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Near-Infrared Dual Greenhouse Gas Sensor Based on Hollow-Core Photonic Crystal Fiber for Gas-Cell In-Situ Applications. SENSORS (BASEL, SWITZERLAND) 2024; 24:1670. [PMID: 38475206 DOI: 10.3390/s24051670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2024] [Revised: 02/05/2024] [Accepted: 02/28/2024] [Indexed: 03/14/2024]
Abstract
A greenhouse gas sensor has been developed to simultaneously detect multiple gas species within a hollow-core photonic bandgap fiber (HC-PBF) structure entirely composed of fibers. To enhance sensitivity, the gas cell consists of HC-PBF enclosed between two single-mode fibers fused with a reflective end surface to double the absorption length. The incorporation of side holes for gas diffusion allows for analysis of the relationship between gas diffusion speed, number of drilled side holes, and energy loss. As the number of drilled holes increases, the response time decreases to less than 3 min at the expense of energy loss. Gas experiments demonstrated detection limits of 0.1 ppm for methane and 2 ppm for carbon dioxide, with an average time of 50 s. In-situ testing conducted in rice fields validates the effectiveness of the developed gas detection system using HC-PBF cells, establishing all-fiber sensors with high sensitivity and rapid response.
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Core and Shell Contributions to the Phonon Spectra of CdTe/CdS Quantum Dots. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:921. [PMID: 36903799 PMCID: PMC10004847 DOI: 10.3390/nano13050921] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/13/2023] [Revised: 02/20/2023] [Accepted: 03/01/2023] [Indexed: 06/18/2023]
Abstract
The parameters of the shell and interface in semiconductor core/shell nanocrystals (NCs) are determinant for their optical properties and charge transfer but are challenging to be studied. Raman spectroscopy was shown earlier to be a suitable informative probe of the core/shell structure. Here, we report the results of a spectroscopic study of CdTe NCs synthesized by a facile route in water, using thioglycolic acid (TGA) as a stabilizer. Both core-level X-ray photoelectron (XPS) and vibrational (Raman and infrared) spectra show that using thiol during the synthesis results in the formation of a CdS shell around the CdTe core NCs. Even though the spectral positions of the optical absorption and photoluminescence bands of such NCs are determined by the CdTe core, the far-infrared absorption and resonant Raman scattering spectra are dominated by the vibrations related with the shell. The physical mechanism of the observed effect is discussed and opposed to the results reported before for thiol-free CdTe Ns as well as CdSe/CdS and CdSe/ZnS core/shell NC systems, where the core phonons were clearly detected under similar experimental conditions.
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Correlation between Infrared Absorption and Lithium Sublattice Disorder in Magnesium-Doped Lithium Niobate. MATERIALS (BASEL, SWITZERLAND) 2023; 16:797. [PMID: 36676531 PMCID: PMC9867136 DOI: 10.3390/ma16020797] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Revised: 12/29/2022] [Accepted: 01/09/2023] [Indexed: 06/17/2023]
Abstract
Lithium niobate is a ferro- and piezoelectric material with excellent optical properties and a wide variety of applications. The defect structures of congruent and Mg-doped crystals are still under intense discussion. In this work, undoped lithium niobate and magnesium-doped lithium niobate grown from congruent melt with the addition of 0 to 9 mol% MgO were investigated by infrared absorption, establishing the dependence of the absorbance on the Mg-doping level in two bands related to OH- stretching vibrations. The absorption band at 3485 cm-1 peaks at a MgO concentration in melt of 1 mol% and vanishes for MgO concentrations above the threshold level for optical damage suppression (4.8 mol%). A corresponding peak occurs in the minimum yield of the 7Li(p,α)4He reaction during ion channeling measurements, indicating a maximum of disorder in the Li sublattice. A possible explanation for this correlation is the attribution of this absorption band to ilmenite stacking fault sequences instead of isolated NbLi antisites in undoped and low-doped material. On the other hand, the OH- absorption band at 3535 cm-1 stays weak up to the MgO concentration threshold, and then increases, hinting to a defect related to the increase of vacancies due to the lack of charge compensation.
