Approximate analytical solution of the Takagi equations for X-ray diffraction in the backscattering mode from a cylindrically bent crystal

The dynamic diffraction of a spherical X-ray wave from a cylindrically bent crystal in the backscattering mode has been theoretically studied. An approximate analytical solution of the system of Takagi differential equations is obtained under certain conditions imposed on the coordinates of atoms inside the crystal.     

Calculation of the optimum parameters of a copper-vapor laser lidar for remote probing of H2

A numerical solution of the lidar equation is obtained for Raman backscattering by hydrogen molecules and the optimum radiation powers of a copper laser are determined at distances of 100–6000 m. Pis’ma Zh. Tekh. Fiz. 24, 32–35 (February 26, 1998)     

Visible and near-infrared backscattering spectroscopy for sizing spherical microparticles

Scattering is a useful tool for the determination of particle size in solution. In particular, spectroscopic analysis of backscattering renders the possibility of a simplified experimental setup and direct data processing using Mie theory. We show that a simple technique based on near-infrared (NIR) backscattering spectroscopy together with the development of the corresponding algorithm based on Fourier transform (FT) and Mie theory are a powerful tool for sizing microparticles in the range from 8 to 60 microm diameter. There are three wavelength intervals in the NIR, within which different diameter ranges were analyzed. In each one, the FT yields a coarse diameter value with an uncertainty dependent on the wavelength range. A more accurate value is obtained by further applying cross correlation between experimental and theoretical spectra. This latter step reduces the uncertainty in diameter determination between 30% and 40%, depending on wavelength interval and particle diameter. These results extend previous information on visible backscattering spectroscopy applied to sizing microparticles in the range between 1 and 24 mum diameter. This technique could be the basis for the construction of a portable and practical instrument.     

Detection of stratospheric sulfuric Acid aerosols with polarization lidar: theory, simulations, and observations

The derivation of backscatter ratio profiles from polarization lidar measurements is discussed. The method is based on differences in depolarization between molecular backscattering and backscattering from spherical aerosol particles. Simulations show that the polarization algorithms yield backscatter ratios with uncertainties comparable with those obtained by Klett's method, provided that the backscattering process is dominated by molecular scattering. The technique could be utilized for monitoring the stratospheric sulfuric acid aerosol layer during periods of background conditions. The polarization analysis method is discussed in light of simulation results and is applied to polarization lidar profiles observed during the ALBATROSS 1996 field measurement campaign.     

On spherical X-ray wave focusing upon backscattering from a parabolic cylinder crystal

The focusing of a spherical X-ray wave upon the Bragg backscattering from a crystal uniaxially bent to form a parabolic cylinder is theoretically studied. Based on geometrical optics, an analytical formula for the size of the crystal surface area involved in the diffraction reflection in the backscattering mode is derived. The analytical expression for the wave intensity distribution at the focus is analyzed and compared to that obtained previously.     

A kinematic approximation for the coefficient of X-ray wave backscattering from a strongly bent crystal

An analytical expression for the coefficient of Bragg backscattering (θ_B≅π/2) of an X-ray wave from a strongly bent thin crystal is obtained. It is shown that the amplitude reflection coefficient for backscattering from a strongly bent crystal differs from the value for a flat crystal of the same thickness by a small phase-dependent factor.     

Light scattering at oblique incidence on two coaxial cylinders

A solution for the problem of a plane wave at oblique incidence on two coaxial cylinders is presented. The solution of the wave equation is determined for various geometric regions, and boundary conditions are applied at the material interfaces. The resulting solution consists of a system of eight equations in eight unknown coefficients. Expressions for two of the Mueller-scattering matrix elements (S(11) and S(12)) and the extinction, scattering, and backscattering cross sections are derived. A numerical algorithm for the solution is developed and implemented. The algorithm is tested for several limiting cases: homogeneous, hollow, and metal-core cylinders at various angles of incidence for TM and TE waves. Comparisons of the results of the algorithm with the results of studies reported in the literature are made. The comparisons are favorable, achieving good agreement with published work. For two coaxial cylinders, the numerical calculations show that if one is to use light scattering as a diagnostic tool, both of the Mueller-scattering matrix elements S(11) and S(12) must be measured simultaneously. In addition, the backscattering cross section is very sensitive for monitoring change in the radii of the cylinders.     

