Showing papers on "Fresnel zone published in 2013"

Single shot high resolution digital holography

Abstract: We demonstrate a novel computational method for high resolution image recovery from a single digital hologram frame. The complex object field is obtained from the recorded hologram by solving a constrained optimization problem. This approach which is unlike the physical hologram replay process is shown to provide high quality image recovery even when the dc and the cross terms in the hologram overlap in the Fourier domain. Experimental results are shown for a Fresnel zone hologram of a resolution chart, intentionally recorded with a small off-axis reference beam angle. Excellent image recovery is observed without the presence of dc or twin image terms and with minimal speckle noise.

Demonstration of focus-tunable diffractive Moiré-lenses.

Abstract: In an earlier publication [Appl. Opt. 47, 3722 (2008)] we suggested an adaptive optical lens, which consists of two cascaded diffractive optical elements (DOEs). Due to the Moire-effect the combined optical element acts as a Fresnel zone lens with a refractive power that can be continuously adjusted by a mutual rotation of the two stacked DOEs. Here we present an experimental realization of this concept. Four designs of these Moire-DOEs (MDOEs) were fabricated in thin (0.7 mm) glass slides by lithography and subsequent etching. Each element was realized as a 16 phase level DOE designed for 633 nm illumination. Our experimental investigation shows that the Moire-lenses have a broad adjustable refractive power range with a high efficiency, which allows one to use them for flexible beam steering and for imaging applications.

Switchable Fresnel lens based on micropatterned alignment

Abstract: In this Letter we disclose a method to fabricate a liquid crystal (LC) Fresnel zone lens (FZL) with higher efficiency The LCFZL, based on alternate twisted nematic (TN) and planar aligned (PA) regions, has been prepared by means of a two-step photo-alignment process The FZL profile for both optical regimes, ie, in TN and PA alignment domains, generates the same focal length (f) Thus, the proposed LCFZL manifests double light intensity at the focal point and therefore offers double the efficiency of existing FZLs Moreover, because of lower driving voltage and fast response, these elements could find application in many modern devices

Rapid prototyping of Fresnel zone plates via direct Ga(+) ion beam lithography for high-resolution X-ray imaging.

Abstract: A significant challenge to the wide utilization of X-ray microscopy lies in the difficulty in fabricating adequate high-resolution optics. To date, electron beam lithography has been the dominant technique for the fabrication of diffractive focusing optics called Fresnel zone plates (FZP), even though this preparation method is usually very complicated and is composed of many fabrication steps. In this work, we demonstrate an alternative method that allows the direct, simple, and fast fabrication of FZPs using focused Ga+ beam lithography practically, in a single step. This method enabled us to prepare a high-resolution FZP in less than 13 min. The performance of the FZP was evaluated in a scanning transmission soft X-ray microscope where nanostructures as small as sub-29 nm in width were clearly resolved, with an ultimate cutoff resolution of 24.25 nm, demonstrating the highest first-order resolution for any FZP fabricated by the ion beam lithography technique. This rapid and simple fabrication scheme il...

Full field tabletop EUV coherent diffractive imaging in a transmission geometry

Abstract: We demonstrate the first general tabletop EUV coherent microscope that can image extended, non-isolated, non-periodic, objects. By implementing keyhole coherent diffractive imaging with curved mirrors and a tabletop high harmonic source, we achieve improved efficiency of the imaging system as well as more uniform illumination at the sample, when compared with what is possible using Fresnel zone plates. Moreover, we show that the unscattered light from a semi-transparent sample can be used as a holographic reference wave, allowing quantitative information about the thickness of the sample to be extracted from the retrieved image. Finally, we show that excellent tabletop image fidelity is achieved by comparing the retrieved images with scanning electron and atomic force microscopy images, and show superior capabilities in some cases.

Ion beam lithography for Fresnel zone plates in X-ray microscopy.

