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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Detection and Signal Processing for Near-Field Nanoscale Fourier Transform Infrared Spectroscopy

Researchers from a broad spectrum of scientific and engineering disciplines are increasingly using scattering-type near-field infrared spectroscopic techniques to characterize materials non-destructively with nanoscale spatial resolution. However, a sub-optimal understanding of a technique's implementation can complicate data interpretation and act as a barrier to entering the field. Here the key detection and processing steps involved in producing scattering-type near-field nanoscale Fourier transform infrared spectra (nano-FTIR) are outlined. The self-contained mathematical and experimental work derives and explains: i) how normalized complex-valued nano-FTIR spectra are generated, ii) why the real and imaginary components of spectra qualitatively relate to dispersion and absorption respectively, iii) a new and generally valid equation for spectra which can be used as a springboard for additional modeling of the scattering processes, and iv) an algebraic expression that can be used to extract an approximation to the sample's local extinction coefficient from nano-FTIR. The algebraic model for weak oscillators is validated with nano-FTIR and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectra on samples of polystyrene and Kapton and further provides a pedagogical pathway to cementing some of the technique's key qualitative attributes.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Identifying Differential Equations in Fourier Domain (FourierIdent)

We investigate identifying differential equations in the frequency domain. Fourier analysis is an important tool in theoretical analysis and numerical solvers of differential equations, yet there is limited work in exploring this connection in the identification of differential equations. This paper aims to identify the underlying differential equation in the frequency domain, from a given single realization of the differential equation perturbed by noise. Such setting imposes difficulties which are different from other identification methods where computation is carried out in the physical domain. We propose several ways to mitigate the challenges arising from noise in data and large differences in the magnitudes of frequency responses. The main takeaways are that identifying differential equations solely in the frequency domain is challenging, the method we propose is based on a form of domain partitions in the frequency domain, and this method shows benefits for complex data even with high level of noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain and to enhance the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms, and shows advantages on complex data with many frequency modes, even under high level of noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Microstructural characterization and assessment of mechanical properties of concrete based on combined elemental analysis techniques and Fast-Fourier transform-based simulations

This paper presents a pixel-based modeling approach of concrete which combines an experimental characterization of concrete and the Fast-Fourier transform simulations. High-resolution phase maps created from experimental characterization by micro X-ray fluorescence, energy dispersive X-ray analysis, and X-ray diffraction contain 9 different phases, including 22.17 vol.% of hydrated cement paste, 54.21 vol.% of minerals, and 23.62 vol.% of interfaces. These phases provide the input for determining the effective elastic properties, coupled with Fast-Fourier transform-based simulation. The simulation results show that the effective range of Young’s modulus of concrete is comparable with the range of experimental values ~ 37 ± 4 GPa with the assumption of realistic properties of interfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone

Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For one such process as liquid-metal dealloying (LMD), phase field models have been developed to understand the mechanisms leading to complex morphologies. However, the LMD governing equations in these models often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, numerical stiffness in the PDEs requires an extremely refined time step size (on the order of 10 -12 s or smaller). This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required. This motivates the development of surrogate models capable of leaping forward in time, by skipping several consecutive time steps at-once. In this paper, we propose a U-shaped adaptive Fourier neural operator (U-AFNO), a machine learning (ML) based model inspired by recent advances in neural operator learning. U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields, and passes the latent space through a vision transformer (ViT) implemented in the Fourier space (AFNO). We use U-AFNOs to learn the dynamics of mapping the field at a current time step into a later time step. We also identify global quantities of interest (QoI) describing the corrosion process (e.g., the deformation of the liquid-metal interface, lost metal, etc.) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in spite of the chaotic nature of LMD. Most notably, our model reproduces the key microstructure statistics and QoIs with a level of accuracy on par with the high-fidelity numerical solver, while achieving a significant 11, 200 × speed-up on a high-resolution grid when comparing the computational expense per time step. Finally, we also investigate the opportunity of using hybrid simulations, in which we alternate forward leaps in time using the U-AFNO with high-fidelity time stepping. We demonstrate that while advantageous for some surrogate model design choices, our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Fourier-based three-dimensional multistage transformer for aberration correction in multicellular specimens