Analytic model of ocean color

Ocean color is determined by spectral variations in reflectance at the sea surface. In the analytic model presented here, reflectance at the sea surface is estimated with the quasi-single-scattering approximation that ignores transspectral processes. The analytic solutions we obtained are valid for a vertically homogeneous water column. The solution provides a theoretical expression for the dimensionless, quasi-stable parameter (r), with a value of ~0.33, that appears in many models in which reflectance at the sea surface is expressed as a function of absorption coefficient (a) and backscattering coefficient (b(b)). In the solution this parameter is represented as a function of the mean cosines for downwelling and upwelling irradiances and as the ratio of the upward-scattering coefficient to the backscattering coefficient. Implementation of the model is discussed for two cases: (1) that in which molecular scattering is the main source of upwelling light, and (2) that in which particle scattering is responsible for all the upwelled light. Computations for the two cases are compared with Monte Carlo simulations, which accounts for processes not considered in the analytic model (multiple scattering, and consequent depth-dependent changes in apparent optical properties). The Monte Carlo models show variations in reflectance with the zenith angle of the incident light. The analytic model can be used to reproduce these variations fairly well for the case of molecular scattering. For the particle-scattering case also, the analytic and Monte Carlo models show similar variations in r with zenith angle. However, the analytic model (as implemented here) appears to underestimate r when the value of the backscattering coefficient b(b) increases relative to the absorption coefficient a. The errors also vary with the zenith angle of the incident light field, with the maximum underestimate being approximately 0.06 (equivalent to relative errors from 12 to 17%) for the range of b(b)/a studied here. One implication of this result is that the model could also be used to obtain approximate solutions for the Q factor, defined for a given look angle as the ratio of the upwelling irradiance at the surface to the upwelling radiance at the surface at that angle. This is a quantity that is important in remote-sensing applications of ocean-color models. An advantage of the model discussed here is that its implementation requires inputs that are in principle accessible only in a remote-sensing context.     

Ultraviolet DIAL measurements of O3 profiles in regions of spatially inhomogeneous aerosols

The differential absorption lidar (DIAL) technique generally assumes that atmospheric optical scattering is the same at the two laser wavelengths used in the DIAL measurement of a gas concentration profile. Errors can arise in this approach when the wavelengths are significantly separated, and there is a range dependence in the aerosol scattering distribution. This paper discusses the errors introduced by large DIAL wavelength separations and spatial inhomogeneity of aerosols in the atmosphere. A Bernoulli solution for determining the relative distribution of aerosol backscattering in the UV region is presented, and scattering ratio boundary values for these solutions are discussed. The results of this approach are used to derive a backscatter correction to the standard DIAL analysis method. It is shown that for the worst cases of severe range dependence in aerosol backscattering, the residual errors in the corrected DIAL O3 measurements were <10 ppbv for DIAL wavelengths at 286 and 300 nm.     

Raman detection of proteomic analytes

The compatibility of nonenhanced Raman spectroscopy with chromatographic and mass spectroscopic proteomic sensing is demonstrated for the first time. High-quality normal Raman spectra are derived from protein solutions with concentrations down to 1 microM and 1 fmol of protein nondestructively probed within the excitation laser beam. These results are obtained using a drop coating deposition Raman (DCDR) method in which the solution of interest is microdeposited (or microprinted) on a compatible substrate, followed by solvent evaporation and backscattering detection. Representative applications include the DCDR detection of insulin derived from an HPLC fraction, nondestructive DCDR followed by MALDI-TOF of lysozyme, the DCDR detection of protein spots deposited using an ink-jet microprinter, and the identification of spectral differences between glycan isomers of equal mass (such as those derived from posttranslationally modified proteins).     

Rapid free-vibration analysis with model reduction based on coherent nodal clusters

Modal expansion is a workhorse used in many engineering analysis algorithms. One example is the coupled boundary element-finite element computation of the backscattering target strength of underwater elastic objects. To obtain the modal basis, a free-vibration (generalized eigenvalue) problem needs to be solved, which tends to be expensive when there are many basis vectors to compute. In the above-mentioned backscattering example it could be many hundreds or thousands. Excellent algorithms exist to solve the free-vibration problem, and most use some form of the Rayleigh-Ritz (RR) procedure. The key to an efficient RR application is a low-cost transformation into a reduced basis. In this work, a novel, inexpensive a priori transformation is constructed for solid-mechanics finite element models based on the notion of coherent nodal clusters. The inexpensive RR procedure then leads to significant speedups of the computation of an approximate solution to the free vibration problem.     

