Fluorescence lifetime optical tomography in weakly scattering media in the presence of highly scattering inclusions

We consider the problem of fluorescence lifetime optical tomographic imaging in a weakly scattering medium in the presence of highly scattering inclusions. We suggest an approximation to the radiative transfer equation, which results from the assumption that the transport coefficient of the scattering media differs by an order of magnitude for weakly and highly scattering regions. The image reconstruction algorithm is based on the variational framework and employs angularly selective intensity measurements. We present numerical simulation of light scattering in a weakly scattering medium that embeds highly scattering objects. Our reconstruction algorithm is verified by recovering optical and fluorescent parameters from numerically simulated datasets.     

Ocean source and optical property estimation from explicit and implicit algorithms

We solve an inverse problem of ocean optics for estimating spatially dependent absorption and scattering coefficients and for determining sources such as fluorescence, bioluminescence, or Raman scattering. The solution requires in situ measurement of the downward and upward plane irradiances and scalar irradiances and a priori estimation of the angular shape of the volume scattering function. Both an explicit algorithm and an implicit one are developed from new two-stream radiative-transfer equations that utilize an asymptotic radiance approximation to close the set of equations. A comparison of numerical tests for the two algorithms is given.     

双层球形颗粒的光散射计算

在光散射颗粒测量技术中,Mie散射理论的计算非常重要。本文中讨论了双层球形颗粒光散射的计算方法,对计算过程中不同函数参量选用了合适的递推计算方法,改进的计算方法克服了以前算法在实际运算中遇到的误差。计算了若干物理量,如消光系数、散射系数、吸收系数以及CPU运算速度。计算结果表明,选用的方法简单、迅速、稳定且误差小。     

Simulation of light scattering from a particle upon a wafer surface

We simulated light scattering from a particle located on a smooth surface. We developed a new approach utilizing the discrete sources method based on a strict mathematical model for this scattering problem. The main features of the corresponding numerical algorithm are presented. The results of modeling and comparisons with other theoretical results and experimental data are shown as well.     

Application of the sinc basis moment method to the reconstruction of infinite circular cylinders

A solution of the ultrasonic scattering and inverse scattering problem has been obtained by solving the inhomogeneous Helmholtz wave equation by the sinc basis moment method. In this numerical study, the algorithm of S.A. Johnson and M.L. Tracy (1983) has been applied to the reconstruction of an infinite circular cylinder that is subject to an incident cylindrical wave of ultrasound and is surrounded by a homogeneous coupling medium. For weak scattering cylinders, successful reconstructions have been obtained using the known exact solution for the scattered field as the input data for the algorithm. A detailed discussion of sampling requirements for this algorithm is presented, and the threshold derived correlates well with results of a numerical study of variation of the sampling density. Effects of varying object contrast, object size, grid size, sampling density, and method of iteration are investigated. Because the algorithm is slow, optimization of computation is described.     

Inverse scattering with a wave-front-matching algorithm

We propose and study a numerical procedure for the reconstruction of surface profiles from far-field scattering data. The algorithm, based on wave-front-matching principles, is used to reconstruct one-dimensional surface profiles from amplitude scattering data calculated by using rigorous techniques. The study is complemented by the development of a sampling strategy and considerations of the tolerance of the algorithm to noise in the data.     

Imaging strongly scattering media using a multiple frequency distorted Born iterative method

The distorted Born iterative (DBI) method is a powerful approach for solving the inverse scattering problem for ultrasound tomographic imaging. This method alternates between solving the inverse scattering problem for the scattering function and the forward scattering problem for the total field and the inhomogeneous Green's function. The algorithm is initialized using the basic Born inverse solution. One fundamental problem is the algorithm diverges for strongly scattering media. This is caused by the limitation of the Born assumption in estimating the initial step of the algorithm. We present a multiple frequency DBI approach to alleviate this problem, thus extending the applicability of the DBI method to the level of dealing with biological tissue. In this multiple frequency approach, a low frequency DBI-based solution, is used to initialize the algorithm at higher frequencies. The low frequency allows convergence of the algorithm to a contrast level that is close to the true level, however, with a poor spatial resolution. The high frequency improves the spatial resolution while preserving convergence because the difference between the true contrast and the initial contrast is relatively small. We present numerical simulations that demonstrate the ability of this method to reconstruct strongly scattering regions.     

