Joint 3D traveltime calculation based on fast marching method and wavefront construction

3D traveltime calculation is widely used in seismic exploration technologies such as seismic migration and tomography. The fast marching method （FMM） is useful for calculating 3D traveltime and has proven to be efficient and stable. However, it has low calculation accuracy near the source, which thus gives it low overall accuracy. This paper proposes a joint traveltime calculation method to solve this problem. The method firstly employs the wavefront construction method （WFC）, which has a higher calculation accuracy than FMM in calculating traveltime in the small area near the source, and secondly adopts FMM to calculate traveltime for the remaining grid nodes. Due to the increase in calculation precision of grid nodes near the source, this new algorithm is shown to have good calculation precision while maintaining the high calculation efficiency of FMM, which is employed in most of the computational area. Results are verified using various numerical models.

High-contrast imaging based on wavefront shaping to improve low signal-to-noise ratio photoacoustic signals using superpixel method

Photoacoustic(PA) imaging has drawn tremendous research interest for various applications in biomedicine and experienced exponential growth over the past decade. Since the scattering effect of biological tissue on ultrasound is two-to three-orders magnitude weaker than that of light, photoacoustic imaging can effectively improve the imaging depth.However, as the depth of imaging further increases, the incident light is seriously affected by scattering that the generated photoacoustic signal is very weak and the signal-to-noise ratio(SNR) is quite low. Low SNR signals can reduce imaging quality and even cause imaging failure. In this paper, we proposed a new wavefront shaping and imaging method of low SNR photoacoustic signal using digital micromirror device(DMD) based superpixel method. We combined the superpixel method with DMD to modulate the phase and amplitude of the incident light, and the genetic algorithm(GA) was used as the wavefront shaping algorithm. The enhancement of the photoacoustic signal reached 10.46. Then we performed scanning imaging by moving the absorber with the translation stage. A clear image with contrast of 8.57 was obtained while imaging with original photoacoustic signals could not be achieved. The proposed method opens new perspectives for imaging with weak photoacoustic signals.

Comparison of Iterative Wavefront Estimation Methods

The iterative reconstruction methods of the wavefront phase estimation from a set of discrete phase slope measurements have been considered. The values of the root-mean-square difference between the reconstructed and original wavefront have been received for Jacobi, Gauss-Seidel, Successive over-relaxation and Successive over-relaxation with Simpson Reconstructor methods. The method with the highest accuracy has been defined.

Low-order Wavefront Error Compensation for Multi-field of Lithography Projection Objective Based on Interior Point Method

Low-order wavefront error account for a large proportion of wave aberrations.A compensation method for low order aberration of projection lithography objective based on Interior Point Method is presented.Compensation model between wavefront error and degree of movable lens freedom is established.Converting over-determined system to underdetermined system,the compensation is solved by Interior Point Method(IPM).The presented method is compared with direct solve the over-determined system.Then,other algorithm GA,EA and PS is compared with IPM.Simulation and experimental results show that the presented compensation method can obtained compensation with less residuals compared with direct solve the over-determined system.Also,the presented compensation method can reduce computation time and obtain results with less residuals compare with AGA,EA and PS.Moreover,after compensation,RMS of wavefront error of the experimental lithography projection objective decrease from 56.05 nm to 17.88 nm.

GLOBAL STABILITY OF TRAVELING WAVEFRONTS FOR NONLOCAL REACTION-DIFFUSION EQUATIONS WITH TIME DELAY

This paper is concerned with the stability of traveling wavefronts for a population dynamics model with time delay. Combining the weighted energy method and the comparison principle, the global exponential stability of noncritical traveling wavefronts （waves with speeds c 〉 c＊, where c=c＊ is the minimal speed） is established, when the initial perturbations around the wavefront decays to zero exponentially in space as x → -∞, but it can be allowed arbitrary large in other locations, which improves the results in[9, 18, 21].

