Effects of Noise and Detection Error in a Dynamic Adaptive Optics System

It is well known that noise and detection error can affect the performances of an adaptive optics (AO) system. Effects of noise and detection error on the phase compensation effectiveness in a dynamic AO system are investigated by means of a pure numerical simulation in this paper. A theoretical model for numerically simulating effects of noise and detection error in a static AO system and a corresponding computer program were presented in a previous article. A numerical simulation of effects of noise and detection error is combined with our previous numeral simulation of a dynamic AO system in this paper and a corresponding computer program has been compiled. Effects of detection error, readout noise and photon noise are included and investigated by a numerical simulation for finding the preferred working conditions and the best performances in a practical dynamic AO system. An approximate model is presented as well. Under many practical conditions such approximate model is a good alternative to the more accurate one. A simple algorithm which can be used for reducing the effect of noise is presented as well. When signal to noise ratio is very low, such method can be used to improve the performances of a dynamic AO system.

Evaluation of influence of multiple scattering effect in light-scattering-based applications

The extinction cross sections of a system containing two particles are calculated by the T-matrix method, and the results are compared with those of two single particles with single-scattering approximation. The necessity of the correction of the refractive indices of water and polystyrene for different incident wavelengths is particularly addressed in the calculation. By this means, the volume fractions allowed for certain accuracy requirements of single-scattering approximation in the light scattering experiment can be evaluated. The volume fractions calculated with corrected refractive indices are compared with those obtained with fixed refractive indices which have been rather commonly used, showing that fixed refractive indices may cause significant error in evaluating multiple scattering effect. The results also give a simple criterion for selecting the incident wavelength and particle size to avoid the 'blind zone' in the turbidity measurement, where the turbidity change is insensitive to aggregation of two particles.

Large-eddy simulation of turbulent collision of heavy particles in isotropic turbulence

The small-scale motions relevant to the collision of heavy particles represent a general challenge to the conventional large-eddy simulation (LES) of turbulent particle-laden flows. As a first step toward addressing this challenge, we examine the capability of the LES method with an eddy viscosity subgrid scale (SGS) model to predict the collision-related statistics such as the particle radial distribution function at contact, the radial relative velocity at contact, and the collision rate for a wide range of particle Stokes numbers. Data from direct numerical simulation (DNS) are used as a benchmark to evaluate the LES using both a priori and a posteriori tests. It is shown that, without the SGS motions, LES cannot accurately predict the particle-pair statistics for heavy particles with small and intermediate Stokes numbers, and a large relative error in collision rate up to 60% may arise when the particle Stokes number is near St_K=0.5. The errors from the filtering operation and the SGS model are evaluated separately using the filtered-DNS (FDNS) and LES flow fields. The errors increase with the filter width and have nonmonotonic variations with the particle Stokes numbers. It is concluded that the error due to filtering dominates the overall error in LES for most particle Stokes numbers. It is found that the overall collision rate can be reasonably predicted by both FDNS and LES for St_K>3. Our analysis suggests that, for St_K<3, a particle SGS model must include the effects of SGS motions on the turbulent collision of heavy particles. The spectral analysis of the concentration fields of the particles with different Stokes numbers further demonstrates the important effects of the small-scale motions on the preferential concentration of the particles with small Stokes numbers.

Effect of elliptical manufacture error of an axicon on the diffraction-free beam patterns

Based on the generalized Huygens-Fresnel diffraction integral theory and the stationary-phase method, we analyze the influence on diffraction-free beam patterns of an elliptical manufacture error in an axicon. The numerical simulation is compared with the beam patterns photographed by using a CCD camera. Theoretical simulation and experimental results indicate that the intensity of the central spot decreases with increasing elliptical manufacture defect and propagation distance. Meanwhile, the bright rings around the central spot are gradually split into four or more symmetrical bright spots. The experimental results fit the theoretical simulation very well. (C) 2008 Society of Photo-Optical Instrumentation Engineers.

IMPROVED PEAK POWER METHOD FOR MEASURING FREQUENCY RESPONSES OF PHOTODETECTORS IN A SELF-HETERODYNE SYSTEM

An improved peak power method for measuring frequency responses of photodetectors in a self-heterodyne system consisting of a distributed Bragg reflector laser is proposed. The time-resolved spectrum technique is used to measure the peak power of the beat signal and the intrinsic linewidth of heat signal for calibration. The experimental results show that the impact of the thermal-induced frequency drift, which is the main reason for producing an error in measurement by conventional peak power method and spectrum power method, can be removed.

