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.     

Experimental determination of photon propagation in highly absorbing and scattering media

Optical imaging and tomography in tissues can facilitate the quantitative study of several important chromophores and fluorophores. Several theoretical models have been validated for diffuse photon propagation in highly scattering and low-absorbing media that describe the optical appearance of tissues in the near-infrared (NIR) region. However, these models are not generally applicable to quantitative optical investigations in the visible because of the significantly higher tissue absorption in this spectral region compared with that in the NIR. We performed photon measurements through highly scattering and absorbing media for ratios of the absorption coefficient to the reduced scattering coefficient ranging approximately from zero to one. We examined experimentally the performance of the absorption-dependent diffusion coefficient defined by Aronson and Corngold [J. Opt. Soc. Am. A 16, 1066 (1999)] for quantitative estimations of photon propagation in the low- and high-absorption regimes. Through steady-state measurements we verified that the transmitted intensity is well described by the diffusion equation by considering a modified diffusion coefficient with a nonlinear dependence on the absorption. This study confirms that simple analytical solutions based on the diffusion approximation are suitable even for high-absorption regimes and shows that diffusion-approximation-based models are valid for quantitative measurements and tomographic imaging of tissues in the visible.     

Optical properties of normal and carcinomatous bronchial tissue

To understand better the optical characteristics and autofluorescence properties of normal and carcinomatous bronchial tissue, we measured the absorption coefficient, scattering coefficient, and anisotropy factor from 400 to 700 nm. We made the measurements by using an integrating sphere with a collimated white-light beam to measure total reflectance and transmittance of samples. The unscattered transmittance of the samples was measured through polarized on-axis light detection. The inverse adding-doubling solution was utilized to solve the equation of radiative transfer and to determine the absorption coefficient and reduced scattering coefficient. The scattering coefficient and anisotropy factor were derived from the unscattered transmittance of the sample and the reduced scattering coefficient. The measured parameters allow us to simulate photon propagation in normal bronchial and tumoral tissue by using Monte Carlo modeling.     

Predictions and measurements of scattering and absorption over broad wavelength ranges in tissue phantoms

Predictions from Mie theory regarding the wavelength dependence of scattering in tissue from the near UV to the near IR are discussed and compared with experiments on tissue phantoms. For large fiber separations it is shown that rapid, simultaneous measurements of the elastic scatter signal for several fiber separations can yield the absorption coefficient and reduced scattering coefficient. With this information, the size of the scattering particles can be estimated, and this is done for Intralipid. Measurements made at smaller source detector separations support Mie theory calculations, demonstrating that the sensitivity of elastic scatter measurements to morphological features, such as scatterer size, is enhanced when the distance between the source and detector fibers is small.     

Optical characterization of biological tissues: determining absorption and scattering coefficients

We have measured the spectra of diffuse reflection and the total and collimated transmission of the mucous membrane of the stomach in the normal state by the methods of integrating spheres and single scattering in a wavelength range from 350 to 750 nm. The optical characteristics of this biological tissue were determined by solving the inverse scattering problem using the Kubelka-Munk three-flux model and the diffusion method. A comparative analysis of the results is presented.     

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.     

In vivo scattering measurement of biological tissue by the use of a pyroelectric polymer transducer

We propose a new method, to our knowledge, for noninvasive scattering measurements of tissues by the use of a pyroelectric polymer transducer, poly(vinylidene fluoride trifluoroethylene) film. In this method, samples are irradiated with nanosecond, low-energy light pulses delivered from an optical fiber, and the pyroelectric signal induced by the diffuse reflectance is measured with a transducer. The signal is then converted into diffuse reflectance by use of a calibration factor. The validity of this method was confirmed by our measuring the scattering coefficient of a white acrylic resin within an accuracy of +/- 15%. We attempted to apply this method to the estimation of scattering coefficients of normal and burned skins in rats in vivo.     

