Random Tilt Research Articles

Iterative phase-shifting algorithm immune to random phase shifts and tilts

An iterative phase-shifting algorithm based on the least-squares principle is developed to overcome the random piston and tilt wavefront errors generated from the phase shifter. The algorithm iteratively calculates the phase distribution and the phase-shifting map to minimize the sum of squared errors in the interferograms. The performance of the algorithm is evaluated via computer simulations and validated by the Fizeau interferometer measurements. The results show that the proposed algorithm has a fast convergence rate and satisfactory phase-estimation accuracy, improving the measurement precision of the phase-shifting interferometers with significant phase-shifter errors.

A method for structure analysis of nanomaterials by electron diffraction: Phase identification and unit cell determination

We report a quick and easy method for a random selected area electron diffraction (SAED) pattern without rotating and tilting the specimen to perform phase identification and unit cell determination by combined with the XRD softwares. If your TEM is well aligned and camera length is carefully corrected, two-dimensional (2D)-SAED pattern can be directly transformed to 1D-profile after the center determination of pattern, this profile is then imported to XRD analysis packages. Finally, phase identification and unit cell determination can be performed after peak search or precise peak position determined by profile fitting. Two examples, flaky-like TiO2 nanomaterial and TiO2 nanotubes precipitated by the silver nanoparticles, were tested and verified for the validation of phase identification and unit cell determination using this method; the successful crystallographic analysis of one single gold nanocrystal indicates it is still validate for the nanocrystals with the smaller diffraction volume, but need two or more random tilt SAED patterns. This method could be further used in the quantitative phase analysis, structure determination and Rietveld refinement for the nanomaterials if the reliable integrated intensity can be extracted.

Automated correlation of single particle tilt pairs for Random Conical Tilt and Orthogonal Tilt Reconstructions

One of the major methodological challenges in single particle electron microscopy is obtaining initial reconstructions which represent the structural heterogeneity of the dataset. Random Conical Tilt and Orthogonal Tilt Reconstruction techniques in combination with 3D alignment and classification can be used to obtain initial low-resolution reconstructions which represent the full range of structural heterogeneity of the dataset. In order to achieve statistical significance, however, a large number of 3D reconstructions, and, in turn, a large number of tilted image pairs are required. The extraction of single particle tilted image pairs from micrographs can be tedious and time-consuming, as it requires intensive user input even for semi-automated approaches. To overcome the bottleneck of manual selection of a large number of tilt pairs, we developed an algorithm for the correlation of single particle images from tilted image pairs in a fully automated and user-independent manner. The algorithm reliably correlates correct pairs even from noisy micrographs. We further demonstrate the applicability of the algorithm by using it to obtain initial references both from negative stain and unstained cryo datasets.

Speckle contrast for flat-topped field profiles

Speckle contrast is evaluated for flat-topped field profiles where the characterization and evaluation of speckle contrast are based on mathematical formulation and theoretical parameter variation. The speckle field which is represented by the random phase shift and the random phase tilt is multiplied by the flat-topped shaped field. The increase in the source size of the flat-topped field first causes the speckle contrast to increase, then reaches saturation. Increase in the variance of the phase shift of a flat-topped field causes an appreciable increase in the speckle contrast. Depending on the diffraction characteristics of the finite sized flat-topped field distribution, upon changing the variance of the phase shift, the speckle contrast exhibits different behavior at short and long propagation distances. However, especially for small variances of phase tilts, the speckle contrast seems to monotonically increase as the propagation distance becomes larger. The effect of the order of flatness on the speckle contrast is small at short propagation distances which can be appreciable at long propagation distances.

An SPM/PO-based Polarimetrie Two-Scale Model

A polarimetric two-scale scattering model employed to retrieve the surface parameters of bare soils from polarimetric SAR data is presented. The scattering surface is here considered as composed of randomly tilted rough facets, for which the SPM or the PO hold. The facet random tilt causes a random variation of the local incidence angle, and a random rotation of the local incidence plane around the line-of-sight, which in turn causes a random rotation of the facet scattering matrix. Unlike other similar already existing approaches, our method considers both these effects. The proposed scattering model is then used to retrieve bare soil moisture and large-scale roughness from the co-polarized and cross-polarized ratios.