Ultrasonic Backscattering in Cubic Polycrystals with Ellipsoidal Grains and Texture

An ultrasonic model for backscattering from polycrystalline microstructure is developed for polycrystals with uniaxial texture and elongated cubic crystallites. The uniaxial texture or crystallographic orientation of the grains is described by a modified Gaussian orientation distribution function (ODF) with a texture parameter. Macroscopically such a textured polycrystalline medium exhibits hexagonal symmetry. The preferred texture direction and elongation are independently defined in a global system. The dependence of backscattering coefficients and their directional ratios on both texture and grain anisotropy are discussed. Attenuation coefficients in the high frequency range for arbitrary wave propagation direction are obtained and then the ratios in the three axis directions are studied. The model is compared with experimental data available in the literature for Al rolled alloys and shows good agreement when accounting for both texture and grain anisotropy effects.     

Effect of the particle-size distribution on the backscattering ratio in seawater

Mie theory is used to model the backscattering ratio (the ratio of the backscattering coefficient to the total scattering coefficient) of marine particles with the assumption that they follow a Junge-type size distribution. Results show that the backscattering ratio is very sensitive to the presence of submicrometer particles and depends strongly on the shape of the size distribution. However, it is not affected significantly by absorption and does not vary with wavelength over the visible range. The implications for modeling of backscattering and ocean color in terms of phytoplankton pigment concentration are discussed.     

Extracting electron backscattering coefficients from backscattered electron micrographs

Electron backscattering micrographs possess the so-called Z-contrast, carrying information about the chemical compositions of phases present in microstructures. The intensity at a particular point in the backscattered electron micrograph is proportional to the signal detected at a corresponding point in the scan raster, which is, in turn, proportional to the electron backscattering coefficient of a phase at that point. This article introduces a simple method for extracting the electron backscattering coefficients of phases present in the microstructure, from the backscattered electron micrographs. This method is able to convert the micrograph's greyscale to the backscattering-coefficient-scale. The prerequisite involves the known backscattering coefficients for two phases in the micrograph. In this way, backscattering coefficients of other phases can be determined. The method is unable to determine the chemical compositions of phases or the presence of an element only from analysing the backscattered electron micrograph. Nevertheless, this method was found to be very powerful when combined with energy dispersive spectroscopy, and the calculations of backscattering coefficients.     

Ultrasonic Propagation and Scattering in Duplex Microstructures with Application to Titanium Alloys

A general model for elongated duplex microstructures is proposed for modeling scattering-induced ultrasonic longitudinal attenuation in hexagonal polycrystals for application to titanium alloys. The material system consists of microtextured regions (MTRs) which are formed by much smaller ?? crystallites with preferred orientations. Their preferred orientation is represented by a modified Gaussian orientation distribution function. Scattering induced by MTRs and by crystallites is added to obtain ultrasonic attenuation in the medium. The effective elastic properties of MTRs are determined and used to obtain the scattering-induced MTR attenuation and backscattering. Crystallite attenuation is estimated by the untextured attenuation coefficient factored by a texture transition function. The total attenuation is obtained by combining solutions for microtextured region attenuation and crystallite attenuation. Spectroscopic attenuation and backscattering measurements are performed on a forged sample of titanium alloy. Reasonable agreement is found between experiment and the model predictions with a given texture parameter.     

Effect of suspended particulate-size distribution on the backscattering ratio in the remote sensing of seawater

Mie theory is used to study the influence of the particle-size distribution (PSD) on the backscattering ratio for case 1 and 2 waters. Several in situ measured PSDs from coastal water and the open ocean, representing typical case 2 and 1 waters, were used in this investigation. Calculation of the backscattering ratio requires integration of the PSD over a much broader size range than is usually measured. Consequently extrapolation from fitted data is necessary. To that purpose the measured data are fitted with hyperbolic (Junge) and the two-component model of the PSD. It is shown that the result of extrapolation, hence the backscattering ratio, critically depends on the chosen PSD model. For a particular PSD model the role of submicrometer particles and the applied integration limits on the backscattering ratio is discussed. The use of the hyperbolic PSD model largely overestimates the number of small (submicrometer) particles that significantly contribute to backscattering and consequently leads to an erroneously high backscattering ratio. The two-component model proves to be an adequate PSD model for use in backscattering/scattering calculations providing satisfactory results complying with experimental data. The results are relevant for the inversion of remotely sensed data and the prediction of optical properties and the concentration of phytoplankton pigments, suspended sediment, and yellow substance.     

