Fresnel zone

About: Fresnel zone is a research topic. Over the lifetime, 2337 publications have been published within this topic receiving 37650 citations.

Source Focusing and Coherent Imaging of a Microscopic Object at Weak Spatial Coherence of the Synchrotron Radiation Beam

Abstract: Experimental results are presented on the measurement of a holographic (phase-contrast) image of a boric fiber (100-μm-diameter boric cylinder with a 20-μm-diameter tungsten core) and on radiation focusing by Fresnel zone plates using the Kurchatov synchrotron radiation source. By comparison of the obtained hologram with theoretically calculated data, the vertical size of the source was determined to be 325 ± 25 μm. This value was also confirmed by measuring the half-width of the direct image of the source. Features of image recording on a photographic film are discussed.

Applicability of geometrical optics to in-plane liquid-crystal configurations

Abstract: We study the applicability of geometrical optics to inhomogeneous dielectric nongyrotropic optically anisotropic media typically found in in-plane liquid-crystal configurations with refractive indices no=1.5 and ne=1.7. To this end, we compare the results of advanced ray- and wave-optics simulations of the propagation of an incident plane wave to a special anisotropic configuration. Based on the results, we conclude that for a good agreement between ray and wave optics, a maximum change in optical properties should occur over a distance of at least 20 wavelengths.

Gaussian-Beam-Kirchhoff prestack depth migration

Abstract: SUMMARYDuetoimagingproblemsofaseismicwavefieldincomplexgeologicalregionsbytheuseofzeroorderraytheoryasGreenfunction,wereporton a Gaussian-Beam (GB) type operator in the kernel of a finite-offsettrue-amplitude prestack depth migration Kirchhoff operator. This op-erator is a weighted GB superposistion integral constrained to the pro-jected Fresnel zone of a seismic experiment. The current migrationoperator is applied to a simple synthetic example and is compared tothe conventional Kirchhoff-PSDM in a complex synthetic geologicalmodel of the Solim˜oes Basin (Brazil). The depth images in all thecases showed an increase in horizontal resolution and a reduction ofmigration artifacts.INTRODUCTIONKirchhoff-type time or depth migration has been used as workhorseby oil industry since the pioneering work of Hagedoorn (1954), inwhich the surfaces of maximum convexity were later related to thescalar wave equation and became familiar in the geophysics litera-ture as “Kirchhoff migration” (Schneider, 1978). In the last threedecades, however, Kirchhoff migration in the meaning stated aboveevolved from a single imaging only operator to a inversion operator.This has led to the development of a miscellaneous of other imagingtechniques (Tygel et al., 1993), where the resulting operators are ableto handle AVO/AVA data, those ones important in the characterizationof oil-bearing reserves.The basic algorithm that supports Kirchhoff migration is based on thekinematicanddynamicraytracing(Cervenˇ ´y,2001),i.e.,zeroorderraytheory. However, ray theory may not correctly simulate the seismicwavefield in some determined regions of the velocity model. In orderto bypass these drawbacks, along the years several methods have beenused, including the paraxial ray theory (Bortfeld, 1989). The paraxialray theory is essentially a real theory (Cervenˇ ´y, 2001); its extension toa complex character lead us to the Gaussian beam concept, which areparaxial rays with an amplitude factor that exponentially decays withrespect to the distance from the so called central ray, in a Gaussianmanner. Unlike ray theory, which is a mathematical representation ofthe energy path of the wavefield, the GB’s are physical quantities thatcan be measured, and in being so, they exist in regions of the velocitymodel where common rays (i.e., central rays) cannot be numericallytraced. Besides that, in some situations where the wavefield is notregular (i.e., the amplitudes tend to infinity, in caustic regions), theGB’s are regular, granting the numerical stability of the method.Toourknowledge, thefirstworkstodealwithGB’sasanimagingtoolwereduetoRaz(1987)andCosta(1989). Later,Hill(1990)developeda GB migration for poststack data by using the decomposition of thewavefieldinplanewaves. InHill(2001),theGBmigrationisextendedto 3D prestack data, where using the Kirchhoff downward extrapo-lation principle (Schneider, 1978) and the Claerbout (1971) imagingprinciple, it is shown that in the midpoint coordinates this process canbeseenasalocalslantstackingofeachwavefieldelementdecomposedin beams (Hale, 1992).In this work, we present the theoretical and numerical results of a 3DKirchhoff-type prestack depth migration operator where we make useof a weighted GB superposition integral as a Green function of theimaging problem. In order to adequately control the parameters thatdefine the half-width of a GB, we use as a physical constraint forthe determination of the “beam parameters” the Fresnel volume, es-pecifically speaking the Fresnel zone of a seismic experiment and itscounterpart, projected towards the acquisition surface. By using thediffraction stacking principle (Schleicher et al., 1993), we calculatethe Fresnel volume elements by dynamic raytracing. Then, we de-termine a radius of influence, inside of which we stack the seismicreflections corresponding to reflectors elements in the neighbour of areflection point and that influences on the resolution of the final im-age. Our process is compromised with the true amplitude of reflec-tion events, by correcting seismic data from the effects of geometricalspreading losses. The interaction between the weight-function of theGB superposition integral and the weight-function of the true ampli-tude migration operator has led to a weight-function of the GB super-position integral that is proportional to the value of the Fresnel zonematrix. In our opinion, this leads to a new physical interpretation ofthereferredweight-function,whencomparedtotheanalysisofKlimˇes(1984), wherenoconstrainttothenumberofparaxialraystobesuper-posed on a observation point (i.e., on the geophone) is stated (Ferreiraand Cruz, 2005). We have applied our algorithm to a complex syn-thetic model of the Solimoes Basin, Brazil. The migrated results have˜shown a sensible reduction in the number of migration artifacts and agood horizontal resolution.THEORYThemigrationoperatortobeconsideredisgivenby(FerreiraandCruz,2005)I(M,t)=−12π

Focusing and imaging properties of diffractive optical elements with star-ring topological structure

Abstract: A kind of diffractive optical elements (DOE) with star-ring topological structure is proposed and their focusing and imaging properties are studied in detail. The so-called star-ring topological structure denotes that a large number of pinholes distributed in many specific zone orbits. In two dimensional plane, this structure can be constructed by two constrains, one is a mapping function, which yields total potential zone orbits, corresponding to the optical path difference (OPD); the other is a switching sequence based on the given encoded seed elements and recursion relation to operate the valid zone orbits. The focusing and imaging properties of DOE with star-ring topological structure are only determined by the aperiodic sequence, and not relevant to the concrete geometry structure. In this way, we can not only complete the traditional symmetrical DOE, such as circular Dammam grating, Fresnel zone plates, photon sieves, and their derivatives, but also construct asymmetrical elements with anisotropic diffraction pattern. Similarly, free-form surface or three dimensional DOE with star-ring topological structure can be constructed by the same method proposed. In consequence of smaller size, lighter weight, more flexible design, these elements may allow for some new applications in micro and nanphotonics.