Frequency domain optical tomography using a conjugate gradient method without line search

A conjugate gradient method without line search (CGMWLS) is presented. This method is used to retrieve the local maps of absorption and scattering coefficients inside the tissue-like test medium, with the synthetic data. The forward problem is solved with a discrete-ordinates finite-difference method based on the frequency domain formulation of radiative transfer equation. The inversion results demonstrate that the CGMWLS can retrieve simultaneously the spatial distributions of optical properties inside the medium within a reasonable accuracy, by reducing cross-talk between absorption and scattering coefficients.     

一维梯度折射率介质光学特性的反演

在单个方波脉冲入射情况下,利用共轭梯度法对一维梯度折射率介质的折射率、吸收系数以及散射系数进行了反演.正问题采用间断有限元法求解,反问题的解则在正问题的基础上通过共轭梯度法得到.研究结果表明,利用单个方波脉冲入射情况下的时域半球反射率以及时域半球透射率作为测试值能够有效地反演一维梯度折射率介质的光学特性及其分布情况.     

基于快速蒙特卡罗的散射介质光学参量干涉测量方法研究

提出了一种散射介质光学参量的干涉测量方法. 在蒙特卡罗数值模拟的基础上引入聚焦高斯光源模型和基于比例缩放的压缩算法, 实现了对光子后向散射分布和干涉特性的快速模拟. 利用计算数据训练了前向人工神经网络进行了介质光学参量的反向求解. 实验中以脂肪乳注射剂和生物染色剂印度墨水组成的悬混液为样本, 通过光学干涉系统测量得到了后向散射光依赖于深度的干涉光强分布, 并对其中散射和吸收系数进行了反向计算. 所得结果能够正确反映散射和吸收系数与散射和吸收物质浓度之间的线性关系, 验证了该方法的可行性.     

基于快速蒙特卡罗的散射介质光学参量干涉测量方法研究

提出了一种散射介质光学参量的干涉测量方法.在蒙特卡罗数值模拟的基础上引入聚焦高斯光源模型和基于比例缩放的压缩算法,实现了对光子后向散射分布和干涉特性的快速模拟.利用计算数据训练了前向人工神经网络进行了介质光学参量的反向求解.实验中以脂肪乳注射剂和生物染色剂印度墨水组成的悬混液为样本,通过光学干涉系统测量得到了后向散射光依赖于深度的干涉光强分布,并对其中散射和吸收系数进行了反向计算.所得结果能够正确反映散射和吸收系数与散射和吸收物质浓度之间的线性关系,验证了该方法的可行性.     

Light propagation in porous ceramics: porosity and optical property studies using tunable diode laser spectroscopy

By integrating gas in scattering media absorption spectroscopy and frequency domain photon migration a new method is developed for the study of optical porosity and optical properties of porous media, in our case ceramics. The optical porosity is defined as the ratio of the path length through the gas-filled pores and the physical path length through the whole medium. The effective refractive index of the porous ceramics is also retrieved based on the optical porosity, which is then used to evaluate the reduced scattering coefficients of the porous ceramics. The combined method provides a new way to study light propagation in porous media. A modified Looyenga model is proposed to study the relationship between the physical porosity and the effective refractive index of the porous medium, which also connects the optical and physical porosities, and provides the possibility to use the present method for porosimetry analysis.     

Influence of structural characteristics on the thermal conductivity of polycrystalline diamond films

By analyzing the signal formed by the photoacoustic effect as a function of the light modulation frequency, it is shown that this effect may be used to determine the thermal conductivity of diamond materials. The method is checked experimentally for two types of polycrystalline diamond films grown by chemical vapor deposition with the gaseous medium activated by a dc discharge and a microwave discharge. The data obtained on the thermal conductivity of the films are discussed with reference to the results of an investigation of the optical absorption, Raman light scattering, and cathodoluminescence of similar films. It is shown that the thermal conductivity of polycrystalline diamond films depends on the structural characteristics, which are determined by the deposition conditions. Fiz. Tverd. Tela (St. Petersburg) 40, 1221–1225 (July 1998)     

Optical tomography using the time-independent equation of radiative transfer—Part 2: inverse model

