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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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Pattern-enhanced Resonant Soft X-ray Scattering for Operando monitoring of electrochemical solid-liquid interfaces

Unveiling interfaces at sub-nanometer scales is essential for advancing the understanding of complex chemical transformations. However, characterizing solid-liquid interfaces with high dimensional sensitivity and temporal resolution remains challenging, due to their dynamic nature and inaccessibility by conventional probes. Here we present an approach, Pattern-enhanced Resonant Soft X-ray Scattering, to overcome the challenges. Rooted in a “sample-as-optics” philosophy, this technique utilizes precisely engineered line-grating nanopatterns to modulate near-field X-ray illumination, coherently enhancing scattering signals from the line-gratings. We implement the method using Ni line-grating nanopatterns in electrochemical water oxidation. The periodic nanostructures serve as diffractive optical elements to reveal the Ni oxidation gradients and structural dynamics at the electrode-electrolyte interfaces. Finite-element simulations corroborate the observed trends by modeling variations in compositions and structures during electrocatalysis. Through integrating advanced sample design with coherent wave nature of soft X-rays, our approach opens accessible pathways to operando exploring chemical evolution and sub-nanometer dimensional variations simultaneously in electrochemical systems. This non-destructive method is efficient and element-specific, making it valuable for probing chemical and dimensional dynamics with appropriate modeling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Nanoscale Chemical Reaction Imaging at the Solid-Liquid Interface via TERS

Plasmon-enhanced chemical transformations at the solid-liquid interface can be imaged with high sensitivity, chemical selectivity, and nanoscale precision through tip-enhanced Raman scattering (TERS). We demonstrate the latter for the first time through measurements aimed at (i) locating plasmonic hotspots at the solid-liquid interface at which chemical transformations take place, (ii) monitoring the evolution from reactants to products through their distinct Raman spectra, and (iii) 2D correlation analysis of Raman time trajectories to unambiguously extract the spectral components that mark chemical transformation and to understand the correlations between the product and parent signatures. For our proof-of-principle study, we select a model plasmon-enhanced chemical process, namely, the dimerization of p-nitrothiophenol to dimercaptoazobenzene, but now, at the solid-liquid interface. Our plasmonic construct otherwise consists of chemically functionalized gold microplates in aqueous solution, which we image using a gold-coated TERS probe irradiated at 633-nm. Overall, we demonstrate chemical reaction imaging in aqueous solution via TERS for the first time, herein, at a pixel-limited lateral spatial resolution of 10 nm.

Bhattarai, Ashish↗
DOE OSTI2016

Laser induced structural transformation in chalcogenide based superlattices

Superlattices made of alternating layers of nominal GeTe and Sb{sub 2}Te{sub 3} have been studied by micro-Raman spectroscopy. A structural irreversible transformation into ordered GeSbTe alloy is induced by high power laser light exposure. The intensity ratio of anti-Stokes and Stokes scattering under laser illumination gives a maximum average temperature in the sample of 177 °C. The latter is lower than the growth temperature and of 400 °C necessary by annealing to transform the structure in a GeSbTe alloy. The absence of this configuration after in situ annealing even up to 300 °C evidences an electronic excitation induced-transition which brings the system into a different and stable crystalline state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1976

Effects of multiple scattering on light pulses reflected by turbid atmospheres

Multiple scattering contributions to lidar returns from turbid atmospheres are derived by means of an analytical theory. It is assumed that scattering takes place mainly at small angles except for one event that scatters the light backward. The phase functions are approximated by the sum of Gaussian functions of the scattering angle in both the forward and backward directions. The three-dimensional radiative transfer equation is transformed to a one-dimensional problem by means of Fourier transforms. Neumann solutions to the transformed equation of radiative transfer are then found. A number of examples are presented for cloud, fog and haze models. The results are found to be in satisfactory agreement with results obtained from the Monte Carlo analysis of Kunkel (1974) and the theory of light pulses doubly scattered by turbid atmospheres which was developed by Eloranta (1972).

