The influence of the sampling dots on the analysis of the wave front aberration by using the covariance matrix method

The covariance matrix method is a simple method for solving the Zernike polynomial with the higher fitting precision. In this paper, it was used to analyze the several optical wave fronts of the fine polished aluminum disk surface captured by a Twyman-Green interferometer system. We had found that the PV (peak-to-valley) and rms (root-mean-square) values of the wave front aberration changes with changing the Zernike term and the expressions for the several optical wave fronts with the different sampling dots were wrong. By analyzing the relations among the condition number of the coefficients matrix, the Zernike term, and the number of the sampling dots, it was indicated that the number of the sampling dots had only reduced the fluctuation the PV and the rms value while the Zernike term increases, but did not change the case that the expressions for the wave front aberration were wrong when the Zernike term is larger than 14, especially when the number of the sampling dots is less. Such an analysis will be valuable in solving the Zernike polynomial for the wave front aberration analysis by using the covariance matrix method in optical testing.     

Reducing phase retrieval errors in Fourier analysis of 2-dimensional digital model interferograms

In order to measure the displacements of facets on a growing spherical Cu_2−δSe crystal with sub-nanometre resolution, we investigated the reliability and accuracy of standard method of Fourier analysis of digital laser interferograms. Guided by realistic experimental conditions (two-dimensional (2D) interferograms), starting from 2D model interferograms and using original custom designed Gaussian filtering window and multistage unwrapping procedure of the retrieved phase, we demonstrate for a considerable parameter range the non-negligible inherent phase retrieval error due to non-integer number of fringes within the digital image. Our results indicate an intermediate parameter range where the error is acceptably small. We introduce an algorithm modification that significantly reduces the error, especially for low and high fringe densities. In the experimentally most common case of diagonal fringes the reduced error is an order of magnitude smaller than for nearly one-dimensional case within almost entire parameter space.     

Measurement of surface form deviation of the plane optical element using grid line method

A method for automatically measuring the surface form deviation of the plane optical element is presented. It uses the image pre-processing technique to obtain the centerlines of the interference fringes, the grid line technique to search the average fringe spacing and the maximum curvature of the interference fringes, and the normalization to obtain the value of surface form deviation of the optical element. The experimental results show that the measuring precision of the surface form deviation of the plane optical element reaches the value of 0.1 and the method improves the adaptation capability of processing the interference fringes, which indicates that the method can substitute the visual interpretation of interference fringes in high-noise workshop environment.     

Reverberation-ray matrix analysis for wave propagation in multiferroic plates with imperfect interfacial bonding

The dispersion behavior of waves in multiferroic plates with imperfect interfacial bonding has been investigated via the method of reverberation-ray matrix, which is directly established from the three-dimensional equations of magneto-electro-elasticity in the form of state space formalism. A generalized spring-layer model is employed to characterize the interfacial imperfection. By introducing a dual system of local coordinates for each single layer, the numerical instability usually encountered in the state space method can be avoided. Based on the proposed method, a typical sandwich plate made of piezoelectric and piezomagnetic phases is considered in numerical examples to calculate the dispersion curves and mode shapes. It is demonstrated that the results obtained by the present method is unconditionally stable as compared to the traditional state space method. The influence of different interfacial bonding conditions on the dispersion characteristics and corresponding mode shapes is investigated.     

Diagnostic analysis of experimental artefacts in DOSY NMR data by covariance matrix of the residuals

Multivariate curve resolution (MCR) has been applied to separate pure spectra and pure decay profiles of DOSY NMR data. Given good initial guesses of the pure decay profiles, and combined with the nonlinear least square regression (NLR), MCR can result in good separation of the pure components. Nevertheless, due to the presence of artefacts in experimental data, validation of a MCR model is still necessary. In this paper, the covariance matrix of the residuals (CMR), obtained by postmultiplying the residual matrix with its transpose, is proposed to evaluate the quality of the results of an experimental data set. Plots of the rows of this matrix give a general impression of the covariance in the frequency domain of the residual matrix. Different patterns in the plot indicate possible causes of experimental imperfections. This new criterion can be used as diagnosis in order to improve experimental settings as well as suggest appropriate preprocessing of DOSY NMR data.     

Development of a practical performance aberration retrieval method from spot intensity images using inverse analysis

A “practically applicable” spot images based aberration retrieval method was developed. The method was systemized with the following techniques. 1) The real part and imaginary part of the spatial spectrum of the focal plane were expanded with the finite lower Zernike polynomials, respectively, and the method was reduced to the nonlinear least squares problem which calculates these coefficients. This technique will identify both the aberration and the intensity distribution of the spatial spectrum. 2) The intensity distributions of spot images were calculated using the Nijboer-Zernike polynomials in order to avoid a long calculation time and the numerical errors caused by Fourier transform or convolution. 3) Two noise reduction methods were applied to the present method, and some numerical and practical experiments were performed to demonstrate the technique’s effectiveness. Four kinds of practical experiment based on theories were performed, and all of them showed good agreement with the theories.     