Measurement of optical transport properties of normal and malignant human breast tissue

We report measurement of optical transport parameters of normal and malignant (ductal carcinoma) human breast tissue. A spatially resolved steady-state diffuse reflectance technique was used for measurement of the reduced scattering coefficient (mu(s)?) and the absorption coefficient (mu(a)) of the tissue. The anisotropy parameter of scattering (g) was estimated by goniophotometric measurements of the scattering phase function. The values of mu(s)? and mu(a) for malignant breast tissue were observed to be larger than those for normal breast tissue over the wavelength region investigated (450-650 nm). Further, by using both the diffuse reflectance and the goniophotometric measurements, we estimated the Mie equivalent average radius of tissue scatterers to be larger in malignant tissue than in normal tissue.     

Optical sectioning using a fiber probe with an angled illumination-collection geometry: evaluation in engineered tissue phantoms

We present a fiber optic probe that combines polarized illumination and detection with an angled distal probe geometry to detect the size-dependent scattering at a specific depth within epithelium. Analysis of the scattering signal by use of Mie theory allows the extraction of scatterer size and size distribution-key parameters for precancer detection. The probe was evaluated in two tissue phantoms: polystyrene beads atop collagen gel and multiple layers of cancer cells atop collagen. We also present in vivo measurements in the oral cavity of normal volunteers. The sizes of scatterers extracted from the scattering spectra corresponded to independently measured values.     

Airborne polarized lidar detection of scattering layers in the ocean

A polarized lidar technique based on measurements of waveforms of the two orthogonal-polarized components of the backscattered light pulse is proposed to retrieve vertical profiles of the seawater scattering coefficient. The physical rationale for the polarized technique is that depolarization of backscattered light originating from a linearly polarized laser beam is caused largely by multiple small-angle scattering from particulate matter in seawater. The magnitude of the small-angle scattering is determined by the scattering coefficient. Therefore information on the vertical distribution of the scattering coefficient can be derived potentially from measurements of the time-depth dependence of depolarization in the backscattered laser pulse. The polarized technique was verified by field measurements conducted in the Middle Atlantic Bight of the western North Atlantic Ocean that were supported by in situ measurements of the beam attenuation coefficient. The airborne polarized lidar measured the time-depth dependence of the backscattered laser pulse in two orthogonal-polarized components. Vertical profiles of the scattering coefficient retrieved from the time-depth depolarization of the backscattered laser pulse were compared with measured profiles of the beam attenuation coefficient. The comparison showed that retrieved profiles of the scattering coefficient clearly reproduce the main features of the measured profiles of the beam attenuation coefficient. Underwater scattering layers were detected at depths of 20-25 m in turbid coastal waters. The improvement in dynamic range afforded by the polarized lidar technique offers a strong potential benefit for airborne lidar bathymetric applications.     

Microscopic origin of light scattering in tissue

A newly designed instrument, the static light-scattering (SLS) microscope, which combines light microscopy with SLS, enables us to characterize local light-scattering patterns of thin tissue sections. Each measurement is performed with an illumination beam of 70-microm diameter. On these length scales, tissue is not homogeneous. Both structural ordering and small heterogeneities contribute to the scattering signal. Raw SLS data consist of a two-dimensional intensity distribution map I(theta, phi), showing the dependence of the scattered intensity I on the scattering angle theta and the azimuthal angle phi. In contrast to the majority of experiments and to simulations that consider only the scattering angle, we additionally perform an analysis of the azimuthal dependence I(phi). We estimate different contributions to the azimuthal scattering variation and show that a significant fraction of the azimuthal amplitude is the result of tissue structure. As a demonstration of the importance of the structure-dependent part of the azimuthal signal, we show that this function of the scattered light alone can be used to classify tissue types with surprisingly high specificity and sensitivity.     