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Low-temperature grown vertically aligned carbon nanotube array for an optimal infrared bolometer. NANOTECHNOLOGY 2021; 32:505719. [PMID: 34547736 DOI: 10.1088/1361-6528/ac28dc] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2021] [Accepted: 09/21/2021] [Indexed: 06/13/2023]
Abstract
Vertically aligned carbon nanotube (VACNT) arrays have been explored as an absorber of thermal-type photodetectors. A long and dense VACNT array absorbs a wide spectral range of incident light with high absorption rate, but has a high thermal mass that results in a low response speed. To achieve a small thermal mass, a shorter and less dense VACNT array is needed. In addition, the high temperature needed to grow the VACNTs is detrimental to the functional sensing materials of the photodetector. The height, density, and growth temperature of VACNTs need to be optimized to achieve a working absorber that has high absorption rate and a high response speed. In this work, a low-temperature plasma enhanced chemical vapor deposition process is used to prepare various VACNT arrays with different heights and densities by controlling the CNT growth parameters. The absorption coefficients of the resulting samples are measured with Fourier transform infrared spectroscopy. An effective medium theory (EMT) is adopted to establish a working model of the VACNTs. Using experimentally extracted CNT density and height as fitting parameters, the EMT model is fitted to obtain theoretical absorption coefficients, which are found to be comparable to the experimentally measured absorption coefficients. Our experimental and theoretical investigations pave the way for future studies to integrate CNTs with infrared photodetectors.
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Eco-Friendly AgBiS 2 Nanocrystal/ZnO Nanowire Heterojunction Solar Cells with Enhanced Carrier Collection Efficiency. ACS APPLIED MATERIALS & INTERFACES 2021; 13:3969-3978. [PMID: 33448786 DOI: 10.1021/acsami.0c19435] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
AgBiS2 nanocrystals (NCs) are nontoxic, lead-free, and near-infrared absorbing materials. Eco-friendly solar cells were constructed using interdigitated layers of ZnO nanowires (NWs) and AgBiS2 NCs, with the aim of elongating the otherwise short carrier diffusion length of the AgBiS2 NC assembly. AgBiS2 NCs were uniformly infiltrated into the ZnO NW layers using a low-cost and easily scalable dip coating method. The resulting ZnO NW/AgBiS2 NC interdigitated structures provided efficient carrier pathways in constructed nanowire solar cells (NWSCs), composed of a transparent electrode/ZnO NW/AgBiS2 NC interdigitated layer/P3HT hole transport layer/Au. The photocurrent external quantum efficiency (EQE) in the visible to near-infrared regions was enhanced compared to those of the control solar cells made with ZnO/AgBiS2 tandem layered structures. The maximum EQE for the NWSCs reached 82% in the visible region, which is higher than the EQE values previously reported for solar cells fabricated with ZnO/AgBiS2 NCs. Air stability tests on unsealed NWSCs demonstrated that 90% or more of the initial power conversion efficiency was maintained even after 6 months.
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Dependence of Heat Transport in Solids on Length-Scale, Pressure, and Temperature: Implications for Mechanisms and Thermodynamics. MATERIALS 2021; 14:ma14020449. [PMID: 33477677 PMCID: PMC7831911 DOI: 10.3390/ma14020449] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/04/2020] [Revised: 01/10/2021] [Accepted: 01/14/2021] [Indexed: 11/24/2022]
Abstract
Accurate laser-flash measurements of thermal diffusivity (D) of diverse bulk solids at moderate temperature (T), with thickness L of ~0.03 to 10 mm, reveal that D(T) = D∞(T)[1 − exp(−bL)]. When L is several mm, D∞(T) = FT−G + HT, where F is constant, G is ~1 or 0, and H (for insulators) is ~0.001. The attenuation parameter b = 6.19D∞−0.477 at 298 K for electrical insulators, elements, and alloys. Dimensional analysis confirms that D → 0 as L → 0, which is consistent with heat diffusion, requiring a medium. Thermal conductivity (κ) behaves similarly, being proportional to D. Attenuation describing heat conduction signifies that light is the diffusing entity in solids. A radiative transfer model with 1 free parameter that represents a simplified absorption coefficient describes the complex form for κ(T) of solids, including its strong peak at cryogenic temperatures. Three parameters describe κ with a secondary peak and/or a high-T increase. The strong length dependence and experimental difficulties in diamond anvil studies have yielded problematic transport properties. Reliable low-pressure data on diverse thick samples reveal a new thermodynamic formula for specific heat (∂ln(cP)/∂P = −linear compressibility), which leads to ∂ln(κ)/∂P = linear compressibility + ∂lnα/∂P, where α is thermal expansivity. These formulae support that heat conduction in solids equals diffusion of light down the thermal gradient, since changing P alters the space occupied by matter, but not by light.