High signal-to-noise ratio sensing with Shack–Hartmann wavefront sensor based on auto gain control of electron multiplying CCD

High signal-to-noise ratio can be achieved with the electron multiplying charge-coupled-device（EMCCD） applied in the Shack–Hartmann wavefront sensor（S–H WFS） in adaptive optics（AO）.However,when the brightness of the target changes in a large scale,the fixed electron multiplying（EM） gain will not be suited to the sensing limitation.Therefore an auto-gain-control method based on the brightness of light-spots array in S–H WFS is proposed in this paper.The control value is the average of the maximum signals of every light spot in an array,which has been demonstrated to be kept stable even under the influence of some noise and turbulence,and sensitive enough to the change of target brightness.A goal value is needed in the control process and it is predetermined based on the characters of EMCCD.Simulations and experiments have demonstrated that this auto-gain-control method is valid and robust,the sensing SNR reaches the maximum for the corresponding signal level,and especially is greatly improved for those dim targets from 6 to 4 magnitude in the visual band.

Optical transfer function analysis of circular-pupil wavefront coding systems with separable phase masks

This paper proposes a simple method to achieve the optical transfer function of a circular pupil wavefront coding system with a separable phase mask in Cartesian coordinates. Based on the stationary phase method, the optical transfer function of the circular pupil system can be easily obtained from the optical transfer function of the rectangular pupil system by modifying the cut-off frequency and the on-axial modulation transfer function. Finally, a system with a cubic phase mask is used as an example to illustrate the way to achieve the optical transfer function of the circular pupil system from the rectangular pupil system.

Stability of Traveling Wavefronts for a Spatially Nonlocal Population Model with Delay

The stability of traveling wavefronts for a spatially nonlocal population model with quasi-monotonicity and delay is discussed in this article.It is shown that all monostable wavefronts are exponentially stable for large speed with the help of weightedenergy method and comparison principle.The proper selection of the weighted function is necessary to overcome the difficulty caused by the nonlocal nonlinearity for establishing the energy estimates of solutions.

大尺寸优质Cr^(3+)∶BeAl_(2)O_(4)晶体生长与性能研究

本文采用感应加热提拉法结合上称重自动控径技术,成功生长出大尺寸、高质量的翠绿宝石(Cr^(3+)∶BeAl_(2)O_(4))晶体。晶坯等径圆柱体尺寸达到ϕ70 mm×140 mm,晶坯质量超过2800 g。通过冷光源照射晶坯,发现晶坯中心区域ϕ10~15 mm存在气泡。采用5 mW绿光激光照射ϕ8 mm×130 mm的翠绿宝石晶体棒,晶体内部无散射颗粒。利用Zygo激光平面干涉仪对晶体棒进行测试,波前畸变为0.3λ@632.8 nm。用电感耦合等离子体原子发射光谱法测定了翠绿宝石晶体的铬离子掺杂浓度,并计算出轴向浓度梯度为0.5×10^(-4)~1.9×10^(-4)cm^(-1)(摩尔分数)。用Perkin Elmer Lambda-950紫外可见近红外分光光度计测试了不同掺杂浓度的翠绿宝石晶体在室温下的吸收光谱,并计算了吸收系数。这些研究结果为翠绿宝石晶体的应用提供了重要的基础数据。

界面二次源波前扩展法全局最小走时射线追踪技术

以Moser方法为代表的最短路径射线追踪算法可以快速稳定地获得整个追踪区域的全局最小走时和路径,但它存在两个缺陷:一是射线大多由折线呈锯齿状相连,长度和位置偏离真实射线路径;二是在低变速区容易出现射线路径多值现象.本文提出的界面二次源波前扩展法全局最小走时射线追踪技术(以下简称界面源法)旨在解决上述两个问题.不同于Moser方法,界面源法只在物性分界面上设置子波源点,子波出射射线可以到达任何不穿越物性界面而直接到达的空间点和界面离散点,在均匀块体内或层内地震波以精确的射线路径传播.显然,界面源法的子波出射方向数远远大于传统方法,算法的追踪误差主要由界面离散引起的,因此,界面源法很好地解决了Moser法存在的问题,大大提高了追踪的精度.同时,由于界面源法的子波源点数远远小于Moser法,因而效率也很高.模型实算证实了该算法的高效性.

