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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

TMD factorisation for diffractive jets in photon-nucleus interactions

Abstract Using the colour dipole picture and the colour glass condensate effective theory, we study the diffractive production of two or three jets via coherent photon-nucleus interactions at high energy. We consider the hard regime where the photon virtuality and/or the transverse momenta of the produced jets are much larger than the saturation momentumQ s of the nuclear target. We show that, despite this hardness, the leading-twist contributions are controlled by relatively large parton configurations, with transverse sizesR~ 1/Q s , which undergo strong scattering and probe gluon saturation. We demonstrate that these leading-twist contributions admit transverse-momentum dependent (TMD) factorisation, in terms of quark and gluon diffractive TMD distribution functions, for which we obtain explicit expressions from first principles. We go beyond our previous work by evaluating the contributions involving the quark diffractive distributions and by establishing that their DGLAP evolution emerges via controlled calculations within the colour dipole picture. We find the same expression for the quark diffractive TMD in two different processes (semi-inclusive diffraction and the diffractive production of quark-gluon dijets), thus demonstrating its universality.

Physics↗
DOE OSTI2024

Phase Identification in Synchrotron X-ray Diffraction Patterns of Ti–6Al–4V Using Computer Vision and Deep Learning

X-ray diffraction patterns contain information about the atomistic structure and microstructure (defect population) of materials, extracting detailed information from diffraction patterns is complex, demanding and relies on prior knowledge. Here, we hypothesize that deep-learning techniques can help to perform an effective and accurate analysis with high throughput rates. To demonstrate this concept, we applied a novel deep learning framework to determine the evolution of the β-phase volume fraction in a Ti–6Al–4V alloy during heat-treatment from video sequences of 2D diffraction patterns recorded in transmission and with highly monochromatic radiation in a synchrotron beamline. In particular, we studied the impact of network design on prediction reliability and computational performance. Networks of different architectures were trained using 3008 experimental 2D patterns. A well-tuned model was found to reproduce the phase fractions of another experimental data set, consisting of 1100 diffraction patterns, with a mean-square error as small as 2.6 x 10 -4 . The average prediction error of β-phase volume fraction was within 1.6 x 10 -2 (in each diffraction pattern) of the values obtained by conventional methods. Our work demonstrates that convolutional neural networks can evaluate high energy X-ray diffraction patterns with a remarkable level of reliability. Furthermore, it demonstrates the significance of network design on the reliability of predictions and computational performance. The most complex models do not necessarily result in highest accuracy and may even fail to learn from the data.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Unsupervised anomaly detection in MeV ultrafast electron diffraction

MeV ultrafast electron diffraction (MUED) is a pump-probe technique used to study the dynamic structural evolution of materials. An ultrashort laser pulse triggers structural changes, which are then probed by an ultrashort relativistic electron beam. To overcome low signal-to-noise ratios, diffraction patterns are averaged over thousands of shots. However, shot-to-shot instabilities in the electron beam can distort individual patterns, introducing uncertainty. Improving MUED accuracy requires detecting and removing these anomalous patterns from large datasets. In this work, we developed a fully unsupervised methodology for the detection of anomalous diffraction patterns. Using a convolutional autoencoder, we calculate the reconstruction mean squared error of the diffraction patterns. Based on the statistical analysis of this error, we provide the user an estimation of the probability that the pattern is normal, which also allows a posterior visual inspection of the images that are difficult to classify. This method has been trained with only 100 diffraction patterns and tested on 1521 patterns, resulting in a false positive rate between 0.2% and 0.4%, with a training time of 10 s per image and a test time of about 1 s per image. Here, the proposed methodology can also be applied to other diffraction techniques in which large datasets are collected that include faulty images due to instrumental instabilities.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Nonlinear encoding in diffractive information processing using linear optical materials

Nonlinear encoding of optical information can be achieved using various forms of data representation. Here, we analyze the performances of different nonlinear information encoding strategies that can be employed in diffractive optical processors based on linear materials and shed light on their utility and performance gaps compared to the state-of-the-art digital deep neural networks. For a comprehensive evaluation, we used different datasets to compare the statistical inference performance of simpler-to-implement nonlinear encoding strategies that involve, e.g., phase encoding, against data repetition-based nonlinear encoding strategies. We show that data repetition within a diffractive volume (e.g., through an optical cavity or cascaded introduction of the input data) causes the loss of the universal linear transformation capability of a diffractive optical processor. Therefore, data repetition-based diffractive blocks cannot provide optical analogs to fully connected or convolutional layers commonly employed in digital neural networks. However, they can still be effectively trained for specific inference tasks and achieve enhanced accuracy, benefiting from the nonlinear encoding of the input information. Our results also reveal that phase encoding of input information without data repetition provides a simpler nonlinear encoding strategy with comparable statistical inference accuracy to data repetition-based diffractive processors. Our analyses and conclusions would be of broad interest to explore the push-pull relationship between linear material-based diffractive optical systems and nonlinear encoding strategies in visual information processors.

