabrication methods have been developed to fabricate Fresnel zone plates for focusing x-rays in the 5 - 25 keV energy region. These two fabrication methods are discussed in terms of spatial resolution and focusing efficiency, which are two important parameters that characterize the performance of a Fresnel zone plate. Experimental characterization of the zone plates fabricated by the two methods are described and the results are discussed.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Stigmatic imaging by zone plates: a generalized treatment

Abstract: We present a new and succinct formulation for the zone radii of zone plates in terms of the focal length and the object-to-image throw of the imaging configuration. This treatment enables us to develop a method for dimensionless analysis of zone-plate parameters for stigmatic imaging of axial-object points. A set of graphs depicts the essential design parameters of zone plates over a wide range of the electromagnetic spectrum, from the infrared to x-ray wavelengths. These nomographs are useful in designing zone plates for given applications, particularly in rapid assessment of the feasibility of zone plates for specified requirements in the early stages of design.

Thin film deposition: an alternative technique for the fabrication of binary optics with high efficiency

Abstract: Binary optics were fabricated by an ion-beam sputter deposition technique on different substrate materials for the wavelengths of 1.52 mu m and 0.63 mu m respectively. The blazed profile of thin film dielectric gratings was approximated by a 2 and 4 phase level profile and the kinoform profile in each zone of the Fresnel zone lenses was approximated by a 2,4,8,16 and a 32 level profile. Such stepped profiles were realized with several masks, written with electron-beam and with photolithographic technology. The microlenses were coated with an anti-reflection coating. The reflection of these lenses was optimized on the basis of an angular spectrum approach. A minimum reflectivity as low as 1*10/sup -4/ was realized using in situ controlled multilayers of TiO/sub 2/ and SiO/sub 2/. The measurements reveal, that the spot-sizes of the fabricated microlenses are close to the diffraction limited values. The highest measured diffraction efficiencies for the 32 level structures are 97%. The effects of fabrication errors, such as level heights, alignment and linewidths errors, on the diffraction efficiency of Fresnel zone lenses were discussed. >

Dielectric resin electromagnetic lens and production thereof

Abstract: PURPOSE:To provide the planar electromagnetic lens of a fixed thickness, to easily adjust, fix and set the radio wave axis of the lens and to reduce a manufacture cost by discretizing the phase zone of a Fresnel zone by a discontinuous finite position value, constituting the respective phase zones as a dielectric packing material to fluorinated resin and integrally and simultaneously forming the whole with the uniform thickness. CONSTITUTION:Phases are rounded by the discontinuous finite value and respective zone sections in the lens zoned by the Fresnel zone are constituted of divided parts whose thickness in a radio wave transmission direction is approximately uniform for the respective phases rounded from the center axis of the lens to a peripheral direction. The divided parts are constituted of a pure fluorinated resin material part 101 as base material resin, the phase zone 102 designed so as to make a phase amount in the direction of the thickness (d) be a prescribed amount in the thickness (d) for which dielectric powder whose relative dielectric constant is high is tilled in the pure fluorinated resin material part 101 and the phase zone 103 designed so as to make the phase amount larger than the phase zone 102 by a similar procedure further and make the phase amount be the prescribed phase amount in the thickness (d).

Blazed Fresnel zone lenses approximated by discrete step profiles: effects of fabrication errors

Abstract: Blazed Fresnel zone lenses for 1.5 j.m wavelength were fabricated in quartz glass by means of microstructuringtechnology. The blazed profile in each zone of the lenses was approximated by 2, 4, and 8 discrete levels. The effects offabrication errors, such as depth and alignment errors, on the diffraction efficiency of the different Fresnel zone lenses were investigated. Further the location and intensity of the parasitic foci appearing due to the discrete level approximation are calculated. Theoretical results along with experimental measurements are presented.1. INTRODUCTIONDiffractive optical lenses are beginning to play an important role in a variety of applications'. This is especially true for those lenses that can be fabricated with microstructuring techniques that are adapted from microelectronic technology. The most common of these diffractive lenses are Fresnel zone lenses that are recorded as surface reliefgratings. In order to obtain the maximum diffraction efficiency, the shape of the grating profiles must be blazed.Unfortunately, such blazed profiles are difficult to fabricate, so they must be approximated by a staircase-like profilehaving a number of discrete levels.Multilevel zone plate lenses can reach high efficiencies depending on the number of discrete levels that are used. Thefabrication of these elements involves multiple steps of repeated pattern transfer and either anisotropic etching orthin film deposition3 to build up the desired surface profile. During these steps a variety of fabrication errors can beintroduced that degrade the optical quality and reduce the diffraction efficiency significantly. Some of these errors andtheir effects have been considered in applications with visible and far infra-red radiations2'.

Fresnel zones on the screen

Abstract: For λ real, we consider the pattern given by the value modulo 2 of the integer part of λ(X 2 + y 2, where (x, y) ∈ Z × Z. We study the periodicity and other geometric properties of this pattern, and show that it can provide, by visual inspection and an elementary computation, a diophantine approximation for λ. We conclude with similar results for other moduli.

Stigmatic Imaging by Spherical Fresnel Zone Plates

Abstract: We present a succinct and convenient formulation for the zone radii of a spherical Fresnel zone plate that produces the stigmatic image of an axial object at a specific finite/infinite distance from the zone plate. By ‘image’ we imply the first order or primary image produced by the zone plate. The variation in zone radii for different conjugate positions and for different values of curvature of the spherical zone plate is demonstrated with the help of numerical results. In order to bring forth the significance of this variation for Fresnel zone plates operating at different regions of the electromagnetic spectrum, the variation is shown for one representative wavelength at each of the four regions of the electromagnetic spectrum, namely, the infrared, the visible, the extreme ultraviolet and the soft X-rays.

Two-dimensional array of AR-coated diffractive microlenses fabricated by thin-film deposition

Abstract: Two dimensional arrays of Fresnel zone micro lenses were fabricated and coated with antireflection layers by ion-beam-sputter deposition technique. The thickness of the layers was controlled by a reflection-wideband-monitoring-system with high accuracy. The lenses have a circular aperture of 2 mm and focal lengths of 70 mm and 20 mm for the wavelength of 0.63 micrometers and focal lengths of 29 mm, 8 mm, and 5.6 mm for the wavelength of 1.52 micrometers . The blazed profile in each zone was approximated by an eight level profile. Such stepped profiles were recorded with several masks, written with e-beam and with photolithographic technology. Our measurements reveal that the spot-sizes of the fabricated microlenses are close to the diffraction limited values, and the diffraction efficiency for the eight level structure is 83 percent.

Characteristics pathlength Fresnel number equations and ideal lens wavefront Kirchhoff formulation: analysis of focused spherical wave diffraction fields

Abstract: The characteristic optical pathlength Fresnel number equation for a paraxial Gaussian laser beam diffracted and spherically focused by an ‘ideal’ circular lens is derived. The maximum inside and outside pathlength Fresnel numbers are quantified. The maximum outside pathlength Fresnel number, simplified via the paraxial approximation, is shown to be equal to the classical focal Fresnel number of the lens-aperture combination. A unique Kirchhoff diffraction integral formulation of this configuration is derived, and calculations show that the diffraction fields for a circular-aperture-truncated focused Gaussian beam are identical in characteristic shape to the same but non-focused diffraction fields, as long as significant focal shift effects are not present. Example applications of the optical pathlength Fresnel number equation are given.