Abstract: Fresnel Zone Plates (FZP) are to date very successful focusing optics for X-rays. Established methods of fabrication are rather complex and based on electron beam lithography (EBL). Here, we show that ion beam lithography (IBL) may advantageously simplify their preparation. A FZP operable from the extreme UV to the limit of the hard X-ray was prepared and tested from 450 eV to 1500 eV. The trapezoidal profile of the FZP favorably activates its 2nd order focus. The FZP with an outermost zone width of 100 nm allows the visualization of features down to 61, 31 and 21 nm in the 1st, 2nd and 3rd order focus respectively. Measured efficiencies in the 1st and 2nd order of diffraction reach the theoretical predictions.

Modulation of a super-Gaussian optical needle with high-NA Fresnel zone plate.

Abstract: A high NA Fresnel zone plate (FZP) is studied using vectorial angular spectrum theory for realizing the sharpest possible super-Gaussian optical needle with purely longitudinal polarization illuminated by a radially polarized vector beam. Strong dispersion of the FZP results in a light field resembling a super-Gaussian optical needle by selecting an optimal FZP structural wavelength relative to the illumination wavelength and inserting a narrow comb window function into the center-shaded FZP. A 25 μm long longitudinally polarized flattop optical needle with a transverse beam width of about 0.366λ is focused at a distance of 222.5 μm away from a binary amplitude 3.46 mm diameter FZP for a 532.4 nm wavelength in free space.

Angular spectrum simulation of X-ray focusing by Fresnel zone plates

Abstract: A computing simulation routine to model any type of circularly symmetric diffractive X-ray element has been implemented. The wavefield transmitted beyond the diffractive structures is numerically computed by the angular spectrum propagation method to an arbitrary propagation distance. Cylindrical symmetry is exploited to reduce the computation and memory requirements while preserving the accuracy of the numerical calculation through a quasi-discrete Hankel transform algorithm, an approach described by Guizar-Sicairos & Gutierrez-Vega [J. Opt. Soc. Am. A, (2004), 21, 53–58]. In particular, the code has been used to investigate the requirements for the stacking of two high-resolution Fresnel zone plates with an outermost zone width of 20 nm.

A Deterministic Round Earth Loss Model for Open-Sea Radio Propagation

Abstract: This paper proposes a deterministic path-loss model for the open-sea environment. The model accounts for different effects including effective reflection, divergence, and diffraction due to rough sea and earth curvature. The model results show excellent agreement with experimental results from our recent measurement campaign, which investigated propagation at 2 GHz with a maximum distance of 45 km. Channel parameters like mean-square surface slope and standard deviation of surface height are evaluated, from which it can be concluded that the shadowing and scattering effects on the reflection ray will influence the fading amplitude within the distance of 0.6 First Fresnel Zone clearance.

Nonuniform sampled scalar diffraction calculation using nonuniform fast Fourier transform

Abstract: Scalar diffraction calculations, such as the angular spectrum method (ASM) and Fresnel diffraction, are widely used in the research fields of optics, x rays, electron beams, and ultrasonics. It is possible to accelerate the calculation using fast Fourier transform (FFT); unfortunately, acceleration of the calculation of nonuniform sampled planes is limited due to the property of the FFT that imposes uniform sampling. In addition, it gives rise to wasteful sampling data if we calculate a plane having locally low and high spatial frequencies. In this Letter, we developed nonuniform sampled ASM and Fresnel diffraction to improve the problem using the nonuniform FFT.

Focusing and imaging of a virtual all-optical tunable terahertz Fresnel zone plate.

Abstract: A virtual all-optical tunable terahertz Fresnel zone plate is achieved utilizing the localized distribution of the transient electron plasma on a silicon wafer. Its focusing and imaging performance are experimentally demonstrated. Experimental results show that the effect of the virtual zone plate is the same as an actual one. Adjusting the spatial pattern of the electron plasma, the central wavelength and the focal length of the virtual zone plate can be all-optically dynamically steered. The research is a significant step to the development of tunable optical imaging elements.

