Measuring the centroid gain of a Shack-Hartmann quad-cell wavefront sensor by using slope discrepancy

Shack-Hartmann wavefront sensors (SH WFS) are used by many adaptive optics (AO) systems to measure the wavefront. In this WFS, the centroid of the spots is proportional to the wavefront slope. If the detectors consist of 2 x 2 quad cells, as is the case in most astronomical AO systems, then the centroid measurement is proportional to the centroid gain. This quantity varies with the strength of the atmospheric turbulence and the angular extent of the beacon. The benefits of knowing the centroid gain and current techniques to measure it are discussed. A new method is presented, which takes advantage of the fact that, in a SH-WFS-based AO system, there are usually more measurements than actuators. Centroids in the null space of the wavefront reconstructor, called slope discrepancy measurements, contain information about the centroid gain. Tests using the W. M. Keck Observatory AO system demonstrate the accuracy of the algorithm.     

Iteration of phase window correlation and least-squares fit for Young's fringe pattern processing

Correlation by means of phase windows that artificially create phase shifts is combined with the least-squares fit to provide a processing algorithm. A Young's pattern is correlated by means of the phase windows to generate four patterns with phase shifts of 0 degrees , 90 degrees , 180 degrees , and 270 degrees . The phase of the Young's pattern is derived from the four patterns. Then the derived phase is least-squares fitted to a phase plane. The above steps are repeated once to improve accuracy. Speckle noise is suppressed by the correlation operations, as well as a loop including phase calculation, fringe reconstruction, and smoothing. The magnitude and direction of the displacement associated with Young's pattern are determined from the phase plane. The algorithm takes less calculation time than the fast Fourier transform method and does so with improved accuracy. Software has been developed and is used in the experiment.     

Evolution of the scintillation index and the optical vortex density in speckle fields after removal of the least-squares phase

Knowledge of the behavior of stochastic optical fields can aid the understanding of the scintillation of light propagating through a turbulent medium. For this purpose, we perform a numerical investigation of the evolution of the scintillation index and the optical vortex density in a speckle field after removing its continuous phase. We find that both the scintillation index and the vortex density initially drop and then increase again to reach an equilibrium level. It is also found that the initial rate of decrease in both cases is 1 order of magnitude faster than the eventual rate of increase. Their detail shapes are however different. Therefore different empirical functions are used to fit the shapes of these curves.     

A least-squares front-tracking finite element method analysis of phase change with natural convection

This paper focuses on the numerical modelling of phase-change processes with natural convection. In particular, two-dimensional solidification and melting problems are studied for pure metals using an energy preserving deforming finite element model. The transient Navier–Stokes equations for incompressible fluid flow are solved simultaneously with the transient heat flow equations and the Stefan condition. A least-squares variational finite element method formulation is implemented for both the heat flow and fluid flow equations. The Boussinesq approximation is used to generate the bulk fluid motion in the melt. The mesh motion and mesh generation schemes are performed dynamically using a transfinite mapping. The consistent penalty method is used for modelling incompressibility. The effect of natural convection on the solid/liquid interface motion, the solidification rate and the temperature gradients is found to be important. The proposed method does not possess some of the false diffusion problems associated with the standard Galerkin formulations and it is shown to produce accurate numerical solutions for convection dominated phase-change problems.     

Supersolidus liquid phase sintering of moulded metal components

The influence of supersolidus liquid phase sintering (SLPS) on the density of sintered components manufactured using a Ni-base superalloy powder (N18) has been studied. A compression moulding technique was employed to simulate the metal injection moulding (MIM) process using coarse N18 powder, with a particle size distribution of 40–63 m, as opposed to fine powders of less than 10m normally used in conventional MIM. The study has demonstrated how the problem of low sintered density, encountered in solid-state sintering using coarse powders, can been overcome by SLPS and that the sintered densities of the N18 powder via the moulding process route were comparable with those produced by conventional die pressing and sintering.     

Redistribution of gas phase components during spark discharge

Changes in the composition of the gas phase during spark discharge operation in a closed volume has been studied. Equations that describe the kinetics of this process are derived and used to calculate the real variation of partial pressures of all significant gas phase components involved in the plasmachemical interaction. Rate constants of the main reactions are determined for plasma discharge in air in a closed volume.     

