多程脉冲激光放大器的宽带放大逆问题研究

宽带放大逆问题对于研究高功率激光系统的放大性能十分重要。将极化强度时域解析法应用于亚纳秒量级的宽带放大研究，通过Gerchberg-Saxton(GS)和遗传算法的混合算法，详细模拟和研究了脉冲激光的宽带放大逆问题，即给定输出脉冲的时间和空间分布，结合放大系统参数，逆向反演注入放大器脉冲的时空波形。极化强度时域解析法应用于宽带放大具有计算耗时少的优点，混合智能算法简化了激光放大器的逆问题模型，加快了逆问题求解的收敛速度。     

一种通用的辐射聚焦器设计方法

本文把辐射聚焦器设计当作逆衍射问题求解，在吸收“模拟退火”思想的基础上，提出了一种通用性强、抗局部极值性好的优化算法──Ｉｍｐｒｏｖｅｄ－ＡＬＯＰＥＸ法，并就如何控制优化过程中的温度与步长两参量，进行了详细的讨论，剔除了ＡＬＯＰＥＸ法中存在的一些问题，最后比较了Ｅｒｒｏｒ－Ｒｅｄｕｃｔｉｏｎ法和本方法的设计结果。     

一种新的求解脑磁逆问题的搜索方法

给出一种新的求解真实头模型下脑磁逆问题的搜索方法.通过不同位置的源的相互关系，由上一个搜索源的计算结果通过简单计算，直接得到下一个搜索源的结果，避免了繁琐耗时的边界元积分方法，简化了求解过程，提高了求解速度. 关键词： 脑磁图 逆问题 搜索方法     

求解光学CT图象重建问题的广义脉冲谱技术研究

间接法是目前实现医学诊断用近红外光三维成象(光CT)的最有潜力的手段之一.该方法基于以下假设,即给定分别对应于不同点激励源作用下成象组织体表面各点的传输光测量.在组织体内存在着与上述检测量相对应的、唯一的光学参数三维分布.由此,图象重建变成了特定光子传输模型的逆问题.本文提出采用广义脉冲谱技术(Generalized Pulse Spectrum Technique,GPST)进行光学CT图象重建逆问题的求解.给出了GPST在扩散方程光子传输模型逆问题求解中的具体实现,数值实验结果表明,通过选择合适的复频率点,采用GPST算法的图象重建结果优于其它现有算法,且响应时间合理.最后,本文还初步讨论了吸收和散射系数重建中复频率点选择的一些基本原则。     

基于BP神经网络的排爆机械臂逆运动学分析

机械臂逆运动学是已知末端执行器的位姿求解机械臂各关节变量,主要用于机械臂末端执行器的精确定位和轨迹规划,如何高效的求解机械臂运动学逆解是机械臂轨迹控制的难点。针对传统的机械臂逆运动学求解方法复杂且存在多解等问题,提出一种基于BP神经网络的机械臂逆运动学求解方法。以四自由度机械臂为研究对象,对其运动学原理进行分析,建立BP神经网络模型并对神经网络算法进行改进,最后使用MATLAB进行仿真验证。仿真结果表明：使用BP神经网络模型求解机械臂逆运动学问题设计过程简单,求解精度较高,一定程度上避免了传统方法的不足,是一种可行的机械臂逆运动学求解方法。     

材料热物性与热源强度辨识的改进遗传算法

建立二维非线性导热逆问题(IHCP)的数学模型.通过对基本遗传算法逐步改进得到三种不同改进阶段的遗传算法,分别用于反演导热问题中材料的导热系数及其内部热源强度,并比较遗传算法在各改进阶段用于求解导热逆问题时的收敛速度与求解精度,寻求一种使导热逆问题求解效率与计算精度更高的遗传算法改进策略.结果表明:提出的遗传算法改进策略达到了预期目的.     