Acoustic attenuation analysis of network systems by using impedance matrix method

An impedance matrix method is proposed to predict the acoustic attenuation characteristics of network systems. The system may contain several silencer modules and each module may be composed of complex components such as multiply connected tubes, portions with any-shaped cross-section and dissipative parts. The technique of substructuring is adopted and the system is divided into several substructure modules. Three strategies: boundary element method (BEM), numerical point collocation approach and numerical mode matching technique are introduced and the impedance matrix of each module may be computed by a certain appropriate methodology according to the dimensions and geometry of the substructure. Impedance matrix synthesis is employed to obtain the resultant impedance matrix and then transmission loss may be calculated. All the calculation results are verified by experimental measurements and 3-D BEM predictions.     

Early transient responses of multi-span stepped single-walled carbon nanotubes using the method of reverberation ray matrix

The early transient responses of multi-span stepped single walled carbon nanotubes (SWCNTs) under impact loadings are studied by the method of reverberation ray matrix (MRRM). The dynamics model of the carbon nanotubes is established in the Fourier phase space on the basis of the nonlocal Timoshenko beam model. The wave solutions of SWCNTs with arbitrary boundary conditions are obtained by the wave method. The reverberation ray matrix of the multi-span stepped SWCNTs is the product of scattering, phase and permutation matrices, which can be determined by the impact loadings, continuous conditions and boundary conditions. The early transient responses can be calculated by the inverse Fourier transform of the sum of initial ray groups. It can be found that the early transient displacement response in the very short time subjected to the impact loading is very small, while the transient transverse shear strain becomes large in the very short time. The influences of nanotubes span number, nanotubes type and boundary conditions on the early transient responses of multi-span stepped SWCNTs are investigated.     

车载摄影摄像装置图像偏移与动态几何像差的分析

对利用车载摄影摄像装置进行路面检测的检测车,由于检测车行驶时车身存在振动,其检测精度由图像偏移量与动态几何像差决定。为提高检测精度,必须确定任一时刻的图像偏移量与动态几何像差并对其进行补偿。利用刚体绕定点有限转动的欧拉定理推导了图像偏移函数与动态几何像差函数,计算了为使图像清晰而需在任一时刻对图像的偏移进行补偿的补偿量和对焦距、像面位置、透镜位置进行调整的调整量。研究为图像偏移和动态几何像差补偿的实现奠定了理论基础。     

利用 CCD 图像分析法测定激光横向光场分布

运用Matlab的数字图像处理功能,编写程序分析了CCD相机所拍摄的基模TEM00和TEM10模在靶上的反射光斑,得出光场分布的曲线,并与理论曲线进行对比,验证了由基尔霍夫衍射积分方程推导得到的光场分布函数的正确性。     

Analysis of a right-angle conical reflector resonator by the transfer matrix method

A resonator with a right-angle conical reflector has been proposed to produce high-power CO₂ laser beams. To analyze eigenfields of the right-angle conical reflector resonator, this paper adopts and demonstrates the transfer matrix method. In this paper, the mode-fields and corresponding losses are described as eigenvectors and eigenvalues of a transfer matrix according to the self-reproducing principle of laser field. By solving the transfer matrix for eigenvectors and eigenvalues, we obtain field distributions and losses of the dominant eigenmodes. The calculation results reveal that the right-angle conical reflector resonator could be used for a high-power CO₂ laser to achieve low-order modes. However, the beam quality is reduced due to the residual blind-hole, which is in accord with the experimental result.     

基于子结构技术的光机装置反射镜组件的稳定性分析

反射镜组件是光机装置的重要组成部分,反射镜片的转角稳定性对光路的传输有着直接影响。为了分析获得在地脉动载荷作用下反射镜片的转角响应,分别基于整体结构建模技术和子结构技术建立了某光机装置简化结构的有限元模型,并分析获得了装置中两个反射镜片的转角响应。两种方法得到的反射镜片的转角响应差别分别为3.99%,11.84%,说明基于子结构技术开展光机装置反射镜架组件的稳定性分析是可行的。     

非线性演化方程孤立波的同伦分析法求解

利用同伦分析法求解了Burgers方程，得到了其扭结形孤立波的近似解析解，该解非常接近于相应的精确解.结果表明，同伦分析法可用来求解非线性演化方程的孤立波解.同时，也对所用方法进行了一定扩展，得到了Kadomtsev-Petviashvili(KP)方程的钟形孤立子解.经过扩展后的方法能够更方便地用于求解更多非线性演化方程的高精度近似解析解. 关键词： Burgers方程 同伦分析法 KP方程 孤立波解     

