Random media characterization using the analysis of diffusing light data on the basis of an effective medium model

The transport properties of dense random media such as rutile powder layers and polyball suspensions are analyzed in visible and near infrared on the basis of experimental data on coherent backscattering, diffuse transmittance, and low-coherence interferometry. The developed technique of retrieval of the transport parameters of examined scattering media allows the evaluation of the transport mean free path l* and the effective refractive index n(ef) of the medium without a priori knowledge of the optical properties of the scattering particles. It is found that with decreasing wavelength lambda(0) the value of localization parameter 2pin(ef)l*/lambda(0) of the studied rutile samples abruptly drops and approaches approximately 2.6 at 473 nm. This peculiarity is caused by the very large scattering efficiency of scatterers in the vicinity of the first Mie resonance.     

Selective polarization imager for contrast enhancements in remote scattering media

Conventional intensity imaging through turbid media suffers from rapid loss of image contrast due to light scattering from particles or random variations of refractive index. This paper features the development of an active imaging, snapshot, system design and postprocessing algorithms that differentiate between radiation that scatters or reflects from remote, obscured objects and the radiation from the scattering media itself through a combination of polarization difference imaging, channel blurring, and Fourier spatial filtering. The produced sensor acquires and processes image data in real time, yielding improved image contrasts by factors of 10 or greater for dense water vapor obscurants.     

Light scattering by a random distribution of particles embedded in absorbing media: full-wave Monte Carlo solutions of the extinction coefficient

We present a numerical investigation of the light scattering in an absorbing medium with randomly distributed scatterers. The extinction coefficient is derived from an ensemble of numerical solutions of Maxwell's equations for many different realizations of the system. Results are in good agreement with the predictions given by the effective medium theory under the independent-scattering approximation. Beyond the independent-scattering approximation, we explore the domain of validity of an effective medium theory that takes into account correlations between pairs of scatterers. A good agreement is obtained with a filling ratio up to 30% for scatterers with a relative refractive index contrast lower than 20% and size parameters near unity.     

Two-color excitation fluorescence microscopy through highly scattering media

We study the performance of two-color excitation (2CE) fluorescence microscopy [Opt. Lett. 24, 1505 (1999)] in turbid media of different densities and anisotropy. Excitation is achieved with two confocal excitation beams of wavelengths lambda(1) and lambda(2), which are separated by an angular displacement theta, where lambda(1) not equal lambda(2), 1/lambda(e) = 1/lambda(1) + 1/lambda(2), and lambda(e) is the single-photon excitation wavelength of the sample. 2CE fluorescence is generated only in regions of the sample where the two excitation beams overlap. The 2CE fluorescence intensity is proportional to the product of the two excitation intensities and could be detected with a large-area photodetector. The requirement of spatiotemporal simultaneity for the two excitation beams makes 2CE fluorescence imaging a promising tool for observing microscopic objects in a highly scattering medium. Optical scattering asymmetrically broadens the excitation point-spread function and toward the side of the focusing lens that leads to the contrast deterioration of the fluorescence image in single- or two-photon (lambda(1) = lambda(2)) excitation. Image degradation is caused by the decrease in the excitation energy density at the geometrical focus and by the increase in background fluorescence from the out-of-focus planes. In a beam configuration with theta not equal 0, 2CE fluorescence imaging is robust against the deleterious effects of scattering on the excitation-beam distribution. Scattering only decreases the available energy density at the geometrical focus and does not increase the background noise. For both isotropic and anisotropic scattering media the performance of 2CE imaging is studied with a Monte Carlo simulation for theta = 0, pi/2, and pi, and at different h/d(s) values where h is the scattering depth and d(s) is the mean-free path of the scattering medium.     

Particle size analysis of turbid media with a single optical fiber in contact with the medium to deliver and detect white light

Wavelength-dependent elastic-scattering spectra of highly scattering media measured with only a single fiber for both light delivery and collection are presented. White light is used as a source, and oscillations of the detected light intensities are seen as a function of wavelength. The maximum and minimum of the oscillations can be used to determine scatterer size for monodisperse distributions of spheres when the refractive indices are known. In addition, several properties of the probe relevant to tissue diagnosis are examined and discussed including the effects of absorption, a broad distribution of scatterers, and the depth probed.     

Polarized pulse waves in random discrete scatterers

In recent years there has been increasing interest in the use of polarization for imaging objects in a cluttered environment. Examples are optical imaging through clouds, optical detection of objects in a biological medium, and microwave detection of objects in clutter. We extend previous studies of continuous-wave scattering to pulse-polarization scattering in discrete scatterers. We solve the time-dependent vector radiative transfer equation for a plane-parallel medium by using Mie scattering and the discrete ordinates method. The time-dependent degree of polarization and cross-polarization discrimination are calculated and verify the advantages of circular over linear polarization in maintaining greater copolarized components rather than cross-polarized components.     

