自聚焦透镜的长度对斐索干涉仪面形测量的影响

讨论了自聚焦透镜的长度对自聚焦透镜斐索干涉仪面形测量的影响 ,给出了面形干涉图中相邻干涉条纹半径的平方差随自聚焦透镜长度和面形曲率半径变化的三维曲线、待测面 R→∞时的二维曲线以及自聚焦透镜的长度对面形测量范围的影响 ,并用平面作待测面给出实验值 ,验证了实验与理论的一致性     

轴向温度梯度对红外透镜光学性能的影响

运用有限元分析软件ANSYS建立了透镜组件的有限元模型,并对其进行热应力分析。用Zernike多项式对变形后的镜面面形进行拟合,并将得到的Zernike系数导入光学设计软件ZEMAX中,分析了轴向温度梯度对红外透镜光学性能的影响。结果表明:透镜面形的PV值、RMS值以及透镜表面曲率半径的变化量(ΔR)均随轴向温度梯度的增大而增大;轴向温度梯度使透镜面形发生了变化,从而导致了透镜光学性能的下降。     

方形自聚焦透镜的折射率分布研究

为了获得方形自聚焦透镜的折射率分布,提出了一种求解其折射率分布的半经验方法。该方法利用圆形边界条件下获得的扩散方程的解去近似方形边界条件下扩散方程的解,该近似解中的4个待定系数用雅明干涉法测得的方形自聚焦透镜4个位置点上的折射率来确定。该方法避免了在方形边界条件下求解扩散方程的复杂过程,得到的半经验公式形式简单、计算方便,利用半经验公式计算得到的折射率与实验结果吻合得较好,二者之间的最大相对误差为0.94%,平均相对误差不超过0.3%。该公式为以后研究方形自聚焦透镜阵列成像问题提供了可供参考的理论依据。     

基于频谱傅里叶变换的平行光管液晶显示屏测透镜焦距研究

为了提高平行光管测透镜焦距的质量,采用频谱傅里叶变换和液晶显示屏方法.首先给出系统结构图以及测量方程;接着根据液晶显示屏上光斑位置变化的距离,鉴别出平行光管是否离焦,通过液晶显示屏最小像元尺寸计算最大检焦分辨率;然后基于频谱傅里叶变换对液晶显示屏定焦;最后给出了误差分析.实验测量显示液晶显示屏比目视法有更高的精度,测量重复性好.     

单端输入非线性波导耦合器的稳定性及其自开关效应

分析了单端输入非线性光波导耦合器的稳定性，给出了非线性耦合波方程的近似解析解，用近似解析解计算的结果与严格解的结果以及Ａ．Ｔ．Ｐｈａｍ等的近似结果进行了比较，数值分析表明本文的结果比Ａ．Ｔ．Ｐｈａｍ等的结果更接近严格解，还分析了非线性光波导耦合器的调制特性和自开关效应     

基于电场操控面形的非球面复合透镜制作

介绍了一种制作非球面复合透镜的新方法.根据电场作用改变液滴透镜面形的原理,利用SU-8光固胶直接在双凹透镜表面制作液滴复合透镜,以电场作用操控液滴复合透镜的面形得到非球面,并实时检测其面形和焦斑图像,在检测到较好的透镜面形和聚焦状态时,用紫外光固化得到低像差的非球面复合透镜.研制了基于电场操控面形的非球面复合透镜制作实验平台,实验检测并讨论了复合透镜在电场中的变形,计算了其主曲率和焦距的变化规律.与原有的平凸非球面液滴透镜相比,此透镜具有更长的焦距和更大的变焦范围,并能保持低像差,改进了基于电场操控面形的非球面透镜制作技术,拓宽了非球面液滴透镜的应用范围.     