Determination of optical coefficients and fractal dimensional parameters of cancerous and normal prostate tissues

Optical extinction and diffuse reflection spectra of cancerous and normal prostate tissues in the 750 to 860 nm spectral range were measured. Optical extinction measurements using thin ex vivo prostate tissue samples were used to determine the scattering coefficient (μ(s)), while diffuse reflection measurements using thick prostate tissue samples were used to extract the absorption coefficient (μ(a)) and the reduced scattering coefficient (μ'(s)). The anisotropy factor (g) was obtained using the extracted values of μ(s) and μ'(s). The values of fractal dimension (D(f)) of cancerous and normal prostate tissues were obtained by fitting to the wavelength dependence of μ'(s). The number of scattering particles contributing to μ(s) as a function of particle size and the cutoff diameter d(max) as a function of g were investigated using the fractal soft tissue model and Mie theory. Results show that d(max) of the normal tissue is larger than that of the cancerous tissue. The cutoff diameter d(max) is observed to agree with the nuclear size for the normal tissues and the nucleolar size for the cancerous tissues. Transmission spectral polarization imaging measurements were performed that could distinguish the cancerous prostate tissue samples from the normal tissue samples based on the differences between their absorption and scattering parameters.     

Unsupervised segmentation of RF echo into regions with different scattering characteristics

Recent experimental results verify that the probability distribution function of the diffuse component of the RF echo depends primarily on the concentration of the diffuse scatterers in the resolution cell. In this paper we apply these results to develop an unsupervised segmentation scheme that partitions an RF A-scan or B-scan image into statistically homogeneous regions that reflect the underlying scattering characteristics. The proposed segmentation scheme is based on a nonparametric homogeneity test that compares two regions of interest (ROI) for possible merging utilizing information about both the coherent and the diffuse component of the RF echo. For the coherent component, homogeneity is defined in terms of the estimated average spacing of each ROI. For the diffuse component, we use the nonparametric Kolmogorov-Smirnov (K-S) homogeneity statistical test that compares two empirical distributions associated with any two ROIs. This test can be used to obtain a segmentation into regions with different scattering characteristics regardless of the nature of the scattering conditions (e.g., Rayleigh regions with different scatterer concentration, different non-Rayleigh regions, or different coherent scattering regions). Finer segmentation can be obtained by learning the distributions associated with the various homogeneous regions obtained from the coarse segmenter. The proposed segmentation scheme is applied on simulated RF scans with different scatterer concentration per resolution cell, on phantom data which mimic tissue, and on liver scans. The results demonstrate the effectiveness of the segmentation algorithm even in cases of subtle differences in the scattering characteristics of each region (for example, diffuse component with scatterer density of 16 and 32 scatterers per resolution cell).     

Optical properties of highly scattering media determined from changes in attenuation, phase, and modulation depth

The optical properties of scattering media determine the attenuation (A) and the transit time (?t?) of light reflected from the medium as well as the phase (?) and modulation depth (M) of an intensity-modulated lightwave. Our primary finding is that the ratio of changes in A, ?, and M is approximately independent of the scattering properties and gives a good estimate of the absorption coefficient. These changes can be induced either by small changes in the absorption coefficient of the medium, by the tuning of the wavelength, or by changes in the light source-detector distance. The application for the in vivo monitoring of hemoglobin and oxyhemoglobin concentrations in human tissue is discussed.     

Longitudinal wave scattering from rough crack-like defects

The roughness of crack-like defects affects ultrasonic wave scattering and this, in turn, affects defect detection and characterization. The first part of this paper is concerned with the efficient numerical modeling of scattering from rough cracks, i.e., a finite element local scattering (FELS) model. The scattered field is presented in the form of a scattering matrix, which describes the far-field scattering coefficient for all possible combinations of incident and scattering directions. The scattering matrices for many different realizations of rough cracks are simulated using both a FELS model and a model based on the Kirchhoff approximation. It is shown that the difference between scattering matrices extracted from the Kirchhoff model and the FELS model is less than 8%, for rough cracks with a standard deviation less than 0.3 wavelengths and a correlation length longer than 0.5 wavelengths, at incident and scattering angles ranging from -80° to 80° relative to the normal direction of the mean surface. Because the Kirchhoff model is significantly more efficient than the FELS model, it is used for subsequent simulations in which many realizations of rough cracks are studied to gain insight into the statistical nature of the scattering process. In line with previous work, a distinction is made between the coherent and diffuse contributions to the overall scattered field, in which the former represents the ensemble average over multiple surface realizations. The coherent and diffuse contributions of scattered field from various types of rough cracks are simulated. It is shown that surface roughness directly affects the coherent contribution to scattering behavior, whereas the diffuse contribution is affected by both surface roughness and correlation length, especially for rougher cracks.     