Tabletop single-shot extreme ultraviolet Fourier transform holography of an extended object.

Abstract: We demonstrate single and multi-shot Fourier transform holography with the use of a tabletop extreme ultraviolet laser. The reference wave was produced by a Fresnel zone plate with a central opening that allowed the incident beam to illuminate the sample directly. The high reference wave intensity allows for larger objects to be imaged compared to mask-based lensless Fourier transform holography techniques. We obtain a spatial resolution of 169 nm from a single laser pulse and a resolution of 128 nm from an accumulation of 20 laser pulses for an object ~11x11μm2 in size. This experiment utilized a tabletop extreme ultraviolet laser that produces a highly coherent ~1.2 ns laser pulse at 46.9 nm wavelength.

Efficient focusing of 8 keV X-rays with multilayer Fresnel zone plates fabricated by atomic layer deposition and focused ion beam milling

Abstract: Fresnel zone plates (FZPs) recently showed significant improvement by focusing soft X-rays down to ∼10 nm. In contrast to soft X-rays, generally a very high aspect ratio FZP is needed for efficient focusing of hard X-rays. Therefore, FZPs had limited success in the hard X-ray range owing to difficulties of manufacturing high-aspect-ratio zone plates using conventional techniques. Here, employing a method of fabrication based on atomic layer deposition (ALD) and focused ion beam (FIB) milling, FZPs with very high aspect ratios were prepared. Such multilayer FZPs with outermost zone widths of 10 and 35 nm and aspect ratios of up to 243 were tested for their focusing properties at 8 keV and shown to focus hard X-rays efficiently. This success was enabled by the outstanding layer quality thanks to ALD. Via the use of FIB for slicing the multilayer structures, desired aspect ratios could be obtained by precisely controlling the thickness. Experimental diffraction efficiencies of multilayer FZPs fabricated via this combination reached up to 15.58% at 8 keV. In addition, scanning transmission X-ray microscopy experiments at 1.5 keV were carried out using one of the multilayer FZPs and resolved a 60 nm feature size. Finally, the prospective of different material combinations with various outermost zone widths at 8 and 17 keV is discussed in the light of the coupled wave theory and the thin-grating approximation. Al2O3/Ir is outlined as a promising future material candidate for extremely high resolution with a theoretical efficiency of more than 20% for as small an outermost zone width as 10 nm at 17 keV.

Accelerating and Abruptly-Autofocusing Beam Waves in the Fresnel Zone of Antenna Arrays

Abstract: We introduce the concept of spatially accelerating (curved) beam waves in the Fresnel region of properly designed antenna arrays. These are transversely localized EM waves that propagate in free space in a diffraction-resisting manner, while at the same time laterally shifting their amplitude pattern along a curved trajectory. The proposed beams are the radiowave analogue of Airy and related accelerating optical waves, which, in contrast to their optical counterparts, are produced by the interference of discrete radiating elements rather than by the evolution of a continuous wavefront. Two dyadic array configurations are proposed comprising 2D line antennas: linear phased arrays with a power-law phase variation and curved power-law arrays with in-phase radiating elements. Through analysis and numerical simulations, the formation of broadside accelerating beams with power-law trajectories is studied versus the array parameters. Furthermore, the abrupt autofocusing effect, that occurs when beams of this kind interfere with opposite acceleration, is investigated. The concept and the related antenna setups can be of use in radar and wireless communications applications.

Depth resolution enhancement in double-detection optical scanning holography

Abstract: We propose an optical scanning holography system with enhanced axial resolution using two detections at different depths. By scanning the object twice, we can obtain two different sets of Fresnel zone plates to sample the same object, which in turn provides more information for the sectional image reconstruction process. We develop the computation algorithm that makes use of such information, solving a constrained optimization problem using the conjugate gradient method. Simulation results show that this method can achieve a depth resolution up to 1 μm.