High-resolution tissue imaging is often compromised by sample-induced optical aberrations that degrade resolution and contrast. Although wavefront sensor-based adaptive optics (AO) can measure these aberrations, such hardware solutions are typically complex, expensive to implement and slow when serially mapping spatially varying aberrations across large fields of view. Here we introduce AOViFT (adaptive optical vision Fourier transformer)—a machine learning-based aberration sensing framework built around a three-dimensional multistage vision transformer that operates on Fourier domain embeddings. AOViFT infers aberrations and restores diffraction-limited performance in puncta-labeled specimens with substantially reduced computational cost, training time and memory footprint compared to conventional architectures or real-space networks. We validated AOViFT on live gene-edited zebrafish embryos, demonstrating its ability to correct spatially varying aberrations using either a deformable mirror or postacquisition deconvolution. By eliminating the need for the guide star and wavefront sensing hardware and simplifying the experimental workflow, AOViFT lowers technical barriers for high-resolution volumetric microscopy across diverse biological samples.

Alshaabi, Thayer [Howard Hughes Medical Institute,↗
DOE OSTI2020

RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrors

With the rapid evolution of synchrotron X-ray sources, the demand for high-precision X-ray mirrors has greatly increased. Single nanometer profile error is required to keep imaging capability at the diffraction limit. Ion Beam Figuring (IBF), as a highly deterministic surfacing technique, has been used for ultra-precision finishing of mirrors. One crucial step that guides the IBF process is dwell time calculation. A valid dwell time solution should be non-negative and duplicate the shape of the desired removal map. Another important aspect is to minimize the total dwell time. In this study, we propose a Robust Iterative Fourier Transform-based dwell time Algorithm (RIFTA) that automatically fulfills these requirements. First, the thresholded inverse filtering in Fourier transform-based deconvolution is stabilized and automated by optimizing the threshold value using the Nelder-Mead simplex algorithm. Second, a novel two-level iterative scheme is proposed to guarantee the minimized total dwell time with its non-negativity at each dwell point. Third, a bicubic resampling is employed to flexibly adapt the calculated dwell time map to any IBF process intervals. The performance of RIFTA is first studied with simulation, followed by a comparison with the other state-of-the-art dwell time algorithms. We then demonstrate with an experiment that, using the dwell time calculated by the RIFTA, the total dwell time is shortened by a factor of two and the RMS in a 5 × 50 mm clear aperture was reduced from 3.4 nm to 1.1 nm after one IBF run, which proves the effectiveness and the efficiency of the proposed algorithm.

42 ENGINEERING↗
DOE OSTI2020

Correlations between azimuthal anisotropy Fourier harmonics in PbPb collisions at sNN =2.76 TeV in the HYDJET++ model and in the multiphase transport model

Correlations between azimuthal anisotropy Fourier harmonics vn (n=2,3,4) are studied using the events from PbPb collisions at sNN=2.76 TeV generated by the HYDJET++ and multiphase transport (AMPT) models, and compared to the corresponding experimental results obtained by the ATLAS Collaboration. The Fourier harmonics vn are measured over a wide centrality range using the two-particle azimuthal correlation method. The slopes of the v2-v3 correlation from both models are in a good agreement with the ATLAS data. The HYDJET++ model predicts a stronger slope for the v2-v4 and v3-v4 correlations than the ones experimentally measured, while the results from the AMPT model are in a rather good agreement with the experimental results. In contrast to the HYDJET++ predictions, the AMPT model predicts a boomeranglike shape in the structure of the correlations as found in the experimental data. © 2020 American Physical Society.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Perturbation theory models for LSST-era galaxy clustering: Tests with subpercent mock catalog measurements in Fourier and configuration space