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Nondispersive Infrared Gas Analyzer for Partial Pressure Measurements of a Tantalum Alkylamide During Vapor Deposition Processes. APPLIED SPECTROSCOPY 2020; 74:1219-1229. [PMID: 31617384 DOI: 10.1177/0003702819885182] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
A nondispersive infrared gas analyzer was demonstrated for investigating metal alkylamide precursor delivery for microelectronics vapor deposition processes. The nondispersive infrared analyzer was designed to simultaneously measure the partial pressure of pentakis(dimethylamido) tantalum, a metal precursor employed in high volume manufacturing vapor deposition processes to deposit tantalum nitride, and dimethylamine, the primary decomposition product of pentakis(dimethylamido) tantalum at typical delivery conditions for these applications. This sensor was based on direct absorption of pentakis(dimethylamido) tantalum and dimethylamine in the fingerprint spectral region. The nondispersive infrared analyzer optical response was calibrated by measuring absorbance as a function of dimethylamine and pentakis(dimethylamido) tantalum density. The difference between the mass of material removed from the ampoule during flow tests as measured gravimetrically and as determined optically, by calculating flow rates from the nondispersive infrared analyzer measurements, was only ≈2 %. The minimum detectable molecular densities for pentakis(dimethylamido) tantalum and dimethylamine were ≈2 × 1013 cm-3 and ≈5 × 1014 cm-3, respectively (with no signal averaging and for a sampling rate of 200 Hz), and the corresponding partial pressures were ≈0.1 Pa and ≈2 Pa for pentakis(dimethylamido) tantalum and dimethylamine, respectively (for an optical flow cell temperature of 93 ℃). Pentakis(dimethylamido) tantalum could be detected at all conditions of this investigation and likely the majority of conditions relevant to high volume manufacturing tantalum nitride deposition. Dimethylamine was not detected at all conditions in this study, because of a lower nondispersive infrared analyzer sensitivity to dimethylamine compared to pentakis(dimethylamido) tantalum and because conditions of this study were selected to minimize DMA production. While this nondispersive infrared gas analyzer was specifically developed for pentakis(dimethylamido) tantalum and dimethylamine, it is suitable for characterizing the vapor delivery of other metal alkylamide precursors and the corresponding amine decomposition products, although in the case of some metal alkylamides a different bandpass filter would be required.
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Self-Assembly of Carbon Black/AAO Templates on Nanoporous Si for Broadband Infrared Absorption. ACS APPLIED MATERIALS & INTERFACES 2020; 12:4081-4087. [PMID: 31875671 DOI: 10.1021/acsami.9b19107] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Broadband absorption in the mid-infrared region is of significance for wide applications, such as photo/thermal detection, infrared stealth, and thermal imaging. Recently, metal-based plasmonic absorbers have been developed in the mid-infrared region. However, the fabrication cost, thickness, and bandwidth of these absorbers applied in aerospace still need to be improved. In this study, we propose and experimentally demonstrate a large-area, rather thin, metal-free absorber with broadband mid-infrared absorption based on a low-cost self-assembly process. The metal-free absorber is fabricated by spraying carbon black nanoparticles onto 5 μm-thick transferrable anodic aluminum oxide (AAO) templates on nanoporous Si graded-index films, which are fabricated by ion irradiation. Experimental results show that the average absorbance can reach 97.5% in the range of 2.5-15.3 μm. Full-wave numerical simulations show that the electromagnetic fields are greatly enhanced into pores, as these random carbon black particles serve as scatter centers and couple light into 5 μm-thick AAO templates, enhancing the interaction of light with carbon black significantly, and reveal that the high-performance broadband absorption is attributed to the light-trapping effect. The significant light absorption combined with a low-cost, high-production self-assembly technique suggests that the absorber can be used in the fields of optoelectronics and integrated photonics.
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Abstract
We report updated infrared (IR) absorption measurements on vapor-deposited cryogenic parahydrogen (pH2) solids that indicate a ≈10% systematic error in our previous approach for determining a pH2 solid's thickness (S. Tam and M.E. Fajardo. Appl. Spectrosc. 2001. 55(12): 1634-1644). We provide corrected values for the integrated absorption intensities of the Q1(0)+S0(0) and S1(0)+S0(0) bands calculated over the 4495-4520 cm-1 and 4825-4855 cm-1 regions, respectively. New polarized IR absorption spectroscopy data demonstrate the insensitivity to polarization effects of the peak intensity of the QR(0) phonon sideband near 4228 cm-1. This feature provides an even quicker way for determining the thickness of a pH2 solid than via the integrated absorptions.
