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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Time‐Lapse Image Classification Using a Diffractive Neural Network

Diffractive deep neural networks (D 2 NNs), comprised of spatially engineered passive surfaces, collectively process optical input information at the speed of light propagation through a thin diffractive volume, without any external computing power. Diffractive networks were demonstrated to achieve all‐optical object classification and perform universal linear transformations. Herein, a “time‐lapse” image classification scheme using a diffractive network is demonstrated for the first time, significantly advancing its classification accuracy and generalization performance on complex input objects by using the lateral movements of the input objects and/or the diffractive network, relative to each other. In a different context, such relative movements of the objects and/or the camera are routinely being used for image super‐resolution applications; inspired by their success, a time‐lapse diffractive network is designed to benefit from the complementary information content created by controlled or random lateral shifts. The design space and performance limits of time‐lapse diffractive networks are numerically explored, revealing a blind testing accuracy of 62.03% on the optical classification of objects from the CIFAR‐10 dataset. This constitutes the highest inference accuracy achieved so far using a single diffractive network on the CIFAR‐10 dataset. Time‐lapse diffractive networks will be broadly useful for the spatiotemporal analysis of input signals using all‐optical processors.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Artifact identification in X-ray diffraction data using machine learning methods

In situ synchrotron high-energy X-ray powder diffraction (XRD) is highly utilized by researchers to analyze the crystallographic structures of materials in functional devices ( e.g. battery materials) or in complex sample environments ( e.g. diamond anvil cells or syntheses reactors). An atomic structure of a material can be identified by its diffraction pattern along with a detailed analysis of the Rietveld refinement which yields rich information on the structure and the material, such as crystallite size, microstrain and defects. For in situ experiments, a series of XRD images is usually collected on the same sample under different conditions ( e.g. adiabatic conditions) yielding different states of matter, or is simply collected continuously as a function of time to track the change of a sample during a chemical or physical process. In situ experiments are usually performed with area detectors and collect images composed of diffraction patterns. For an ideal powder, the diffraction pattern should be a series of concentric Debye–Scherrer rings with evenly distributed intensities in each ring. For a realistic sample, one may observe different characteristics other than the typical ring pattern, such as textures or preferred orientations and single-crystal diffraction spots. Textures or preferred orientations usually have several parts of a ring that are more intense than the rest, whereas single-crystal diffraction spots are localized intense spots owing to diffraction of large crystals, typically >10 µm. In this work, an investigation of machine learning methods is presented for fast and reliable identification and separation of the single-crystal diffraction spots in XRD images. The exclusion of artifacts during an XRD image integration process allows a precise analysis of the powder diffraction rings of interest. When it is trained with small subsets of highly diverse datasets, the gradient boosting method can consistently produce high-accuracy results. The method dramatically decreases the amount of time spent identifying and separating single-crystal diffraction spots in comparison with the conventional method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1974

The dyadic diffraction coefficient for a curved edge

A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edge formed by perfectly conducting curved or plane surfaces is obtained. This diffraction coefficent remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. The method is on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresnel integrals, which ensure that the total field is continuous at shadow and reflection boundaries. The diffraction coefficients have the same form for the different types of edge illumination; only the arguments of the Fresnel integrals are different. Since diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved edge.

Kouyoumjian, R. G.↗
NASA NTRS2005

Diffraction-based optical correlator

Method and system for wavelength-based processing of a light beam. A light beam, produced at a chemical or physical reaction site and having at least first and second wavelengths, ?1 and ?2, is received and diffracted at a first diffraction grating to provide first and second diffracted beams, which are received and analyzed in terms of wavelength and/or time at two spaced apart light detectors. In a second embodiment, light from first and second sources is diffracted and compared in terms of wavelength and/or time to determine if the two beams arise from the same source. In a third embodiment, a light beam is split and diffracted and passed through first and second environments to study differential effects. In a fourth embodiment, diffracted light beam components, having first and second wavelengths, are received sequentially at a reaction site to determine whether a specified reaction is promoted, based on order of receipt of the beams. In a fifth embodiment, a cylindrically shaped diffraction grating (uniform or chirped) is rotated and translated to provide a sequence of diffracted beams with different wavelengths. In a sixth embodiment, incident light, representing one or more symbols, is successively diffracted from first and second diffraction gratings and is received at different light detectors, depending upon the wavelengths present in the incident light.