用Zernike多项式进行波面拟合的几种算法

介绍了几种实现波面Ｚｅｒｎｉｋｅ 多项式拟合的常用算法。为避免因直接构造法方程组而引入计算误差，这些方法归结为两种思路：一是从基底函数系入手，通过变换函数族的基底来改善法方程组状态；二是直接从矛盾方程组入手，应用Ｈｏｕｓｅｈｏｌｄｅｒ变换把系数矩阵正交三角化，直接求解拟合系数。特别是第二种方法由本文第一次提出，它避免了构造法方程组，从而避免了以前的方法因构造的法方程组出现严重病态而引入的计算误差，并且易于编程，因而是一种比较理想的实现Ｚｅｒｎｉｋｅ 多项式拟合的算法。

基于波面面形的滤波计算

为提高光学干涉测量的精度,研究了用来消除干涉条纹图噪声的滤波算法。讨论了不同波面和不同干涉仪噪声下不同滤波方法的滤波效果。考虑干涉仪噪声对条纹图的影响与检测中的不同波面情况,基于泽尼克多项式原理用matlab仿真法建立了离焦、像散、彗差、球差4种不同的干涉条纹图,计算了滤波后不同波面面形的PV值和GRMS值差别的大小。结果表明：同种噪声与滤波器情况下,在离焦、像散、彗差、球差4种面型中,滤波后球差波面的PV差值最大,高达0.11λ,与在乘性噪声下其它波面的最高PV值0.08λ相比,滤波效果较差;滤波后像散波面的PV差值最小,除乘性噪声中值滤波情况外,PV差值均在0.05λ以下,最低达0.01λ,滤波效果较好。此外,彗差波面滤波情况要略优于离焦波面。滤波器中,低通滤波稳定性高,PV差值局限于0.01λ~0.04λ,滤波效果相对好;而空域滤波后波面的PV差值最高达0.09λ,但噪声针对性更好。

高功率光学元件畸变波前位相均方根梯度计算

根据实际光学元件的畸变波前建立了畸变波前模型,分析了位相均方根梯度计算过程中,三种波前数据处理方式的各自特点及优劣,并得出最佳处理方式,即对波前边缘增添零采样点、加汉宁窗处理、傅里叶变换、低通滤波、傅里叶逆变换、乘上逆汉宁窗,最后截取原始长度的数据。讨论了畸变波前边缘增添零采样点的个数、波前口径、波前抽样间距与均方根误差之间的相互关系。计算证明,对于口径为300 mm×300 mm、抽样间隔为0.5 mm的随机波前,当取截止频率为33 mm-1、初始波前两边分别添14 个点即波前尺寸扩大7mm长时,其均方根误差最小,此时该值为0.008λ,恢复的波前最理想,计算所得的位相均方根梯度也最合理。

薄反射镜主动光学实验系统

用口径400mm、厚12mm的薄反射镜作为实验镜进行了主动光学实验。支撑系统由背部12个主动支撑点和3个固定支撑点组成,主动支撑点采用由压电陶瓷促动器和压力传感器组成的力促动器,用于控制实验镜面形,固定支撑点用于控制实验镜的定位。通过Shack-Harmann波前传感器测量镜面面形并拟合出Zernike像差,用阻尼最小二乘法计算出校正力,通过PID算法闭环控制各促动器施加力的过程。通过主动校正,将初始支撑状态下的1.16λ(λ=632.8nm)RMS面形精度校正到0.07λRMS,优于镜面抛光后的0.1λRMS。