Platform Tilt Perturbation as an Intervention for People With Chronic Vestibular Dysfunction

Training to improve responses to perturbations may be beneficial for individuals with unilateral vestibular dysfunction. We evaluated the effects of an incrementally increasing surface tilt perturbation intervention for individuals with chronic vestibular pathology on gait, activities of daily living, and dizziness. Participants (n = 29) were randomly assigned to 1 of 3 groups. The first group received random surface tilt perturbations of increasing angles and speed, half of the trials with vision-occluding goggles, 3 times weekly for 3 weeks (P group). The second group received tilt perturbation intervention (as above) plus a home program of vestibular rehabilitation exercises (P+EX group). The third group performed only the vestibular rehabilitation exercises (EX group). Outcome measures included temporospatial gait measures, Dynamic Gait Index (DGI), Dizziness Handicap Inventory (DHI), Patient Specific Functional Scale (PSFS), and a Perceived Outcomes Scale (POS). The P and P+EX groups showed greater improvement on the PSFS and the POS compared to the EX group. DGI scores indicated decreased fall risk in 8 of 9 individuals who participated in P or P+EX training and who initially scored below the 19-point cutoff score. Both the P and P+EX groups showed significant within-group changes on some gait characteristics, DGI, DHI, PSFS, and POS measures. The EX group showed within-group change only on the DHI. Surface tilt perturbation training appears to be more effective for improving abilities at the activities and participation levels than vestibular exercises alone. In addition, tilt perturbation training reduced fall risk as measured by the DGI.

Retrieval of Soil Surface Parameters via a Polarimetric Two-Scale Model

We propose a polarimetric two-scale surface scattering model employed to retrieve the surface parameters of bare soils from polarimetric synthetic aperture radar or scatterometer data. The scattering surface considered here is composed of slightly rough randomly tilted facets, for which the small perturbation scattering method holds. The facet random tilt causes both a random variation of the local incidence angle and a random rotation of the local incidence plane around the line of sight. Unlike other similar already existing approaches, our method considers both these stochastic effects in the analytical evaluation of the facet scattering matrix, and their statistical modeling is derived from a proper statistical description of the scattering surface. In particular, we assume that the facet slope (i.e., the slope of the large-scale surface roughness) is a Gaussian random variable, in agreement with both classical and fractal surface models. The proposed scattering model is then used to retrieve bare soil moisture and (large-scale) roughness from the co- and cross-polarized ratios. The performance of the resulting retrieval algorithm and its validity limits are finally assessed by comparing obtained results to “ in situ” measurements. To this aim, data from different measurement campaigns available in literature are employed.

Grain Boundary Migration in Fe–3mass%Si Alloy Bicrystals under a Magnetic Field

Grain boundary migration under a magnetic field was studied using Fe–3mass%Si alloy bicrystals with ‹001›/Σ5 (φ=36°) and ‹001›/random (φ=45°) tilt boundaries at temperatures between 1223 K and 1323 K. A capillarity method (Sun and Bauer method) was used to observe grain boundary migration. A 6 T magnetic field was applied parallel to the [100] direction, which is one of easy magnetization directions, in a grain whose area increases with occurring grain boundary migration. It was found that the application of a magnetic field observably increased the velocity of grain boundary migration for both bicrystals. The abrupt change in the velocity of grain boundary migration was observed at a critical capillary driving force irrespective of whether the magnetic field was applied. However, this critical driving force was decreased by application of a magnetic field. It was suggested that the magnetic field act as a driving force for grain boundary migration rather than increase its mobility.