激光放大一维问题的解

在变率方程的基础上解析求解了一维的包含损耗在内的光脉冲传输的正问题与逆问题，并通过数值计算加以验证。     

三维声波方程逆问题的共轭梯度法求解

考虑一个完整的三维声波方程的逆问题．通过构造一个表面声压偏差平方和形式的目标泛函，把声波方程的逆问题转化为一个控制声学特性参数分布使得目标泛函达到最小伍的优化问题．采用共轭梯度法来求解这个优化问题．通过引入一个对偶函数u（x，t），文中用微扰法求得了目标泛函梯度值的解析表达式，从而克服了以往用共轭梯度法求解偏微分方程控制的优化问题时计算目标活函梯度的困难，大大压缩了共轭梯度法计算目标泛函梯度的时间，而且提高了梯度值的计算精度．还进一步进行了反演声学特性参数三维分布的数值仿真计算．共轭梯度法完整解决了三维声波方程的逆问题．     

光学CT二维正向问题有限元法数值模拟的研究

简述了光学ＣＴ正模型的有限元解理论，给出了二维圆形组织体光学ＣＴ正问题的有限元法解的数值模拟结果，该结果对于生物组织体内光子传输行为以及光ＣＴ逆问题的理论和实验研究具有重要的指导意义。     

基于奇异值分解的数字波前拟合算法

提出了基于奇异值分解、采用泽尼克多项式拟合干涉波前的算法,该算法直接从线性方程组入手,对矩阵进行奇异值分解分解,在求解逆矩阵的过程中,采用阈值法对奇异值的倒数进行非常规的置换(∞→0),可直接得到系数向量。理论分析和实验证明,相对于传统的格拉姆施密特正交法,该算法可首先通过求解条件数判断线性方程矩阵是否奇异,对于解决病态方程组或奇异矩阵的最小二乘问题,有很好的稳定性,避免了由最小二乘构造的法方程组出现病态而引入的计算误差,且易于编程。     

Light propagation for time-domain fluorescence diffuse optical tomography by convolution using lifetime function

Time-domain light propagation in biological tissue is studied by solving the forward problem for fluorescence diffuse optical tomography using a convolution of the zero-lifetime emission light and the exponential function for a finite lifetime. We firstly formulate the fundamental equations in a time-domain assuming that the fluorescence lifetime is equal to zero, and then the solution including the lifetime is obtained by convolving the emission light and the lifetime function. The model is a two-dimensional (2-D) 10 mm-radius circle with the optical properties simulating biological tissue for the near infrared light, and contains some inclusions with fluorophores. Temporal and spatial profiles of excitation and emission light are calculated and discussed for several models with different inclusions. The results are physically reasonable and will be used for the inverse problem of fluorescence diffuse optical tomography.     

Theory and analysis of frequency-domain photoacoustic tomography

A new frequency-domain approach to photoacoustic tomography has recently been proposed, promising to overcome some of the shortcomings associated with the pulsed photoacoustic approach. This approach offers many of the benefits of pulsed photoacoustics but requires a different set of equations for modeling of the forward and inverse problems due to the longer time scales involved in the optical input signal. The theory of photoacoustic tomography with an optical input that is not necessarily a short pulse is considered in this paper. The full optical, thermal, and acoustic governing equations are derived. A transfer function approach is taken for the solution and analysis of this problem. The results and implications are compared with those of pulsed photoacoustics and traditional ultrasonic diffraction tomography. A Fourier diffraction theorem is also presented, which could be used as a basis for the development of tomographic imaging algorithms.     

吸收散射性三维矩形介质内辐射源项的反问题

提出了一种由边界出射辐射强度反演吸收散射性三维矩形介质内辐射源项分布的方法。该方法是在辐射传递方程离散坐标近似的基础上,用求目标函数极小值的共轭梯度法进行反演计算。通过对介质辐射特性、光学厚度等参数对反演精度影响的分析,结果表明,即使存在测量误差,本文所提出的方法可较精确地反演辐射源项。     

Index to volume 72

A numerical analysis of wave propagation in one dimensional inhomogeneous media is presented in this paper, the first (Part I) of two companion papers. The aim is to provide a natural and physical basis for the solution of the inverse scattering problem in one dimension. The paper includes (i) a discussion of some aspects of the numerical solution of the direct problem, (ii) typical results of calculation and (iii) a comparison between exact solutions and forward scattering approximation (FSA) solutions of the direct problem. It is shown that the FSA allows accurate calculations of the reflected wave and thus constitutes a sound basis for the solution of the inverse problem treated in Part II.     