Abnormal phenomenon of the dependence of the retention factors for uncharged species on applied voltage in capillary electrochromatography

Polymethacrylate-based monolithic columns were prepared for capillary electrochromatography (CEC) by in situ copolymerization of butyl methacrylate (BMA), 2-acrylamido-2-methyl-1-propanesulfonic acid (AMPS), and ethylene dimethacrylate (EDMA) in the presence of a porogen in fused-silica capillaries of 100 mum I.D. The abnormal phenomenon that retention factors for neutral species decreases with applied voltage in CEC was observed. Capillary electrophoresis (CE) instruments usually require a period of time to increase voltage from 0 kV to desired value, which is called as ramp time. Such ramp time and any error in the determination of dead time should be taken into account during the accurate calculation of retention factors. After the correction of the retention factors, the plots of the corrected factors for alkylbenzene versus applied voltage were made, the absolute value of the plot slopes are less than 1.8 X 10(-4), Which indicates that the corrected retention times for neutral species do not show any dependence on applied voltage. Further, the plots of the corrected retention times for acidic and basic compounds versus the reciprocal of applied voltage were drawn, where the target compounds were eluted in neutral form. The very nice linearity of the plots was obtained. The linear correlation coefficients are over 0.999. Here, the slopes of the plots represent

Studies of instrumental spreading in gel permeation chromatography by coupling with a two-angle laser light scattering detector

The instrumental spreading of a high temperature gel permeation chromatograph (GPC) was evaluated by coupling with a two-angle laser light scattering (TALLS) detector, using narrow polystyrene, polyethylene, and syndiotactic polypropylene samples. The determined spreading factor increased with increasing molecular weight of polymers, and no maximum for spreading 174 tor was observed in the studied retention volume, while the spreading factors for single low molecular weight alkanes are independent of their molecular weight. Neglecting of the spreading effect for GPC would not introduce much error in molecular weight calculation when high quality high performance columns were used, especially when equipped with a laser light scattering detector. The scaling relationship between radius of gyration and molecular weight of polymer, determined by GPC with a TALLS detector, was independent of the instrumental spreading.

WAVELENGTH POSITIONING ERRORS AND TRUE DETECTION LIMIT IN RELATION TO MULTICOMPONENT ANALYSIS TECHNIQUES FOR THE CORRECTION OF LINE INTERFERENCES IN INDUCTIVELY COUPLED PLASMA ATOMIC EMISSION-SPECTROMETRY

The present paper deals with the evaluation of the relative error (DELTA(A)) in estimated analyte concentrations originating from the wavelength positioning error in a sample scan when multicomponent analysis (MCA) techniques are used for correcting line interferences in inductively coupled plasma atomic emission spectrometry. In the theoretical part, a quantitative relation of DELTA(A) with the extent of line overlap, bandwidth and the magnitude of the positioning error is developed under the assumption of Gaussian line profiles. The measurements of eleven samples covering various typical line interferences showed that the calculated DELTA(A) generally agrees well with the experimental one. An expression of the true detection limit associated with MCA techniques was thus formulated. With MCA techniques, the determination of the analyte and interferent concentrations depend on each other while with conventional correction techniques, such as the three-point method, the estimate of interfering signals is independent of the analyte signals. Therefore. a given positioning error results in a larger DELTA(A) and hence a higher true detection limit in the case of MCA techniques than that in the case of conventional correction methods. although the latter could be a reasonable approximation of the former when the peak distance expressed in the effective width of the interfering line is larger than 0.4. In the light of the effect of wavelength positioning errors, MCA techniques have no advantages over conventional correction methods unless the former can bring an essential reduction ot the positioning error.

EVALUATION OF THE EFFECT OF WAVELENGTH POSITIONING ERRORS ON KALMAN FILTERING RESULTS IN INDUCTIVELY COUPLED PLASMA ATOMIC EMISSION-SPECTROMETRY

This work evaluates the effect of wavelength positioning errors in spectral scans on analytical results when the Kalman filtering technique is used for the correction of line interferences in inductively coupled plasma atomic emission spectrometry (ICP-AES). The results show that a positioning accuracy of 0.1 pm is required in order to obtain accurate and precise estimates for analyte concentrations. The positioning error in sample scans is more crucial than that in model scans. The relative bias in measured analyte concentration originating from a positioning error in a sample scan increases linearly with an increase in the magnitude of the error and the peak distance of the overlapping lines, but is inversely proportional to the signal-to-background ratio. By the use of an optimization procedure for the positions of scans with the innovations number as the criterion, the wavelength positioning error can be reduced and, correspondingly, the accuracy and precision of analytical results improved.

