Number Of Fresnel Zones Research Articles

Acoustic scattering by smooth and rough elastic cylinders insonified by directional sonars

Realistic sonars radiate spherically spreading waves and have directivity. Therefore, they insonify a target over a finite number of Fresnel zones and span a continuum of oblique incident angles, even when the center of the beam is at normal incidence. These effects strongly influence both the overall scattered pressure levels and resonances. For example, because of the spreading of the beam and associated oblique insonification within the beam, axially propagating guided waves are generated that would not have otherwise existed for an idealized incident plane wave. This investigation illustrates practical sonar properties and their effects on cylinder scattering both theoretically and experimentally. An approximate theoretical formulation for acoustic scattering by elastic cylinders is proposed in the form of a simple line integral accounting for these properties. Laboratory measurements are also presented to test the range of validity of the formulation for smooth cylinders under both monostatic and bistatic configurations. This study is further extended for the case of rough elastic cylinders.

Acoustic scattering from cylinders for aquaculture applications

In aquaculture farms, long-lines are used to grow kelp for food, pharmaceuticals, and biofuel. As these farms become larger and move offshore, acoustic sensing with high-frequency broadband echosounders is likely a scalable option for large-scale monitoring, making understanding of the scattering properties of the long-lines critical. However, the boundary conditions for the long-lines are complicated, and field data show that the long-lines occupy only a small number of Fresnel zones. To determine the influence of Fresnel zone interference, cylindrical targets with known boundary conditions but a small number of Fresnel zones insonified were studied. Using a formulation involving a monopole line source and an infinitely long cylinder excited at normal incidence relative to the cylinder axis, an apparent volume flow is derived for the case of a spherically spreading source with Bessel function transceiver directivity. Element pressure derived using this volume flow is integrated along the length of the cylinder to yield the scattered field. Theoretical results using this method are validated experimentally at angles near normal incidence. The theoretical formulation is then extended for larger angles by deriving the volume flow based on the analytic solution to an obliquely excited infinite elastic cylinder. [Work funded by ARPA-E.]

Accuracy Check of GTD MER with Weighted Fringe Wave Using Fresnel Zone Number for Grazing Incidence and Slope Wave Diffraction

Accuracy Check of GTD MER with Weighted Fringe Wave Using Fresnel Zone Number for Grazing Incidence and Slope Wave Diffraction

Empirical Validation Of Effective Earth Radius Adjustment Factors For Earth Bulge and Diffraction Loss Parameters Computation

In this paper, the effect of effective earth radius adjustment factors (k-adjustment factors) on various parameters associated with single knife edge diffraction loss is studied. The parameters considered are, the earth bulge, Fresnel-Kirchoff diffraction parameter and the number of Fresnel zones that are partially or fully blocked by obstruction in the signal path. The k-adjustment factors analytical expressions are derived and then validated using empirical elevation profile data for line-of-sight (LOS) communication link between Eket and Akwa Ibom state University. Also, k-factors considered in this paper are k1 = 0.5, k2 = 0.9 and k3= 1.333. In all, the results show that when the value of any of the three parameters is known at a given k-factor, k1, then the value of that parameter can be determined at any other k-factor, k2 by adding the k1-to-tk2 adjustment factor of that parameter to the value of the parameter at k1. The result is essential is evaluating the influence of variations in effective earth radius factor on the parameters associated with single knife edge diffraction loss.

Modified Edge Representation (MER) Consisting of Keller’s Diffraction Coefficients With Weighted Fringe Waves and Its Localization for Evaluation of Corner Diffraction

Equivalent edge currents (EECs) for high-frequency diffraction analysis are intermediate concepts between ray theory and wave optics [physical optics (PO)]. The methods of EEC present some ambiguity in the definition of currents at general edge points, which do not satisfy the diffraction law. Modified edge representation (MER) is a unique concept for a complete definition of EEC with simple and classical Keller-type knife-edge diffraction coefficients. Although singularities in the definition of EEC exist, the line integration of MER EEC results uniform and accurate fields everywhere including geometrical boundaries except for the case of grazing incidence, where reflection and incidence shadow boundaries (RSB and ISB) are close to each other. In this paper, fringe wave (FW) part of MER EEC is modified by introducing the weighting in terms of Fresnel zone number (FZN) distance from the reflection point to improve the accuracy at and near shadow boundaries even in grazing incidence. Next, the corner diffraction, a contribution coming from edge point which does not satisfy the diffraction law, is extracted in MER by introducing another weighting function using the FZN distance from scattering centers on edge. Its remarkable accuracy fully validates MER EECs at general edge points. The dipole wave scattering from flat square and triangular plates are discussed with numerical examples.