Evaluation of a preconditioned conjugate-gradient algorithm for weighted least-squares unwrapping of digital speckle-pattern interferometry phase maps

Inasmuch as current fringe analysis techniques used in digital speckle-pattern interferometry (DSPI) yield a phase map modulo 2pi, phase unwrapping is the final step of any data evaluation process. The performance of a recently published algorithm used to unwrap DSPI phase maps is investigated. The algorithm is based on a least-squares minimization technique that is solvable by the discrete cosine transform. When phase inconsistencies are present, they are handled by exclusion of invalid pixels from the unwrapping process through the assignment of zero-valued weights. Then the weighted unwrapping problem is solved in an iterative manner by a preconditioned conjugate-gradient method. The evaluation is carried out with computer-simulated DSPI phase maps, an approach that permits the generation of phase fields without inconsistencies, which are then used to calculate phase deviations as a function of the iteration number. Real data are also used to illustrate the performance of the algorithm.     

Deformation analysis of notched components and assessment of approximate methods

Finite element modelling was conducted on notched members subjected to proportional and non-proportional loading. A recently developed cyclic plasticity model capable of accurately describing cyclic material behaviour was implemented into a finite element code. A plate with a central hole and a shaft with a circumference groove were studied. Approximate methods for the notched problems were critically evaluated using the finite element results.     

Reconstruction of spatial, phase, and coherence properties of light

Image reconstruction of partially coherent light is interpreted as quantum-state reconstruction. An efficient method based on the maximum-likelihood estimation is proposed for acquiring information from blurred intensity measurements affected by noise. Connections with incoherent-image restoration are pointed out. The feasibility of the method is demonstrated numerically. Spatial and correlation details significantly below the diffraction limit are revealed in the reconstructed pattern.     

Stability assessment of earth slope using modified particle swarm optimization

This paper has proposed an effective method to determine the minimum factor of safety (FS) and associated critical failure surface in slope stability analysis. The search for the minimum FS based on limit equilibrium methods is a complex optimization problem as the objective function is non-smooth and non-convex. Recently, particle swarm optimization (PSO) as a meta-heuristic optimization algorithm has been developed with success in treating various types of problems. In the current study, a new approach of PSO is proposed to calculate the safety factor of earth slopes. The safety factors of the general slip surfaces are calculated using Spencer method of slices, and each new slip surface is randomly generated by straight line technique. The reliability and efficiency of the proposed algorithm are examined by considering a number of published cases. The results indicate that the new method can predict a more critical failure mechanism with a lower FS and can outperform the other methods in the literature as well as standard PSO. Finally, the proposed method will be validated by considering an existing slope failure in Ulu Klang, Malaysia.     

Life assessment of multiaxially cyclic loaded turbine components

Rotors of turbines are exposed to high thermo-mechanical loads, especially during start-up and shut-down procedures. Especially in the notched region of the blade-connection to the rotor a complex multiaxial elastic-plastic stress state is present. The reason is the multi-surface contact in combination with fatigue and creep-fatigue load. Within the scope of this work the blade-disc-connection of a gas turbine made of the nickel-based alloys IN792 (blades) and IN718 (disc) was investigated at typical local service temperature of 550 °C. The aim was the investigation of mutual influence of adjoining blades as well as the effect on cycles to failure by variation of friction behaviour due to different coatings on the surface of the blade root. An already existing life assessment method based on a local strain approach could be confirmed for this more complex loading situation.
In contrast to this, a blade-shaft-connection of a steam turbine made of X12CrMoWVNbN10-1-1 was investigated at its typical service temperature of 600 °C. During cyclic loading, the martensitic 10Cr steel reacts with ongoing cyclic softening. The fundamental result of the work discussed here is the development of a new life assessment method based on a damage parameter, which is a function of accumulated plastic strain. This damage parameter is included in a complex material model considering static, cyclic and viscoplastic materials behaviour. Thus, the life assessment method could be verified with inelastic finite element calculations of the model specimens, which were especially designed for the low-cycle fatigue tests of blade-shaft-connection presented in this paper.     

Pressure–impulse diagrams for the behavior assessment of structural components

Theoretical and numerical methods for deriving pressure–impulse (P–I) diagrams for structural elements subjected to transient loads are described in this paper. Three different search algorithms for deriving P–I diagrams numerically were developed by the authors and are presented. The P–I diagrams of a linear elastic system under rectangular and triangular load pulses are derived using both theoretical and numerical methods and the results are compared. The application of these approaches to the behavior assessment of tested structural elements is illustrated.     