Raman and fluorescent scattering matrix of spherical microparticles

In this paper, we have investigated the main properties of the Raman and fluorescent matrix of scattering by microspheres using the matrix scattering formalism. The coherent and incoherent inelastic scattering of incident light by a microsphere is described by the Stokes parameters. We demonstrate the main symmetry properties of the coherent and incoherent Raman and fluorescent scattering matrices. Numerical results are presented to illustrate the Raman scattering efficiency, cross-phase coefficient, and some other parameters of scattering by microspheres.     

Effect of the scattering delay on time-dependent photon migration in turbid media

We modified the diffusion approximation of the time-dependent radiative transfer equation to account for a finite scattering delay time. Under the usual assumptions of the diffusion approximation, the effect of the scattering delay leads to a simple renormalization of the light velocity that appears in the diffusion equation. Accuracy of the model was evaluated by comparison with Monte Carlo simulations in the frequency domain for a semi-infinite geometry. A good agreement is demonstrated for both matched and mismatched boundary conditions when the distance from the source is sufficiently large. The modified diffusion model predicts that the neglect of the scattering delay when the optical properties of the turbid material are derived from normalized frequency- or time-domain measurements should result in an underestimation of the absorption coefficient and an overestimation of the transport coefficient. These observations are consistent with the published experimental data.     

室内声场模拟中的界面声散射

室内声场模拟中引入扩散反射对提高模拟的准确性具有重要意义,但采用单值散射系数无法完整表示界面的扩散反射特性。受几何声学中扩散反射模拟方法的限制,界面有效散射系数存在不确定性。通过改变一个矩形房间中的吸声量、吸声布置方式及表面几何复杂程度等声场条件,对混响时间的模拟值与实测值进行比较,分析了由界面散射系数不确定性产生的模拟偏差与房间内声场扩散的关系。     

Biogeo-optics: particle optical properties and the partitioning of the spectral scattering coefficient of ocean waters

We propose a direct method of partitioning the particulate spectral scattering coefficient of the marine hydrosol based on the concurrent determination of the concentrations of particulate mineral and organic matter (the total mass of optically active scattering material exclusive of water) with the particulate spectral scattering coefficient. For this we derive a Model II multiple linear regression model. The multiple linear regression of the particulate spectral scattering coefficient against the independent variables, the concentrations of particulate inorganic matter and particulate organic matter, yields their mass-specific spectral scattering cross sections. The mass-specific spectral scattering cross section is simply the particle scattering cross section normalized to the particle mass, a fundamental optical efficiency parameter for the attenuation of electromagnetic radiation [Absorption and Scattering of Light by Small Particles, (Wiley-Interscience, 1983), pp. 80-81, 289]. It is possible to infer the optical properties of the suspended matter from the mass-specific spectral scattering cross sections. From these cross sections we partition the particulate spectral scattering coefficient into its major components.     

Simultaneous reconstruction of absorption and scattering maps with ultrasound localization: feasibility study using transmission geometry

We report the experimental results of the simultaneous reconstruction of absorption and scattering coefficient maps with ultrasound localization. Near-infrared (NIR) data were obtained from frequency domain and dc systems with source and detector fibers configured in transmission geometry. High- or low-contrast targets located close to either the boundary or the center of the turbid medium were reconstructed by using NIR data only and NIR data with ultrasound localization. Results show that the mean reconstructed absorption coefficient and the spatial distribution of the absorption map have been improved significantly with ultrasound localization. The improvements in the mean scattering coefficient and the spatial distribution of the scattering coefficient are moderate. When both the absorption and the scattering coefficients are reconstructed the performance of the frequency-domain systemis much better than that of the dc system.