Weinman, J. A.↗
DOE OSTI2018

Infrared and Raman spectroscopy of α-ZrW 2 O 8 : A comprehensive density functional perturbation theory and experimental study

We report that cubic zirconium tungstate (α-ZrW 2 O 8 ), a well-known negative thermal expansion material, has been investigated within the framework of density functional perturbation theory (DFPT), combined with experimental characterization to assess and validate computational results. Using combined Fourier transform infrared measurements and DFPT calculations, new and extensive assignments were made for the far-infrared (<400 cm -1 ) spectrum of α-ZrW 2 O 8 . Lastly, a systematic comparison of DFPT-simulated infrared, Raman, and phonon density-of-state spectra with Fourier transform far-/mid-infrared and Raman data collected in this study, as well as with available inelastic neutron scattering measurements, shows the superior accuracy of the PBEsol exchange-correlation functional over standard PBE calculations for studying the spectroscopic properties of this material.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Toward accurate measurement of electromagnetic field by retrieving and refining the center position of non-uniform diffraction disks in Lorentz 4D-STEM

Recent advancement in scanning transmission electron microscopy (STEM) allows the use of 4D-STEM, a technique that captures an electron diffraction pattern at each scan point in STEM, to measure electrostatic and magnetic potential and field in materials. However, accurate measurement, separation of the magnetic and electric signals, and removal of artifacts remain challenging, especially in the presence of complex non-uniform diffraction contrast within the disks. In this work, based on dynamic simulations of 4D-STEM patterns built upon superstructures consisting of millions of atoms to account for different sample thickness and edge geometries, we show how the shape and intensity distribution of the central disk are affected by multiple scattering. We propose a robust refinement procedure through iteration of the spin-sensitive peak position of the disk-center in the circular Hough transform filtered images from experimental Lorentz 4D-STEM dataset after minimizing the possible artifacts, such as those due to the change of thickness, dynamic scattering, and scanning process. We verify that caution must be taken as in practice the rigid-disk-shift model used to reconstruct induction maps can easily break down due to disk-protrusion when there exists a nonconstant phase gradient or thickness within the width of the probe. Through quantitative analysis and comparing experiment with calculation the effect of the non-spin-related intensity distribution inside the disk as well as that causes the disk shift due to the intensity-protrusion can be removed, and high-quality magnetic field mapping is possible.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Efficient scatter distribution estimation and correction in CBCT using concurrent Monte Carlo fitting

Purpose: X-ray scatter is a significant impediment to image quality improvements in cone-beam CT (CBCT). The authors present and demonstrate a novel scatter correction algorithm using a scatter estimation method that simultaneously combines multiple Monte Carlo (MC) CBCT simulations through the use of a concurrently evaluated fitting function, referred to as concurrent MC fitting (CMCF). Methods: The CMCF method uses concurrently run MC CBCT scatter projection simulations that are a subset of the projection angles used in the projection set, P, to be corrected. The scattered photons reaching the detector in each MC simulation are simultaneously aggregated by an algorithm which computes the scatter detector response, S{sub MC}. S{sub MC} is fit to a function, S{sub F}, and if the fit of S{sub F} is within a specified goodness of fit (GOF), the simulations are terminated. The fit, S{sub F}, is then used to interpolate the scatter distribution over all pixel locations for every projection angle in the set P. The CMCF algorithm was tested using a frequency limited sum of sines and cosines as the fitting function on both simulated and measured data. The simulated data consisted of an anthropomorphic head and a pelvis phantom created from CT data, simulated with and without the use of a compensator. The measured data were a pelvis scan of a phantom and patient taken on an Elekta Synergy platform. The simulated data were used to evaluate various GOF metrics as well as determine a suitable fitness value. The simulated data were also used to quantitatively evaluate the image quality improvements provided by the CMCF method. A qualitative analysis was performed on the measured data by comparing the CMCF scatter corrected reconstruction to the original uncorrected and corrected by a constant scatter correction reconstruction, as well as a reconstruction created using a set of projections taken with a small cone angle. Results: Pearson’s correlation, r, proved to be a suitable GOF metric with strong correlation with the actual error of the scatter fit, S{sub F}. Fitting the scatter distribution to a limited sum of sine and cosine functions using a low-pass filtered fast Fourier transform provided a computationally efficient and accurate fit. The CMCF algorithm reduces the number of photon histories required by over four orders of magnitude. The simulated experiments showed that using a compensator reduced the computational time by a factor between 1.5 and 1.75. The scatter estimates for the simulated and measured data were computed between 35–93 s and 114–122 s, respectively, using 16 Intel Xeon cores (3.0 GHz). The CMCF scatter correction improved the contrast-to-noise ratio by 10%–50% and reduced the reconstruction error to under 3% for the simulated phantoms. Conclusions: The novel CMCF algorithm significantly reduces the computation time required to estimate the scatter distribution by reducing the statistical noise in the MC scatter estimate and limiting the number of projection angles that must be simulated. Using the scatter estimate provided by the CMCF algorithm to correct both simulated and real projection data showed improved reconstruction image quality.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