温度变化对胶粘结透镜面形精度的影响

为了保证透镜的面形精度受温度影响较小,透镜采用低应力胶粘结要优于采用机械方式装夹。首先对比了胶粘结透镜在16℃,20℃,26℃时透镜轴向应力大小和面形的变化。实验验证了在不同温度下,胶粘结透镜面形的峰谷(PV)值(0.073λ,0.064λ,0.085λ)要优于机械方式装夹的透镜面形PV值(0.204λ,0.108λ,0.105λ)。最后对不同温度下胶粘结透镜面形变化的理论计算、仿真和实验结果的误差进行了分析。实验结果表明在温度变化时,采用胶粘结透镜的面形精度要优于机械装夹的透镜面形精度,并且能有效控制温度变化对透镜面形精度的影响。     

金属包层非均匀平板介质波导传输特性分析

用微扰理论和多层分割法求得到金属包层非均匀介质波导导模的传播常数的一级和二级近似解,与用复本征方程求得的精确解进行比较,给出了与精确值符合相当好的数值结果,结果表明微扰法是相当好的近似方法,二级近似结果对一级近似结果的修正很小,一级近似已可以给出足够精确的结果。     

用于室内照明的自由曲面均匀配光透镜设计

以非成像光学为基础,设计了一种在大发散角范围内均匀配光的大功率LED室内照明二次配光透镜方案。采用划分网格法建立光源LED和接收面的映射关系,推导透镜自由曲面面形的一般方程,采用差分法求解透镜面形方程获得面形轮廓数据,再用三维软件建立透镜模型,通过光学仿真软件对所建模型进行光线追迹。结果表明:此方案适用于40°～140°配光角度要求的均匀配光;仿真配光角度120°的照明系统,当透镜的口径与LED发光面直径之比大于等于10时,照明系统的均匀性优于0.9,能量利用率大于92%,且照明效果不受接收面高度的影响。该设计方法为实现大功率LED室内均匀照明系统的小型化和简单化提供了一种有效的途径。     

用单个薄透镜进行模式匹配

根据单个薄透镜进行高斯模匹配的物理原理,提出一种由已知束腰尺寸和位置来确定透镜的位置和焦距的简单方法。在二次方程的基础上得出明确的分析结果。当束腰之比接近于1时,给出一个近似解。匹配透镜的位置可用图解法确定。     

High precision approximate analytical solutions to ODE using LS-SVM

The problem of solving differential equations and the properties of solutions have always been an important content of differential equation the study. In practical application and scientific research, it is difficult to obtain analytical solutions for most differential equations. In recent years, with the development of computer technology, some new intelligent algorithms have been used to solve differential equations. They overcomes the drawback of traditional methods and provide the approximate solution in closed form (i.e., continuous and differentiable). The least squares support vector machine (LS-SVM) has nice properties in solving differential equations. In order to further improve the accuracy of approximate analytical solutions and facilitative calculation, a novel method based on numerical methods and LS-SVM methods is presented to solve linear ordinary differential equations (ODEs). In our approach, a high precise of the numerical solution is added as a constraint to the nonlinear LS-SVM regression model, and the optimal parameters of the model are adjusted to minimize an appropriate error function. Finally, the approximate solution in closed form is obtained by solving a system of linear equations. The numerical experiments demonstrate that our proposed method can improve the accuracy of approximate solutions.     

A new method of analysis for PWM switching power converters

A new method of analysis for pulse-width modulation (PWM) switching power converters is presented. It allows one to find an approximate periodic solution for the converter vector state variable. The converter is modelled by a differential equation with periodic coefficients. This equation is substituted by an equivalent system of linear differential equations with constant coefficients. Only the forced (steady-state) solutions should be found for each equation of this system. The equations are solved in sequence. The final steady-state solution of the PWM differential equation is obtained as the sum of these forced solutions. The method allows one to find the converter dc transfer function and efficiency, to evaluate their frequency dependences, and to find the critical frequency and ripple. The first three equations of the equivalent system are usually adequate for practical purposes, and these equations are obtained by an easy formal procedure. One can also obtain the dynamic equation of the state variable dc component, and calculate the converter line to output and duty cycle to output transfer functions. A boost converter is used as an example to confirm the analytical results by numerical simulation.     

A new fast locking charge pump PLL: analysis and design

In this paper a new structure for a fast locking charge pump phase locked loop (CPPLL) is introduced which overcomes the trade-off between the settling time and overshoot of the system. This fast locking PLL uses an auxiliary bang–bang frequency comparator (BBFC) as a lock-aid. An additional charge pump current controlled by the output of the BBFC is injected into the main loop filter capacitor to accelerate the locking process. An analytical approach to extract the differential equation governing on the system’s dynamics is used to evaluate the performance of this fast locking PLL. A heuristic method that results in an approximate solution for the extracted differential equation is also proposed. The correctness of the presented differential equation and its closed-form solutions are verified by comparing the obtained closed-form solutions and simulation results. Using the obtained closed-form solutions, we predict the behavior of the system and design a fast BBFC-CPPLL which meets the system’s requirements. Correctness of the differential equation and its closed-form solutions are verified by comparing the obtained closed-form solutions and simulation results.     