Characterization and correction of spherical aberration due to glass substrate in the design and fabrication of Fresnel zone lenses

Abstract: As with a conventional lens, a Fresnel zone lens (FZL) can be used to image objects at infinity or nearby In the latter case, the FZL converts a diverging spherical wavefront into a converging spherical wavefront The glass substrate on which the FZL is fabricated introduces spherical aberration resulting in a shift of the image plane and blurring of the image Two novel schemes for correction of this spherical aberration are proposed and studied in this paper To demonstrate them, FZLs are designed with and without aberration correction They are fabricated using electron beam direct writing The devices are evaluated and the accuracy of the proposed aberration correction schemes is validated

Multiresolution imaging of mantle reflectivity structure using SS and P′P′ precursors

Abstract: SUMMARY Knowledge of the mantle reflectivity structure is highly dependent on our ability to efficiently extract, and properly interpret, small seismic arrivals. Among the various data types and techniques, long-period SS/PP precursors and high-frequency receiver functions are routinely utilized to increase the confidence of the recovered mantle stratifications at distinct spatial scales. However, low resolution and a complex Fresnel zone are glaring weaknesses of SS precursors, while over-reliance on receiver distribution is a formidable challenge for the analysis of converted waves from oceanic regions. A promising high frequency alternative to receiver functions is PPprecursors, which are capable of resolving mantle structures at verticalandlateralresolutionof ∼5and ∼200km,respectively,owingtotheirspectralcontent, shallow angle of incidence and near-symmetric Fresnel zones. This study presents a novel processing method for both SS (or PP) and PPprecursors based on deconvolution, stacking, Radon transform and depth migration. A suite of synthetic tests is performed to quantify the fidelity and stability of this method under different data conditions. Our multiresolution survey of the mantle at targeted areas near Nazca-South America subduction zone reveal both olivine and garnet related transitions at depths below 400km. We attribute a depressed 660 to thermal variations, whereas compositional variations atop the upper-mantle transition zone are needed to explain the diminished or highly complex reflected/scattered signals from the 410km discontinuity. We also observe prominent PPreflections within the transition zone, and the anomalous amplitudes near the plate boundary zone indicate a sharp (∼10km thick) transition that likely resonates with the frequency content of PPprecursors. The migration of SS precursors in this study shows no evidence of split 660 reflections, but potential majorite-ilmenite (590-640km) and ilmenite-perovskite transitions (740-750km) areidentifiedbasedonsimilarlyprocessedhigh-frequencyPPprecursors.Additionalfindings of severely scattered energy in the lithosphere and distinct lower mantle reflections at ∼800km could be potentially important but require further verifications. Overall, our improved imaging methods and the strong sensitivity of PPprecursors to the existence, depth, sharpness and strengthofreflective structuresoffersignificant futurepromisefortheunderstanding ofmantle mineralogy and dynamics.

X-ray wavefront characterization of a Fresnel zone plate using a two-dimensional grating interferometer

Abstract: The x-ray wavefront downstream of a Fresnel zone plate (FZP) was characterized using a two-dimensional grating interferometer. Transverse wavefront slope maps, measured using a raster phase-stepping scan, allowed accurate phase reconstruction of the x-ray beam. Wavefront measurements revealed that the wavefront error is very sensitive to the input beam entering the FZP. A small stack of one-dimensional compound refractive lenses was used to introduce astigmatism in the probing x-ray beam to investigate the contribution of the incoming beam in contrast to the optical aberrations. Experimental data were shown to be consistent with theoretical calculations.

Multilayer Laue Lenses with Focal Length of 10 mm

Abstract: Multilayer laue lenses are diffractive optics with a high potential for producing X-ray foci in the order of 10 nm or even below. Particularly for hard X-rays (E > 6 keV) these optics promise better resolution and higher efficiencies than currently available Fresnel zone plates. Magnetron sputter deposition has been used for the fabrication of multilayer laue lenses using the layer materials MoSi2 and Si. The lens design has been defined to get focal length in the order of 10 mm. One of the lenses with an aperture of about 20 μm has been used as focusing optics in the nanoprobe beamline P06 at PETRA III. Ptychography has been applied to characterize the caustic of the focused beam and to determine the size of the X-ray focus. A spot size of about 39 nm could be obtained with a photon energy of 21 keV and a focal length of 9.9 mm.

