Showing papers on "Fresnel zone published in 1987"
TL;DR: In this article, a phase-correcting Fresnel zone plate is described, and its characteristics are given when used in the millimeter-wave region for imaging or frequency filtering in place of a lens.
Abstract: A focusing element called the phase-correcting Fresnel zone plate is described, and its characteristics are given when used in the millimeter-wave region for imaging or frequency filtering in place of a lens. Two versions are discussed, one where alternate concentric annular grooves are cut in a single piece of low-loss dielectric, and a second where two (or more) dielectrics are used in alternate concentric rings. For the latter case, an appropriate choice of parameters produces a design of constant thickness (i.e., a flat disk), named the "planar lens." Design formulas and curves, as well as measured results, are given for both types, and an analytical description is derived for the far-field patterns. Compared with lenses, zone plates are simpler to construct and have lower absorption loss, thickness, and weight.
152 citations
TL;DR: In this article, the authors proposed a scheme for deriving a high-resolution zone plate from a coarser one by interfering the light from two positive-order foci, which is called spatial-frequency multiplication.
Abstract: We propose a scheme for deriving a high-resolution zone plate from a coarser one by interfering the light from two positive-order foci. We give a theorteical analysis of the process, which we call spatial-frequency multiplication. The analysis requires calculation of diffracted intensities far off axis, and we derive validity conditions for the application of approximate methods to this calculation. Specifically, we show that the Fresnel approximation is useful in many cases, whereas the method of stationary phase is valid for all cases of technological interest. Some practically useful parameter choices are considered for implementation of the zone-plate fabrication method. An example calculation suggests that a zone plate with smallest zone spacing of 13.8 nm may be possible.
37 citations
01 Nov 1987-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this article, the experimental results of observing hard X-ray focusing during Bragg diffraction on a perfect crystal with Fresnel zone surface structure were reported, and the possibilities of developing Xray Bragg optics were considered.
Abstract: The experimental results of observing hard X-ray focusing during Bragg diffraction on a perfect crystal with Fresnel zone surface structure are reported. Possibilities of developing X-ray Bragg optics are considered.
37 citations
TL;DR: In this article, the authors show a relationship between the multiplicity of CDP coverage of a 3D survey and that of a 2D survey with the same signal-to-uncorrelated-noise ratio.
Abstract: Three-dimensional seismic surveys, in general, do not need the same high degree of CDP coverage as 2-D surveys to achieve a certain signal-to-noise ratio after migration.
This can be shown theoretically for Kirchhoff migration and laterally uncorrelated noise. More precisely, there exists a formal relationship between the multiplicity of CDP coverage of a 3-D survey and that of a 2-D survey with the same signal-to-uncorrelated-noise ratio. Frequency and aperture are parameters in the corresponding expression. Heuristically the relationship can be obtained by applying the concept of the Fresnel zone.
Though the mathematics in this paper refer to laterally uncorrelated noise, the underlying concepts can probably also be used for weakly correlated noise, e.g., for multiple reflections and for the low-frequency remnants of surface waves.
26 citations
TL;DR: In this paper, the three-dimensional intensity distribution near the focus is investigated for systems with Fresnel numbers N < 0.5 and isophotes (contours of equal intensity) are presented that demonstrate the structure of the field deep within the region of Fresnel diffraction.
Abstract: Investigations of the three-dimensional intensity distribution near the focus are extended here to systems with Fresnel numbers N < 0.5. Isophotes (contours of equal intensity) are presented that demonstrate the structure of the field deep within the region of Fresnel diffraction.
22 citations
TL;DR: In this article, the authors examined the effect of scatterers being in the Fresnel zone of one another on the backscattering coefficient of both disc-shaped and needle-shaped leaves.
16 citations
TL;DR: An analytic approximation of an iterative method of image reconstruction from Fresnel-zone magnitude data is discussed in this paper, where the method of stationary phase is used to estimate both the Fresnelzone transform and the inverse Fresnel zone transform.