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Gas Leak Detection by Dilution of Atmospheric Oxygen. SENSORS 2017; 17:s17122804. [PMID: 29206133 PMCID: PMC5751694 DOI: 10.3390/s17122804] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/31/2017] [Revised: 11/18/2017] [Accepted: 11/30/2017] [Indexed: 11/16/2022]
Abstract
Gas leak detection is an important issue in infrastructure monitoring and industrial production. In this context, infrared (IR) absorption spectroscopy is a major measurement method. It can be applied in an extractive or remote detection scheme. Tunable laser spectroscopy (TLS) instruments are able to detect CH₄ leaks with column densities below 10 ppm·m from a distance of 30 m in less than a second. However, leak detection of non-IR absorbing gases such as N₂ is not possible in this manner. Due to the fact that any leaking gas displaces or dilutes the surrounding background gas, an indirect detection is still possible. It is shown by sensitive TLS measurements of the ambient background concentration of O₂ that N₂ leaks can be localized with extractive and standoff methods for distances below 1 m. Minimum leak rates of 0.1 mbar·L/s were determined. Flow simulations confirm that the leakage gas typically effuses in a narrow jet. The sensitivity is mainly determined by ambient flow conditions. Compared to TLS detection of CH₄ at 1651 nm, the indirect method using O₂ at 761 nm is experimentally found to be less sensitive by a factor of 100. However, the well-established TLS of O₂ may become a universal tool for rapid leakage screening of vessels that contain unknown or inexpensive gases, such as N₂.
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Nondispersive Infrared Gas Analyzer for Vapor Density Measurements of a Carbonyl-Containing Organometallic Cobalt Precursor. APPLIED SPECTROSCOPY 2017; 71:2632-2642. [PMID: 28707985 DOI: 10.1177/0003702817716939] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
A nondispersive infrared (NDIR) gas analyzer was demonstrated for measuring the vapor-phase density of the carbonyl-containing organometallic cobalt precurso μ2-η2-(tBu-acetylene) dicobalthexacarbonyl (CCTBA). This sensor was based on direct absorption by CCTBA vapor in the C≡O stretching spectral region and utilized a stable, broadband IR filament source, an optical chopper to modulate the source, a bandpass filter for wavelength isolation, and an InSb detector. The optical system was calibrated by selecting a calibration factor to convert CCTBA absorbance to a partial pressure that, when used to calculate CCTBA flow rate and CCTBA mass removed from the ampoule, resulted in an optically determined mass that was nominally equal to a gravimetrically-determined mass. In situ Fourier transform infrared (FT-IR) spectroscopy was performed simultaneously with the NDIR gas analyzer measurements under selected conditions in order to characterize potential spectroscopic interferences. Interference due to CO evolution from CCTBA was found to be small under the flow conditions employed here. A CCTBA minimum detectable molecular density as low as ≈3 × 1013 cm-3 was calculated (with no signal averaging and for a sampling rate of 200 Hz). While this NDIR gas analyzer was specifically tested for CCTBA, it is suitable for characterizing the vapor delivery of a range of carbonyl-containing precursors.
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Raman and Conductivity Analysis of Graphene for Biomedical Applications. MATERIALS 2016; 9:ma9110897. [PMID: 28774016 PMCID: PMC5457257 DOI: 10.3390/ma9110897] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/05/2016] [Revised: 11/01/2016] [Accepted: 11/01/2016] [Indexed: 11/16/2022]
Abstract
In this study, we present a comprehensive investigation of graphene's optical and conductive properties using confocal Raman and a Drude model. A comparative analysis between experimental findings and theoretical predictions of the material's changes and improvements as it transitioned from three-dimensional graphite is also presented and discussed. Besides spectral recording by Raman, which reveals whether there is a single, a few, or multi-layers of graphene, the confocal Raman mapping allows for distinction of such domains and a direct visualization of material inhomogeneity. Drude model employment in the analysis of the far-infrared transmittance measurements demonstrates a distinct increase of the material's conductivity with dimensionality reduction. Other particularly important material characteristics, including carrier concentration and time constant, were also determined using this model and presented here. Furthermore, the detection of micromolar concentration of dopamine on graphene surfaces not only proves that the Raman technique facilitates ultrasensitive chemical detection of analytes, besides offering high information content about the biomaterial under study, but also that carbon-based materials are biocompatible and favorable micro-environments for such detection. Such information is valuable for the development of bio-medical sensors, which is the main application envisioned for this analysis.