准分子激光原位角膜磨镶术对近视眼高阶像差的影响

目的 :观察并分析准分子激光原位角膜磨镶术(LASIK)对近视患者的波前像差 ,尤其是眼高阶像差的影响 ,探讨术后眼高阶像差与角膜屈光力、角膜厚度的关系。方法 :应用波前像差仪对 33例 ( 6 4只眼 )近视患者LASIK手术前及术后 1个月、1 0个月的眼波前像差进行测量 ;用裂隙扫描式角膜地形图进行手术前后的K1、K2及角膜厚度检查 ,将术前术后的高阶像差、K1、K2及角膜厚度分别进行比较分析。结果 :①LASIK术前的波前像差分布以低阶像差占优势 ,为 81 .7% ,彗差和其他高阶像差分别占 1 3.9%和 4 .4 %。②LASIK术后 1个月高阶像差显著增加 ,差异有显著性(P <0 .0 0 1 ) ,彗差和其他高阶像差分别占 51 .8%和 2 0 .9% ,低阶像差占 2 7.8% ,高阶像差整体平均增加 2 .96倍 ,以二次彗差增加最多 ,达到 3.1 7倍 (P <0 .0 0 1 )。③LASIK术后 1 0个月彗差和其他高阶像差分别占 4 0 .8%和 1 7.0 % ,低阶像差占 38.1 % ,与术后 1个月相比 ,高阶像差均有所减少 ,差异有显著性 (P <0 .0 0 1 ) ,与术前相比 ,整体高阶像差差异仍有显著性 (P <0 .0 1 ) ,表现为二次彗差和二次球差仍比术前有显著增加 ,差异有显著性 (P <0 .0 0 1 ) ,但优势高阶像差彗差、球差逐渐恢复到术前水平 ,差异无显著性 (P >0 .0 5)。

基于最小二乘法的波面函数拟合

采用最小二乘法对特殊波面函数进行数据拟合 ,并得到通用性公式。为制作产生特殊波面的计算全息元件打下了数学基础。

板条增益介质波前畸变诊断方法

对波前重构算法中的区域法进行了改进,使其能够应用于板条增益介质的波前畸变诊断。利用该方法对47块Nd:YAG板条增益介质沿厚度方向波前畸变进行测量,指出镀膜和加工等环节对增益介质的波前畸变可能造成的影响。按照波前畸变峰谷(PV)值对测量结果进行了统计,结果表明:增益介质造成的静态波前畸变参差不齐,测量样本中静态畸变PV值最多可达5μm以上,且仅有4.1%的增益介质静态畸变PV值小于1μm。通过选取某些增益介质使之级联,测量其组合波前畸变,发现在系统中使用两块波面互补的增益介质有助于减小系统的静态波前畸变。

基于完全三叉树堆排序的波前扩展有限差分地震波走时快速算法

波前扩展有限差分地震波走时算法具有物理意义明确、因果稳定性强的特点,但每次波前扩展都要寻找波前面上的最小走时点。当计算网格点数较多,特别是涉及到三维走时计算时,寻找波前面上的最小走时点是一项十分耗时的工作。研究发现,波前扩展有限差分地震波走时算法的波前点具有两个突出特点:①波前点更新十分频繁,通常每次取出波前最小走时点后都要插入若干新的波前点;②新计算出的波前点的走时通常比较大。数据结构中的二叉树堆排序方法可以提高寻找波前面上最小走时点的效率,根据特点①,在原始二叉树堆排序方法的基础上,优化了插入新波前点和移除波前面上最小走时点的流程,实际计算结果表明,与原始的二叉树堆排序方法相比,改进后的二叉树堆排序方法可以提高大约20%的计算效率。根据特点②,将原始的二叉树堆排序方法推广到多叉树,实际计算结果表明,完全三叉树堆排序方法优于二叉树和四叉树堆排序方法,可以再提高5%的计算效率。

基于波前构建法的TTI介质射线追踪

射线(群速度)方向与旅行时梯度(相速度)方向不一致,使得TTI介质的射线追踪变得非常困难。传统的以弹性参数表示的各向异性射线追踪系统比各向同性条件下要复杂得多,而且在每一步都要求通过解特征值问题来计算极化矢量,使得整个射线追踪过程相当耗时。鉴于此,本文引入一种用相速度和群速度重构的射线追踪系统,该射线追踪系统与各向同性条件下的完全相似,从而简化了TTI介质的射线追踪问题。在综合考虑多种走时计算方法的优劣后,选择波前构建法进行射线追踪和波前传播的计算。将简化的射线追踪系统与波前构建法的优势相结合,得到了简单、高效的TTI介质射线追踪方法,并通过模型试算验证了此法的可行性。

斐索型球面干涉仪移相误差的探讨

本文对斐索型球面干涉仪的移相原理误差进行了理论推导和计算；应用移相干涉术的三步法和五步法，分析和比较了球面移相误差对波面复原精度的影响，并给出了有关数据和曲线。最后，提出了几种减小球面测量误差的措施。