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Results for “Fourier Transform”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Supercontinuum Fourier transform spectrometry with balanced detection on a single photodiode

We demonstrate a method of combining a supercontinuum light source with a commercial Fourier transform spectrometer, using a novel approach to dual-beam balanced detection, implemented with phase-sensitive detection on a single light detector. A 40 dB reduction in the relative intensity noise is achieved for broadband light, analogous to conventional balanced detection methods using two matched photodetectors. Unlike conventional balanced detection, however, this method exploits the time structure of the broadband source to interleave signal and reference pulse trains in the time domain, recording the broadband differential signal at the fundamental pulse repetition frequency of the supercontinuum. The method is capable of real-time correction for instability in the supercontinuum spectral structure over a broad range of wavelengths and is compatible with commercially designed spectrometers. A proof-of-principle experimental setup is demonstrated for weak absorption in the 1500-1600 nm region.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Automatic Fourier transform and self-Fourier beams due to parabolic potential

We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fourier transforms are the beams themselves.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Big Data in Reciprocal Space: Sliding Fast Fourier Transforms for Determining Periodicity

Significant advances in atomically resolved imaging of crystals and surfaces have occurred in the last decade allowing unprecedented insight into local crystal structures and periodicity. Yet, the analysis of the long-range periodicity from the local imaging data, critical to correlation of functional properties and chemistry to the local crystallography, remains a challenge. Here, we introduce a Sliding Fast Fourier Transform (FFT) filter to analyze atomically resolved images of in-situ grown La5/8Ca3/8MnO3 films. We demonstrate the ability of sliding FFT algorithm to differentiate two sub-lattices, resulting from a mixed-terminated surface. Principal Component Analysis (PCA) and Independent Component Analysis (ICA) of the Sliding FFT dataset reveal the distinct changes in crystallography, step edges and boundaries between the multiple sub-lattices. The method is universal for images with any periodicity, and is especially amenable to atomically resolved probe and electron-microscopy data for rapid identification of the sub-lattices present.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy

The dephasing of the Fermi edge singularity excitations in two modulation doped single quantum wells of 12 nm and 18 nm thickness and in-well carrier concentration of ∼4 × 10{sup 11} cm{sup −2} was carefully measured using spectrally resolved four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. Although the absorption at the Fermi edge is broad at this doping level, the spectrally resolved FWM shows narrow resonances. Two peaks are observed separated by the heavy hole/light hole energy splitting. Temperature dependent “rephasing” (S{sub 1}) 2DFT spectra show a rapid linear increase of the homogeneous linewidth with temperature. The dephasing rate increases faster with temperature in the narrower 12 nm quantum well, likely due to an increased carrier-phonon scattering rate. The S{sub 1} 2DFT spectra were measured using co-linear, cross-linear, and co-circular polarizations. Distinct 2DFT lineshapes were observed for co-linear and cross-linear polarizations, suggesting the existence of polarization dependent contributions. The “two-quantum coherence” (S{sub 3}) 2DFT spectra for the 12 nm quantum well show a single peak for both co-linear and co-circular polarizations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Integrated Silicon Fourier Transform Spectrometer with Broad Bandwidth and Ultra‐High Resolution

An ultra-high resolution Fourier transform spectrometer (FTS) realized in silicon photonic platform that can operate with broad band, narrow band as well as a combination of broad band and narrow band signals is reported. The ultra-high resolution of the spectrometer is achieved by exploiting multiple techniques: a Michelson interferometer (MI) structure to increase the optical path delay (OPD), a hybrid waveguide design to reduce insertion loss, an optimized heater and air trenches to achieve higher thermal efficiency. Here, to further increase the OPD of the spectrometer to increase its resolution, a novel multiple interferometers approach is employed which combines balanced MI with N statically imbalanced MIs, thereby increasing the OPD of a single MI by factor of N + 1. An FTS spectrometer consisting of N = 2 such MIs is fabricated and experimentally characterized using unknown broad bandwidth input signal spectra of about 180 nm centered around 1550 nm, a narrow line laser input signal, and a combination of broad and narrow band signals demonstrating spectral resolution of about 0.16 nm.

Li, Ang↗
DOE OSTI2021

Maskless Fourier transform holography

Fourier transform holography is a lensless imaging technique that retrieves an object's exit-wave function with high fidelity. It has been used to study nanoscale phenomena and spatio-temporal dynamics in solids, with sensitivity to the phase component of electronic and magnetic textures. However, the method requires an invasive and labor-intensive nanopatterning of a holography mask directly onto the sample, which can alter the sample properties, forces a fixed field-of-view, and leads to a low signal-to-noise ratio at high resolution. In this work, we propose using wavefront-shaping diffractive optics to create a structured probe with full control of its phase at the sample plane, circumventing the need for a mask. We demonstrate in silico that the method can image nanostructures and magnetic textures and validate our approach with a visible light-based experiment. The method enables investigation of a plethora of phenomena at the nanoscale including magnetic and electronic phase coexistence in solids, with further uses in soft and biological matter research.