Optical tomography is a novel imaging modality that is employed to reconstruct cross-sectional images of the optical properties of highly scattering media given measurements performed on the surface of the medium. Recent advances in this field have mainly been driven by biomedical applications in which near-infrared light is used for transillumination and reflectance measurements of highly scattering biological tissues. Many of the reconstruction algorithms currently utilized for optical tomography make use of model-based iterative image reconstruction (MOBIIR) schemes. The imaging problem is formulated as an optimization problem, in which an objective function is minimized. In the simplest case the objective function is a normalized-squared error between measured and predicted data. The predicted data are obtained by using a forward model that describes light propagation in the scattering medium given a certain distribution of optical properties.In part I of this two-part study, we presented a forward model that is based on the time-independent equation of radiative transfer. Using experimental data we showed that this transport-theory-based forward model can accurately predict light propagation in highly scattering media that contain void-like inclusions. In part II we focus on the details of our image reconstruction scheme (inverse model). A crucial component of this scheme involves the efficient and accurate determination of the gradient of the objective function with respect to all optical properties. This calculation is performed using an adjoint differentiation algorithm that allows for fast calculation of this gradient. Having calculated this gradient, we minimize the objective function with a gradient-based optimization method, which results in the reconstruction of the spatial distribution of scattering and absorption coefficients inside the medium. In addition to presenting the mathematical and numerical background of our code, we present reconstruction results based on experimentally obtained data from highly scattering media that contain void-like regions. These types of media play an important role in optical tomographic imaging of the human brain and joints.     

Accurate reconstruction of the optical parameter distribution in participating medium based on the frequency-domain radiative transfer equation

Reconstructing the distribution of optical parameters in the participating medium based on the frequency-domain radiative transfer equation(FD-RTE) to probe the internal structure of the medium is investigated in the present work.The forward model of FD-RTE is solved via the finite volume method(FVM). The regularization term formatted by the generalized Gaussian Markov random field model is used in the objective function to overcome the ill-posed nature of the inverse problem. The multi-start conjugate gradient(MCG) method is employed to search the minimum of the objective function and increase the efficiency of convergence. A modified adjoint differentiation technique using the collimated radiative intensity is developed to calculate the gradient of the objective function with respect to the optical parameters. All simulation results show that the proposed reconstruction algorithm based on FD-RTE can obtain the accurate distributions of absorption and scattering coefficients. The reconstructed images of the scattering coefficient have less errors than those of the absorption coefficient, which indicates the former are more suitable to probing the inner structure.     

An inverse radiative transfer problem of simultaneously estimating profiles of temperature and radiative parameters from boundary intensity and temperature measurements

A parallel-plane space filled with absorbing, emitting, isotropically scattering, gray medium is studied in this paper. The boundary intensity and boundary temperature profiles are calculated for the inverse analysis. For the simultaneous estimation of temperature, absorption and scattering coefficient profiles in the medium, the sum of residuals of boundary intensity and temperature after being weighted by a balance factor is minimized through using a Newton-type iteration algorithm and the least-squares method. To avoid over-updating for the parameters, the relative updating magnitude during the iteration process is constrained not to be >0.5. It is shown that the boundary intensity measurement alone is not enough to estimate simultaneously the temperature (source) and the radiative properties (both absorption and scattering coefficients) when the measurement data contain sensitive random errors. The boundary temperature measurement can serve as a necessary supplementation to the boundary intensity to make this kind of inverse radiative transfer problem resolvable. It was shown that a compensation relationship between absorption and scattering coefficients makes it difficult to fix them accurately. Parabolic profiles for the three parameters are used to validate the estimation method. When the optical thickness approaches 4.0, the results for the radiative properties are not acceptable, although the result for temperature profile is reasonable. This means the method needs further improvements.     

Numerical developments for short-pulsed Near Infra-Red laser spectroscopy. Part II: inverse treatment

Indirect optical spectroscopy or tomography, that is, mapping of optical properties in scattering and absorption inside a medium given a set of measurements at the boundaries, is highly dependent on the radiative transfer model used to track radiative energy propagation in semi-transparent materials. In the first part of this study, a numerical tool adapted for treating radiative transfer in the frame of short-pulsed laser beam interaction with non-homogeneous matter has been presented. In this paper, it is intended to show how such numerical tools can undergo inversion through adjoint treatment or reverse differentiation.Adjoint models, as well as reverse differentiation, are used in order to allow an efficient computation of the gradient, in the unknown optical parameters space, of an objective or cost function estimating the residual between data obtained at the boundary and predictions by numerical simulations. This gradient is a crucial indication as to update, through line minimization, the set of internal optical properties of the medium.First, the theoretical background of the inverse treatments, both reverse differentiation and adjoint model, for the transient radiative transfer equation model introduced in Part I is developed. Second, different reconstruction configurations are presented. Time-dependent sampling and time filtering effects of the measurements are addressed. Image reconstructions from simulated data are achieved for material phantoms of simple geometry.     