SU-E-J-23: An Accurate Algorithm to Match Imperfectly Matched Images for Lung Tumor Detection Without Markers

Purpose: In order to locate lung tumors on projection images without internal markers, digitally reconstructed radiograph (DRR) is created and compared with projection images. Since lung tumors always move and their locations change on projection images while they are static on DRRs, a special DRR (background DRR) is generated based on modified anatomy from which lung tumors are removed. In addition, global discrepancies exist between DRRs and projections due to their different image originations, scattering, and noises. This adversely affects comparison accuracy. A simple but efficient comparison algorithm is reported. Methods: This method divides global images into a matrix of small tiles and similarities will be evaluated by calculating normalized cross correlation (NCC) between corresponding tiles on projections and DRRs. The tile configuration (tile locations) will be automatically optimized to keep the tumor within a single tile which has bad matching with the corresponding DRR tile. A pixel based linear transformation will be determined by linear interpolations of tile transformation results obtained during tile matching. The DRR will be transformed to the projection image level and subtracted from it. The resulting subtracted image now contains only the tumor. A DRR of the tumor is registered to the subtracted image to locate the tumor. Results: This method has been successfully applied to kV fluoro images (about 1000 images) acquired on a Vero (Brainlab) for dynamic tumor tracking on phantom studies. Radiation opaque markers are implanted and used as ground truth for tumor positions. Although, other organs and bony structures introduce strong signals superimposed on tumors at some angles, this method accurately locates tumors on every projection over 12 gantry angles. The maximum error is less than 2.6 mm while the total average error is 1.0 mm. Conclusion: This algorithm is capable of detecting tumor without markers despite strong background signals.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Classical eikonal from Magnus expansion

In a classical scattering problem, the classical eikonal is defined as the generator of the canonical transformation that maps in-states to out-states. It can be regarded as the classical limit of the log of the quantum S-matrix. In a classical analog of the Born approximation in quantum mechanics, the classical eikonal admits an expansion in oriented tree graphs, where oriented edges denote retarded/advanced worldline propagators. The Magnus expansion, which takes the log of a time-ordered exponential integral, offers an efficient method to compute the coefficients of the tree graphs to all orders. We exploit a Hopf algebra structure behind the Magnus expansion to develop a fast algorithm which can compute the tree coefficients up to the 12th order (over half a million trees) in less than an hour. In a relativistic setting, our methods can be applied to the post-Minkowskian (PM) expansion for gravitational binaries in the worldline formalism. We demonstrate the methods by computing the 3PM eikonal and find agreement with previous results based on amplitude methods. Importantly, the Magnus expansion yields a finite eikonal, while the naïve eikonal based on the time-symmetric propagator is infrared-divergent from 3PM on.

Black Holes↗
DOE OSTI2021

Toward nonthermal control of excited quantum materials: framework and investigations by ultrafast electron scattering and imaging