Spremo, Stevan M.↗
DOE OSTI2022

Computing diffraction patterns of microstructures from phase-field simulations

The diffraction pattern of a material contains information not only on the crystal structures of its constituting phases, but also on its mesoscale spatial distributions of phases, grains, and ferroelastic, ferroelectric, and ferromagnetic domains. While diffraction patterns from experiments such as X-ray diffraction are presented in the reciprocal or Fourier space, mesoscale microstructure models such as the phase-field method naturally produce real-space images of spatial distribution of chemical composition, structural, and ferroic domains. Although one could rather readily compute the Fourier amplitudes of chemical and structural domain distributions generated by mesoscale simulations, they only contain information about the length scale and alignment of the real-space chemical and structure domains. Therefore, a direct comparison between diffraction experiments and mesoscale microstructure simulations is not possible. Here, we develop a theoretical approach to directly compute the crystal diffraction patterns of microstructures predicted by phase-field simulations. In particular, we consider five representative examples of microstructure patterns involving purely compositional domains, a single pair of tetragonal twin structures, multiple twin variants in a hexagonal system, ferroelectric polar vortices, and polycrystalline grains. The results are compared with previous experimental observations as well as X-ray diffraction experiments performed in the present study. Furthermore, the theoretical framework allows one to directly connect material microstructures and diffraction patterns predicted from phase-field simulations and the corresponding diffraction patterns from experiments, and thus providing guidance to experimental diffraction characterization and interpretation of microstructures.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Beamline K11 DIAD: a new instrument for dual imaging and diffraction at Diamond Light Source

The Dual Imaging and Diffraction (DIAD) beamline at Diamond Light Source is a new dual-beam instrument for full-field imaging/tomography and powder diffraction. This instrument provides the user community with the capability to dynamically image 2D and 3D complex structures and perform phase identification and/or strain mapping using micro-diffraction. The aim is to enable in situ and in operando experiments that require spatially correlated results from both techniques, by providing measurements from the same specimen location quasi-simultaneously. Using an unusual optical layout, DIAD has two independent beams originating from one source that operate in the medium energy range (7–38 keV) and are combined at one sample position. Here, either radiography or tomography can be performed using monochromatic or pink beam, with a 1.4 mm × 1.2 mm field of view and a feature resolution of 1.2 µm. Micro-diffraction is possible with a variable beam size between 13 µm × 4 µm and 50 µm × 50 µm. One key functionality of the beamline is image-guided diffraction, a setup in which the micro-diffraction beam can be scanned over the complete area of the imaging field-of-view. This moving beam setup enables the collection of location-specific information about the phase composition and/or strains at any given position within the image/tomography field of view. The dual beam design allows fast switching between imaging and diffraction mode without the need of complicated and time-consuming mode switches. Real-time selection of areas of interest for diffraction measurements as well as the simultaneous collection of both imaging and diffraction data of (irreversible) in situ and in operando experiments are possible.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Refinement for single-nanoparticle structure determination from low-quality single-shot coherent diffraction data

With the emergence of X-ray free-electron lasers, it is possible to investigate the structure of nanoscale samples by employing coherent diffractive imaging in the X-ray spectral regime. In this work, we developed a refinement method for structure reconstruction applicable to low-quality coherent diffraction data. The method is based on the gradient search method and considers the missing region of a diffraction pattern and the small number of detected photons. We introduced an initial estimate of the structure in the method to improve the convergence. The present method is applied to an experimental diffraction pattern of an Xe cluster obtained in an X-ray scattering experiment at the SPring-8 Angstrom Compact free-electron LAser (SACLA) facility. It is found that the electron density is successfully reconstructed from the diffraction pattern with a large missing region, with a good initial estimate of the structure. The diffraction pattern calculated from the reconstructed electron density reproduced the observed diffraction pattern well, including the characteristic intensity modulation in each ring. Our refinement method enables structure reconstruction from diffraction patterns under difficulties such as missing areas and low diffraction intensity, and it is potentially applicable to the structure determination of samples that have low scattering power.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Resonant Tender X-ray Diffraction for Disclosing the Molecular Packing of Paracrystalline Conjugated Polymer Films