Speckle diagnostics of multiple scattering media with the use of frequency-modulated laser radiation

A method for probing randomly inhomogeneous multiple scattering media with the use of frequency-modulated laser radiation is considered. The method is based on analysis of the dependence of the blinking index of time-averaged speckles formed upon scattering of the probing radiation in a medium on the frequency modulation depth of the probing radiation. In the case of a binary frequency modulation, the blinking index of the detected speckle-modulated radiation is determined by the cosine Fourier transform of the probability density of the optical path-length difference of partial components of the scattered field in the probed medium. The values of the probability density of the optical path-length difference reconstructed with the use of the proposed method from the measured blinking index of speckles for model scattering media (fluoroplastic layer and layer of TiO₂ particles on a glass substrate) are in a good agreement with the results of statistical simulation of the probing radiation transfer in multiple scattering media.     

Study of dispersion and absorption of an ensemble of spherical particles inside an optical cavity and new possibilities of predicting the optical characteristics of biological media by intracavity laser spectroscopy

Optical characteristics, namely, dispersion and absorption spectra of an ensemble of spherical particles randomly oriented inside an optical cavity are investigated. The study is based on the self-consistent matching of new data from the inhomogeneous optical cavity with data from the scattering of an ensemble of spherical particles of different size, randomly oriented in free space. As a result, a new model, which self-consistently accounts for multiple scattering in the optical cavity, has been developed to predict absorption and dispersion of ensembles of spherical particles. This model is supposed to enhance potentiality of the intracavity method for plotting wavelength dependences of optical characteristics of media. A specific calculation of dispersion and absorption dependences on the wavelength shows that this method can be used for investigation of biological media consisting of spherical particles, in particular, erythrocyte suspension.     

混浊大气介质调制传递函数的一般特征

基于混浊介质的调制传递函数(MTF)和在各向同性漫射光源照射下平行平面混浊介质出射光强度分布之间的等效原理,利用辐射传输算法DISORT数值计算了几种典型的均匀大气混浊介质的MTF,获得了整个空间频域内MTF的一般特征.结果显示,大气介质的MTF不但依赖于介质的光学厚度(散射和吸收),也依赖于介质的散射相函数.给出了大...     

Analysis of Electromagnetic Waves Scattering by a Finite Size Dielectric and Metal Cylinder in a Rectangular Waveguide

The paper presents a rigorous solution of the scattering problem by a circular dielectric and perfectly conducting cylinders of any radius and any height in the rectangular waveguide oriented perpendicularly to a wall. The method is based on the representation of fields in waveguide and dielectric medium by cylindrical eigenfunctions and application of boundary conditions on surfaces of the cylinder to evaluate the fields inside and outside the cylinder. The reflection and transmission coefficients are expressed through the fields. As an example the reflection and transmission coefficients versus frequency for various dielectric and metallic cylinders are computed. The comparison of numerical with experimental data is presented.     

基于漫反射光谱的组织光学参数测量系统与方法研究

在体组织光学参数测量是生物医学光子学研究重点,不仅为人体成分无创检测、光学成像、光动力疗法等研究提供基础,并且可以快速获取人体光学参数变化,为临床诊断提供依据。研究了利用单一源探距离漫反射光谱在体测量光学参数的测量系统与反构方法。漫反射光谱测量系统由宽谱光源、高分辨光纤光谱仪及光纤探头组成,结构简单,测量方便,可准确快速测量样品漫反射光谱。在光纤探头几何形状基础上,研究了光纤收集及系统传递函数,在此基础上对反构算法进行了校正。光学参数反构算法中正向模型基于Monte Carlo以及神经网络方法,适用光学参数范围大,计算速度快;逆向算法采用主成分分析与非线性建模拟合相结合的方法,可抑制测量噪声影响。在测量系统及反构算法基础上,进行了组织仿体光学参数测量实验,结果表明,利用单一源探距离下漫反射谱,可以较为准确获取吸收系数以及约化散射系数,均方根误差分别达到4.58%以及7.92%。为保证系统测量准确性,测量波长范围应覆盖样品中所含吸收物质吸收峰范围。所研究的在体组织光学参数测量方法为人体成分无创检测及测量条件变化获取提供了基础。     

光学介质表面波度的计算机模型

任一光学介质表面波度对光散射具有不可忽视的影响.本文对用激光轮廓仪所测物体表面曲线进行研究,运用傅里叶级数和最小二乘法拟合光学介质表面波形形态分布,建立了光学介质表面波度的计算机一维模型.     