Estimation of the Radio Refractivity Gradient From Diffraction Loss Measurements

Abstract: The aim of this paper is to show that the gradient of the vertical radio refractivity profile of air near the ground can be estimated from measurements of electromagnetic wave strength. Diffraction can be used as the basic physical principle for non-line-of-sight radio links, where an obstacle covers some parts of the Fresnel zones, and therefore, the strength of electromagnetic wave is proportional to the ratio of coverage. The method, which is simple and easy to implement, is verified by measured data, and comparisons with meteorological measurements are presented.

Seismic Imaging of the Waltham Canyon Fault, California: Comparison of Ray‐Theoretical and Fresnel Volume Prestack Depth Migration

Abstract: Near‐vertical faults can be imaged using reflected refractions identified in controlled‐source seismic data. Often theses phases are observed on a few neighboring shot or receiver gathers, resulting in a low‐fold data set. Imaging can be carried out with Kirchhoff prestack depth migration in which migration noise is suppressed by constructive stacking of large amounts of multifold data. Fresnel volume migration can be used for low‐fold data without severe migration noise, as the smearing along isochrones is limited to the first Fresnel zone around the reflection point. We developed a modified Fresnel volume migration technique to enhance imaging of steep faults and to suppress noise and undesired coherent phases. The modifications include target‐oriented filters to separate reflected refractions from steep‐dipping faults and reflections with hyperbolic moveout. Undesired phases like multiple reflections, mode conversions, direct P and S waves, and surface waves are suppressed by these filters. As an alternative approach, we developed a new prestack line‐drawing migration method, which can be considered as a proxy to an infinite frequency approximation of the Fresnel volume migration. The line‐drawing migration is not considering waveform information but requires significantly shorter computational time. Target‐oriented filters were extended by dip filters in the line‐drawing migration method. The migration methods were tested with synthetic data and applied to real data from the Waltham Canyon fault, California. The two techniques are applied best in combination, to design filters and to generate complementary images of steep faults.

Single-focus x-ray zone plate by stagger arrangement of zones.

Abstract: In this paper a novel single-focus x-ray zone plate is proposed by stagger arrangement of zones, which would be technically easier to manufacture. Theoretical design shows that the transmission function of the plate is a cosine function of radius, like that of a Gabor zone plate. Numerical simulation at the wavelength of 0.275 nm shows that the plate is of single-order focusing, with spatial resolution limit the same as that of the corresponding conventional zone plate, and the first-order diffraction efficiency of 11.5%. The plate can also work for single-order focusing at other x-ray wavelengths.

The Beynon Gabor zone plate: a new tool for de Broglie matter waves and hard X-rays? An off axis and focus intensity investigation

Abstract: Optical elements based on Fresnel zones are used in a range of applications, from X-ray telescopy to microscopy and recently also in the manipulation of de Broglie matter waves. In 1992 Beynon and co-workers presented a binary Gabor type zone plate (henceforth referred to as the Beynon Gabor zone plate). Because this zone plate has no higher order foci, it is in principle a very attractive candidate for focusing of de Broglie matter waves and in some cases X-rays. So far the Beynon Gabor zone plate investigations presented in the literature have concentrated on the intensity distribution along the optical axis and in the focal plane. Here we present a detailed numerical investigation of the Beynon Gabor zone plate, including an investigation of the off-optical axis, off focal plane intensity distribution for point source illumination. We show that at integer fractions of the focal length, the beam becomes nearly toroidal (doughnut-shaped). This offers potentially interesting new possibilities for de Broglie matter wave and X-ray optics, for example in STED-like applications. We further show that the increased intensity at the focal point predicted in the literature for a particular Beynon Gabor zone plate transmission function configuration is an artifact due to the lack of sampling nodes. We support our calculations with experimental measurements in the visible light range, using a Beynon Gabor zone plate fabricated with electron beam lithography.