Effective medium theories for irregular fluffy structures: aggregation of small particles

The extinction efficiencies as well as the scattering properties of particles of different porosity are studied. Calculations are performed for porous pseudospheres with small size (Rayleigh) inclusions using the discrete dipole approximation. Five refractive indices of materials covering the range from 1.20+0.00i to 1.75+0.58i were selected. They correspond to biological particles, dirty ice, silicate, and amorphous carbon and soot in the visual part of the spectrum. We attempt to describe the optical properties of such particles using Lorenz-Mie theory and a refractive index found from some effective medium theory (EMT) assuming the particle is homogeneous. We refer to this as the effective model. It is found that the deviations are minimal when utilizing the EMT based on the Bruggeman mixing rule. Usually the deviations in the extinction factor do not exceed approximately 5% for particle porosity P = 0 - 0.9 and size parameters x(porous) = 2 pi r(s,porous)/lambda < or approximately = 25. The deviations are larger for scattering and absorption efficiencies and smaller for particle albedo and the asymmetry parameter. Our calculations made for spheroids confirm these conclusions. Preliminary consideration shows that the effective model represents the intensity and polarization of radiation scattered by fluffy aggregates quite well. Thus the effective models of spherical and nonspherical particles can be used to significantly simplify the computations of the optical properties of aggregates containing only Rayleigh inclusions.     

A frame-based approach for wideband correlation-inversion of lossless scatterers

Presented here is an ultra-wideband-correlation-based scheme for imaging and inversion of an unknown weak and lossless scatterer embedded in a known background medium. The scheme uses an excitation and reception of ultra wideband/short-pulsed fields by an array of transducers located outside the imaging domain. The scatterer image is formed by cross correlating (in the short-pulsed domain or via spectral integration in the ultra wideband domain) the numerically/ analytically back-propagated, measured, and scattered data set with the forward-propagation excitations. It is shown that in the ultra wideband domain, the forward-backward propagation functions form a frame set in a finite Hilbert space. Within the weak scattering assumption (Born approximation) the scatterer's image and object function (velocity profile) are related via the corresponding frame operator. Therefore, an exact inversion scheme of the frame operator is readily available to yield the object function via an iterative scheme or using the dual frame set. Numerical examples that demonstrate the performance of the imaging and inversion schemes for scatterers with various velocity profiles are presented. It is shown that the scatterer image is generally of poor resolution. However, on inversion, a high-quality velocity profile is obtained that captures the scatterer fine details.     

Use of polarimetric lidar for the study of oriented ice plates in clouds

A polarization lidar operating at 532 nm was converted into an automatic, polarimetric lidar capable of measuring the entire Stokes vector of backscattered light and its derived quantities. Among these quantities, circular and linear depolarizations were studied as tools for investigating the presence of anisotropic scattering media. Isotropic scatterers show a simple relationship between linear and circular depolarization, a relation that we confirm theoretically and experimentally. Deviations from this relation, which are possible in the presence of anisotropic scatterers such as horizontally oriented ice plates when they are observed with a slant lidar, were studied both numerically and experimentally.     

Analysis of time-gated imaging through scattering media by a Fourier optics approach

The method of Fourier optics is applied to the problem of time-gated imaging through scattering media. Tb adapt the problem to this treatment, appropriate alterations are made: The continuous medium is replaced by a cascade of thin scatterers, and a spatial filtering process is substituted for the conventional gating processes. Closed-form solutions are derived.     

基于小波变换利用超声估计生物组织散射元平均间距

生物组织散射元平均间距是描述生物组织微观结构和生物组织和超声散射特性和重要参数,文中构建并物理仿真了生物组织散射元一维超声散射模型,用小波变换方法估计了仿一物组织散射元的平均间距。     

Optical properties of high-density dispersions of particles: application to intralipid solutions

We propose to study the scattering properties of dense distributions of spherical scatterers by resorting to an iterative solution of the Foldy-Twersky equation for the propagation of the coherent field. As a result of the first step of the iterative procedure, the host medium is substituted by an effective medium of complex refractive index to account for the multiple-scattering processes that occur among the particles. Although we truncate the above-mentioned iterative procedure to the second step, the results of our calculations are in excellent agreement with previous experimental results of Zaccanti et al. ("Measurement of optical properties of high-density media," to be published in Applied Optics) for the scattering coefficient of Intralipid solutions up to a volume density of 15% and show a limited disagreement at a volume density of 22%.     

Electromagnetic phase differences in the coherent backscattering enhancement mechanism for random media consisting of large nontransparent spheres