The performance of optoelectronic devices based on conjugated polymers is critically dependent upon molecular packing; however, the paracrystalline nature of these materials limits the amount of information that can be extracted from conventional X-ray diffraction. Resonant diffraction (also known as anomalous diffraction) occurs when the X-ray energy used coincides with an X-ray absorption edge in one of the constituent elements in the sample. The rapid changes in diffraction intensity that occur as the X-ray energy is varied across an absorption edge provide additional information that is lost in a conventional nonresonant experiment. Taking advantage of the fact that many conjugated polymers contain sulfur as heteroatoms, here we reveal pronounced resonant diffraction effects at the sulfur K-edge with a particular focus on the well-studied electron transporting polymer poly([N,N'-bis(2-octyldodecyl)-naphthalene-1,4,5,8-bis(dicarboximide)-2,6-diyl]-alt-5,5'-(2,2'-bithiophene)), P(NDI2OD-T2). The observed behavior is found to be consistent with the theory of resonant diffraction, and by simulating the energy-dependent peak intensity based on proposed crystal structures for P(NDI2OD-T2), we find that resonant diffraction can discriminate between different crystalline packing structures. The utilization of resonant diffraction opens up a new way to unlock important microstructural information about conjugated polymers for which only a handful of diffraction peaks are typically available.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Universal linear intensity transformations using spatially incoherent diffractive processors

Abstract Under spatially coherent light, a diffractive optical network composed of structured surfaces can be designed to perform any arbitrary complex-valued linear transformation between its input and output fields-of-view (FOVs) if the total number ( N ) of optimizable phase-only diffractive features is ≥~2 N i N o , where N i and N o refer to the number of useful pixels at the input and the output FOVs, respectively. Here we report the design of a spatially incoherent diffractive optical processor that can approximate any arbitrary linear transformation in time-averaged intensity between its input and output FOVs. Under spatially incoherent monochromatic light, the spatially varying intensity point spread function ( H ) of a diffractive network, corresponding to a given, arbitrarily-selected linear intensity transformation, can be written as H ( m , n ; m ′, n ′) = | h ( m , n ; m ′, n ′)| 2 , where h is the spatially coherent point spread function of the same diffractive network, and ( m , n ) and ( m ′, n ′) define the coordinates of the output and input FOVs, respectively. Using numerical simulations and deep learning, supervised through examples of input-output profiles, we demonstrate that a spatially incoherent diffractive network can be trained to all-optically perform any arbitrary linear intensity transformation between its input and output if N ≥ ~2 N i N o . We also report the design of spatially incoherent diffractive networks for linear processing of intensity information at multiple illumination wavelengths, operating simultaneously. Finally, we numerically demonstrate a diffractive network design that performs all-optical classification of handwritten digits under spatially incoherent illumination, achieving a test accuracy of >95%. Spatially incoherent diffractive networks will be broadly useful for designing all-optical visual processors that can work under natural light.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Advances in the electron diffraction characterization of atomic clusters and nanoparticles

Nanoparticles and metallic clusters continue to make a remarkable impact on novel and emerging technologies. In recent years, there have been impressive advances in the controlled synthesis of clusters and their advanced characterization. One of the most common ways to determine the structures of nanoparticles and clusters is by means of X-ray diffraction methods. However, this requires the clusters to crystallize in a similar way to those used in protein studies, which is not possible in many cases. Novel methods based on electron diffraction have been used to efficiently study individual nanoparticles and clusters and these can overcome the obstacles commonly encountered during X-ray diffraction methods without the need for large crystals. These novel methodologies have improved with advances in electron microscopy instrumentation and electron detection. Here, we review advanced methodologies for characterizing metallic nanoparticles and clusters using a variety of electron diffraction procedures. These include selected area electron diffraction, nanobeam diffraction, coherent electron diffraction, precession electron diffraction, scanning transmission electron microcopy diffraction, and high throughput data analytics, which leverage deep learning to reduce the propensity for data errors and translate nanometer and atomic scale measurements into material data.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
NASA NTRS1977