光学CT图象重建的数值模拟研究─Kosenbrock坐标轮换法

时间分辨光学 ＣＴ技术因其对生物组织体的无损性，在生物成象领域引起了广泛的兴趣和研究，已提出许多方案，意在克服由于生物组织体中的多光散射效应所造成的成象障碍．本文简述了基于扩散方程近似的光学ＣＴ正向问题有限元解法，提出采用直接搜索优化算法一Ｒｏｓｅｎｂｒｏｃｋ坐标轮换法求解时间分辨光学 ＣＴ中的图象重建问题，给出了基于积分光强和光子平均飞行时间及其加权组合的二维图象重建问题的数值模拟结果，证实了该方法的可行性．     

Sensitivity of atmospheric-surface parameters retrieval to the spectral stability of channels in thermal IR

Sensitivity of the solutions of forward and inverse problems of the atmospheric-surface parameters retrieval to spectral shifts of channels is considered. The solution of the forward problem is obtained by radiative transfer simulation. The retrieval (solution of the inverse problem) is obtained by linear (optimal interpolation) and non-linear (variational) techniques. It is shown that atmospheric temperature profiles exhibit high sensitivity to the spectral shift, while the humidity profiles are moderately sensitive while the sea surface temperatures retrievals are insensitive. Two approaches are proposed to reduce the effect of channel spectral shift, one is based on channel selection and the other approach is related to proper calibration of the cost function. We performed the numerical simulations using the parameters of AIRS spectrometer to illustrate the sensitivity of forward and inverse problems. The results of the simulation show that the inversion error can be significantly reduced by the proposed techniques.     

光学CT图象重建的数值模拟研究─Kosenbrock坐标轮换法

时间分辨光学CT技术因其对生物组织体的无损性,在生物成象领域引起了广泛的兴趣和研究,已提出许多方案,意在克服由于生物组织体中的多光散射效应所造成的成象障碍.本文简述了基于扩散方程近似的光学CT正向问题有限元解法,提出采用直接搜索优化算法-Rosenbrock坐标轮换法求解时间分辨光学CT中的图象重建问题,给出了基于积分光强和光子平均飞行时间及其加权组合的二维图象重建问题的数值模拟结果,证实了该方法的可行性.     

Numerical evaluation of linearized image reconstruction based on finite element method for biomedical photoacoustic imaging

An image reconstruction algorithm for biomedical photoacoustic imaging is discussed. The algorithm solves the inverse problem of the photoacoustic phenomenon in biological media and images the distribution of large optical absorption coefficients, which can indicate diseased tissues such as cancers with angiogenesis and the tissues labeled by exogenous photon absorbers. The linearized forward problem, which relates the absorption coefficients to the detected photoacoustic signals, is formulated by using photon diffusion and photoacoustic wave equations. Both partial differential equations are solved by a finite element method. The inverse problem is solved by truncated singular value decomposition, which reduces the effects of the measurement noise and the errors between forward modeling and actual measurement systems. The spatial resolution and the robustness to various factors affecting the image reconstruction are evaluated by numerical experiments with 2D geometry.     

An efficient and robust reconstruction method for optical tomography with the time-domain radiative transfer equation

An efficient and robust method based on the complex-variable-differentiation method (CVDM) is proposed to reconstruct the distribution of optical parameters in two-dimensional participating media. An upwind-difference discrete-ordinate formulation of the time-domain radiative transfer equation is well established and used as forward model. The regularization term using generalized Gaussian Markov random field model is added in the objective function to overcome the ill-posed nature of the radiative inverse problem. The multi-start conjugate gradient method was utilized to accelerate the convergence speed of the inverse procedure. To obtain an accurate result and avoid the cumbersome formula of adjoint differentiation model, the CVDM was employed to calculate the gradient of objective function with respect to the optical parameters. All the simulation results show that the CVDM is efficient and robust for the reconstruction of optical parameters.