42 ENGINEERING↗
DOE OSTI2024

X-ray diffraction under grazing incidence conditions

Material properties frequently relate to structures at or near surfaces, particularly in thin films. As a result, it is essential to understand these structures at the molecular and atomistic levels. The most accurate and widely used techniques for characterizing crystallographic order are based on X-ray diffraction. When dealing with thin films or interfaces, standard approaches, such as single crystal or powder diffraction, are not suitable. However, X-ray diffraction under grazing incidence conditions can provide the required information. Here, in this Primer, grazing incidence X-ray diffraction (GIXD) is comprehensively introduced, starting from basic considerations on X-ray diffraction at crystals with reduced dimensionality and the optical properties of X-rays, followed by a more in-depth description of an experimental performance, including X-ray sources, goniometers and detectors. Experimental errors, limitations and reproducibility are discussed. Various applications, from highly ordered inorganic single crystal surfaces to weakly ordered polymer thin films, are presented to illustrate the potential of GIXD. Data visualizations, representations and evaluation strategies are summarized, based on the example of anthracene thin films. The Primer compiles information relevant to perform high-quality GIXD experiments, evaluate data and interpret results, to extend knowledge about X-ray diffraction from surfaces, interfaces and thin films.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Strong-field induced fragmentation and isomerization of toluene probed by ultrafast femtosecond electron diffraction and mass spectrometry

We investigate the fragmentation and isomerization of toluene molecules induced by strong-field ionization with a femtosecond near-infrared laser pulse. Momentum-resolved coincidence time-of-flight ion mass spectrometry is used to determine the relative yield of different ionic products and fragmentation channels as a function of laser intensity. Ultrafast electron diffraction is used to capture the structure of the ions formed on a picosecond time scale by comparing the diffraction signal with theoretical predictions. Through the combination of the two measurements and theory, we are able to determine the main fragmentation channels and to distinguish between ions with identical mass but different structures. In addition, our diffraction measurements show that the independent atom model, which is widely used to analyze electron diffraction patterns, is not a good approximation for diffraction from ions. Here, we show that the diffraction data is in very good agreement with ab initio scattering calculations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Selected topics in diffraction with protons and nuclei: past, present, and future

Here, we review a broad range of phenomena in diffraction in the context of hadron–hadron, hadron–nucleus collisions and deep inelastic lepton–proton/nucleus scattering focusing on the interplay between the perturbative QCD and non-perturbative models. We discuss inclusive diffraction in DIS, phenomenology of dipole models, resummation and parton saturation at low x , hard diffractive production of vector mesons, inelastic diffraction in hadron–hadron scattering, formalism of color fluctuations, inclusive coherent and incoherent diffraction as well as soft and hard diffraction phenomena in hadron–hadron/nucleus and photon–nucleus collisions. For each topic we review key results from the past and present experiments including HERA and the LHC. Finally, we identify the remaining open questions, which could be addressed in the continuing experiments, in particular in photon-induced reactions at the LHC and the future electron–ion collider in the US, large hadron electron collider and future circular collider at CERN.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

The incommensurately modulated structures of low-temperature labradorite feldspars: a single-crystal X-ray and neutron diffraction study

Labradorite feldspars of the plagioclase solid solution series have been known for their complicated subsolidus phase relations and enigmatic incommensurately modulated structures. Characterized by the irrationally indexed e -reflections in the diffraction pattern, e -labradorite shows the largest variation in the incommensurate ordering states among the e -plagioclase structures. The strongly ordered low-temperature e -labradorite is one of the last missing pieces of the e -plagioclase puzzle. Nine plutonic and metamorphic labradorite feldspar samples from Canada, Ukraine, Minnesota (USA), Tanzania and Greenland with compositions ranging from An 52.5 to An 68 were studied with single-crystal X-ray diffraction. Two crystals from Labrador, Canada, and Duluth, MN, USA, with wide enough twin lamellae were analyzed with single-crystal neutron diffraction. The incommensurately modulated structures of e -plagioclase are refined for the first time with neutron diffraction data, which confirmed that the T—O distance modulation in the low-temperature e -plagioclase results from the Al–Si ordering in the framework. Detailed configurations of the M site are also observed in the structures refined from neutron diffraction data, which were not possible to see with X-ray diffraction data. The relation between the q -vectors and the mole% An composition is revealed for the entire compositional range of e -plagioclase, from An 25 to An 75 . The previously proposed two-trend relation depending on the cooling rate and phase transition path is confirmed. A new classification of e -plagioclase ( e α , e β and e γ ) is proposed based on the q -vector of the structure, which makes it an independent character from the presence/absence of density modulation. New parameters are proposed to quantify the ordering states of these complicated aperiodic structures of e -plagioclases, such as the difference between $\langle$T 1 o—O$\rangle$ and $\langle$T 1 m—O$\rangle$ at phase t = 0.2 or the normalized intensity of the (071\bar 1) reflection.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Super-resolution image display using diffractive decoders