Measuring concave diffraction grating efficiencies at grazing incidence

The efficiency of a concave diffraction grating in a given order is obtained by measuring the intensities of the diffracted and incident beams and taking their ratio. A valid measurement requires that both the incident and diffracted beams be collected by the detector. At grazing incidence, however, the diffracted beam may spread beyond the detector due to aberrations. In addition, the diffracted beams of consecutive orders may overlap so that unambiguous efficiency measurements cannot be made. The effect of aberrations on efficiency measurements has been studied, using ray tracing, for the geometry of the measuring instrument in use at the Naval Research Laboratory. This instrument is attached to a VUV monochromator which furnishes a diverging beam. The main effect of aberrations for this instrument is a spread of the diffracted beam in the direction of dispersion. The width of the diffracted beam is wavelength dependent and is minimal at the horizontal focus, spreading to longer and shorter wavelengths. Reducing the divergence of the incident beam reduces the spread but, for small radius gratings, not always sufficiently so that the entire diffracted beam can be collected by the detector. The distance from the detector to the grating can also be adjusted to aid in collecting all the diffracted beam.

Hunter, W. R.↗
NASA NTRS1998

Stratified Diffractive Optic Approach for Creating High Efficiency Gratings

Gratings with high efficiency in a single diffracted order can be realized with both volume holographic and diffractive optical elements. However, each method has limitations that restrict the applications in which they can be used. For example, high efficiency volume holographic gratings require an appropriate combination of thickness and permittivity modulation throughout the bulk of the material. Possible combinations of those two characteristics are limited by properties of currently available materials, thus restricting the range of applications for volume holographic gratings. Efficiency of a diffractive optic grating is dependent on its approximation of an ideal analog profile using discrete features. The size of constituent features and, consequently, the number that can be used within a required grating period restricts the applications in which diffractive optic gratings can be used. These limitations imply that there are applications which cannot be addressed by either technology. In this paper we propose to address a number of applications in this category with a new method of creating high efficiency gratings which we call stratified diffractive optic gratings. In this approach diffractive optic techniques are used to create an optical structure that emulates volume grating behavior. To illustrate the stratified diffractive optic grating concept we consider a specific application, a scanner for a space-based coherent wind lidar, with requirements that would be difficult to meet by either volume holographic or diffractive optic methods. The lidar instrument design specifies a transmissive scanner element with the input beam normally incident and the exiting beam deflected at a fixed angle from the optical axis. The element will be rotated about the optical axis to produce a conical scan pattern. The wavelength of the incident beam is 2.06 microns and the required deflection angle is 30 degrees, implying a grating period of approximately 4 microns. Creating a high efficiency volume grating with these parameters would require a grating thickness that cannot be attained with current photosensitive materials. For a diffractive optic grating, the number of binary steps necessary to produce high efficiency combined with the grating period requires feature sizes and alignment tolerances that are also unattainable with current techniques. Rotation of the grating and integration into a space-based lidar system impose the additional requirements that it be insensitive to polarization orientation, that its mass be minimized and that it be able to withstand launch and space environments.