A Toolbox for ab initio 3-D reconstructions in single-particle electron microscopy

Structure determination of a novel macromolecular complex via single-particle electron microscopy depends upon overcoming the challenge of establishing a reliable 3-D reconstruction using only 2-D images. There are a variety of strategies that deal with this issue, but not all of them are readily accessible and straightforward to use. We have developed a "toolbox" of ab initio reconstruction techniques that provide several options for calculating 3-D volumes in an easily managed and tightly controlled work-flow that adheres to standard conventions and formats. This toolbox is designed to streamline the reconstruction process by removing the necessity for bookkeeping, while facilitating transparent data transfer between different software packages. It currently includes procedures for calculating ab initio reconstructions via random or orthogonal tilt geometry, tomograms, and common lines, all of which have been tested using the 50S ribosomal subunit. Our goal is that the accessibility of multiple independent reconstruction algorithms via this toolbox will improve the ease with which models can be generated, and provide a means of evaluating the confidence and reliability of the final reconstructed map.

The Orientational Order in So-Called de Vries Materials

There is a great interest in smectic materials that show no layer shrinkage (NLS) in the transition from smectic A to smectic C. Such materials are often discussed in terms of “de Vries materials” or “de Vries behavior” after A. de Vries, who proposed different mechanisms for this NLS behavior, involving a significant tilt β of the individual molecules in the smectic A phase. According to the original proposition of de Vries, the molecules are already tilted in this kind of smectic A phase, with a large constant tilt and the same tilt direction in each layer but random tilt direction between different layers. Despite the individual molecular tilt the smectic A phase remains uniaxial and the transition to the biaxial smectic C state is seen as a global ordering in the tilt directions. The model thus ad hoc predicts that there is zero layer shrinkage at the A – C transition. We refer to this model as the “hollow cone distribution”. As later pointed out by de Vries there are, however, other possible models for describing a tilt disorder (thermodynamically unavoidable) in the A phase. Nevertheless, the hollow cone has been a widely accepted model in the literature and is repeatedly referred to in discussing de Vries behavior or even taken as a basis for theories describing it. We discuss different smectic A orientational distribution functions that could be related to de Vries behavior or de Vries transitions. We find that two opposite models have comparable predictive power but only one gives a consistent picture together with existing data. Our conclusion is that the smectic A – smectic C transition can have a continuously changing character from a “pure tilt” to a “pure de Vries”, and we illustrate the orientational distribution functions in the A and C phases for these two limiting cases. We find that de Vries behavior is not related to any exotic distribution of hollow cone or similar kind in the A phase, but instead to an unusual combination of low nematic order and high smectic order in the de Vries smectic A. As the technical interest in such materials is considerable, a directed effort toward the synthesis of new optimized materials would be important.

Cover Picture: On the Origin of the “Giant” Electroclinic Effect in a “De Vries”‐Type Ferroelectric Liquid Crystal Material for Chirality Sensing Applications (ChemPhysChem 6/2009)

AbstractThe cover picture shows characteristics of a new ‘de Vries’‐type ferroelectric liquid crystal in which the ferroelectric transition is an order–disorder transition where the directions of molecular tilt inside a smectic layer order into a certain direction. Since the rod‐like molecules (drawn as cylinders) are tilted in the paraelectric SmA* (with random tilt directions) as well as in the ferroelectric SmC* phase, the ferroelectric transition is connected with a rather weak contraction of the smectic layer thickness (even though the optical tilt θ reaches values of about 25°). On page 890, F. Giesselmann et al. show that this new ferroelectric material exhibits a remarkably weak temperature dependence of its giant electroclinic effect (the coupling between tilt and elelctric field) in the SmA* phase. The origin of this striking electroclinic effect is the co‐occurrence of a ‘de Vries’‐type ordering with a weak first‐order tilting transition.magnified image

Electrochemical deposition of Cu 2O on stainless steel substrates: Promotion and suppression of oriented crystallization

Cu 2O coatings with 111 orientation comprising crystallites with a triangular pyramidal morphology could be deposited at pH = 12 from baths stabilized with a variety of ligating agents showing that oriented crystallization is independent of the ligand structure. When the deposition is carried out at very high [OH −] concentrations (pH > 14), the coatings are unoriented and comprise crystallites with octahedral morphology. In some of these coatings, the loss of orientation is attributed to the random tilt of the long axes of the crystallites with respect to the normal to the substrate. In others, the loss of orientation is due to the redissolution of pre-grown faceted crystallites. Given that the dominant morphology of the crystallites obtained under these conditions is octahedral, crystal growth takes place under conditions of thermodynamic control.