基于单频数据重构散射障碍的新型线性采样方法

散射及反散射的数学理论与计算一直是应用数学领域中的重要课题，其成果在地质勘探、无损探测、医学成像等领域都具有广泛的应用．线性采样方法（LSM）是近年来反散射理论中一类非常流行的非迭代型重建算法，但是这种方式很难推广到如半空间中障碍反散射等更为复杂的问题中．本文基于单频数据研究Dirichlet障碍反散射问题的数值重建算法．通过构造带有阻尼边界条件的辅助边值问题，提出了一类新型的线性采样方法，并在理论上严格证明了该方法在任意给定的波数下重构障碍形状及位置的有效性．     

Ultrasonic imaging by local shape function method with CGFFT

A numerical algorithm for the reconstruction of the density and the compressibility of a biological body from ultrasonic scattering data is presented. The reconstruction algorithm is based on the local shape function method (LSF) combined with the conjugate gradient method with fast Fourier transform (CGFFT). The nonlinearity due to the multiple scattering has been accounted for in an iterative minimization scheme. Numerical examples of simulation data and real experimental data are given showing the capability of this algorithm     

Frequency domain modeling of reradiation in highly scattering media

We present a straightforward procedure for frequency domain modeling of reradiation in a highly scattering medium with an arbitrary, finite three-dimensional geometry. We use a finite difference numerical solver to determine the fluence distribution at the excitation wavelength, which is then coupled to the emission wavelength with an array of equivalent reradiating sources. We then calculate the fluence distribution at the emission wavelength with a second, independent numerical simulation with new optical parameters appropriate to the emission wavelength, using the distributed reradiating sources as the excitation. We compare three-dimensional simulations of a fluorophore distributed in a scattering medium with experimental data. We also compare simulations of the Raman reradiation of small diamonds in a scattering medium with experiment.     

Robust determination of the anisotropic polarizability of nanoparticles using coherent confocal microscopy

A coherent confocal microscope is proposed as a means to fully characterize the elastic scattering properties of a nanoparticle as a function of wavelength. Using a high numerical aperture lens, two-dimensional scanning, and a simple vector-beam shaper, the rank-2 polarizability tensor is estimated from a single confocal image. A method for computationally efficient data processing is described, and numerical simulations show that this algorithm is robust to noise and uncertainty in the focal plane position. The proposed method is a generalization of techniques that provide an estimate of a limited set of scattering parameters, such as a single orientation angle for rodlike particles. The measurement of the polarizability obviates the need for a priori assumptions about the nanoparticle.     

A numerical reconstruction method in inverse elastic scattering

In this paper a new numerical method for the shape reconstruction of obstacles in elastic scattering is proposed. Initially, the direct scattering problem for a rigid body and the mathematical setting for the corresponding inverse one are presented. Inverse uniqueness issues for the general case of mixed boundary conditions on the boundary of our obstacle, which are valid for a rigid body as well are established. The inversion algorithm based on the factorization method is presented into a suitable form and a new numerical scheme for the reconstruction of the shape of the scatterer, using far-field measurements, is given. In particular, an efficient Tikhonov parameter choice technique, called Improved Maximum Product Criterion (IMPC) and its linchpin within the framework of the factorization method is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no a priori knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples involving a kite, an acorn, and a peanut-shaped object.     

Scattering-reduction effect with overcoated rough surfaces: theory and experiment.

We show that a scattering-reduction effect is obtained by coating a rough surface with an antireflection layer. This research is a generalization of Amra's [J. Opt. Soc. Am. A 10, 365-374 (1993)] study of smooth surfaces conducted with a first-order theory to the case of rough surfaces. We show that the differential method with the R matrix algorithm can be used to study scattering from multilayered rough surfaces. A comparison between numerical and experimental results is given.     