Chambers, Diana M.↗
NASA NTRS2000

Phase-Shifting Liquid Crystal Point-Diffraction Interferometry

Microgravity fluid physics experiments frequently measure concentration and temperature. Interferometers such as the Twyman Green illustrated have performed full-field measurement of these quantities. As with most such devices, this interferometer uses a reference path that is not common with the path through the test section. Recombination of the test and reference wavefronts produces interference fringes. Unfortunately, in order to obtain stable fringes, the alignment of both the test and reference paths must be maintained to within a fraction of the wavelength of the light being used for the measurement. Otherwise, the fringes will shift and may disappear. Because these interferometers are extremely sensitive to bumping, jarring and transmitted vibration, they are typically mounted on optical isolation tables. Schlieren deflectometers or the more recent Shack-Hartmann wavefront sensors also measure concentration and temperature in laboratory fluid flows. Ray optics describe the operation of both devices. In a schlieren system, an expanded, collimated beam passes through a test section where refractive index gradients deflect rays. A lens focuses the beam to a filter placed in the rear focal plane of the decollimating lens. In a quantitative color schlieren system, gradients in the index of refraction appear as colors in the field of view due to the action of the color filter. Since sensitivity is a function of the focal length of the decollimating lens, these systems are rather long and filter fabrication and calibration is rather difficult. A Shack-Hartmann wavefront sensor is an array of small lenslets. Typical diameters are on the order of a few hundred microns. Since these lenslets divide the test section into resolution elements, the spatial resolution can be no smaller than an individual lenslet. Such a device was recently used to perform high-speed tomography of heated air exiting a 1.27 cm diameter nozzle. While these wavefront sensors are very compact, the limited spatial resolution and the methods required for data reduction suggest that a more useful instrument needs to be developed. The category of interferometers known as common path interferometers can eliminate much of the vibration sensitivity associated with traditional interferometry as described above. In these devices, division of the amplitude of the wavefront following the test section produces the reference beam. Examples of these instruments include shearing and point diffraction interferometers. In the latter case, shown schematically, a lens focuses light passing through the test section onto a small diffracting object. Such objects are typically either a circle of material on a high quality glass plate or a small sphere in a glass cell. The size of the focused spot is several times larger than the object so that the light not intercepted by the diffracting object forms the test beam while the diffracted light generates a spherical reference beam. While this configuration is mechanically stable, phase shifting one beam with respect to the other is difficult due to the common path. Phase shifting enables extremely accurate measurements of the phase of the interferogram using only gray scale intensity measurements and is the de facto standard of industry. Mercer and Creath 2 demonstrated phase shifting in a point diffraction interferometer using a spherical spacer in a liquid crystal cell as the diffracting object. By changing the voltage across the cell, they were able to shift the phase of the undiffracted beam relative to the reference beam generated by diffraction from the sphere. While they applied this technology to fluid measurements, the device shifted phase so slowly that it was not useful for studying transient phenomena. We have identified several technical problems that precluded operation of the device at video frame rates and intend to solve them to produce a phase-shifting liquid crystal point-diffraction interferometer operating at video frame rates. The first task is to produce high contrast fringes. Since the diffracted beam is much weaker than the transmitted beam, interferograms have poor contrast unless a dye is added to the liquid crystal to reduce the intensity of the undiffracted light. Dyes previously used were not rigorously characterized and suffered from hysteresis in both the initial alignment state of the device and the electro-optic switching characteristics. Hence, our initial effort will identify and characterize dyes that do not suffer from these difficulties and are readily soluble in the liquid crystal host. Since the ultimate goal of this research is to produce interferometers capable of phase shifting at video frame rates, we will quantify the difference in switching times between ferroelectric and nematic liquid crystals. While we have more experience with nematic crystals, they typically switch more slowly than ferroelectric cells. As part of that effort, we will investigate the difference in the modulation of the interferograms as a function of the type of liquid crystal in the cell. Because the temporal switching response of a liquid crystal cell is directly related its thickness, we intend to explore techniques required to produce cells that are as thin as possible. However, the cells must still produce a total phase shift of two pi radians.

Griffin, DeVon W.↗
NASA NTRS2002

Diffraction hardware testbed and model validation

Optical systems, which operate over a wide range of Fresnel numbers, are often times performance-limited by diffraction effects. In order to characterize such effects at the 40-100 picometer level, a diffraction testbed has been built which has the capability of measuring diffraction effects at this level. Concurrently, mathematical diffraction modeling tools have been developed that propagate an input wavefront through an optical train, while retaining amplitude and phase information at a grid resolution sufficient for yielding picometer-resolution diffraction test data. This paper contains a description of this diffraction hardware testbed, the diffraction modeling approach, and a comparison of the modeled and hardware test results, which then serves as validation of the diffraction modeling methodology.