Abstract: An analytic approximation of an iterative method of image reconstruction from Fresnel-zone magnitude data is discussed The method of stationary phase is used to estimate both the Fresnel-zone transform and the inverse Fresnel-zone transform With this theory we can explain why fewer iterations are needed for good images to be obtained at locations in the Fresnel-zone region of an optical processor that are farther from the Fourier-transform plane
13 citations
TL;DR: In this paper, the optical matching characteristics of undulator radiation with some condenser zone plates were investigated in the soft X-ray region using an undulator beamline at the Photon Factory.
Abstract: Optical matching characteristics of undulator radiation with some condenser zone plates were investigated in the soft X-ray region using an undulator beamline at the Photon Factory. It was confirmed that the monochromatization of the first harmonic of the undulator radiation was made by meams of a system consisting of a zone plate and a pinhole, but the transmission efficiency and the wavelength resolution of the system were lower than expected. Analyses show that the results can be attributed to the finite source size of the undulator radiation which is determined by the present storage ring operation and also to the longer focal lengths of the zone plates used. It was also found that the virtual source point of the undulator radiation should be assigned at the position of the undulator itself.
9 citations
15 Jun 1987
9 citations
TL;DR: In this article, a cylindrical system Fresnel lens-absorber with uniform concentration and normal incoming rays to the absorber is considered, and the unique solution to the problem is obtained.
Abstract: A cylindrical system Fresnel lens-absorber with uniform concentration and normal incoming rays to the absorber is considered. In the approximation of the Sun as a point source the unique solution to the problem is obtained.
9 citations
TL;DR: In this article, a method of calculating the radial intensity distribution of the Fresnel diffraction pattern of a circular aperture is presented. But this method can also be applied to calculations of more complicated apertures.
Abstract: The author presents a method of calculating the radial intensity distribution of the Fresnel diffraction pattern of a circular aperture. The method uses the concept of counting whole or partial Fresnel zones and has an accuracy of about five per cent of the maximum intensity, although it can be refined to improve this figure somewhat. The method can also be applied to calculations of the Fresnel diffraction patterns of more complicated apertures.
TL;DR: Using the Hopkins algorithm, expressions for the intensity patterns, in both the Fresnel and far-field regions, associated with the diffraction of a plane-wave elliptical Gaussian beam truncated by an elliptical aperture were derived in this paper.
Abstract: Using the Hopkins algorithm, expressions are derived for the intensity patterns, in both the Fresnel and far-field regions, associated with the diffraction of a plane-wave elliptical Gaussian beam truncated by an elliptical aperture This is accomplished by evaluating the diffraction integral subject to the Fresnel approximation Numerical results are presented that indicate how the truncation parameter affects the side-lobe level in the Fresnel and far-field regions
TL;DR: In contrast to the continuous character of reflectors seen in seismic data from the sedimentary column, a pervasive feature of deep crustal reflections is their laterally discontinuous nature.
Abstract: Summary. In contrast to the continuous character of reflectors seen in seismic data from the sedimentary column, a pervasive feature of deep crustal reflections is their laterally discontinuous nature. Deep reflections often appear on the seismic section as groups of flat-lying or dipping segments. The length of the individual segments may vary by an order of magnitude. Moreover, the segments are often shorter than the Fresnel zone for a specular reflection. The apppearance of deep flat-lying reflectors of this type has motivated geologic hypotheses of a layered and heterogeneous lower crust. Dipping bands of discontinuous reflectors are interpreted variously as decollement surfaces, sutures, or faults penetrating to midcrustal or deeper levels. A significant geophysical concern is whether truly discontinuous reflectors in the deep crust can be distinguished from an inaccurate or incoherent image. Incoherence can result from the presence of signal-generated noise created at the earth's surface or along the transmission path. Given the types of signal-generated noise likely to be present in deep crustal data, we wish to know how well we can resolve both laterally continuous and discontinuous reflectors using standard reflection data acquisition and processing. To test the effects of such noise on the CMP stack we have conducted finite-difference synthetic seismogram experiments for two similar layered models each having two specular reflectors. One model contained an irregular surface layer, the other contained a zone of random velocity fluctuations between the two reflectors. We processed the data normally, from shot gather to CMP stack and migrated section. The two numerical experiments produced CMP sections with substantially different character. Processing the surface model data produced a clear image of the two deep reflectors as the CMP stack suppressed noise generated in the irregular surface layer. The surface generated noise limited the vertical resolution as it degraded the action of predictive deconvolution applied before stack. Signal-generated noise in the second model did not affect the deconvolution process because the scatterers were located below the zone of surface layer reverberations. The laterally inhomogeneous zone degraded the image of the deepest reflector. The signal-generated noise in the second model may be viewed as signal reflected from the random zone. The dip-filtering action of the CMP stack resulted in reflection events from the random zone having greater horizontal continuity than is present in the velocity model, causing further smearing by a standard time-migration technique.