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Multiple, consecutive, fully-extended 2.0₅-helix peptide conformation. Biopolymers 2016; 100:621-36. [PMID: 23893391 DOI: 10.1002/bip.22267] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2013] [Revised: 04/16/2013] [Accepted: 04/19/2013] [Indexed: 02/01/2023]
Abstract
The peptide 2.0(5)-helix does exist. It has been experimentally authenticated both in the crystalline state (by X-ray diffraction) and in solution (by several spectroscopic techniques). It is the most common conformation for C(α)-tetrasubstituted α-amino acids with at least two atoms in each side chain, provided that cyclization on the C(α)-atom is absent. X-Ray diffraction has allowed a detailed description of its geometrical and three-dimensional (3D)-structural features. The infrared absorption and the nuclear magnetic resonance parameters characteristics of this multiple, consecutive, fully-extended structure have been described. Conformational energy calculations are in agreement with the experimental findings. As the contribution per amino acid residue to the length of this helix is the longest possible, its exploitation as a molecular spacer is quite promising. However, it is a rather fragile 3D-structure and particularly sensitive to solvent polarity. Interestingly, in such a case, it may reversibly convert to the much shorter 3(10)-helix, thus generating an attractive molecular spring.
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Direct Determination of the Simplest Criegee Intermediate (CH2OO) Self Reaction Rate. J Phys Chem Lett 2014; 5:2224-2228. [PMID: 26279538 DOI: 10.1021/jz5008406] [Citation(s) in RCA: 55] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The rate of self-reaction of the simplest Criegee intermediate, CH2OO, is of importance in many current laboratory experiments where CH2OO concentrations are high, such as flash photolysis and alkene ozonolysis. Using laser flash photolysis while simultaneously probing both CH2OO and I atom by direct absorption, we can accurately determine absolute CH2OO concentrations as well as the UV absorption cross section of CH2OO at our probe wavelength (λ = 375 nm), which is in agreement with a recently published value. Knowing absolute concentrations we can accurately measure kself = 6.0 ± 2.1 × 10(-11)cm(3) molecule(-1) s(-1) at 297 K. We are also able to put an upper bound on the rate coefficient for CH2OO + I of 1.0 × 10(-11) cm(3) molecule(-1) s(-1). Both of these rate coefficients are at least a factor of 5 smaller than other recent measurements of the same reactions.
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Spectral filtering for improved pulsed photothermal temperature profiling in agar tissue phantoms. JOURNAL OF BIOMEDICAL OPTICS 2008; 13:064002. [PMID: 19123649 PMCID: PMC2671995 DOI: 10.1117/1.2998477] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We present a systematic experimental comparison of pulsed photothermal temperature profiling utilizing the customary spectral band of the InSb radiation detector (lambda=3.0 to 5.6 microm) and a narrowed acquisition band (4.5 to 5.6 microm). We use custom tissue phantoms composed of agar gel layers separated by thin absorbing layers. The laser-induced temperature profiles are reconstructed within the customary monochromatic approximation, using a custom minimization algorithm. In a detailed numerical simulation of the experimental procedure, we consider several acquisition spectral bands with the lower wavelength limit varied between 3.0 and 5.0 microm (imitating application of different long-pass filters). The simulated PPTR signals contain noise with amplitude and spectral characteristics consistent with our experimental system. Both experimental and numerical results indicate that spectral filtering reduces reconstruction error and broadening of temperature peaks, especially for shallower and more complex absorbing structures. For the simulated PPTR system and watery tissues, numerical results indicate an optimal lower wavelength limit of 3.8 to 4.2 microm.
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Single Particle Motions in Liquids: Qualitative Features of Memory Functions. JOURNAL OF RESEARCH OF THE NATIONAL BUREAU OF STANDARDS. SECTION A, PHYSICS AND CHEMISTRY 1974; 78A:413-420. [PMID: 32189792 DOI: 10.6028/jres.078a.025] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
Memory functions, which enter into the equations of motion for time correlation functions, are constructed from neutron scattering, infrared absorption and light scattering data involving single particle motions in liquids. The qualitative features of these memory functions are related to the shape of the corresponding time correlation functions. It is found that a negative portion to the memory function is indicative of a rapid loss of correlation in time while strong temporal correlations imply a memory function which does not go negative. The mathematical structure of a memory function is examined for the case of the ideal gas by expanding and evaluating the projection operator representation of the function. The resulting expression has a rich mathematical structure and can be expressed in a closed form only for its Laplace transform.
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