Keskinbora, Kahraman↗
DOE OSTI2017

Surface-Induced Dissociation of Protein Complexes in a Hybrid Fourier Transform Ion Cyclotron Resonance Mass Spectrometer

Mass spectrometry continues to develop as a valuable tool in the analysis of proteins and protein complexes. In protein complex mass spectrometry studies, surface-induced dissociation (SID) has been successfully applied in quadrupole time-of-flight (Q-TOF) instruments. SID provides structural information on non-covalent protein complexes that is complementary to other techniques. However, the mass resolution of Q-TOF instruments can limit the information that can be obtained for protein complexes by SID. Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) provides ultrahigh resolution and ultrahigh mass accuracy measurements. In this study, an SID device was designed and successfully installed in a hybrid FT-ICR instrument in place of the standard gas collision cell. The SID-FT-ICR platform has been tested with several protein complex systems (homooligomers, a heterooligomer, and a protein-ligand complex, ranging from 53 kDa to 85 kDa), and the results are consistent with data previously acquired on Q-TOF platforms, matching predictions from known protein interface information. SID fragments with the same m/z but different charge states are well-resolved based on distinct spacing between adjacent isotope peaks, and the addition of metal cations and ligands can also be isotopically resolved with the ultrahigh mass resolution available in FT-ICR.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2020

Novel Strategy To Analyze Fourier Transform Ion Cyclotron Resonance Mass Spectrometry Data of Biomass Pyrolysis Oil for Oligomeric Structure Assignment

Among the most prominent challenges for the analysis of biomass pyrolysis products is the characterization of the abundant oligomer fraction of bio-oil. This fraction is principally made up of pyrolytic lignins and dehydrated, highly modified sugar oligomers, called humins, in liquid phase. An emerging technique for analysis of this oligomer fraction is high-resolution Fourier transform-ion cyclotron resonance mass spectrometry (FT-ICR MS), which allows for accurate determination of C x H y O z formulae for detected oligomers. Additionally, using simple dehydration and fragmentation reaction schemes, similar formulae can be developed from cellulose-, hemicellulose- and lignin-derived oligomers, which are primary depolymerization products. In this paper, FT-ICR MS analysis is coupled with combinatoric dehydration and fragmentation modeling in order to match experimentally detected bio-oil oligomers with hypothetical pathways for their formation during pyrolysis. In this way, we present a novel strategy by which oligomeric structures can be proposed for bio-oils. Using this approach, it becomes possible to advance the understanding of both the molecular structures comprising the bio-oil oligomer fraction and the pathways by which these structures form during biomass pyrolysis reactions.

09 BIOMASS FUELS↗
DOE OSTI2020

Quantum Fourier transform revisited

Summary The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a particular matrix decomposition of the discrete Fourier transform (DFT) matrix. In this paper, we show that the quantum Fourier transform (QFT) can be derived by further decomposing the diagonal factors of the FFT matrix decomposition into products of matrices with Kronecker product structure. We analyze the implication of this Kronecker product structure on the discrete Fourier transform of rank‐1 tensors on a classical computer. We also explain why such a structure can take advantage of an important quantum computer feature that enables the QFT algorithm to attain an exponential speedup on a quantum computer over the FFT algorithm on a classical computer. Further, the connection between the matrix decomposition of the DFT matrix and a quantum circuit is made. We also discuss a natural extension of a radix‐2 QFT decomposition to a radix‐ d QFT decomposition. No prior knowledge of quantum computing is required to understand what is presented in this paper. Yet, we believe this paper may help readers to gain some rudimentary understanding of the nature of quantum computing from a matrix computation point of view.

Camps, Daan↗
DOE OSTI2024

Highly-efficient quantum Fourier transformations for certain non-Abelian groups

Quantum Fourier transformations are an essential component of many quantum algorithms, from prime factoring to quantum simulation. While the standard Abelian QFrT is well studied, important variants corresponding to non-Abelian groups of interest have seen less development. In particular, fast non-Abelian Fourier transformations are important components for both quantum simulations of field theories as well as approaches to the non-Abelian hidden subgroup problem. In this work, we present fast quantum Fourier transformations for a number of non-Abelian groups of interest for high energy physics, B T , B O , 6 Δ ( 27 ) , Δ ( 54 ) , and Σ ( 36 × 3 ) . For each group, we derive explicit quantum circuits and estimate resource scaling for fault-tolerant implementations. Our work shows that the development of a fast Fourier transformation can substantively reduce simulation costs by an up to three orders of magnitude for the finite groups that we have investigated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Direct interpolative construction of the discrete Fourier transform as a matrix product operator

The quantum Fourier transform (QFT), which can be viewed as a reindexing of the discrete Fourier transform (DFT), has been shown to be compressible as a low-rank matrix product operator (MPO) or quantized tensor train (QTT) operator. However, the original proof of this fact does not furnish a construction of the MPO with a guaranteed error bound. Meanwhile, the existing practical construction of this MPO, based on the compression of a quantum circuit, is not as efficient as possible. We present a simple closed-form construction of the QFT MPO using the interpolative decomposition, with guaranteed near-optimal compression error for a given rank. This construction can speed up the application of the QFT and the DFT, respectively, in quantum circuit simulations and QTT applications. We also connect our interpolative construction to the approximate quantum Fourier transform (AQFT) by demonstrating that the AQFT can be viewed as an MPO constructed using a different interpolation scheme.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Fast Fourier Transform for multivariate aggregate claims

The Fast Fourier Transform provides an alternative approximate method to evaluate the distribution of aggregate losses in insurance and finance. The efficiency of this method has already been proved for univariate and bivariate insurance models; therefore, in this paper, we extend it to a multivariate setting by considering its application to a particular model that includes losses of different types and dependency between them. Since the Fourier transform method works with truncated claims distributions, it can generate aliasing errors by wrapping around the probability mass that lies at the truncation point below this point. To eliminate this problem, we also discuss a suitable change of measure called exponential tilting that forces the tail of the distribution to decrease at exponential rate. Other possible errors are also discussed. We also illustrate the method on several numerical examples.

97 MATHEMATICS AND COMPUTING↗