Journal Article•
TL;DR: Focusing performance of Fresnel-zone-type ultrasonic focusing systems is evaluated by calculating field distributions for an equivalent radiator composed of concentric annular-transducer elements, and is compared with that of a concave radiator.
Abstract: Focusing performance of Fresnel-zone-type ultrasonic focusing systems is evaluated by calculating field distributions for an equivalent radiator composed of concentric annular-transducer elements, and is compared with that of a concave radiator. It is demonstrated that the Fresnel-zone-type radiator presents almost the same focused field as the corresponding concave one and gives reduced sidelobes uner the existence of propagation loss. Focusing characteristics of radiators with inactivated transducer elements in the central part are also examined.
TL;DR: Focusing performance of Fresnel-zone-type ultrasonic focusing systems is evaluated by calculating field distributions for an equivalent radiator composed of concentric annular-transducer elements, and is compared with that of a concave radiator as mentioned in this paper.
Abstract: Focusing performance of Fresnel-zone-type ultrasonic focusing systems is evaluated by calculating field distributions for an equivalent radiator composed of concentric annular-transducer elements, and is compared with that of a concave radiator. It is demonstrated that the Fresnel-zone-type radiator presents almost the same focused field as the corresponding concave one and gives reduced sidelobes uner the existence of propagation loss. Focusing characteristics of radiators with inactivated transducer elements in the central part are also examined.
TL;DR: The effects of quantization on the width of and power in the main lobe and the level of the sidelobes are studied and the results are cast in terms of normalized parameters and are applicable in general.
Abstract: Recently, various high-precision digital graphic systems have been used to generate patterns for diffractive and computer generated holographic optical elements. These plotting systems with submicron accuracy have a common drawback, namely, the patterns drawn have to be quantized. In this paper, the effects of pattern quantization on the optical beams are studied. Specifically, the fields of perfect cylindrical zone plates and cylindrical zone plates with quantized stripes are compared with that of conventional refractive cylindrical lenses. In particular, the effects of quantization on the width of and power in the main lobe and the level of the sidelobes are studied. The results are cast in terms of normalized parameters and are applicable in general.
TL;DR: In this article, a comparison of synthetic seismic reflection sections calculated using a relatively inexpensive ray theory and a relatively expensive generalized reflectivity algorithm for a complex, laterally inhomogeneous model of the oceanic Moho demonstrates that ray theory provides a close approximation to the full-wave theory.
Abstract: The algorithm chosen for the calculation of synthetic seismograms often represents a compromise between the realistic representation of complex geology and economy. Comparison of synthetic seismic reflection sections calculated using a relatively inexpensive ray theory and a relatively expensive generalized reflectivity algorithm for a complex, laterally inhomogeneous model of the oceanic Moho demonstrates that ray theory provides a close approximation to the full-wave theory. The chief difference between the two synthetic sections is the more accurate variation in amplitude with horizontal range predicted by the reflectivity synthetics, due to its inclusion of the horizontal smoothing of the reflected amplitudes over the width of the First Fresnel Zone. While this Fresnel zone smoothing will become increasingly important with increasing reflector depth, the results shown here suggest that inexpensive ray theory synthetics may have sufficient accuracy in many similar applications.
TL;DR: In this paper, a micro-zone plate of 250 zones and 55 nm outermost ring width at the electron storage ring BESSY in Berlin was used for X-ray microscopy.
Patent•
20 Aug 1987
TL;DR: In this paper, the alignment mark of a Fresnel zone target is formed in a predetermined semiconductor chip, which is formed by a scribing line, and the mask is aligned by forming the surface of the semiconductor chips disposed under the target.