Quantum material systems upon applying ultrashort laser pulses provide a rich platform to access excited material phases and their transformations that are not entirely like their equilibrium counterparts. The addressability and potential controls of metastable or long-trapped out-of-equilibrium phases have motivated interests both for the purposes of understanding the nonequilibrium physics and advancing the quantum technologies. Thus far, the dynamical spectroscopic probes eminently focus on microscopic electronic and phonon responses. For characterizing the long-range dynamics, such as order parameter fields and fluctuation effects, the ultrafast scattering probes offer direct sensitivity. Bridging the connections between the microscopic dynamics and macroscopic responses is central toward establishing the nonequilibrium physics behind the light-induced phases. Here, we present a path toward such understanding by cross-examining the structure factors associated with different dynamical states obtained from ultrafast electron scattering, imaging, and modeling. We give the basic theoretical framework on describing the non-equilibrium scattering problems and briefly describe how such framework relates to the out-of-equilibrium phenomena. We give effective models outlining the emergences of nonthermal critical points, hidden phases, and non-equilibrium relaxational responses from vacuum-suspended rare-earth tritellurides, tantalum disulfides thin films, and vanadium dioxide nanocrystalline materials upon light excitations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Interfacial Reactivity and Speciation Emerging from Na-Montmorillonite Interactions with Water and Formic Acid at 200 °C: Insights from Reactive Molecular Dynamics Simulations, Infrared Spectroscopy, and X-ray Scattering Measurements

Reactive organic fluid - mineral interactions at elevated temperatures contribute to the evolution of planetary matter. One of the less studied but important transformations in this regard involves the reactions of formic acid with naturally occurring clays such as sodium montmorillonite. To advance a mechanistic understanding of these interactions, we use ReaxFF reactive molecular dynamics simulations in conjunction with infrared (IR) spectroscopy and X-ray scattering experiments to investigate the speciation behavior of water-formic acid mixtures on sodium montmorillonite interfaces at 473 K and 1 atm. Using a newly developed reactive forcefield, we show that the experimental IR spectra of unreacted and reacted mixture can be accurately reproduced by ReaxFF/MD. We further benchmark the simulation predictions of sodium carbonate and bicarbonate formation in the clay interlayers using Small and Wide-Angle X-ray Scattering measurements. Subsequently, leveraging the benchmarked forcefield, we interrogate the pathway of speciation reactions with emphasis on carbonate, formate, and hydroxide groups elucidating the energetics, transition states, intermediates, and preferred products. Further, we also delineate the differences in reactivities and catalytic effects of clay edges, facets, and interlayers owing to their local chemical environments, which have far reaching consequences in their speciation behavior. The experimental and simulation approaches described in this study and the transferable forcefields can be applied translationally to advance the science of clay-fluid interactions for several applications including subsurface fluid storage and recovery and clay-pollutant dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Microstructure evolution and properties of graphene nanoplatelets reinforced aluminum matrix composites

Highlights: • Lamellar structure of GNPs fibers and Al matrix was obtained in the rolling direction. • Stacking faults were observed in Al grains due to greatly increased GNPs/Al interfaces. • Strength of Al-0.2 wt% GNPs increased 36.8% with negligible electrical conductivity loss. - Abstract: Aluminum matrix composites reinforced with graphene nanoplatelets (GNPs) were prepared by continuous casting and subsequent rolling. Al-GNPs master alloy, prepared by ball milling and cold pressing, was added into Al melts to fabricate the composites. Microstructure evolution of the composites were observed using scanning electron microscopy (SEM), transmission electron microscopy (TEM) and electron back scattered diffraction (EBSD). GNPs distributed uniformly in the as-cast specimen and then transformed into fibers in the rolling direction after deformation and finally a lamellar structure formed in the composites. Raman spectra showed that the structural damage of GNPs mainly came from ball milling. The interface between GNPs and Al was well combined in general while a few microcracks were observed, which reduced the ductility of the composites and no adverse aluminum carbide (Al{sub 4}C{sub 3}) was detected at the interface. Stacking faults were observed interior of the aluminum grain, which may due to the existence of plentiful interface introduced by GNPs. Fracture observation revealed that the load transferred from Al matrix to GNPs. The ultimate tensile strength of Al-0.2 wt% GNPs composites was about 36.8% higher than that of pure Al with the same casting and rolling process, which should result from the lamellar structure and load transfer, while the conductivity of the composites decreased slightly, indicating that interface scattering between Al and GNPs is very limited. The investigation results show that Al-GNPs composite is potential for high strength and high conductivity application.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

Hydrogen Diffusivity Measurements of YH 1.87 Moderator Material with Incoherent Quasielastic Neutron Scattering

