Small-dynamic-angle measurement using tangent relationship and phase-modulating technique

A method using two prisms for measurement of small dynamic angles is proposed in which the measurement is based on a simple tangent equation and a phase-modulating interferometer with a laser diode to measure dynamic optical path differences with higher accuracy. Owing to the simple tangent equation, the symmetry requirement on the two prisms in the optical configuration is eliminated, and easy measurement of the separations between two parallel beams with a position-sensitive detector is achieved. Small-dynamic-angle measurements are experimentally demonstrated with high accuracy. (C) 2007 Society of Photo-Optical Instrumentation Engineers.

Tolerance analysis for incident angle of volume phase holographic grating used in optical channel performance monitor

Transmission Volume Phase Holographic Grating (VPHG) is adopted as spectral element in the real-time Optical Channel Performance Monitor (OCPM), which is in dire need in the Dense Wavelength -division-multiplexing(DATDM) system. And the tolerance of incident angle, which can be fully determined by two angles: 6 and (p, is finally inferred in this paper. Commonly, the default setting is that the incident plane is perpendicular to the fringes when the incident angle is mentioned. Now the situation out of the vertical is discussed. By combining the theoretic analysis of VPHG with its use in OCPM and changing 6 and (0 precisely in the computation and experiment, the two physical quantities which can fully specify the performance of VPHG the diffraction efficiency and the resolution, are analyzed. The results show that the diffraction efficiency varies greatly with the change of 6 or (p. But from the view of the whole C-band, only the peak diffraction efficiency drifts to another wavelength. As for the resolution, it deteriorates more rapidly than diffraction efficiency with the change of (p, while more slowly with the change of theta. Only if \phi\less than or equal to+/-1degrees and alpha(B) -0.5 less than or equal to theta less than or equal to alpha(B) + 0.5, the performance of the VPHG would be good enough to be used in OCPM system.

USE OF RETRODIRECTIVE ARRAY PHASE CONJUGATION CIRCUITRY FOR NEAR- AND FAR-FIELD POSITION ANGLE OF ARRIVAL DETECTION

In this article, we present position indication functionality as obtained by using a retrodirective array, thereby allowing location information extraction of the position of the remote transmitter with which the retrodirective array is cooperating. This is carried out using straightforward circuitry with no requirement for complex angle of arrival algorithms, thereby giving a result in real time enabling tracking of fast moving transmitters. We show using a 10 x element retrodirective array, operating at 2.4 GHz that accuracies of far-field angle of arrival of within +/- 1 degrees over the arrays +/- 30 degrees azimuth field of view are possible. While in the near-field for angles of arrival of +/- 10 degrees it is possible to extract the position of a dipole source down to a resolution of 032 lambda. (C) 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 1031-1034, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.25097

Small-angle x-ray scattering study of the structural evolution of the drying of sonogels with the liquid phase exchanged by acetone

The structural evolution on the drying of wet sonogels of silica with the liquid phase exchanged by acetone, obtained from tetraethoxisilane sonohydrolysis, was studied in situ by small-angle x-ray scattering (SAXS). The periods associated to the structural evolution as determined by SAXS are in agreement with those classical ones established on basis of the features of the evaporation rate of the liquid phase in the obtaining of xerogels. The wet gel can be described as formed by primary particles (microclusters), with characteristic length a ∼ 0.67 nm and surface which is fractal, linking together to form mass fractal structures with mass fractal dimension D=2.24 in a length scale ξ∼6.7 nm. As the network collapses while the liquid/vapor meniscus is kept out of the gel volume, the mass fractal structure becomes more compacted by increasing D and decreasing ξ, with smoothing of the fractal surface of the microclusters. The time evolution of the density of the wet gels was evaluated exclusively from the SAXS parameters ξ, D, and a. The final dried acetone-exchanged gel presents Porod's inhomogeneity length of about 2.8 nm and apparently exhibits an interesting singularity D →3, as determined by the mass fractal modeling used to fit the SAXS intensity data for the obtaining of the parameters ξ and D.

Operator's manual : grinding kit, valve seat, electric 35 degree angle type concentric drive, 1/4 horsepower, AC/DC, single phase, 115-volt, 14000 RPM rated no load speed (K.O. Lee Company model P300BB) (4910-060-9983) and (K.O. Lee Company model P300BB-M2) (4910-473-6437).