Method of monitoring the shape of an atomic force (tunneling) microscope tip using backscattering spectrometry

A method is proposed to monitor the shape of an atomic force microscope tip, which can combine the operations of ion etching and shape monitoring, by using the intensity of the backscattering of ions from the same or a different beam to monitor the shape. Relationships have been obtained to monitor the shape of the probe using the measured dependence of the backscattering intensity on the parameters of the incident beam. Pis’ma Zh. Tekh. Fiz. 23, 88–92 (June 12, 1997)     

Raman lidar observations of cloud liquid water

We report the design and the performances of a Raman lidar for long-term monitoring of tropospheric aerosol backscattering and extinction coefficients, water vapor mixing ratio, and cloud liquid water. We focus on the system's capabilities of detecting Raman backscattering from cloud liquid water. After describing the system components, along with the current limitations and options for improvement, we report examples of observations in the case of low-level cumulus clouds. The measurements of the cloud liquid water content, as well as the estimations of the cloud droplet effective radii and number densities, obtained by combining the extinction coefficient and cloud water content within the clouds, are critically discussed.     

Effect of Poly-Alkylene-Glycol Quenchant on the Distortion,Hardness, and Microstructure of 65Mn Steel

Currently, the 65Mn steel is quenched mainly by oil media. Even though the lower cooling rate of oil compared to water reduces the hardness of steel post quenching, the deforming and cracking of parts are often minimized. On the other hand, the oil media also has the disadvantage of being flammable, creating smoke that adversely affects the media. The poly alkylene glycol (PAG) polymer quenchant is commonly used for quenching a variety of steels based on its advantages such as non-flammability and flexible cooling rate subjected to varying concentration and stirring speed. This article examines the effect of PAG polymer quenching solution (with concentrations of 10% and 20%) on deformation, hardness, and microstructure of C-ring samples made of 65Mn steel. Furthermore, the performance of PAG polymer quenchant is also compared with those of two common quenching solutions: Water and oil. When cooling in water, the C-ring samples had the largest deformation and 2 times higher than the results obtained when a 10% PAG solution was used. In particular, similar levels of deformation on the C-ring samples were observed in both cases of 20% PAG solution and oil as the primary quenching media. Furthermore, the hardness level measured between the sampled parts quenched in the 20% PAG solution appeared to be more uniform than that obtained from the oil-quenched sample. The study of the microscopic structure of steel by optical microscopy combined with X-ray diffraction showed that the water hardened sample exhibited cracks and comprised of two phases, martensite and retained austenite. According to the results of Electron Back Scattering Diffraction (EBSD) analysis and backscattering electronic image (BSE), the content of austenite residue in the sample when the sample was cooled in PAG 10 and 20% solution was 3.21% and 4.73%, respectively and smaller than the measurements obtained from oil quenching solution. Thus, the 65Mn steel is cooled in 20% PAG solution for high hardness and more evenly distributed than when it is quenched in oil while still ensuring a small level of deformation. Therefore, the PAG 20% solution can completely replace oil as the main media used to quench the 65Mn steel.     

Design of fractal patch antenna for size and radar cross-section reduction

This research study presents a novel design of star-shaped fractal patch antenna for miniaturisation and backscattering radar cross-section (RCS) reduction. The proposed fractal antenna gives 50% size reduction compared with a conventional circular microstrip patch (CCMP) antenna. The antenna is studied experimentally for return loss behaviour using vector network analyser R&S ZVA40. It can be useful for wireless application in 0.85-4 GHz frequency band. Further, the study focuses on backscattering RCS (both monostatic and bistatic) reduction by the proposed antenna compared with the CCMP antenna. It is found that increase in number of fractal iterations included in the conventional patch to design fractal antenna geometry reduces backscattering RCS at multiband compared to the conventional patch antenna. This reduction in backscattering RCS by the antenna is observed at multiband. The antenna can be tuned for low backscattering by variation in the substrate dielectric constant and thickness and the superstrate dielectric constant and thickness. For maximum RCS reduction by the antenna, optimisation of substrate thickness becomes necessary. The study also deals with effect of frequency and aspect angle variation on backscattering RCS reduction.