Analysis of square Fresnel Zone Plate Lens for dual band detectors

Dust emission is used in space applications for star-formation characterization normally acquired by different detectors operating at Infrared (IR) and sub-millimeter wave (sub-mm wave) frequencies. An integrated dual band detector working at both frequency ranges is described in this paper. The proposed configuration implements a spiral antenna working at sub-millimeter wave frequencies whose design is based on Fresnel zones theory. At the same time, this spiral antenna is used as Fresnel lens to focus IR power (12 μm) into an IR detector. The paper describes the influence of implementing a sub-mm wave spiral antenna based on square Fresnel zones. In particular, the effects on the focal distance and the focal gain at IR frequencies and the radiation features at sub-mm wave frequencies are studied. Further- more, the importance of the number of Fresnel zones used in the design of the sub-mm spiral antenna is also determined.

Physical Optics Radiation Integrals with Frequency-Independent Number of Division utilizing Fresnel Zone Number Localization and Adaptive Sampling Method

Physical Optics Radiation Integrals with Frequency-Independent Number of Division utilizing Fresnel Zone Number Localization and Adaptive Sampling Method

Relief-phase diffractive optical elements on formed revolution surfaces having the high diffraction efficiency

The equations of microstructure reliefs of the single-layer diffractive optical elements disposed on curvilinear interfaces of two mediums are given. These reliefs provide the demanded form of a wave front and 100 p.c. the diffraction efficiency on one wave length irrespective of number of Fresnel zones. Recommendations about use of the given equations for manufacturing of the double-layer two-relief structures providing high diffraction efficiency within the given spectral range are given.

The efficiency of relief-phase diffractive elements at a small number of Fresnel zones

A technique and investigation results are presented on the effect of the number of Fresnel zones on the diffraction efficiency and quality of the wave front formed by a diffractive optical element. Equations are presented for the microstructure reliefs of diffractive optical elements making (regardless of the number of Fresnel zones) the wavefront shape coinciding with the calculated one and ensuring 100% diffraction efficiency at a single wavelength and, in the case of two-layer structures, almost 100% diffraction efficiency in a wide spectral range.

Fresnel Zone Criterion to Implement Locality in the Method of Moments and PO-MoM Hybrid Method for the Reduction of Unknowns

Locality of high frequency electromagnetic scattering phenomena is embodied and imported to the Method of Moments (MoM) to reduce computational load. The proposed method solves currents on small areas only around inner and edge stationary phase points (SPPs) on the scatterer surfaces. The range of MoM area is explicitly specified in terms of Fresnel zone number as a function of frequency, source and observer positions. Based upon this criterion, scatterer of arbitrary size and shape can be solved with almost frequency independent number of unknowns. In some special cases like focusing systems, locality disappears and the method reduces to the standard MoM. The hybrid method called PO-MoM is complementarily introduced to cope with these cases, where Fresnel zone number with analogous but different definition is used. The selective use of Local-MoM and PO-MoM provides frequency insensitive number of unknowns for general combination of source and observation points. Numerical examples of RCS calculation for two dimensional flat and curved surfaces are presented to demonstrate the accuracy and reduction of unknowns of this method. The Fresnel zone, introduced in the scattering analysis for the first time, is a useful indicator of the locality or the boundary for MoM areas.

Fresnel zone antenna for dual-band detection at millimeter and infrared wavelengths

In this work the concept of a Fresnel zone antenna for dual-band detection in the IR and millimeter wave region is presented. The design is based on a Fresnel zone plate lens in the IR that is transformed to serve as a millimeter-wave antenna. Two different designs are presented, a circular-zone design that gives a high diffractive efficiency in the IR and a square-zone design that gives a higher response in the millimeter band but a lower focusing efficiency in the IR. Both designs have an operation bandwidth with the same low frequency limit of 400 GHz (750 microm), which can be tailored by changing the number of Fresnel zones, and a high frequency limit of 4.5 THz (65 microm) for the circular-zone design and 5 THz (59 microm) for the square-zone design.