Abstract: PURPOSE:To accurately align masks by forming the surface of a semiconductor chip disposed under a Fresnel zone target formed on the mask in a projection or a recess. CONSTITUTION:The alignment mark 33 of a Fresnel zone target is formed in a predetermined semiconductor chip 32 formed by a scribing line 31. Recess regions 34 and projection regins 35 are repeatedly formed at a pitch l, for example, of 5mum on the periphery of the mark 33. When the size l' from the surface A of the region 34 to the surface B of the region 35 becomes 1/4 lambda, where lambda is the wavelength of alignment light. Thus, since the light arrived at the surface f a semiconductor wafer 1 through the surface of the mask 2 and reflected on the surface does not partly coincide with the light reflected on the surface of the mask, they do not extremely strengthen nor weaken each other. Therefore, a difficulty of the erasure of the spot of the Fresnel zone target on the mask can be avoided.
TL;DR: In this paper, a method for finding optimal scales in Gaussian field expansions for circular aperture antennas is given, paralleling the method for rectangular antennas presented in an earlier paper, which leads to approximations structured in the sense that the number of lobes in the approximation corresponds to the number number of terms retained in the expansion.
Abstract: Gaussian field expansions for circular aperture antennas are reviewed, and a method for finding optimal scales in these expansions is given, paralleling the method for rectangular antennas presented in an earlier paper. This procedure is shown to lead to approximations structured in the sense that the number of lobes in the approximation corresponds to the number of terms retained in the expansion. An example is given of the development of a cosine distribution from the aperture, through the Fresnel region, to the far field.
Patent•
17 Feb 1987
TL;DR: In this article, the halfwidth of a bright line spectrum of a luminescent line was used to measure the distance between a mask and a wafer at all times, by using the half-width of the spectrum for matching the position of the mask with that of the wafer.
Abstract: PURPOSE:To accurately measure a distance between a mask and a wafer at all times, by using the half-width of a bright line spectrum of a luminescent line for matching the position of the mask with that of the wafer CONSTITUTION:A mask 1 where prescribed linear Fresnel zone targets are formed and a wafer whereon diffraction gratings are formed are disposed opposite to each other, and then parallel beams 5 of light are projected from above the surface of the mask The beams of light diffracted by the linear Fresnel zone targets, which are converged on the wafer 2, are reflected by the diffraction gratings 4 on the wafer 2, and a spectrum of light is displayed While the displayed spectrum of light is varied in luminance and half-width according to a distance between the wafer 2 and the mask 1, the half-width can be detected irrespective of an absolute level, and therefore it can be used not only for matching the position of the mask 1 with that of the wafer 2, but also for measuring an arbitrary distance between the two
TL;DR: In this article, a method was developed using high-resolution Fresnel zone plates and synchrotron radiation by which large-scale masks (eg prepared on an X-ray transmitting substrate by optical exposure) may be reduced by projection to sub-micron feature size.
01 Jan 1987
TL;DR: In this article, an analytical description of the far-field pattern has been developed for a new type of flat lens, which is used as a quasi-optical focusing or frequency-filtering element at frequencies from 35 to 210 GHz.
Abstract: Characteristics are given for Fresnel zone plates used as quasi-optical focusing or frequency-filtering elements at frequencies from 35 to 210 GHz. An analytical description of the far-field pattern has been developed. Design data, measured results are given for a new type of flat lens.
01 Jan 1987
TL;DR: In this article, it was shown that the carbon material from which the absorbing zones are formed is semitransparent to soft x-rays and this lack of opacity results in a reduction of focusing efficiency of about a factor of ten compared to the theoretical figure.