Yttrium hydride is an optimal choice of moderator material for thermal neutron spectrum reactors requiring small core volumes. The Transformation Challenge Reactor (TCR) program at Oak Ridge National Laboratory (ORNL) aims to develop an additively manufactured microreactor core by leveraging recent advances in materials, manufacturing, data analytics, and high-fidelity modeling and simulation. Yttrium hydride was selected as the moderator material for TCR due to its high moderating power, which enables the spatially efficient reactor design and thermal stability that is superior when compared with zirconium hydride. Hydrogen desorption from yttrium hydride is expected at elevated temperatures, posing safety and performance concerns. As a lifetime component in advanced reactors, appropriate strategies to mitigate hydrogen release from yttrium hydride over long-term reactor operation are required. Understanding hydrogen mobility in yttrium hydride provides the scientific basis for developing a hydrogen barrier for hydride moderator and predicting the hydrogen redistribution within the material during various operational conditions. This study investigated the hydrogen motion in YH 1.87 as a function of temperature ranging from 200 to 1,173 K using incoherent quasielastic neutron scattering (IQNS) at the Spallation Neutron Source (SNS). The results are presented and discussed in terms of hydrogen self-diffusion coefficients, activation energy for translational hydrogen motion, and hydrogen jump distances. Based on the IQNS data, YH 1.87 is found to be stable at high temperatures with no translational H motion below 1,023 K within the IQNS detection limits. In the temperature range of 1,073–1,173 K, hydrogen diffusivity in YH 1.87 is $D = 4.57 X 10^{⁻3} [m^2/s] exp (⁻\frac{1.73[eV]}{RT}$). The hydrogen concentration’s dependence on hydrogen diffusivity is also discussed in this report.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Solitons in lattice field theories via tight-binding supersymmetry

Reflectionless potentials play an important role in constructing exact solutions to classical dynamical systems (such as the Korteweg-de Vries equation), non-perturbative solutions of various large-N field theories (such as the Gross-Neveu model), and closely related solitonic solutions to the Bogoliubov-de Gennes equations in the theory of superconductivity. These solutions rely on the inverse scattering method, which reduces these seemingly unrelated problems to identifying reflectionless potentials of an auxiliary one-dimensional quantum scattering problem. There are several ways of constructing these potentials, one of which is quantum mechanical supersymmetry (SUSY). In this paper, motivated by recent experimental platforms, we generalize this framework to develop a theory of lattice solitons. We first briefly review the classical inverse scattering method in the continuum limit, focusing on the Korteweg-de Vries (KdV) equation and SU(N) Gross-Neveu model in the large N limit. We then generalize this methodology to lattice versions of interacting field theories. Our analysis hinges on the use of trace identities, which are relations connecting the potential of an equation of motion to the scattering data. For a discrete Schrödinger operator, such trace identities had been known as far back as Toda; however, we derive a new set of identities for the discrete Dirac operator. We then use these identities in a lattice Gross-Neveu and chiral Gross-Neveu (Nambu-Jona-Lasinio) model to show that lattice solitons correspond to reflectionless potentials associated with the discrete scattering problem. These models are of significance as they are equivalent to a mean-field theory of a lattice superconductor. To explicitly construct these solitons, we generalize supersymmetric quantum mechanics to tight-binding models. We show that a matrix transformation exists that maps a tight-binding model to an isospectral one which shares the same structure and scattering properties. The corresponding soliton solutions have both modulated hopping and onsite potential, the former of which has no analogue in the continuum limit. We explicitly compute both topological and non-topological soliton solutions as well as bound state spectra in the aforementioned models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2000

Time-resolved diffusion tomographic 2D and 3D imaging in highly scattering turbid media

A method for imaging objects in highly scattering turbid media. According to one embodiment of the invention, the method involves using a plurality of intersecting source/detectors sets and time-resolving equipment to generate a plurality of time-resolved intensity curves for the diffusive component of light emergent from the medium. For each of the curves, the intensities at a plurality of times are then inputted into the following inverse reconstruction algorithm to form an image of the medium: wherein W is a matrix relating output at source and detector positions r.sub.s and r.sub.d, at time t, to position r, .LAMBDA. is a regularization matrix, chosen for convenience to be diagonal, but selected in a way related to the ratio of the noise, to fluctuations in the absorption (or diffusion) X.sub.j that we are trying to determine: .LAMBDA..sub.ij =.lambda..sub.j .delta..sub.ij with .lambda..sub.j = /<.DELTA.Xj.DELTA.Xj> Y is the data collected at the detectors, and X.sup.k is the kth iterate toward the desired absorption information. An algorithm, which combines a two dimensional (2D) matrix inversion with a one-dimensional (1D) Fourier transform inversion is used to obtain images of three dimensional hidden objects in turbid scattering media.

