Green functions for diffuse photon-density waves generated by a line source in two nonabsorbing turbid media in contact

Diffuse photon-density waves generated by an instantaneous line source that is parallel to the interface between two semi-infinite turbid media are studied by use of the diffusion approximation. For two nonabsorbing media the Green functions for diffuse light are obtained based on the Green functions for temperature fields that were derived with the Cagniard-de Hoop method. The boundary conditions for diffuse light take into account the discontinuity in the specific intensity at the interface between two media with different refractive indices. The results of the calculations of the specific intensities and the gradient lines for different sets of parameters are presented.     

Propagation of diffuse light in a turbid medium with multiple spherical inhomogeneities

We develop a fast and accurate solver for the forward problem of diffusion tomography in the case of several spherical inhomogeneities. The approach allows one to take into account multiple scattering of diffuse waves between different inhomogeneities. Theoretical results are illustrated with numerical examples; excellent numerical convergence and efficiency are demonstrated. The method is generalized for the case of additional planar diffuse-nondiffuse interfaces and is therefore applicable to the half-space and slab imaging geometries.     

Adaptive calibration for object localization in turbid media with interfering diffuse photon density waves

The amplitude cancellation method that uses dual out-of-phase sources (a phased array system) can sensitively detect and locate small objects in turbid media. The balance of these two sources is crucial to the system's detection sensitivity and accuracy. We describe a convenient method with which to adaptively calibrate the amplitudes of the two sources at each scanning position by use of low-frequency modulation of the intensity of the in-phase and the antiphase sources. We achieve accurate localization ability of the phased array system by accounting for the influence of asymmetrical boundaries and the heterogeneous background absorption. Experimental data on human breast phantoms demonstrate that localization accuracy within several millimeters has been accomplished through this method.     

Modelling of a single object embedded in a layered medium

We present a numerical method based on the method of the fictitious sources to model one or several inclusions of arbitrary shape in stratified media. Our aim is to propose an efficient numerical method for the modelling of plasmonic devices. Indeed, metals impose rapid decays of the electromagnetic fields that are often a problem for methods based on a volume meshing. We give the theoretical basis of the method and also some practical details of its implementation in order to obtain an efficient numerical code. The efficiency of the numerical code is illustrated by modelling a spherical open cavity in a metal layer and a hole in a dielectric layer.     

Theory of a fixed scatterer embedded in a turbid medium: numerical results

Based on a previous theory of diffuse photon density waves by Furutsu [J. Opt. Soc. Am. A 15, 1371 (1998)], several sets of figures are prepared to detect a fixed scatterer (object) embedded in a turbid layer, such as a tumor in tissue, with a source and a detector placed independently along the boundaries on different sides. The relative total intensity of the wave is introduced such that it is reduced to 1 in the case of no scatterer and usually less than that, owing to a shadowing by the scatterer. Sets of curves are presented to demonstrate shadow images of the scatterer observed along the layer boundaries depending on the scatterer's location.     

Monte carlo diffusion hybrid model for photon migration in a two-layer turbid medium in the frequency domain

We propose a hybrid Monte Carlo (MC) diffusion model for calculating the spatially resolved reflectance amplitude and phase delay resulting from an intensity-modulated pencil beam vertically incident on a two-layer turbid medium. The model combines the accuracy of MC at radial distances near the incident beam with the computational efficiency afforded by a diffusion calculation at further distances. This results in a single forward calculation several hundred times faster than pure MC, depending primarily on model parameters. Model predictions are compared with MC data for two cases that span the extremes of physiologically relevant optical properties: skin overlying fat and skin overlying muscle, both in the presence of an exogenous absorber. It is shown that good agreement can be achieved for radial distances from 0.5 to 20 mm in both cases. However, in the skin-on-muscle case the choice of model parameters and the definition of the diffusion coefficient can lead to some interesting discrepancies.     

Ultrafast optical Kerr gate imaging in a poly-disperse turbid medium

The influence of the size parameter of the scatterers on ultrafast optical Kerr gate (OKG) imaging is investigated in highly scattering poly-disperse turbid media. The results show that in a poly-disperse turbid medium, which in our case, is a suspension of two different sized mono-disperse microspheres, the temporal and spatial behaviors of the light pulses transmitted through it are dominated by the smaller microspheres. The contrasts of the OKG images for the poly-disperse microsphere sample are closer to the contrasts of the OKG images for the smaller sized mono-disperse microsphere sample.     

Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium

We have examined the possibility of determining the optical properties of a two-layer medium by using a diffusion approximation radiation transport model [Appl. Opt. 37, 779 (1998)]. Continuous-wave and frequency-domain (FD) low-noise Monte Carlo (MC) data were fitted to the model. Marquardt-Levenberg and a simulated annealing algorithm were used and compared as optimization techniques. Our particular choice of optical properties for the two-layer model was consistent with skin and underlying fat in the presence of an exogenous chromophore [Appl. Opt. 37, 1958 (1998)]. The results are therefore specific to this set of optical properties. It was found that the cw diffusion solution could never be used to estimate all optical properties reliably. The combined cw and FD solutions could not be used to estimate some of the top-layer optical properties to an accuracy of better than 10%, although the absorption and the transport scattering coefficients of the bottom layer could be estimated to within 7% and 0.5%, respectively. No improvement was found from simultaneously fitting MC data at three different modulation frequencies. These results point to the need for a more accurate radiation transfer model at small source-detector separations.     

Diffuse light propagation in a turbid medium with varying refractive index: Monte Carlo modeling in a spherically symmetrical geometry

We report on the development of Monte Carlo software that can model media with spatially varying scattering coefficient, absorption, and refractive index. The varying refractive index is implemented by calculating curved photon paths in the medium. The results of the numerical simulations are compared with analytical solutions obtained using the diffusion approximation. The model under investigation is a scattering medium that contains a spherically symmetrical inclusion (inhomogeneity) created by variation in optical properties and having no sharp boundaries. The following steady-state cases are considered: (a) a nonabsorbing medium with a spherically symmetrical varying refractive index, (b) an inclusion with varying absorption and scattering coefficients and constant refractive index, and (c) an inclusion with varying absorption, scattering, and refractive index. In the latter case it is shown that the interplay between the absorption coefficient and the refractive index may create the effect of a hidden inclusion.     

Mie-scattering formalism for spherical particles embedded in an absorbing medium

Most of the Mie-scattering calculations have been done for a particle embedded in a nonabsorbing host medium. Generalization to an absorbing host medium can be achieved (a) by modifying the calculation of the spherical Bessel functions to account for a complex argument and (b) by accounting properly for the net rate of incident, scattered, and absorbed energy. We present an extended formalism of Mie scattering for the case of an absorbing host medium. Numerical calculations show that for a large spherical particle embedded in an absorbing host medium the extinction efficiency approaches 1 compared with 2 for a nonabsorbing host medium. We conjecture that this difference is due to the suppression of diffraction when the radius of the sphere is large.     

Three-dimensional imaging of objects embedded in turbid media with fluorescence and Raman spectroscopy

We present a single-ended technique for three-dimensional imaging of objects embedded in a turbid medium by the use of time-resolved fluorescence emission or Raman scattering. The technique uses the earliest arriving photons, which we show are not sensitive to the relatively long fluorescence lifetime, and thus can be used to extract the desired spatial information accurately, even at a distance equivalent to 100 mean free paths. The results also demonstrate the feasibility and the potential of one's combining time-resolved optical tomography with fluorescence or Raman spectroscopy to localize and identify the embedded objects. This technique may be valuable for the diagnosis of disease in highly scattering human tissue because it can provide spatial and biochemical information about the composition of embedded lesions.     

Analytical solutions for time-resolved fluorescence lifetime imaging in a turbid medium such as tissue.

An analytical solution is developed to quantify a site-specific fluorophore lifetime perturbation that occurs, for example, when the local metabolic status is different from that of surrounding tissue. This solution may be used when fluorophores are distributed throughout a highly turbid media and the site of interest is embedded many mean scattering distances from the source and the detector. The perturbation in lifetime is differentiated from photon transit delays by random walk theory. This analytical solution requires a priori knowledge of the tissue-scattering and absorption properties at the excitation and emission wavelengths that may be obtained from concurrent time-resolved reflection measurements. Additionally, the solution has been compared with the exact, numerically solved solution. Thus the presented solution forms the basis for practical lifetime imaging in turbid media such as tissue.     

Method for tracing the position of an alien object embedded in a random particulate medium

We have developed a new technique based on light scattering experiments for tracing an alien particle with deterministic potential in a random collection of particles. We have shown that, via a sequence of measurements of light scattered to a far field of a scattering collection, it is possible to locate the center of the alien particle. The analysis of the stability of reconstruction is provided, and it is demonstrated via simulations that the results are stable for sufficiently large wavelength of the incident light and in cases when the size of the alien particle is comparable with the size of the typical particle in the collection.     