Phase curves of intensity are calculated for light scattering in media randomly packed with large nontransparent spheres (x=125), the surfaces of which reflect according to the Fresnel equations. We consider three values of refractive index: m = 0.73 + i5.93 (metal Al), 1.6 + i1.72 (metal Fe), and 1.5 + i0.1 (black glass). We use a Monte Carlo ray-tracing approach. Different kinds of electromagnetic phase differences of reciprocal trajectories are investigated for the second and third orders of scattering; the highest orders give comparatively small contributions due to the backward-scattering indicatrix of large nontransparent spheres. We find that the main electromagnetic phase difference between the direct and time-reversal (reciprocal) trajectories is the outer phase difference that depends only on the relative positions of the first and last points of the ray reflections and the phase angle. The inner phase difference is connected with the changing path length of the ray inside the medium. This depends on the particle size and the phase angle that is the angle between the source and receiver from the scatterer, i.e., 180 degrees minus the scattering angle. The inner phase difference can give oscillations in the phase curve consisting of second-order components if the medium consists of strictly monodisperse spheres. Usually the coherent backscattering enhancement is calculated ignoring the shadow-hiding effect. We show that accounting for the shadowing of the reciprocal trajectory is important for the formation of the backscattering effect. The third-order scattering surge is a superposition of wide and narrow opposition spikes that correspond to two different types of scattering trajectories, closed and opened ones. The first type is due to scattering by two particles; the second one corresponds to scattering by three particles.     

Depolarization and blurring of optical images by biological tissue

We present a study of the image blurring and depolarization resulting from the transmission of a narrow beam of light through a continuous random medium. We investigate the dependence of image quality degradation and of depolarization on optical thickness, correlation length of the inhomogeneities, and incident polarization state. This is done numerically with a Monte Carlo method based on a transport equation that takes into account polarization of light. We compare our results with those for transport in media with discrete spherical scatterers. We show that depolarization effects are different in these two models of biological tissue.     

Intervening attenuation affects first-order statistical properties of ultrasound echo signals

Previous studies show that first-order statistical properties of ultrasound echo signals are related to the effective number of scatterers in the "resolution cell" of a pulse-echo ultrasound system. When the effective number of scatterers is large (~10 or more) this results in echo signals whose amplitude follows a Rayleigh distribution, with the RF echo signal obeying Gaussian statistics; deviation from Rayleigh or Gaussian statistics yields information on scatterer number densities. In this paper, the influence of the medium's attenuation on non-Gaussian properties of the echo signal is considered. Preferential attenuation of higher frequency components of a pulsed ultrasound beam effectively broadens the beam and increases the resolution cell size. Thus, the resultant non-Gaussian parameter for broad bandwidth excitation of the transducer depends not only on the scatterer number density but also on the attenuation in the medium. These effects can be reduced or eliminated by using narrow-band experiments.     

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.     

Quantitative modeling of the anisotropy of ultrasonic backscatterfrom canine myocardium

Reports extensions and new results of the First Time Domain Born approximation model used by Mottley and Miller (1982) to describe the anisotropy of ultrasonic backscatter measured in canine myocardium. The interaction of an ultrasonic plane wave impulse with a single cylindrical scatterer using time and frequency domain approaches is reviewed. Myocardial tissue is modeled as a suspension of aligned cylindrically shaped scatterers uniformly distributed in a homogeneous medium. The authors propose extensions to this model to deal with nonideal scatterer orientation, by introducing axial distribution functions and scatterer size distributions based on histology, modeled as a uniform distribution. The backscatter coefficient in the range 2.0-8.0 MHz is calculated. An algorithm to compute the average differential scattering cross section is presented. Ultrasonic elastic properties of myocardial tissue are discussed. Results of the anisotropy of the numerically computed backscatter parameters for model media having nominal mechanical and acoustic properties of canine myocardial tissue are presented and compared to available experimental data along with discussion of possible conclusions     

Implementing the near- to far-field transformation in the finite-difference time-domain method

When the finite-difference time-domain (FDTD) method is applied to light-scattering computations, the far fields can be obtained by means of integrating the near fields either over the volume bounded by the particle's surface or on a regular surface encompassing the scatterer. For light scattering by a sphere, the accurate near-field components on the FDTD-staggered meshes can be computed from the rigorous Lorenz-Mie theory. We investigate the errors associated with these near- to far-field transform methods for a canonical scattering problem associated with spheres. For a scatterer with a small refractive index, the surface-integral approach is more accurate than its volume counterpart for computation of the phase functions and extinction efficiencies; however, the volume-integral approach is more accurate for computation of other scattering matrix elements, such as P12, P32, and P43, especially for backscattering. If a large refractive index is involved, the results computed from the volume-integration method become less accurate, whereas the surface method still retains the same order of accuracy as in the situation for the small refractive index.     

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).     

Application of Mie theory to assess structure of spheroidal scattering in backscattering geometries

Inverse light scattering analysis seeks to associate measured scattering properties with the most probable theoretical scattering distribution. Although Mie theory is a spherical scattering model, it has been used successfully for discerning the geometry of spheroidal scatterers. The goal of this study was an in-depth evaluation of the consequences of analyzing the structure of spheroidal geometries, which are relevant to cell and tissue studies in biology, by employing Mie-theory-based inverse light scattering analysis. As a basis for this study, the scattering from spheroidal geometries was modeled using T-matrix theory and used as test data. In a previous study, we used this technique to investigate the case of spheroidal scatterers aligned with the optical axis. In the present study, we look at a broader scope which includes the effects of aspect ratio, orientation, refractive index, and incident light polarization. Over this wide range of parameters, our results indicate that this method provides a good estimate of spheroidal structure.