Equivalent line current for cylindrical dipole antennas and its asymptotic behavior

The concept of an equivalent line source for representing the current on a cylindrical dipole antenna is introduced. It is shown that the Fourier series coefficients of this equivalent line source are related to those of the actual antenna current by exponentially growing factors that grow rapidly for the higher order harmonics. This is used to explain why Hallén's integral equation using an approximate kernel does not have an exact solution. The asymptotic behavior of the Fourier coefficients is established. An explanation of why approximate solutions to the approximate integral equation often provide good results for the current and input impedance is also given.     

首次积分与(n+1)维多重sine-Gordon方程的无穷序列新解

通过几种函数变换把(n+1)维多重sine-Gordon方程的求解转化为常微分方程组的求解.利用常微分方程组的首次积分与可求解几种常微分方程的Bcklund变换和解的非线性叠加公式,构造了(n+1)维多重sine-Gordon方程的无穷序列类孤子新解.     

On filtered binary processes

The problem of calculating the probability density function of the output of anRCfilter driven by a binary random process with intervals generated by an equilibrium renewal process is studied. New integral equations, closely related to McFadden's original integral equations, are derived and solved by a matrix approximation method and by iteration. Transformations of the integral equations into differential equations are investigated and a new closed-form solution is obtained in one special case. Some numerical results that compare the matrix and iteration solutions with both exact solutions and approximate solutions based upon the Fokker-Planck equation are presented.     

Surface-potential solutions to the Pao–Sah voltage equation

Surface potential is one of the most important quantities in compact MOSFET (metal-oxide-semiconductor field-effect transistor) modeling. Current trend in compact modeling is moving from the threshold-voltage-based to the surface-potential-based models. The latter require a very accurate solution of the nonlinear implicit Pao–Sah voltage equation. Another past difficulty of the surface-potential-based models was the imaginary and thus unphysical solution when the gate voltage is very close to the flatband voltage. This was recently resolved by Sah physically, consequently mathematical conditioning is no longer necessary, although nonlinearity remains. The solutions to the Pao–Sah voltage equation are graphically demonstrated to illustrate the multiplicity of roots and to help attain the correct solution, but not suitable for numerical computation and analytical compact modeling. The main advantage of the analytical approximate solutions over the numerical one is their faster computation speed. However, all approximate solutions suffer from poor accuracy, in addition to some unexpected results. On the other hand, iterative algorithms may also return erroneous solutions by converging to the wrong roots for the surface potential. With properly chosen initial guess, the Newton–Raphson algorithm for the Pao–Sah voltage equation can converge to the correct solution with controllable high accuracy and computation speed comparable to that of the approximate explicit algorithms. An initial guess that ensures convergence to correct surface potential solution for the newly derived 2004-Sah voltage equation is proposed, which can be used to benchmark other approximate solutions. Comparisons among various approximate solutions with the iterative one are presented, both in wide gate voltage ranges (from strong accumulation to strong inversion) with coarse gate voltage step size and narrow gate voltage range near flatband with fine gate voltage step size.     

On nonlinear fractional Klein-Gordon equation

Numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Gordon equation can be used as numerical algorithm. The behavior of solutions and the effects of different values of fractional order α are shown graphically. Some examples are given to show ability of the method for solving the fractional nonlinear equation.     

New analytical expressions for dark current calculations of highlydoped regions in semiconductor devices

We studied highly doped quasi-neutral regions of semiconductor devices with position dependent doping concentration in the absence of illumination. An important parameter of a highly doped region is its dark current. To clarify how the doping profile influences the dark current, simple analytical expressions are useful. To this end, we first transformed the transport equations to a simple dimensionless form. This enables us to write already existing analytical expressions in an elegant way. It is demonstrated how, from any analytical dark current expression, a direct counterpart can be derived. Next, we derived a dimensionless form for a nonlinear first-order differential equation for the effective recombination velocity. Starting from the analytical solution of this differential equation for uniformly doped regions and using linearization techniques, we obtained two new simple and accurate expressions for the dark current. The expressions are valid for general doping profiles with different minority carrier transparencies. The exact solution is included between both new approximate solutions. The new expressions are compared with previous approximate solutions