Here, we analyze the clustering of galaxies using the z = 1.006 snapshot of the CosmoDC2 simulation, a high-fidelity synthetic galaxy catalog designed to validate analysis methods for the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). We present sub-percent measurements of the galaxy auto-correlation and galaxy-dark matter cross correlations in Fourier space and configuration space for a magnitude-limited galaxy sample. At these levels of precision, the statistical errors of the measurement are comparable to the systematic effects present in the simulation and measurement procedure; nevertheless, using a hybrid-PT model, we are able to model non-linear galaxy bias with 0.5% precision up to scales of k max = 0.5 h/Mpc and r min = 4 Mpc/h. While the linear bias parameter is measured with 0.01% precision, other bias parameters are determined with considerably weaker constraints and sometimes bimodal posterior distributions. We compare our fiducial model with lower dimensional models where the higher-order bias parameters are fixed at their co-evolution values and find that leaving these parameters free provides significant improvements in our ability to model small scale information. We also compare bias parameters for galaxy samples defined using different magnitude bands and find agreement between samples containing equal numbers of galaxies. Finally, we compare bias parameters between Fourier space and configuration space and find moderate to significant tension between the two approaches. Although our model is often unable to fit the CosmoDC2 galaxy samples within the 0.1% precision of our measurements, our results suggest that the hybrid-PT model used in this analysis is capable of modeling non-linear galaxy bias within the percent level precision needed for upcoming galaxy surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Asymptotic behavior of the Fourier coefficients and the analytic structure of the QCD equation of state

In this paper we study the universal properties of the baryon chemical potential Fourier coefficients in quantum chromodynamics. We show that by following a well-defined strategy, the Fourier coefficients can be used to locate Yang-Lee edge singularities associated with chiral phase transition (and by extension with the Roberge-Weiss) in the complex chemical potential plane. We comment on the viability of performing this analysis using lattice QCD data. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2024

Galaxy bispectrum in the spherical Fourier-Bessel basis

The bispectrum, the three-point correlation in Fourier space, is a crucial statistic for studying many effects targeted by the next-generation galaxy surveys, such as primordial non-Gaussianity (PNG) and general relativistic (GR) effects on large scales. In this work we develop a formalism for the bispectrum in the spherical Fourier-Bessel (SFB) basis—a natural basis for computing correlation functions on the curved sky, as it diagonalizes the Laplacian operator in spherical coordinates. Working in the SFB basis allows for line-of-sight effects such as redshift space distortions and GR to be accounted for exactly, i.e., without having to resort to perturbative expansions to go beyond the plane-parallel approximation. Only analytic results for the SFB bispectrum exist in the literature given the intensive computations needed. We numerically calculate the SFB bispectrum for the first time, enabled by a few techniques: We implement a template decomposition of the redshift-space kernel Z 2 into Legendre polynomials, and separately treat the PNG and velocity-divergence terms. We derive an identity to integrate a product of three spherical harmonics connected by a Dirac delta function as a simple sum and use it to investigate the limit of a homogeneous and isotropic Universe. Furthermore, we present a formalism for convolving the signal with separable window functions and use a toy spherically symmetric window to demonstrate the computation and give insights into the properties of the observed bispectrum signal. While our implementation remains computationally challenging, it is a step toward a feasible full extraction of information on large scales via a SFB bispectrum analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Quantum error mitigation for Fourier moment computation

Hamiltonian moments in Fourier space—expectation values of the unitary evolution operator under a Hamiltonian at different times—provide a convenient framework to understand quantum systems. They offer insights into the energy distribution, higher-order dynamics, response functions, correlation information, and physical properties. This paper focuses on the computation of Fourier moments within the context of a nuclear effective field theory on superconducting quantum hardware. The study integrates echo verification and noise renormalization into Hadamard tests using control reversal gates. These techniques, combined with purification and error suppression methods, effectively address quantum hardware decoherence. The analysis, conducted using noise models, reveals a significant reduction in noise strength by two orders of magnitude. Moreover, quantum circuits involving up to 266 gates over five qubits demonstrate high accuracy under these methodologies when run on IBM superconducting quantum devices. Published by the American Physical Society 2025