Plastic deformation mechanisms in nanocrystalline columnar grain structures

We present an atomistic study of the plastic deformation mechanisms occurring in columnar structures of nanocrystalline Ni, with particular emphasis on the process of dislocation emission form the grain boundaries. The samples are constructed with grain boundaries characterized by random tilt misorientations around a common 〈1 1 0〉 type axis. All samples contain the same 36 grains polycrystalline microstructure, with grain sizes ranging from 4 to 20 nm in order to isolate size effects on the deformation mechanisms. Tensile deformations up to 8% were simulated and the strain stress curves observed for these samples show grain size effects in both the elastic and plastic portions. An inverse Hall–Petch effect is observed for the nominal stress at a fixed strain, but disappears when the grain size-dependent elastic modulus is used to construct an 0.5% offset yield stress. Both dislocation emission from the grain boundaries and grain boundary accommodation of plasticity are observed. Dislocation emission comes largely from pre-existing dislocation-like structures in the grain boundaries, and increases rapidly for grain sizes >4 nm. However, the number of dislocations per unit length of grain boundary saturates to a constant value at large grain sizes, indicating a fixed density of pre-existing sources in the grain boundaries. A simple model wherein dislocation emission is prohibited within a small distance from grain triple junctions accounts for the overall density versus grain size. Grain boundary sliding was observed in the same regions of the microstructure in all grain sizes, and to approximately the same degree. A simple model accounting for both dislocations and sliding is consistent with the observed trends in plastic strain versus grain size. The implications of these observations for more realistic three-dimensional samples are briefly discussed.

Compression-shear-induced tilt azimuthal orientation of amphiphilic monolayers at the air-water interface: a C(infinity)-->C2v transition in the flow of a two-dimensional hexatic structure.

Compression-shear-induced tilt azimuthal orientation of amphiphilic monolayer in tilting phases (L2 and L'2) at the air-water interface is analyzed as dynamical equilibrium of the elastic distortion of orthogonally hexagonal structure of the molecules under compression-induced shear flow. It is shown theoretically that the compression can induce molecular tilts lying along and/or against the flow direction. All these tilts makeup the initial random tilt azimuth of the molecular tails along a uniform direction. At a threshold compression speed, it causes a C(infinity)-->C(2v)-symmetry transition at the air-water interface. With Maxwell displacement current and optical second-harmonic generation measurements, the above theoretical results are verified experimentally in a monolayer of 4-heptyloxy-4(')-cyanobiphenyl.

Resonator stability subject to dynamic random-tilt aberration.

We derive the behavior of the average exit time (i.e., the number of reflections before escape) of a ray path traveling between two perfect mirrors subject to dynamic random-tilt aberrations. Our calculation is performed in the paraxial approximation. When small random tilts are taken into account, we may consider an asymptotic regime that generically reduces the problem to the study of the exit time from an interval for a harmonic, frictionless oscillator driven by Gaussian white noise. Despite its apparent simplicity, the exact solution of this problem remains an open mathematical challenge, and we propose here a simple approximation scheme. For flat mirrors, the natural frequency of the oscillator vanishes, and, in this case, the average exit time is known exactly. It exhibits a 2/3 scaling-law behavior in terms of the variance of the random tilts. This behavior also follows from our approximation scheme, which establishes the consistency of the scaling law. Our mathematical results are confirmed with simulation experiments.