High-resolution image projection over a large field of view (FOV) is hindered by the restricted space-bandwidth product (SBP) of wavefront modulators. We report a deep learning–enabled diffractive display based on a jointly trained pair of an electronic encoder and a diffractive decoder to synthesize/project super-resolved images using low-resolution wavefront modulators. The digital encoder rapidly preprocesses the high-resolution images so that their spatial information is encoded into low-resolution patterns, projected via a low SBP wavefront modulator. The diffractive decoder processes these low-resolution patterns using transmissive layers structured using deep learning to all-optically synthesize/project super-resolved images at its output FOV. This diffractive image display can achieve a super-resolution factor of ~4, increasing the SBP by ~16-fold. We experimentally validate its success using 3D-printed diffractive decoders that operate at the terahertz spectrum. This diffractive image decoder can be scaled to operate at visible wavelengths and used to design large SBP displays that are compact, low power, and computationally efficient.

36 MATERIALS SCIENCE↗
NASA NTRS1974

TM surface wave diffraction by a truncated dielectric slab recessed in a perfectly conducting surface

The diffraction of a TM sub o surface wave by a terminated dielectric slab which is flush mounted in a perfectly conducting surface is studied. The incident surface wave gives rise to waves reflected and diffracted by the termination; these reflected and diffracted fields may be expressed in terms of the geometrical theory of diffraction by introducing surface wave reflection and diffraction coefficients which are associated with the termination. In this investigation, the surface wave reflection and diffraction coefficients have been deduced from a formally exact solution to this canonical problem. The solution is obtained by a combination of the generalized scattering matrix technique and function theoretic methods.

Pathak, P. H.↗
NASA NTRS1978

On the use of classical and conical diffraction mountings for XUV gratings

A description is given of the properties of plane diffraction gratings used in conical diffraction. Formulas are given for computing the direction of the diffracted orders. Experiments were performed to investigate the behavior of gratings used on conical diffraction mountings. Comparisons made with classical diffraction mountings show a significant increase in the efficiency of the -1 order. An empirical formula to predict the efficiencies of gratings used in conical diffraction mountings has been verified by the measurements.

Neviere, M.↗
NASA NTRS1979

Applications of diffraction theory to aeroacoustics

A review is given of the fundamentals of diffraction theory and the application of the theory to several problems of aircraft noise generation, propagation, and measurement. The general acoustic diffraction problem is defined and the governing equations set down. Diffraction phenomena are illustrated using the classical problem of the diffraction of a plane wave by a half-plane. Infinite series and geometric acoustic methods for solving diffraction problems are described. Four applications of diffraction theory are discussed: the selection of an appropriate shape for a microphone, the use of aircraft wings to shield the community from engine noise, the reflection of engine noise from an aircraft fuselage and the radiation of trailing edge noise.

Lansing, D. L.↗
NASA NTRS1979

Applications of diffraction theory to aeroacoustics

The fundamentals of diffraction theory were reviewed and applied to several problems of aircraft noise generation, propagation, and measurement. The general acoustic diffraction problem is defined and the governing equations were set down. Diffraction phenomena are illustrated using the classical problem of the diffraction of a plane wave by a half-plane. Infinite series and geometric acoustic methods for solving diffraction problems are described. Four applications of diffraction theory are discussed: the selection of an appropriate shape for a microphone, the use of aircraft wings to shield the community from engine noise, the reflection of engine noise from an aircraft fuselage, and the radiation of trailing edge noise.

Lansing, D. L.↗
NASA NTRS1987

Dihedral corner reflector backscatter using higher order reflections and diffractions

The uniform theory of diffraction (UTD) plus an imposed edge diffraction extension is used to predict the backscatter cross sections of dihedral corner reflectors which have right, obtuse, and acute included angles. The UTD allows individual backscattering mechanisms of the dihedral corner reflectors to be identified and provides good agreement with experimental cross-section measurements in the azimuthal plane. Multiply reflected and diffracted fields of up to third-order are included in the analysis for both horizontal and vertical polarizations. The coefficients of the uniform theory of diffraction revert to those of the geometrical theory of diffraction (GTD) in far-field cross-section analyses, but finite cross sections can be obtained everywhere by considering mutual cancellation of diffractions from parallel edges. Analytic calculations are performed using UTD coefficients; hence the accuracy required in angular measurements is more critical as the distance increases. The common far-field approximation that all rays to the observation point are parallel is too gross an approxiation for the angular parameters in the UTD coefficients in the far field.