Abstract: The resolution obtainable with an x-ray microscope which uses a Fresnel zone plate as the focusing element is primarily dependent on the width of the finest ring of the zone plate and the accuracy of the zone plate pattern (Simpson, 1984). High accuracy zone plates with outermost zone widths of only a few hundred angstroms have been made by carbon contamination e-beam lithography at Kings College London (Buckley et al., 1985). Whilst these zone plates have the finest zone widths yet produced, the fabrication of one zone plate takes ten hours and the carbon material from which the absorbing zones are formed is semitransparent to soft x-rays. This lack of opacity results in a reduction of focusing efficiency of about a factor of ten compared to the theoretical figure. The reduced efficiency increases the length of time required to form an image in a scanning x-ray microscope (Kenney et al., this volume). The time taken to form an image in an x-ray microscope should be as short as possible to minimize specimen deterioration and maximize throughput. For this reason, the replication of carbon zone plates in a higher contrast material, to improve efficiency and minimize imaging times, is highly desirable.
TL;DR: In this article, the validity of the heuristic criteria (HC) of geometric optics and of the geometric theory of diffraction (GTD), suggested in (2-7, 13, 14) and based on identifying the physical volume occupied by the ray with the Fresnel volume (FV) introduced in these papers (i.e., the envelope of the first Fresnel zone), are analyzed.
Abstract: The heuristic criteria (HC) of validity of geometric optics (GO) and of the geometric theory of diffraction (GTD), suggested in (2-7, 13, 14) and based on identifying the physical volume occupied by the ray with the Fresnel volume (FV) introduced in these papers (i.e., the envelope of the first Fresnel zone), are analyzed. Numerous examples of HC invalidity are given, as well as the reasons. In particular, HC provide an incorrect answer for all GO problems with caustics, since in these problems there always exists a ray, whose FV is nonlocal and covers the FV of other rays. The HC are shown to be unsuitable for multiple ray GTD problems, as well as for the simplest problems of diffraction of a cylindrical wave by a half-plane and of a plane wave by a curved half-plane.
TL;DR: In this article, the FZP sampled hologram is sampled with small interval at the central part and large interval at periphery, and the two-dimensional image distribution can be determined for the azimuth and range.
Abstract: The hologram of a single-point object is called a Fresnel zone plate (FZP), and the hologram of a general object is represented as a superposition of FZP's. Since a point image can be reconstructed from the FZP at a reasonable location, there can be considered an image reconstruction method based on FZP. This paper proposes the FZP sampled hologram and the corresponding two-dimensional image reconstruction method. The FZP sampled hologram is sampled with small interval at the central part and large interval at the periphery. By multiplying the phase function with the one-dimensional hologram and performing the Fourier transform, the two-dimensional image distribution can be determined for the azimuth and range. By analyzing the point-image distribution, it is seen that the azimuth resolution of 6 mrad is obtained for the millimeter wave frequency of 35 GHz and the hologram length of 25 cm. It is seen also from the distribution that there exist side peaks of −4.8 dB at an azimuth angle of ± 11 mrad apart from the peak. An experiment was made for the millimeter-wave holography with a simple object, and a satisfactory agreement with the theory was observed.
15 Jun 1987
TL;DR: In this article, a trade-off between the mechanical specifications on the scanning system and the numerical processing complexity must be made, and a suitable numerical processing is then applied for the far field reconstruction.
Abstract: A suitable numerical processing is then applied for the far field reconstruction. Several transformation schemes have been developed for different geometries of the scanning surface, the choice among them being made according to the radiating properties of the antenna under test and to the required hardware complexity. In fact a trade-off between the mechanical specifications on the scanning system and the numerical processing complexity must be made. High accuracy in the reconstructed pattern requires high accuracy in the measured amplitude and phase of the near field. The achievement of such accuracy is much more difficult for the phase measurement than for the amplitude one. In fact the probe positioning errors of the scanning system result essentialy in uncertainities on the detected phase. Furthermore, the phase measurement is more sensitive than the amplitude one to the equipment inaccuracies. In this way tight requirements are to be imposed both on the mechanical and the electrical properties of the scanning system. These problems become critical especially in the millimeter wave range, because the displacement errors are of the same order of magnitude as the wavelenght. Therefore the availability of a transformation procedure based on only amplitude near field measurements is very appealing. Some early results for the spherical Fresnel zone scanning and planar near zone scgnning have been presented in [1,2]. In the following we will discuss some results obtained for the near zone cylindrical scanning. These results can be extended also to the near zone spherical