optical↗
DOE OSTI2023

Snapshot multispectral imaging using a diffractive optical network

Abstract Multispectral imaging has been used for numerous applications in e.g., environmental monitoring, aerospace, defense, and biomedicine. Here, we present a diffractive optical network-based multispectral imaging system trained using deep learning to create a virtual spectral filter array at the output image field-of-view. This diffractive multispectral imager performs spatially-coherent imaging over a large spectrum, and at the same time, routes a pre-determined set of spectral channels onto an array of pixels at the output plane, converting a monochrome focal-plane array or image sensor into a multispectral imaging device without any spectral filters or image recovery algorithms. Furthermore, the spectral responsivity of this diffractive multispectral imager is not sensitive to input polarization states. Through numerical simulations, we present different diffractive network designs that achieve snapshot multispectral imaging with 4, 9 and 16 unique spectral bands within the visible spectrum, based on passive spatially-structured diffractive surfaces, with a compact design that axially spans ~72 λ m , where λ m is the mean wavelength of the spectral band of interest. Moreover, we experimentally demonstrate a diffractive multispectral imager based on a 3D-printed diffractive network that creates at its output image plane a spatially repeating virtual spectral filter array with 2 × 2 = 4 unique bands at terahertz spectrum. Due to their compact form factor and computation-free, power-efficient and polarization-insensitive forward operation, diffractive multispectral imagers can be transformative for various imaging and sensing applications and be used at different parts of the electromagnetic spectrum where high-density and wide-area multispectral pixel arrays are not widely available.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Effect of Collimation on Diffraction Signal-to-Background Ratios at a Neutron Diffractometer

High diffraction signal-to-background ratios (SBRs), the ratios of diffraction peak integrated intensity over its background intensity, are desired for a neutron diffractometer to acquire good statistics for diffraction pattern measurements and subsequent data analysis. For a given detector, while the diffraction peak signals primarily depend on the characteristics of neutron beam and sample coherent scattering, the background largely originates from the sample incoherent scattering and the scattering from the instrument space. In this work, we investigated the effect of collimation on neutron diffraction SBRs of Si powder measurements using one high-angle area detector bank coupled with six different collimation configurations in a large and complex instrument space at the engineering materials diffractometer VULCAN, SNS, ORNL. The results revealed that the diffraction SBRs can be significantly improved by a proper coarse collimator that leaves no gap between the detector and the collimator, and the improvement of SBRs by a fine radial collimator was remarkable with a proper coarse collimator in place but not distinguishable without one. It was also found that the diffraction SBRs were not effectively improved by adding neutron absorbing element boron to the fine radial collimator body, which indicates that either the absorption of secondary scattered neutrons by the added boron is insignificant or the collimator base material (resin and ABS) alone attenuates background scattering sufficiently. These findings could serve as a useful reference for diffractometer developers and/or operators to optimize their collimation to achieve higher diffraction SBRs.

Yu, Dunji↗
NASA NTRS1974

A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface

A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edge formed by perfectly conducting curved or plane surfaces is obtained. This diffraction coefficient remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. Our method is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray-fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresnel integrals, which ensure that the total field is continuous at shadow and reflection boundaries.

Kouyoumjian, R. G.↗
NASA NTRS1993

Diffractive optics fabricated by direct write methods with an electron beam

State-of-the-art diffractive optics are fabricated using e-beam lithography and dry etching techniques to achieve multilevel phase elements with very high diffraction efficiencies. One of the major challenges encountered in fabricating diffractive optics is the small feature size (e.g. for diffractive lenses with small f-number). It is not only the e-beam system which dictates the feature size limitations, but also the alignment systems (mask aligner) and the materials (e-beam and photo resists). In order to allow diffractive optics to be used in new optoelectronic systems, it is necessary not only to fabricate elements with small feature sizes but also to do so in an economical fashion. Since price of a multilevel diffractive optical element is closely related to the e-beam writing time and the number of etching steps, we need to decrease the writing time and etching steps without affecting the quality of the element. To do this one has to utilize the full potentials of the e-beam writing system. In this paper, we will present three diffractive optics fabrication techniques which will reduce the number of process steps, the writing time, and the overall fabrication time for multilevel phase diffractive optics.

Kress, Bernard↗