Microscopic imaging through a turbid medium by use of annular objectives for angle gating

We report a new method for microscopic imaging of an object embedded in a turbid medium. The new method is based on the angle-gating mechanism achieved by the use of polarized annular objectives in the illumination and collection paths of a microscopic imaging system. A detailed experimental study is presented of the effects of the size of annular obstructions on image quality when turbid media, including polystyrene microspheres and milk suspensions, are imaged. Images of 22-mum polystyrene microspheres embedded in the turbid media show that misinterpretation can occur when circular objectives are used, because of the detection of mainly multiply scattered photons (i.e., diffusing photons). However, when annular objectives are employed, diffusing photons from a turbid medium can be efficiently suppressed; thus image contrast appears correctly, and image resolution is increased.     

High-resolution imaging in a deep turbid medium based on an ultrasound-switchable fluorescence technique

The spatial resolution of fluorescence imaging techniques in deep optically turbid media such as tissues is limited by photon diffusion. To break the diffusion limit and achieve high-resolution and deep-tissue fluorescence imaging, a fundamentally different method was demonstrated based on a concept of ultrasound-switchable fluorescence. The results showed that a small fluorescent tube with a diameter of ～180?μm at a depth of ～20?mm in an optical scattering medium ([Formula: see text] and [Formula: see text] cm(-1)) can be clearly imaged with a size of ～260?μm. The depth-to-resolution ratio is shown to be about one order of magnitude better than other deep-tissue fluorescence imaging techniques.     

Interfacial debonding of a spherical inclusion embedded in an infinite medium under remote stress

In the study of strength of particle reinforced composites, it is important to understand the energy release rate due to interfacial debonding between the particle and the matrix which is induced by manufacturing imperfection. This paper is aimed at the investigation of the critical condition for growth of the interfacial debonding and the corresponding volume increase due to void formation. The model used in the study is an isotropic elastic spherical inclusion embedded in an infinite isotropic elastic matrix under remote stress. Initial axisymmetrical interfacial debondings are assumed to exist in the vicinity of poles of the spherical inclusion. Axisymmetrical deformations of the matrix and the inclusion are analyzed based on the theory of three-dimensional elasticity in spherical coordinates. In order to avoid oscillatory stress singularity at the interfacial debonding front between two dissimilar materials, a condition of free slipping without friction at the interface is imposed. A Fredholm integral equation of the first kind is formulated based on the continuity conditions in the normal components of stress and displacement at the contact interface. The kernel function of the integral equation is expressed in terms of an infinite series of Legendre functions. Two types of remote stresses are considered in this study. The first type is the remote tension in the axial direction of the spherical inclusion and the second type is the remote compression in the transverse direction with respect to the axis of the spherical inclusion. Energy release rate is determined according to the rate of change of work done by remote stresses. In this paper, energy release rate and volume of the deformed void due to debonding are computed for any given size of initial interfacial debonding.     

Analytical method for localizing a fluorescent inclusion in a turbid medium

We describe a novel method for localizing a fluorescent inclusion in a homogeneous turbid medium through the use of time-resolved techniques. Based on the calculation of the mean time of the fluorescence curves, the method does not require a priori knowledge of either the fluorescence lifetime or the mean time of the instrument response function since it adopts a differential processing approach. Theoretical expressions were validated and experiments for assessing the accuracy of localization were carried out on liquid optical phantoms with a small fluorescent inclusion. The illumination and detection optical fibers were immersed in the medium to achieve infinite medium geometry as required by the model used. The experimental setup consisted of a time-correlated single-photon counting system. Submillimeter accuracy was achieved for the localization of the inclusion.     

Image contrast enhancement for two-photon fluorescence microscopy in a turbid medium

Image contrast enhancement is investigated for two-photon excitation fluorescence images of a microscopic sample that is buried underneath a turbid medium. The image contrast, which deteriorates rapidly with sample depth because of scattering loss, is enhanced by an increase in the average excitation power of the focused Gaussian (the TEM(00) mode) beam according to a compensation relation that has been derived by use of a Monte Carlo analysis of the scattering problem. A correct increase in the excitation power results in a detected fluorescence signal that remains invariant with sample depth. The scheme is demonstrated on images of DAPI-stained nuclei cells viewed underneath a suspension of 0.105-mum-diameter polystyrene spheres.     

无限介质包围的充液管道中导波的频散特性

利用波传播方法从理论上分析了无限介质包围的充液管道中导波的频散特性.基于经典的薄壳振动理论,求出了不同传输路径中的波数表达式,并利用数值方法对振动方程进行解析研究,分析管道参数和无限介质对导波频散特性的影响.结果表明,管道厚径比、管壁厚度、无限介质和管壁材料与导波频散密切相关.其中管道厚径比和管壁材料对流体主导波(s1...