Near-field distribution and propagation of scattering resonances in Vogel spiral arrays of dielectric nanopillars

Abstract: In this work, we employ scanning near-field optical microscopy, full-vector finite difference time domain numerical simulations and fractional Fourier transformation to investigate the near-field and propagation behavior of the electromagnetic energy scattered at 1.56µm by dielectric arrays of silicon nitride nanopillars with chiral 1-Vogel spiral geometry. In particular, we experimentally study the spatial evolution of scattered radiation and demonstrate near-field coupling between adjacent nanopillars along the parastichies arms. Moreover, by measuring the spatial distribution of the scattered radiation at different heights from the array plane, we demonstrate a characteristic rotation of the scattered field pattern consistent with net transfer of orbital angular momentum in the Fresnel zone, within a few micrometers from the plane of the array. Our experimental results agree with the simulations we performed and may be of interest to nanophotonics applications.

Simultaneous Inversion for Velocity and Reflector Geometry Using Multi-phase Fresnel Volume Rays

Abstract: Traditional ray tomography methods based on the high frequency assumption are sometimes unable to obtain a high resolution tomographic picture due to a deficient coverage of ray paths in real applications, especially for low velocity anomalous regions. In contrast, finite-frequency ray theory is more suitable for handling real seismic propagation problems because the travel time depends not only on the velocity distribution along a central ray (or traditional geometric ray), but also on the velocity values within a region (referred to as the first Fresnel Volume) which incorporates the central ray. In this study, we develop an algorithm to calculate multi-phase Fresnel Volume finite-frequency rays, and then present an inversion method to simultaneous invert for both velocity and reflector geometry by using these multi-phase Fresnel Volume finite-frequency rays. Using synthetic data examples, we compare the reconstructions of the velocity field and the reflector orientation using the Fresnel Volume ray tomographic methods and the traditional ray tomography approach. Results show that the former is advantageous over the latter, especially when the ray density is relatively low. An additional benefit of the Fresnel Volume finite-frequency ray tomographic method is that it can start with a low frequency to capture the coarse velocity structure, thereby mitigating the local minimum trapping problem, and then be tuned to a high frequency for delineating the fine velocity structure.

An asymmetric optical vortex generated by a spiral refractive plate

Abstract: Using a revised Kirchhoff diffraction integral and the finite-difference time-domain method we show that an optical vortex generated by a refractive spiral plate with a relief step has an asymmetric profile. The annular diffraction pattern in the optical vortex beam cross-section is found to be disturbed not only for near-field diffraction but also for the Fresnel zone. For a spiral phase plate with topological charge 3, fabricated on a resist, optical vortex asymmetry has been shown experimentally by near-field scanning optical microscopy.

Fresnel diffraction patterns as accelerating beams

Abstract: We demonstrate that beams originating from Fresnel diffraction patterns are self-accelerating in free space. In addition to accelerating and self-healing, they also exhibit parabolic deceleration property, which is in stark contrast to other accelerating beams. We find that the trajectory of Fresnel paraxial accelerating beams is similar to that of nonparaxial Weber beams. Decelerating and accelerating regions are separated by a critical propagation distance, at which no acceleration is present. During deceleration, the Fresnel diffraction beams undergo self-smoothing, in which oscillations of the diffracted waves gradually focus and smooth out at the critical distance.

Linear fresnel optic for reducing angular spread of light from led array

Abstract: A light source may comprise a cylindrical lens, for example a cylindrical Fresnel lens, a linear array of light-emitting elements, the linear array aligned with and emitting light through the cylindrical Fresnel lens, wherein the cylindrical Fresnel lens reduces the angular spread of light in a widthwise axis of the linear array, the linear array spanning a lens length.