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At least 253 records · Page 14

Massively parallel and universal approximation of nonlinear functions using diffractive processors

Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities. Overcoming this limitation without relying on nonlinear optical materials could unlock unprecedented opportunities for ultrafast and parallel optical computing systems. Here, we demonstrate that large-scale nonlinear computation can be performed using linear optics through optimized diffractive processors composed of passive phase-only surfaces. In this framework, the input variables of nonlinear functions are encoded into the phase of an optical wavefront—e.g., via a spatial light modulator (SLM)—and transformed by an optimized diffractive structure with spatially varying point-spread functions to yield output intensities that approximate a large set of unique nonlinear functions–all in parallel. We provide proof establishing that this architecture serves as a universal function approximator for an arbitrary set of bandlimited nonlinear functions, also covering wavelength-multiplexed nonlinear functions as well as multi-variate and complex-valued functions that are all-optically cascadable. Our analysis also indicates the successful approximation of typical nonlinear activation functions commonly used in neural networks, including the sigmoid, tanh, ReLU (rectified linear unit), and softplus. We numerically demonstrate the parallel computation of one million distinct nonlinear functions, accurately executed at wavelength-scale spatial density at the output of a diffractive optical processor. Furthermore, we experimentally validated this framework using in situ optical learning and approximated 35 unique nonlinear functions in a single shot using a compact setup consisting of an SLM and an image sensor. These results establish diffractive optical processors as a scalable platform for massively parallel universal nonlinear function approximation, paving the way for new capabilities in analog optical computing based on linear materials.

Rahman, Md Sadman Sakib [University of California,↗

Powder Diffraction Crystallography : 98 Years as Plan B?

A historical essay written in 2014 to accompany a talk in the Transactions Symposium "100 Years of Crystallography" at the 2014 American Crystallographic Association Annual Meeting (talk at https://history.amercrystalassn.org/h-brian-toby-videos). Abstract: Powder diffraction patterns were used for structure solution almost contemporaneously with the Bragg’s initial single-crystal determinations. Structures have continued to be determined from powders, in the subsequent century. There has been a nearly explosive growth in this technique since the 1970’s. This was initially driven by neutron diffraction, which prompted the invention of Rietveld analysis, but synchrotrons have gone on to have at least as large an impact. There is no apparent upper limit to the scale of systems that can be structurally studied with powder diffraction; novel protein structures have been determined. When short-range ordering or disordered regions of a material are of interest, the Fourier transform of a powder diffraction pattern, the pair distribution function can be modeled.

Toby, Brian H.↗

Role of depth in optical diffractive neural networks

Free-space all-optical diffractive neural networks have emerged as promising systems for neuromorphic scene classification. Understanding the fundamental properties of these systems is important to establish their ultimate performance. Here we consider the case of diffraction by subwavelength apertures and study the behavior of the system as a function of the number of diffractive layers by employing a co-design modeling approach. We show that adding depth allows the system to achieve high classification accuracies with a reduced number of diffractive features compared to a single layer, but that it does not allow the system to surpass the performance of an optimized single layer. The improvement from depth is found to be limited to the first few layers. These properties originate from the constraints imposed by the physics of light, in particular the weakening electric field with distance from the aperture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Opportunities for inclusive diffraction at EIC

The possibilities for inclusive diffraction in the Electron Ion Collider, EIC, in the US, are analyzed. We find that thanks to the excellent forward proton tagging, the EIC will be able to access a wider kinematical range of longitudinal momentum fraction and momentum transfer of the leading proton than at HERA. This opens up the possibility to measure subleading diffractive exchanges. The extended t-range would allow the precise extraction of 4-dimensional reduced cross section in diffraction. In addition, the varying beam energy setups at the EIC would allow for precise measurements of the longitudinal diffractive structure function.