Kiss, Oriel (ORCID:0000000174613342)↗
DOE OSTI2024

Towards Full Field-of-View Fourier Ptychography for Extreme Ultraviolet Microscope

We evaluate various Fourier ptychographic microscopy (FPM) reconstruction algorithms using both simulated and experimental data acquired from an Extreme Ultraviolet (EUV, 13.5 nm wavelength) microscope. We specifically focus on the algorithms' ability to robustly address field-dependent aberrations, which enables increased spatial resolution and quantitative phase imaging across an expanded field of view. We systematically compare the algorithms' performance under aberrations for a single zoneplate imaging system, utilizing Fourier Ring Correlation (FRC) as a systematic metric for assessing reconstruction quality. Furthermore, we explore the impact of systematic errors on the reconstruction of experimental data, aiming to increase the effective field of view by 25-fold, from the nominal 5x5 um2 diffraction-limited area. Additionally, our evaluation incorporates innovative FPM-adjacent methodologies, including the Angular Ptychographic Imaging with Closed-form method (APIC), for reconstructing EUV images.

Gu, Chaoying↗
DOE OSTI2023

Using an Analytic-Based Magnetic Charge Fourier Series Model to Study a Magnetic Lead Screw when Operating as a Magnetic Spring

A magnetic charge field analysis approach is presented that models an array of magnets by using a magnetic vector Fourier series representation. Using a Fourier series function enables the magnets' relative permeability to be accounted for and also reduces the computational burden. The accuracy of the presented modelling approach is validated by studying the fields and forces created by a magnetic lead screw when acting as a magnetic spring

Kouhshahi, Mojtaba Bahrami↗
DOE OSTI2020

Fourier Analyses of High-Order Continuous and Discontinuous Galerkin Methods

In this paper, we present a Fourier analysis of wave propagation problems subject to a class of continuous and discontinuous discretizations using high-degree Lagrange polynomials. This allows us to obtain explicit analytical formulas for the dispersion relation and group velocity and, for the first time to our knowledge, characterize analytically the emergence of gaps in the dispersion relation at specific wavenumbers, when they exist, and compute their specific locations. Wave packets with energy at these wavenumbers will fail to propagate correctly, leading to significant numerical dispersion. We also show that the Fourier analysis generates mathematical artifacts, and we explain how to remove them through a branch selection procedure conducted by analysis of eigenvectors and associated reconstructed solutions. The higher frequency eigenmodes, named erratic in this study, are also investigated analytically and numerically.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Broadband rapid-scanning phase-modulated Fourier transform electronic spectroscopy

We present a phase-modulated approach for ultrabroadband Fourier transform electronic spectroscopy. To overcome the bandwidth limitations and spatial chirp introduced by acousto-optic modulators (AOMs), pulses from a 1 µm laser are modulated using AOMs prior to continuum generation. This phase modulation is transferred to the continuum generated in a yttrium aluminum garnet crystal. Separately generated phase-modulated continua in two arms of a Mach-Zehnder interferometer interfere with the difference of their modulation frequencies, enabling physical under-sampling of the signal and the suppression of low-frequency noise. By interferometrically tracking the relative time delay of the continua, we perform continuous, rapid-scanning Fourier transform electronic spectroscopy with a high signal-to-noise ratio and spectral resolution. As proof of principle, we measure the linear absorption and fluorescence excitation spectra of a laser dye and various biological samples.

Javed, Ariba↗
NASA NTRS1973

Stress wave calculations in composite plates using the fast Fourier transform.

The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.

Moon, F. C.↗
NASA NTRS1973

A real-time computer for monitoring a rapid-scanning Fourier spectrometer

A real-time Fourier computer has been designed and tested as part of the Lunar and Planetary Laboratory's program of airborne infrared astronomy using Fourier spectroscopy. The value and versatility of this device are demonstrated with specific examples of laboratory and in-flight applications.

Michel, G.↗