Alfano, Robert R.↗
DOE OSTI2017

Understanding Anion, Water, and Methanol Transport in a Polyethylene- b -poly(vinylbenzyl trimethylammonium) Copolymer Anion-Exchange Membrane for Electrochemical Applications

Herein, we report the anion and water transport properties of an anion-exchange membrane (AEM) comprising a block copolymer of polyethylene and poly- (vinylbenzyl trimethylammonium) (PE-b-PVBTMA) with an ion-exchange capacity (IEC) of 1.08 mequiv/g. The conductivity varied little among the anions CO3 2-, HCO3 -, and F-, with a value of Ea ≈ 20 kJ/mol and a maximum fluoride conductivity of 34 mS/cm at 90 °C and 95% relative humidity. The Br- conductivity showed a transition at 60 °C. Pulsed gradient stimulated spin echo nuclear magnetic resonance (PGSE NMR) experiments showed that water diffusion in this AEM is heterogeneous and is affected by the anion present, being fastest in the presence of F-. We determined the methanol self-diffusion in this membrane and observed that it is lower than that in Nafion 117, because of the lower water uptake. This article reports the first measurements of 13C-labeled bicarbonate self-diffusion in an AEM using PGSE NMR spectrometry, which was found to be significantly slower than F- self-diffusion. Back-calculation of the bicarbonate conductivity using the Nernst-Einstein equation gave a value that was significantly lower than the measured value, implying that bicarbonate transport involves OH- in the transport mechanism. Fourier transform infrared spectroscopy, PGSE NMR spectrometry, and small-angle X-ray scattering (SAXS) indicated the presence of different types of waters present in the membrane at different length scales. The SAXS data indicated that there is a water-rich region within the hydrophilic domains of the polymer that has a temperature dependence in intensity at 95% relative humidity (RH).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1980

The effects of seeing on the reflected spectrum of Uranus and Neptune

The results of a redetermination of the rotational periods of Uranus and Neptune, based on spectrograms obtained with the coude spectrograph of the 5 m Hale telescope, are presented. The effects of image motion on the shape of the spectral lines reflected by a planet rotating as a solid body and coherently scattering solar light, has been studied analytically. A general relation between the seeing transformed velocities at any point on the disk and those at the equator is established. It is shown that, for the case of Gaussian seeing, the brightness continuum of the smeared disk contains all the information required to derive the shape of the reflected lines. The shift, change in r.m.s. width, and asymmetry of the seeing transformed lines at the equator have been numerically evaluated for the brightness distribution of Uranus determined from Stratoscope II.

Muench, G.↗
NASA NTRS1999

Time-resolved diffusion tomographic 2D and 3D imaging in highly scattering turbid media

A method for imaging objects in highly scattering turbid media. According to one embodiment of the invention, the method involves using a plurality of intersecting source/detectors sets and time-resolving equipment to generate a plurality of time-resolved intensity curves for the diffusive component of light emergent from the medium. For each of the curves, the intensities at a plurality of times are then inputted into the following inverse reconstruction algorithm to form an image of the medium: ##EQU1## wherein W is a matrix relating output at source and detector positions r.sub.s and r.sub.d, at time t, to position r, .LAMBDA. is a regularization matrix, chosen for convenience to be diagonal, but selected in a way related to the ratio of the noise, to fluctuations in the absorption (or diffusion) X.sub.j that we are trying to determine: .LAMBDA..sub.ij =.lambda..sub.j .delta..sub.ij with .lambda..sub.j = /<.DELTA.Xj.DELTA.Xj> Y is the data collected at the detectors, and X.sup.k is the kth iterate toward the desired absoption information. An algorithm, which combines a two dimensional (2D) matrix inversion with a one-dimensional (1D) Fourier transform inversion is used to obtain images of three dimensional hidden objects in turbid scattering media.

Alfano, Robert R.↗