Slominski, Wojtek↗

LDRD 226360 Final Project Report: Simulated X-ray Diffraction and Machine Learning for Optimizing Dynamic Experiment Analysis

This report is the final documentation for the one-year LDRD project 226360: Simulated X-ray Diffraction and Machine Learning for Optimizing Dynamic Experiment Analysis. As Sandia has successfully developed in-house X-ray diffraction tools for study of atomic structure in experiments, it has become increasingly important to develop computational analysis methods to support these experiments. When dynamically compressed lattices and orientations are not known a priori, the identification requires a cumbersome and sometimes intractable search of possible final states. These final states can include phase transition, deformation and mixed/evolving states. Our work consists of three parts: (1) development of an XRD simulation tool and use of traditional data science methods to match XRD patterns to experiments; (2) development of ML-based models capable of decomposing and identifying the lattice and orientation components of multicomponent experimental diffraction patterns; and (3) conducting experiments which showcase these new analysis tools in the study of phase transition mechanisms. Our target material has been cadmium sulfide, which exhibits complex orientation-dependent phase transformation mechanisms. In our current one-year LDRD, we have begun the analysis of high-quality c-axis CdS diffraction data from DCS and Thor experiments, which had until recently eluded orientation identification.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

High-Energy X-ray Diffraction Microscopy for Nuclear Forensics FY2022 Project Report

Morphological information on nuclear material has been identified using visible light and scanning electron microscopy. These identify qualitative differences in particle morphology. Three-dimensional imaging of materials through alternating scanning electron microscopy imaging and focused ion beam milling has also been used. Unfortunately, these techniques are time- and labor-intensive, with significant sample preparation required and lengthy analysis times. Further, the resulting 3D images are qualitative, require manual identification, and do not capture statistically-representative populations. High energy X-ray 3D imaging using a direct-beam or diffracted-beam (High-Energy Diffraction Microscopy) have been developed at the Advanced Photon Source and can produce quantitative information on grains (phase, location, etc.) and pores (size distribution, sphericity) in a material. These techniques require only minutes to characterize a sample volume and are non-destructive, thus suitable for a wide range of existing samples and for confirmatory analyses to be carried out using conventional microscopy techniques. In this first year of the project, all uranium oxide samples were synthesized and characterized using conventional analyses by the analytical chemistry laboratory. Conventional analysis methods included powder x-ray diffraction, scanning electron microscopy, impurity analysis via inductively coupled plasma mass spectrometry, and infrared spectroscopy. Impurity analysis shows a drop in boron content from UO 3 to the lowest U 3 O 8 calcination temperature, but otherwise no appreciable difference in any sample. Analysis of diffraction data shows a flip of peaks from UO 3 dominated for the 600 °C calcined sample to U 3 O 8 dominated at 700 °C and 800 °C. Analysis of scanning electron microscopy images shows that with increased calcination temperature the size distribution of particles seems to increase and broaden. Both of these last findings are in line with previously published data, though this work used significantly fewer particles to simply show similar trends instead of getting truly quantitative particle analysis. Infrared analysis similarly shows ingrowth of U 3 O 8 as calcination temperature is increased, along with depression of peaks associated with UO 3 and water. Samples were prepared for analysis at the Advanced Photon Source at beamline 1-ID. It is anticipated that analysis will occur in November of 2022. AI/ML techniques to de-noise data coming out of 1-ID during the analyses was also developed during this time using previously gathered data. Preliminary results using a self-supervision technique called Noise2Selfshow good de-noising of data. Once the uranium oxide samples are analyzed, real data will be used to test the de-noising and other AI/ML techniques that may be developed in the second year of the project.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Capability for time-resolved diffraction for material phase in extreme conditions (Q2 FY24 Report)

After a series of development experiments, a new x-ray diffraction diagnostic called FIDDLE (Flexible Imaging Diffraction Diagnostic for Laser Experiments) has been designed, built, and fielded on four shots at NIF. Here we document the initial performance of FIDDLE fielded as the detector in the time-resolved x-ray diffraction experimental platform. Early challenges with EMP have been documented using offline testing in the Target Diagnostics Factory to identify EMP leaks. These techniques were used to guide the application of shielding to weak spots where EM radiation was able to penetrate inside the diagnostic. Application of shielding was found to be effective at reducing EMP leaks, enabling detection of x-ray diffraction on three temporally separated frames during a high pressure (~1Mbar) experiment where lead (Pb) was observed to undergo a phase transition from HCP to BCC.

36 MATERIALS SCIENCE↗

Fresnel diffraction plates are simple and inexpensive

Fresnel plate demonstrates diffraction phenomena simply and inexpensively. A large number of identical diffracting apertures are made in random orientation on photographic film. When a small source of light is viewed through the plate, the diffraction pattern typical of the diffracting aperture is readily seen.