"February 1965."

Operator's manual : grinding machine, valve face, bench mounting, 9/32 inch to 11/16 inch chuck, 0 to 45 degree valve, face angle adjustment, 115-volt, AC/DC, 60-cycle, single phase (Cedar Rapids model "KWIK-WAY" KK) (4910-540-4679).

"6 October 1967."

Monitoring phase behavior of sub- and supercritical CO2 confined in porous fractal silica with 85% porosity

Phase behavior of CO2 confined in porous fractal silica with volume fraction of SiO2 φs = 0.15 was investigated using small-angle neutron scattering (SANS) and ultrasmall-angle neutron scattering (USANS) techniques. The range of fluid densities (0<(FCO2)bulk<0.977 g/cm3) and temperatures (T=22 °C, 35 and 60 °C) corresponded to gaseous, liquid, near critical and supercritical conditions of the bulk fluid. The results revealed formation of a dense adsorbed phase in small pores with sizes D<40 A° at all temperatures. At low pressure (P <55 bar, (FCO2)bulk <0.2 g/cm3) the average fluid density in pores may exceed the density of bulk fluid by a factor up to 6.5 at T=22 °C. This “enrichment factor” gradually decreases with temperature, however significant fluid densification in small pores still exists at temperature T=60°C, i.e., far above the liquid-gas critical temperature of bulk CO2 (TC=31.1 °C). Larger pores are only partially filled with liquid-like adsorbed layer which coexists with unadsorbed fluid in the pore core. With increasing pressure, all pores become uniformly filled with the fluid, showing no measurable enrichment or depletion of the porous matrix with CO2.

Sequential MRI reveals individual level deformities in the growing scoliotic spine that are clinically masked by the Cobb angle

Introduction Clinically, the Cobb angle method measures the overall scoliotic curve in the coronal plane but does not measure individual vertebra and disc wedging. The contributions of the vertebrae and discs in the growing scoliotic spine were measured to investigate coronal plane deformity progression with growth. Methods A 0.49mm isotropic 3D MRI technique was developed to investigate the level-by-level changes that occur in the growing spine of a group of Adolescent Idiopathic Scoliosis (AIS) patients, who received two to four sequential scans (spaced 3-12 months apart). The coronal plane wedge angles of each vertebra and disc in the major curve were measured to capture any changes that occurred during their adolescent growth phase. Results Seventeen patients had at least two scans. Mean patient age was 12.9 years (SD 1.5 years). Sixteen were classified as right-sided major thoracic Lenke Type 1 (one left sided). Mean standing Cobb angle at initial presentation was 31° (SD 12°). Six received two scans, nine three scans and two four scans, with 65% showing a Cobb angle progression of 5° or more between scans. Overall, there was no clear pattern of deformity progression of individual vertebrae and discs, nor between patients who progressed and those who didn’t. There were measurable changes in the wedging of the vertebrae and discs in all patients. In sequential scans, change in direction of wedging was also seen. In several patients there was reverse wedging in the discs that counteracted increased wedging of the vertebrae such that no change in overall Cobb angle was seen. Conclusion Sequential MRI data showed complex patterns of deformity progression. Changes to the wedging of individual vertebrae and discs may occur in patients who have no increase in Cobb angle measure; the Cobb method alone may be insufficient to capture the complex mechanisms of deformity progression.

Sequential MRI of growing scoliotic spines reveals individual level deformities that are clinically masked by the cobb angle