Computer simulation of time-resolved optical imaging of objects hidden in turbid media

We review research on time-resolved optical imaging of objects hidden in strongly scattering media, with emphasis on the application to breast cancer detection. A method is presented to simulate the propagation of light in turbid media. Based on a numerical algorithm to solve the time-dependent diffusion equation, the method takes into account spatial variations of the reduced scattering and absorption factors of the medium due to the presence of objects as well as random fluctuations of these factors. It is shown that the simulation method reproduces, without fitting, experimental results on tissue-like phantoms. Using experimental and simulation results, an assessment is made of the reliability for extracting the reduced scattering and absorption coefficients of the medium from time-resolved reflection and transillumination data. The simulation technique is employed to study the conditions for locating mm-sized objects immersed in a turbid medium, by direct, time-resolved imaging. We discuss a simple method to enhance the imaging power of the time-resolved technique. The mathematical justification of the method, as well as some applications to simple problems, is given. The simulation technique is employed to demonstrate the effectiveness of the data processing technique. Results of time-resolved reflection experiments and simulations are presented, showing that the use of the latter allow us to locate 1 mm diameter objects under conditions which would prevent detection otherwise. Our results demonstrate that the combination of simulation and the appropriate processing of the diffusive part of the time-resolved reflected or transmitted light intensity may substantially increase the potential of the time-resolved near-infrared diffusive light imaging technique as a diagnostic tool for breast cancer detection.     

Effect of Si doping on optical and thermal properties of MOVPE GaN thin layers

Photothermal deflection spectroscopy is used to investigate thermal and optical properties of MOVPE grown GaN thin layers deposited on sapphire substrate. The effects of Si doping on absorption spectrum and gap energy are revealed. Also, doping-induced free carrier absorption is extracted from absorption in the sub-gap region. Moreover, the variations of photothermal signal versus modulation frequency are used to determine thermal properties of these films. The measured thermal conductivity is clearly decreased by Si doping, the main reason should be the phonon scattering on point defects.     

吸收介质中微椭球体颗粒光学参数的研究

本文应用Eikonal近似将微椭球用其等效的球来近似, 结合Mie理论对吸收介质中微椭球体颗粒光学参数进行了数值计算。 结果表明, 椭球位置变化时, 散射和吸收性能发生变化。离心率增大时, 散射和吸收系数都增大, 离心率越大增大的越明显。波长增大时, 在紫光波长为0.4 μm和近红外区波长为1.58 μm处散射系数出现了峰值, 而吸收系数单调增大。相对折射率实部以及虚部变化对光学参数均有影响, 颗粒的吸收性越强, 散射相应地减弱。结果表明这种数值解析方法能有效地计算椭球体颗粒的光学参数。     

Radiative properties of densely packed spheres in semitransparent media: A new geometric optics approach

This contribution presents a new Ray-tracing method for calculating effective radiative properties of densely packed spheres in non-absorbing or semitransparent host medium. The method is restricted to the geometric optic objects and neglects the wave effects. The effective radiative properties such as the absorption and scattering coefficients, and phase function are retrieved from the calculation of mean-free paths of scattering and absorption, and the angular scattering probability of radiation propagating in the dispersed medium. The model accounts for the two geometric effects called here as non-point scattering and ray transportation effects. The successful comparison of the current model with data of radiative properties and transmittances of particle beds in a non-absorbing medium reported in the literature confirm its suitability. It is shown that: (i) for opaque or absorbing particles (not systematically opaque), the non-point scattering is the dominant geometric effects whereas both non-point scattering and ray transportation effects occur for weakly absorbing and transparent particles. In the later cases, these two geometric effects oppose and may cancel out. This may explain why the Independent scattering theory works well for packed of quasi-transparent particles; (ii) the non-point scattering and ray transportation effects can be captured through the scattering and absorption coefficients while using the classical form of phase function. This enables using the standard radiative transfer equation (RTE); (iii) the surrounding medium absorption can be accounted for without any homogenization rule. It contributes to increasing the effective absorption coefficient of the composite medium as expected but, at the same time, it reduces the particle extinction; and (iv) the current transfer calculation predicts remarkably the results of direct Monte Carlo (MC) simulation. This study tends therefore to confirm that the RTE can be applied to densely packed media by using effective radiative properties.