Enhanced lidar backscattering by quasi-horizontally oriented ice crystal plates in cirrus clouds

The backscattering of light by quasi-horizontally oriented hexagonal ice plates is investigated because of its pertinence to lidar measurements of cirrus clouds. For oriented ice crystals, the commonly used geometric optics ray-tracing method is not applicable to the computation of the scattered field in certain scattering directions, in particular, the backscattering direction, because of the singularity problem inherent to the ray-tracing technique. In this study, we solve for the electric field due to scattering by quasi-horizontally oriented ice plates using an approach based on the electromagnetic wave theory. We simplify the analysis by ignoring the effect of the plate's side faces on the internal field inside the particle. This is a reasonable approximation when the ratio of the particle diameter to its thickness is large. This approximation is also valid if the tilt of the particle's symmetric axis from zenith is small and the size parameter is large. The present numerical results indicate that very strong oscillations in the backscattering cross section occur with the variation of size parameter. Furthermore, the bulk backscattering intensity has been calculated by including the effect of a particle size distribution and the random tilt of particle symmetric axis within a small angular region, for example, 2°. A strong dependence is found between the lidar backscattering cross section and the degree of the random tilt of the particles. A combination of the present method with the T-matrix method, which works well for particles having small and moderate size parameters, may provide a more complete picture of the lidar backscattering by quasi-horizontally oriented ice plates.

The effects of molecular shape and quadrupole moment on tilted smectic phase formation

Results are presented from constant NPT Monte Carlo simulations of two systems based on the biaxial internally rotated Gay-Berne (IRGB) potential. First, the effect of increasing molecular elongation is considered, and it is shown that a change in aspect ratio from 3:1 to 4:1 leads to nematic and tilted smectic J phases being replaced by smectic A and tilted smectic G phases, respectively. Second, the effect of a longitudinal electric quadrupole on the phase behaviour of the IRGB model is examined. The presence of a moderate quadrupole moment results in the smectic G phase being replaced by a smectic J; the onset pressure of the smectic J increases monotonically as the quadrupole moment is increased, although the integrity of the tilted layers improves. In addition, the region of smectic A stability is found to persist for moderate quadrupole moment values. For the largest quadrupole moment considered, domains comprising poorly defined, tilted layers are formed but fail to develop into coherent smectic structures. This observation is ascribed to the competition between the unique tilt direction favoured by the biaxial IRGB potential and the random tilt direction of the uniaxial quadrupole-quadrupole interactions.

Peroneal Latency in Normal and Injured Ankles at Varying Angles of Perturbation

The aim of this study was to determine whether there was a difference in latency of the peroneus longus muscle at varying amplitudes of ankle inversion perturbation and between individuals with and without a history of ankle injury. Thirty-four male athletes from different football codes (soccer, rugby) received four random tilts to their left ankles at 5 degrees, 10 degrees, and 15 degrees in the frontal plane on a dual platform trap door. Peroneal latency was defined as the time difference between onset of the trap door movement, as detected by an accelerometer, and the onset of muscle activation above a resting baseline, as recorded using surface electromyography. Latency was determined using an algorithm. A series of repeated measures analyses of variance indicated that the latency was reliable between trials. There was no statistical evidence that history of injury or subjective ankle instability influenced the latency; however, there was a systematic difference between dominant and nondominant legs (dominant, 6.3 ms faster), and there was a small systematic effect (3 ms) for the angle of inversion perturbation. Muscle latency responses in male football players are thought to be influenced more by dominance than by history of injury or amplitude of perturbation.

Mean intensity patterns of mirror telescopes with random tilt errors

The mean intensity of an illuminated mirror with random tilt errors (jitter) is expressed as the transform of the convolution of the pupil function times the tilt-error characteristic function. The result is applied to a mirror with a centered hole.

Order parameters and densities in the smectic C, smectic A and nematic phases of a liquid crystal mixture

Abstract Measurements of the orientational and translational order parameters for the nematic, smectic A and smectic C phases of a commercial liquid crystal material are reported. The order parameters have been obtained by analysis of the angular distribution of the intensity of X-rays scattered by a sample aligned by a magnetic field. Results are presented as a function of temperature, and it is found that the apparent orientational order parameter in the smectic C phase decreases with decrease in temperature. This is explained using a model of random tilt. The experimental order parameters are compared with those calculated from a mean field model.