Residual stresses in the phase components of spark coatings of tungsten and titanium carbides

The X-ray diffraction method is used to study the stressed structural state of spark coatings formed on U8 steel as a result of treatment with T15K6 hard-alloy electrodes. The residual stresses formed in different phase components have different values and signs. Subsequent laser heating decreases compressive and tensile stresses. In the austenitic interlayer of the steel substrate, the residual stresses relax almost completely due to the decrease in the specific volume of the phase in the course of the α → γ transformation. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 5, pp. 115–118, September–October, 2005.     

水相组分对混装乳化炸药的性能影响研究

为研究混装乳化炸药水相各组分质量分数对爆轰性能、乳胶基质稳定性的影响,通过对5组不同组分质量分数配方的爆轰性能进行理论计算,分析水相组分对爆热、爆容、爆速的影响,将设计的5组配方制备成乳胶基质,通过高低温循环模拟温度冲击对储存稳定性的影响。实验结果表明:水相组分中硝酸铵含量从75%增加到79%后,爆轰性能:爆热值从2 360.32 kJ/kg增加到2 658.43 kJ/kg,增加12.6%,爆容值从846.04 L/kg下降到818.61 L/kg,降低3.3%,爆速值从4 573 m/s增加到4 855 m/s,增加6.1%,说明硝酸铵质量分数对爆热的影响最大,对爆容的影响最小。高低温循环次数从5次降到3次,表明增加硝酸铵质量分数对乳胶基质储存稳定性有一定的影响。     

Design methods for reliable fatigue assessment of PM components

The use of PM materials is rapidly expanding with an increasing concentration on highly loaded structural parts such as synchroniser hubs, gears, sprockets or shifting forks. The successful implementation of PM materials for such parts depends on a reliable fatigue design concept. Such a design concept has to consider the local durability, especially in fatigue critical sharply notched areas, depending on the local density of the material and stress gradients. This paper summarises different design methods in order to transfer the fatigue behaviour of specimens to components by considering sharply notched areas. Four different local approaches have been investigated: the highly stressed volume approach, the stress gradient approach, the critical distance method and the stress averaging method according to Neuber. The design methods have been analysed on the basis of fatigue testing results of unnotched and notched fatigue specimens and of synchroniser hubs made from a 4% Ni diffusion‐alloyed steel material (Distaloy AE+0.6%C). The transferability of characteristic fatigue properties from specimens to a sharply notched component, a synchroniser hub, is presented and the practicability of the design methods demonstrated and discussed. These investigations showed that the most reliable concept was the highly stressed volume approach. The accuracy of the approach can be comprehended separating statistical and so called material support effect.     

La3+掺杂对堇青石陶瓷的相组成和性能的影响

为了获得堇青石含量高且具有一定孔隙率的堇青石质耐火材料,用X射线衍射仪,差热分析仪等手段研究了由溶胶-凝胶法（Mg盐、Al盐和正硅酸乙酯按堇青石化学计量比配制）制备堇青石陶瓷时,添加La^3＋对堇青石陶瓷相组成和性能的影响,分析了La^3＋在烧结过程中的作用机理。试验表明,随着烧结温度的提高,La^3＋含量的增加,该陶瓷的致密度、弯曲强度逐渐提高,而气孔率逐渐下降。适量添加La^3＋（质量分数为4％～6％）,显著降低中间相（尖晶石、方石英等）的含量。La^3＋的作用主要是作为烧结助剂,降低烧结温度,提高致密度。     

Application of the least-squares method in processing profilograms

Conclusions The orthogonal-regression-line factors have a nonlinear relationship to the recording scale, and therefore, the median plotted on the profilogram does not correspond to that of the profile. The error in determining the surface-roughness parameters is eliminated by using the formulas (7), (8), and (9). The median of a stationary normal process plotted by means of the least-squares method differs but little from the orthogonal regression line even if the amplitude of waviness is three times greater than that of surface roughness. Moreover, this median's factors have a linear relationship to the scale factors and require a smaller number of mathematical operations for their evaluation. Such a median plotted on the profilogram strictly corresponds to the profile's median.Translated from Izmeritel'naya Tekhnika, No. 2, pp. 84–85, February, 1973.