INTRODUCTION. Clinically, the Cobb angle method measures the overall scoliotic curve in the coronal plane but does not measure individual vertebra and disc wedging. The contributions of the vertebrae and discs in the growing scoliotic spine were measured to investigate coronal plane deformity progression with growth. METHODS. A 0.49mm isotropic 3D MRI technique was developed to investigate the level-by-level changes that occur in the growing spine of a group of Adolescent Idiopathic Scoliosis (AIS) patients, who received two to four sequential scans (spaced 3-12 months apart). The coronal plane wedge angles of each vertebra and disc in the major curve were measured to capture any changes that occurred during their adolescent growth phase. RESULTS. Seventeen patients had at least two scans. Mean patient age was 12.9 years (SD 1.5 years). Sixteen were classified as right-sided major thoracic Lenke Type 1 (one left sided). Mean standing Cobb angle at initial presentation was 31° (SD 12°). Six received two scans, nine three scans and two four scans, with 65% showing a Cobb angle progression of 5° or more between scans. Overall, there was no clear pattern of deformity progression of individual vertebrae and discs, nor between patients who progressed and those who didn’t. There were measurable changes in the wedging of the vertebrae and discs in all patients. In sequential scans, change in direction of wedging was also seen. In several patients there was reverse wedging in the discs that counteracted increased wedging of the vertebrae such that no change in overall Cobb angle was seen. CONCLUSION. Sequential MRI data showed complex patterns of deformity progression. Changes to the wedging of individual vertebrae and discs may occur in patients who have no increase in Cobb angle measure; the Cobb method alone may be insufficient to capture the complex mechanisms of deformity progression.

Evidence of clustering in an aqueous electrolyte solution: a small-angle X-ray scattering study

The work reported hen was motivated by a desire to verify the existence of structure - specifically MP-rich clusters induced by sodium bromide (NaBr) in the ternary liquid mixture 3-methylpyridine (Mf) + water(W) + NaBr. We present small-angle X-ray scattering (SAXS) measurements in this mixture. These measurements were obtained at room temperature (similar to 298 K) in the one-phase region (below the relevant lower consolute points, T(L)s) at different values of X (i.e., X = 0.02 - 0.17), where X is the weight fraction of NaBr in the mixture. Cluster-size distribution, estimated on the assumption that the clusters are spherical, shows systematic behaviour in that the peak of the distribution shifts rewards larger values of cluster radius as X increases. The largest spatial extent of the clusters (similar to 4.5 nm) is seen at X = 0.17. Data analysis assuming arbitrary shapes and sizes of clusters gives a limiting value of cluster size (- 4.5 nm) that is not very sensitive to X. It is suggested that the cluster size determined may not be the same as the usual critical-point fluctuations far removed from the critical point (T-L). The influence of the additional length scale due to clustering is discussed from the standpoint of crossover from Ising to mean-field critical behaviour, when moving away from the T-L.

Esr study of (SO4)2- dynamics in relation to the ferroelectric phase transition in ammonium sulfate

Ferroelectric phase transition in ammonium sulfate has been studied by ESR of CrO43- radical substituting for SO42- ion in (NH4)2SO4. In addition to discontinuous changes at Tc, certain continuous changes are observed in ESR parameters of this probe below Tc, which reflect the role of the sulfate ion in the phase transition. A microscopic mechanism of the phase transition is proposed and discussed in terms of the change of orientation of the sulfate tetrahedron through a finite angle. The degree of the change of orientation below Tc is thought to be the possible order parameter of the phase transition.

Re-entrant Phase Behavior of a Concentrated Anionic Surfactant System with Strongly Binding Counterions

The phase behavior of the anionic surfactant sodium dodecyl sulfate (SDS) in the presence of the strongly binding counterion p-toluidine hydrochloride (PTHC) has been examined using small-angle X-ray diffraction and polarizing microscopy. A hexagonal-to-lamellar transition on varying the PTHC to SDS molar ratio (alpha) occurs through a nematic phase of rodlike micelles (N-C) -> isotropic (I) -> nematic of disklike micelles (N-D) at a fixed surfactant concentration (phi). The lamellar phase is found to coexist with an isotropic phase (l') over a large region of the phase diagram. Deuterium nuclear magnetic resonance investigations of the phase behavior at phi = 0.4 confirm the transition from N-C to N-D on varying alpha. The viscoelastic and flow behaviors of the different phases were examined. A decrease in the steady shear viscosity across the different phases with increasing alpha suggests a decrease in the aspect ratio of the micellar aggregates. From the transient shear stress response of the N-C and N-D nematic phases in step shear experiments, they were characterized to be tumbling and now aligning, respectively. Our studies reveal that by tuning the morphology of the surfactant micelles strongly binding counterions modify the phase behavior and rheological properties of concentrated surfactant solutions.

Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.