Griesser, Timothy↗
NASA NTRS1993

An extended UTD analysis for the scattering and diffraction from cubic polynomial strips

Spline and polynomial type surfaces are commonly used in high frequency modeling of complex structures such as aircraft, ships, reflectors, etc. It is therefore of interest to develop an efficient and accurate solution to describe the scattered fields from such surfaces. An extended Uniform Geometrical Theory of Diffraction (UTD) solution for the scattering and diffraction from perfectly conducting cubic polynomial strips is derived and involves the incomplete Airy integrals as canonical functions. This new solution is universal in nature and can be used to effectively describe the scattered fields from flat, strictly concave or convex, and concave convex boundaries containing edges. The classic UTD solution fails to describe the more complicated field behavior associated with higher order phase catastrophes and therefore a new set of uniform reflection and first-order edge diffraction coefficients is derived. Also, an additional diffraction coefficient associated with a zero-curvature (inflection) point is presented. Higher order effects such as double edge diffraction, creeping waves, and whispering gallery modes are not examined. The extended UTD solution is independent of the scatterer size and also provides useful physical insight into the various scattering and diffraction processes. Its accuracy is confirmed via comparison with some reference moment method results.

Constantinides, E. D.↗
NASA NTRS1994

A uniform geometrical optics and an extended uniform geometrical theory of diffraction for evaluating high frequency EM fields near smooth caustics and composite shadow boundaries

A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly demonstrated and it is shown that the UGO/EUTD results remain valid and uniformly reduce to the classic results away from the transition regions. Mathematical details on the asymptotic properties and efficient numerical evaluation of the canonical functions involved in the UGO/EUTD expressions are also provided.

Constantinides, E. D.↗
NASA NTRS1993

A UGO/EUTD Solution for the Scattering and Diffraction from Cubic Polynomial Strips

A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) solution is developed for the scattering and diffraction from perfectly conducting cubic polynomial strips. The new solution overcomes the difficulties of the classic GO/UTD solution near caustics and composite shadow boundaries. The approach for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the scattered field which is then reduced using a uniform asymptotic procedure. New uniform reflection, zero-curvature diffraction, and edge diffraction coefficients are derived and involve the ordinary and incomplete Airy integrals as canonical functions. Higher order effects such as double edge diffraction, edge-excited creeping waves, and whispering gallery modes are not examined in this work. The UGO/EUTD solution is very efficient and provides useful physical insight into the various scattering and diffraction processes. It is also universal in nature and can be used to effectively describe the scattered fields from flat, strictly concave or convex, and concave-convex boundaries containing edges. Its accuracy is confirmed via comparison with some reference moment method (MM) results.

Constantinides, Evagoras D.↗
NASA NTRS1999

X-Ray Diffraction Techniques for a Field Instrument: Patterns of Lithologic Provences

Future exploration of Mars will attempt to shed light on the mineralogy of surface materials. Instruments deployed from remote platforms should have the capability to conduct both intensive analyses as well as rapid, reconnaissance surveys while they function in the martian environment as surrogate geologists. In order to accommodate the reconnaissance mode of analysis and to compensate for analytical limitations imposed by the space-flight conditions, data analysis methods are being developed that will permit interpretation of data by recognition of signatures or "fingerprints". Specifically, we are developing a technique which will allow interpretation of diffraction patterns by recognition of characteristic signatures of different lithologic provences. This technique allows a remote vehicle to function in a rapid-scan mode using the lithologic signature to determine where a more thorough analysis is needed. An x-ray diffraction pattern is characterized by the angular positions of diffracted x-rays, x-ray intensity levels and background radiation levels. These elements may be used to identify a generalized x-ray signature. Lithologic signatures are being developed in two ways. A signature is composed using the ideal powder diffraction indices from the mineral assembledge common to a specific lithologic provence. This is then confirmed using a laboratory diffraction pattern of a whole rock powder. Preliminary results comparing the diffraction signatures of the major mineral assembledges common to basalt, carbonate, and evaporite basin deposits indicate that lithologies are differentiable as a "fingerprint". Statistical analyses are being performed to establish the confidence levels of this technique.

Marshall, J.↗