Analysis of the resonant scattering of light by cylinders at oblique incidence

We study the resonant scattering of light at oblique incidence by dielectric uncoated and coated cylinders. We develop a stable algorithm that permits us to calculate the resonances of a single dielectric cylinder as the tilting angle varies. This algorithm is based on semiclassical formulas for the distance between resonances. Results show that the resonances and the resonant electromagnetic energy flux near and internal to the cylindrical surface are highly sensitive to variations in the tilting angle. In addition, the coating effects are studied for scattering of light at oblique incidence by an infinite, perfect cylindrical conductor coated by a dielectric layer. In this case the resonance calculations show a peculiar similarity between this light scattering and atomic-molecular scattering. A physical interpretation for these effects is given, based on an analogy of optics and quantum mechanics.     

颗粒超声层析成像的散射特征分析

用数值方法对颗粒超声层析成像进行模拟研究,对单个球形颗粒散射特征的数值解与解析解作对比,验证数值方法的准确性、可靠性,进而对管内放置有单个和3个球形颗粒的散射声场特性进行的数值模拟和分析,并由二值逻辑反投影图像重建算法对其进行空间分布的重建,分析重建图像的误差。结果表明:基于边界元方法的数值模拟和重建方法是可行和有效的。     

Simultaneous recovery of an infinite rough surface and the impedance from near-field data

In this paper, we consider an inverse rough surface scattering problem in near-field optical imaging. This problem is actually to reconstruct the scattering surface as well as its impedance coefficient from multifrequency near-field data, and can be reduced into an integral scheme by employing an integral representation. We solve this integral scheme by a non-linear integral equation method, and further develop a fast inversion algorithm for reconstructing both the rough surface and the impedance coefficient. Numerical experiments are presented to illustrate the effectiveness of the algorithm.     

Simulation of an active underwater imaging through a wavy sea surface

A numerical simulation for underwater imaging through a wavy sea surface has been done. We have used a common approach to model the sea surface elevation and its slopes as an important source of image disturbance. The simulation algorithm is based on a combination of ray tracing and optical propagation, which has taken to different approaches for downwelling and upwelling beams. The nature of randomly focusing and defocusing property of surface waves causes a fluctuated irradiance distribution as an illuminating source of immersed object, while it gives rise to a great disturbance on the image through a coordinate change of image pixels. We have also used a modulation transfer function based on Well’s small angle approximations to consider the underwater optical properties effect on the transferring of the image. As expected, the absorption effect reduces the light intensity and scattering decreases image contrast by blurring the image.     

Comparison among the variants of subspace-based optimization method for addressing inverse scattering problems: transverse electric case

The subspace-based optimization method (SOM) is an efficient approach to addressing the inverse scattering problem. In this paper, a comparative study, on the basis of numerical experiments, is conducted to evaluate the performances of variants of SOM, so as to find the optimal method for the determination of the ambiguous portion, which has a dominant influence on the computational cost and the reconstruction capability of the algorithm.     

Imaging properties of scanning holographic microscopy

Scanning heterodyne holography is an alternative way of capturing three-dimensional information on a scattering or fluorescent object. We analyze the properties of the images obtained by this novel imaging process. We describe the possibility of varying the coherence of the system from a process linear in amplitude to a process linear in intensity by changing the detection mode. We illustrate numerically the properties of the three-dimensional point-spread function of the system and compare it with that of a conventional imaging system with equal numerical aperture. We describe how it is possible, by an appropriate choice of the reconstruction algorithm, to obtain an ideal transfer function equal to unity up to the cutoff frequency, even in the presence of aberrations. Some practical implementation issues are also discussed.     

Matrix algorithms for modeling acoustic waves in piezoelectric multilayers

Matrix algorithms for modeling acoustic waves in piezoelectric multilayers are presented. All the algorithms considered are capable of resolving the numerical instability of transfer matrix at high frequency-thickness product. The formulation of basic matrices for the algorithm building blocks, and the development of recursive algorithms for the stack matrices, are systematically presented for both the conventional scattering and impedance matrices as well as the more recent hybrid matrix. Many variants of the algorithms are discussed, along with their respective usefulness and deficiency. Comparisons are made in their computational efficiency and numerical stability. For unconditional stability throughout large and small thicknesses, both scattering and hybrid matrix algorithms are applicable. For most efficiency, the algorithms that synergize both scattering and hybrid or impedance submatrices are superior, using surface matrix approach. Other aspects of algorithms such as formula conciseness, physical insight, versatility in incorporating boundary conditions, etc., are also noted.