A Multimoment Finite-Volume Shallow-Water Model On The Yin-Yang Overset Spherical Grid

A numerical model for shallow-water equations has been built and tested on the Yin-Yang overset spherical grid. A high-order multimoment finite-volume method is used for the spatial discretization in which two kinds of so-called moments of the physical field [i.e., the volume integrated average ( VIA) and the point value (PV)] are treated as the model variables and updated separately in time. In the present model, the PV is computed by the semi-implicit semi-Lagrangian formulation, whereas the VIA is predicted in time via a flux-based finite-volume method and is numerically conserved on each component grid. The concept of including an extra moment (i.e., the volume-integrated value) to enforce the numerical conservativeness provides a general methodology and applies to the existing semi-implicit semi-Lagrangian formulations. Based on both VIA and PV, the high-order interpolation reconstruction can only be done over a single grid cell, which then minimizes the overlapping zone between the Yin and Yang components and effectively reduces the numerical errors introduced in the interpolation required to communicate the data between the two components. The present model completely gets around the singularity and grid convergence in the polar regions of the conventional longitude-latitude grid. Being an issue demanding further investigation, the high-order interpolation across the overlapping region of the Yin-Yang grid in the current model does not rigorously guarantee the numerical conservativeness. Nevertheless, these numerical tests show that the global conservation error in the present model is negligibly small. The model has competitive accuracy and efficiency.

Effect of nonlinear wave-current interaction on flow fields and hydrodynamic forces

A fifth-order theory for solving the problem of interaction between Stokes waves and exponential profile currents is proposed. The calculated flow fields are compared with measurements. Then the errors caused by the linear superposition method and approximate theory are discussed. It is found that the total wave-current field consists of pure wave, pure current and interaction components. The shear current not only directly changes the flow field, but also indirectly does sx, by changing the wave parameters due to wave-current interaction. The present theory can predict the wave kinematics on shear currents satisfactorily. The linear superposition method may give rise to more than 40% loading error in extreme conditions. When the apparent wave period is used and the Wheeler stretching method is adopted to extrapolate the current, application of the approximate theory is the best.

Symmetry of the Talbot effect and its applications

The Talbot effect is one of the most basic optical phenomena that has received extensive investigations both because its new results provide us more understanding of the fundamental Fresnel diffraction and also because of its wide applications. We summarize our recent results on this subject. Symmetry of the Talbot effect, which was reported in Optics Communications in 1995, is now realized as the key to reveal other rules for explanation of the Talbot effect for array illumination. The regularly rearranged-neighboring-phase-differences (RRNPD) rule, a completely new set of analytic phase equations (Applied Optics, 1999), and the prime-number decomposing rule (Applied Optics, 2001) are the newly obtained results that reflect the symmetry of the Talbot effect in essence. We also reported our results on the applications of the Talbot effect. Talbot phase codes are the orthogonal codes that can be used for phase coding of holographic storage. A new optical scanner based on the phase codes for Talbot array illumination has unique advantages. Furthermore, a novel two-layered multifunctional computer-generated hologram based on the fractional Talbot effect was proposed and implemented (Optics Letters, 2003). We believe that these new results should bring us more new understanding of the Talbot effect and help us to design novel optical devices that should benefit practical applications. (C) 2004 Society of Photo-Optical Instrumentation Engineers.

透镜自重变形引起波像差的有限元分析

在用大口径、长焦距平行光管模拟激光远场特性时，其光组透镜在重力作用下的变形不能忽略，为了分析对出射光束质量的影响，采用有限元分析软件“ANSYS”建立了平行光管光组中声400mm平凸透镜的有限元模型，给出一种分析透镜轴向变形引起的波像差的方法，在不同工况下，计算了平凸透镜在重力作用下轴向变形的峰谷值和均方根值，对轴向变形量均方根值最小工况画出了透镜表面变形的等值线图，计算了声350mm通光口径内的波像差峰谷值和均方根值，对平行光管光组的波像差做出估计，验证了设计的合理性。

SiO_2薄膜折射率的准确拟合分析

精确的光学常数对于设计和制备高品质的光学薄膜非常重要,尤其是那些光学性能对折射率变化敏感的薄膜。SiO_2是一种常用的低折射率材料,因与常用基底折射率相近使其准确拟合有一定难度。实验通过离子束溅射制备了SiO_2单层膜。考虑测量时的误差和基底折射率的影响,采用透射率包络和反射率包络得到了SiO_2的折射率,并用所得折射率进行反演来对这两种途径在实际测量拟合过程中的准确性进行比对。分析表明,剩余反射率在实际的测量过程中误差更小,直接用测量镀膜前后基片的剩余反射率值可以更简便更准确地得到SiO_2的折射率,能达到10~(-2)的精度。