Hoover, R. B.↗

Study of X-ray diffraction on aging alloys with different degrees of volume discrepancy between the precipitation phase and the matrix

Study of the diffraction patterns of X rays diffracted by dispersion-hardened alloys with various degrees of difference between the specific atomic volumes of their precipitation phases and matrices. Experiments were performed on aging alloys KhN77TIuR (nimonic) and KhN67VMTIuO, which have the same types of gamma solid solutions and precipitating gamma prime phases, but differ considerably with respect to the volume factor. It is found that in the decay of supersaturated solid solutions for which the difference between the specific atomic volumes of the precipitation phase and the matrix is small (alloy KhN67VMTIuO) the nature of the intensity distribution of the diffraction lines remains practically unchanged regardless of the aging, while in cases where the volume discrepancy is large (alloy KhN77TIuR) significant changes in the appearance of the diffraction lines are recorded.-

Gitgarts, M. I.↗

Edge diffracted caustic fields

The fields near a caustic created by an edge diffraction process are computed using the equivalent current concept. These fields are shown to have the property commonly associated with ray optical analysis or the Geometrical Theory of Diffraction (GTD), e.g., a 90 deg phase shift as the ray passes through the caustic. The present effort is directed toward consideration of the caustic created by an edge diffraction process. Particular attention is focused on electromagnetic excitation. The acoustic excitation for the hard boundary condition is outlined in an appendix. In addition, goal is to establish the extent of the caustic region. This is of particular importance when a ray optical solution involves multiply-diffracted terms in that the minimum size of the body that can be analyzed may be restricted by the extent of the caustic, i.e., the 90 deg phase shift used in ray optical analysis may be introduced only if the caustic is contained on the surface being studied.

Burnside, W. D.↗

Diffraction by a perfectly conducting rectangular cylinder which is illuminated by an array of line sources

The geometrical theory of diffraction (GTD) is employed to analyze the radiation from a perfectly-conducting rectangular cylinder illuminated by an array of line sources. The excitation of the cylinder by a single electric or magnetic current line source is considered first, and a solution which includes contributions from the geometrical optics rays and all singly- and doubly-diffracted rays is obtained. A new diffraction coefficient valid in the transition regions of the shadow and reflection boundaries is employed to obtain a continuous total field, except for negligible discontinuities in the doubly-diffracted field at its shadow boundaries. Patterns calculated by the GTD method are found to be in excellent agreement with those calculated from an integral equation formulation. Using superposition the solution for array or aperture excitation of the rectangular cylinder is obtained. A computer program for this solution is included.

Kouyoumjian, R. G.↗

An analysis of the radiation from apertures in curved surfaces by the geometrical theory of diffraction

In this paper the geometrical theory of diffraction is extended to treat the radiation from apertures of slots in convex perfectly conducting surfaces. It is assumed that the tangential electric field in the aperture is known so that an equivalent infinitesimal source can be defined at each point in the aperture. Surface rays emanate from this source which is a caustic of the ray system. A launching coefficient is introduced to describe the excitation of the surface ray modes. If the field radiated from the surface is desired, the ordinary diffraction coefficients are used to determine the field of the rays shed tangentially from the surface rays. The field of the surface ray modes is not the field on the surface; hence if the mutual coupling between slots is of interest, a second coefficient related to the launching coefficient must be employed. In the region adjacent to the shadow boundary, the component of the field directly radiated from the source is represented by Fock-type functions. In the illuminated region the incident radiation from the source (this does not include the diffracted field components) is treated by geometrical optics. This extension of the geometrical theory of diffraction is applied to calculate the radiation from slots on elliptic cylinders, spheres, and spheroids.

Pathak, P. H.↗

Programs for calculating cell parameters in electron and X-ray diffraction

Ten programs for calculating cell parameters from single crystal electron diffraction patterns are presented. Most of the programs, written for use with a programmable desk calculator, are also applicable to X-ray diffraction work. The programs can be used to calculate d-spacings from electron diffraction plate measurements, and to determine cell data (including interplanar angles and zone angles) for all crystal systems. A program for rhombohedral-hexagonal conversions and one for matching crystal data from standards with apparent crystal parameters found in diffraction patterns are included. Because they allow rapid determination of data not present in X-ray listings or elsewhere in the literature, the programs facilitate identification of unknowns.