Diffraction criterion for a slit under spherical illumination

A quantitative criterion to determine the type of diffraction produce by a slit, which is an aperture that cannot be circumscribed, is defined. The slit is illuminated with a spherical wave that eliminates the alignment problems produced by filamentary light sources. The determination of the first minimum of intensity in the diffraction pattern was used to define the criterion that differentiates between Fraunhofer and Fresnel diffraction. The criterion is defined in terms of a parameter γ, which is connected to the number of Fresnel zones. Simulations are used to define the criterion and experimental results are presented to corroborate it.

Temporal effects in ultrashort pulsed beams focused by planar diffracting elements

The pulse envelope of an ultrashort pulsed beam is evaluated on the focal points of a Fresnel zone plate. The description of the field dynamics is given in terms of a diffraction-induced pulse train. Within these terms we follow an analytical procedure to characterize the temporal broadening observed at the principal focus, which is significant if the number of Fresnel zones exceeds the number of cycles in the pulse. For Gaussian-type envelopes, the focal field may be accurately expressed in a simple closed form. This expression has a flat-top shape at the principal focus and other odd-order foci, and a two-peak envelope in the case of a low-integer even-order focus. Finally, extremely high orders present a time-domain evolution that emulates a train of uniform pulses with temporal characteristics equivalent to those of the incident beam.

Prevailing effects of interference or diffraction by multiple apertures

The effects of interference and diffraction produced by a bidimensional structure composed of multiple and identical apertures are studied. Such effects are competitive during the propagation, that is, in some planes the interference effects are more visible, while in others prevail the diffraction ones. Using the number of Fresnel zones, the spatial domains where the interference or diffraction effects prevail are defined and parameterized. Simulation and experimental results are further introduced to verify the proposed method.

Minute details detection through Fresnel diffraction domain

The capability of distinguishing fine details or perturbations in simple structures by means of Fresnel-domain diffraction is shown. Through numerical calculations it is shown that the greater the number of Fresnel zones considered in the diffraction setup the larger differentiability is reached. To illustrate our proposal the case of a circular clear aperture in an opaque screen with fine details of variable dimensions and subtending different number of Fresnel zones is studied. It is shown that by taking advantage of the Fresnel-domain diffraction it is possible to distinguish details or defects with area larger than or equal to 1% of the initial structure area, without any kind of mechanical contact between the diffracting structure and the recording media.

Fresnel diffraction supercontinuum generation

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.

Axial intensity distribution behind a Fresnel zone plate

An analytical expression based on an improved Rayleigh–Sommerfeld diffraction formula with evanescent term is derived for analyzing the axial light intensity distribution throughout the whole space behind a Fresnel zone plate. The effects of the number of Fresnel zones and the size of aperture on the axial intensity distribution are calculated for two kinds of Fresnel zone plate with larger and smaller aperture. The validity of the general formulae for calculating the focal lengths and the relative intensities of the foci of a Fresnel zone plate is analyzed.

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

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.

Angular criterion to distinguish between Fraunhofer and Fresnel diffraction

Summary The distinction between Fresnel and Fraunhofer diffraction is an essential condition for the accurate analysis of diffracting structures. In this paper we propose a criterion based on the angle subtended by the first minimum of the diffraction pattern from the centre of the diffracting aperture. The determination of the minimum of the diffraction pattern is the crucial point to assure the accuracy of the criterion. Therefore, the applicability of adequate thresholds for detection is discussed. The criterion is also generalized by expressing it in terms of the number of Fresnel zones delimited by the aperture. Simulations are reported to illustrate the feasibility of the criterion.

Distinguishing between Fraunhofer and Fresnel diffraction by the Young's experiment

Theoretical considerations, simulations and experiments have been carried out to distinguish between Fresnel and the Fraunhofer diffraction regarding the formation of interference patterns by a conventional Young's double-pinhole arrangement with variable separation, which is illuminated by a coherent plane wave. We show that the optical path difference introduced by this setup fits the Fresnel's phase difference between the pinholes. Consequently, it is possible to determine the number of Fresnel zones subtended by a circle centered on one of the pinholes and with radius equals to the pinhole separation. Then, we propose a criterion for distinguishing between Fresnel and Fraunhofer diffraction based on this number of Fresnel zones, which is applicable for diffracting apertures with any shape.