高维非线性演化方程孤立波的同伦分析法求解

利用同伦分析法求解了修正的Kadomtsev-Petviashvili方程, 得到了它的近似孤立波解, 该解与精确解符合得非常好.结果表明，同伦分析法在求解高维非线性演化方程的孤立波解时, 仍然是一种行之有效的方法. 关键词： 同伦分析法 修正的Kadomtsev-Petviashvili方程 孤立波解     

Theoretical study of W-shaped optical fiber with a depression in core center by applying analytical transfer matrix method

Analytical transfer matrix method (ATMM) is a method for calculating the propagation constant in weakly guiding optical fiber. By using ATMM, the optical fiber with a depression in the index profile center and a valley in the cladding layer is analyzed. Compared with Wentzel-Kramers-Brillouin (WKB) method, the simulation result of differential mode delay (DMD) by using ATMM fits well with the experimental results obtained by Takahashi. Based on ATMM, by increasing the depth of central depression in a W-shaped index fiber, the improvement of DMD is also discussed.     

以间质隔离法研究CH3O分子在p-H2间质中的红外吸收光谱

本研究利用低温间质隔离技术搭配红外光谱仪研究CH3ONO在p-H2间质中的光解产生CH3O。实验观察到位于689.3/694.6cm-1、945.9/951.7cm-1、1041.8cm-1、1224.7cm-1、1235.5cm-1、1347.7cm-1、1365.4cm-1、1427.5cm-1、1519.5cm-1、1522.3cm-1等处的CH3O红外吸收谱线,并分析得出各振动模式分别为电子态E1/2a1对称性的ν6、电子态E1/2a2对称性的ν6、电子态E3/2对称性的ν2、电子态E3/2e对称性的ν6、电子态E1/2e对称性的ν6、电子态E1/2a1对称性的ν5、电子态E3/2对称性的ν2、电子态E1/2对称性的ν2、电子态E3/2e对称性的ν5及电子态E1/2e对称性的ν5。     

以间质隔离法研究CH3O分子在p-H2间质中的红外吸收光谱

本研究利用低温间质隔离技术搭配红外光谱仪研究CH3ONO在p-H2间质中的光解产生CH3O。实验观察到位于689.3/694.6cm-1、945.9/951.7cm-1、1041.8cm-1、1224.7cm-1、1235.5cm-1、1347.7cm-1、1365.4cm-1、1427.5cm-1、1519.5cm-1、1522.3cm-1等处的CH3O红外吸收谱线,并分析得出各振动模式分别为电子态E1/2a1对称性的ν6、电子态E1/2a2对称性的ν6、电子态E3/2对称性的ν2、电子态E3/2e对称性的ν6、电子态E1/2e对称性的ν6、电子态E1/2a1对称性的ν5、电子态E3/2对称性的ν2、电子态E1/2对称性的ν2、电子态E3/2e对称性的ν5及电子态E1/2e对称性的ν5。     

A modified transfer matrix method for the study of the bending vibration band structure in phononic crystal Euler beams

We introduce a modified transfer matrix (MTM) method for the calculation of the bending vibration band structure of one-dimensional phononic crystal (PC) Euler beams. A particular combination of hyperbolic functions and triangular functions is introduced to transform the state parameters of the transfer matrix (TM) method into four initial parameters, which have the explicit meanings of the displacement, rotation angle, bending moment and shear force at one beam end. The method is used to calculate the band structures of two PC Euler beams constructed from aluminum–Lucite and 100 kinds of materials. The effectiveness and high efficiency of the MTM method are demonstrated by the results. Several advantages make it a proper choice for the calculation of the bending vibration band structure of PC Euler beams.     

相关分析法确定HL-1M装置磁流体的扰动模式

采用相关分析法模拟分析了HL-1M装置的磁扰动模式,模拟的结果同预期的结果一致。在具有磁流体不稳定性的典型放电中,探测到独立模m=2、3、4,耦合模m=2、3,以及同时出现的耦合模m=4、5和独立模m=5,给出了用扰动幅度的极向截面图分析磁扰动模式的结果,讨论了相关分析法在实验分析中的优点和局限性。     

Advances in pulsed laser weld monitoring by the statistical analysis of reflected light

This paper describes two new techniques for monitoring the quality of laser welds by statistical analysis of the reflected light signal from the weld surface. The first technique involves an algorithm that analyses the variance of the peak values of the reflected signal as a measure of the stability of the surface during pulsed Nd:YAG laser welding in the heat conduction mode. Kalman filtering is used to separate a useful signal from the background noise. A good correlation between weld disruption and signal fluctuation has been identified. This technique could be used in tandem with the present practice of simply using the peak values of reflected (or emitted) light as an indicator of weld quality. The second technique investigated involves an assessment of the temporal shape of the power distribution of individual reflected pulses in comparison with an average of the results from a high quality weld. Once again a high correlation between a poor signal match and inferior quality welding was discovered, which may pave the way towards a new generation of optical weld monitoring devices.