Polkowski, G.↗

Diffraction-limited performance of grazing incidence optical systems

Diffraction effects of X-ray optical systems are often (justifiably) ignored due to the small wavelength of the X-ray radiation. However, the extremely large obscuration ratio inherent to grazing incidence optical systems produces a profound degradation of the diffraction image over that produced by a moderately obscured aperture of the same diameter. The contradictory requirements of large collecting area and relatively short length of optical elements has tended to result in proposed designs containing many concentric shells with increasingly higher obscuration ratios. In this paper it is shown that diffraction effects in such systems can significantly affect the achievable optical performance at the low energy (long wavelength) end of the intended operating spectral range. Parametric diffraction-limited performance predictions for both imaging and spectrographic applications will be presented and compared to AXAF performance goals and/or BBXRT fabrication techniques.

Harvey, James E.↗

Nonprincipal-plane scattering from flat plates: Second-order and corner diffraction and pattern control of horn antennas

Several high-frequency models for nonprincipal-plane scattering from a rectangular, perfectly conducting plate are examined. Two methods, the Method of Equivalent Currents and corner diffraction coefficients, are considered. Formulations for second-order Physical Theory of Diffraction equivalent currents and for corner diffracted fields are presented. Comparisons are made among plate models. Results away from grazing are accurate using only first-order terms. Near grazing, second-order and corner diffraction terms improve the results for many cases. The pattern control of horn antennas using lossy materials to coat the inner walls of the horn is also investigated. Integral Equation and Moment Method techniques are used to formulate the problem. It is clearly demonstrated that side lobe level reduction can be achieved using impedance surfaces on the inner walls of the horn.

Balanis, Constantine A.↗

Diffractive optics technology and the NASA Geostationary Earth Observatory (GEO)

Diffractive (or binary) optics offers unique capabilities for the development of large-aperture, high-performance, light-weight optical systems. The Geostationary Earth Observatory (GEO) will consist of a variety of instruments to monitor the environmental conditions of the earth and its atmosphere. The aim of this investigation is to analyze the design of the GEO instrument that is being proposed and to identify the areas in which diffractive (or binary) optics technology can make a significant impact in GEO sensor design. Several potential applications where diffractive optics may indeed serve as a key technology for improving the performance and reducing the weight and cost of the GEO sensors have been identified. Applications include the use of diffractive/refractive hybrid lenses for aft-optic imagers, diffractive telescopes for narrowband imaging, subwavelength structured surfaces for anti-reflection and polarization control, and aberration compensation for reflective imaging systems and grating spectrometers.

Morris, G. Michael↗

Combining ray-trace and diffraction analysis: A design example

An example is presented of using a combined ray trace and diffraction modeling code to simulate effects of objective-lens tilt in an optical data storage device. In some cases, neither ray-trace analysis nor diffraction analysis can give an adequate description of an optical system. The designer that is faced with the problem of analyzing such a system is forced to use a ray-trace program to determine aberrations in the exit pupil and then introduce aberration coefficients into a diffraction model that simulate the propagation. This approach was found rather awkward, especially if complicated aberrations are present. Our approach is to integrate a diffraction analysis and a ray-trace description of an optical path into one program. Our design is taken from a data storage application, where we must analyze the effects of objective-lens tilt.

Milster, Tom D.↗

Table of interplanar spacings for crystal-structure determinations by X-ray diffraction with molybdenum, copper, cobalt, iron, and chromium radiations

For a simple diffraction pattern, the time required to calculate interplanar distances from measurements of the pattern is not excessive. If more than a few lines are present, however, or if several patterns are to be studied, it is very advantageous to have available a table giving interplanar spacings directly in terms of the linear measurements made on the film of the lines appearing on the diffraction pattern. The preparation of the table given here was undertaken when the expansion of research activities involving X-ray diffraction techniques indicated that such a table would greatly decrease the time required to analyze diffraction patterns. The table was prepared for use with K alpha(sub 1) radiation from the following target materials: molybdenum, copper, cobalt, iron, and chromium.

METALS - STRUCTURES↗