Hyperbolic damped-wave models for transient light-pulse propagation in scattering media

Transient optical transport in highly scattering media such as tissues is usually modeled as a diffusion process in which the energy flux is assumed proportional to the fluence (intensity averaged over all solid angles) gradients. Such models exhibit an infinite speed of propagation of the optical signal, and finite transmission values are predicted even at times smaller than those associated with the propagation of light. If the hyperbolic, or wave, nature of the complete transient radiative transfer equation is retained, the resulting models do not exhibit such drawbacks. Additionally, the hyperbolic equations converge to the solution at a faster rate, which makes them very attractive for numerical applications in time-resolved optical tomography.     

Frequency-resolved interferometer measurements of polarized wave propagation in scattering media

An interferometric technique is utilized to measure both the time- and frequency-domain optical fields scattered by a random medium. The method uses a tunable continuous-wave laser source to make frequency-resolved measurements within a fixed-path-length interferometer. Measured frequency-domain field statistics, with a linearly polarized input, are shown to be zero-mean, circular complex Gaussian for both co- and cross-polarization states. With decreasing scatter, the extracted average impulse responses for co- and cross-polarized states show distinct differences, thereby providing insight into the scattering domain.     

Light propagation in multilayered scattering media beyond the diffusive regime

We describe a method to solve the radiative transfer equation (RTE) in multilayered geometry with index mismatch and demonstrate its potential for modeling light propagation in biological systems. The method is compared to Monte Carlo simulations with high accuracy but is much more efficient in terms of computer time. We illustrate the potential of the method by studying a multilayered system containing a weakly scattering layer surrounded by highly scattering layers, with anisotropic scattering and index mismatched interfaces. The calculation of directional transmitted fluxes has shown that the RTE method can be used to calculate relevant quantities in realistic systems in the presence of non-diffusive behavior.     

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.     

Beam propagation through uniaxial anisotropic media: global changes in the spatial profile

The propagation of electromagnetic beams through uniaxial anisotropic media is investigated. The Maxwell equations are solved in the paraxial limit in terms of the plane-wave spectrum associated with each Cartesian field component. Attention is focused on the global changes in the spatial structure of the beam, which are described by means of the second-order intensity moment formalism. In particular, the propagation law for the intensity moments through this kind of media is obtained. As a consequence it is inferred that it is possible to improve the beam-quality parameter by using these media.     

Role of higher-order scattering in solutions to the forward and inverse optical-imaging problems in random media

From analytical and numerical solutions that predict the scattering of diffuse photon density waves and from experimental measurements of changes in phase shift theta and ac amplitude demodulation M caused by the presence of single and double cylindrical heterogeneities, we show that second- and higher-order perturbations can affect the prediction of the propagation characteristics of diffuse photon density waves. Our experimental results for perfect absorbers in a lossless medium suggest that the performance of fast inverse-imaging algorithms that use first-order Born or Rytov approximations might have inherent limitations compared with inverse solutions that use iterative solutions of a linear perturbation equation or numerical solutions of the diffusion equation.     

Monte carlo procedure for investigating light propagation and imaging of highly scattering media

A Monte Carlo procedure has been developed to study photon migration through highly scattering nonhomogeneous media. When two scaling relationships are used, the temporal response when scattering or absorbing inhomogeneities are introduced can be evaluated in a short time from the results of only one simulation carried out for the homogeneous medium. Examples of applications to the imaging of defects embedded into a diffusing slab, a model usually used for optical mammography, are given. Comparisons with experimental results show the correctness of the results obtained.     

Crack scattering in polycristalline media

The attenuation of plane elastic compressional waves due to scattering by a distribution of thin circular cracks (in Rayleigh approximation) is compared to the attenuation due to grain-scattering in polycristalline media. An estimation of the range of crack distributions we are able to determine in such media by means of attenuation measurements is then proposed. The influence of porosity is also considered.     

Revised Kubelka-Munk theory. III. A general theory of light propagation in scattering and absorptive media

A generally applicable theoretical model describing light propagating through turbid media is proposed. The theory is a generalization of the revised Kubelka-Munk theory, extending its applicability to accommodate a wider range of absorption influences. A general expression for a factor taking into account the effect of scattering on the total photon path traversed in a turbid medium is derived. The extended model is applied to systems of ink-dyed paper sheets-mixtures of wood fibers with dyes-which represent examples of systems that have thus far eluded the original Kubelka-Munk model. The results of simulations of the spectral dependence of Kubelka-Munk coefficients of absorption and scattering show that they compare very well with those derived from experimental results.     

Beam propagation in parabolically tapered graded-index waveguides

To a good approximation, the electromagnetic-propagation characteristics of graded-index waveguides can be written in terms of polynomial-Gaussian modes. For uniform quadratic-index waveguides the behavior of these modes is well known. However, there are sometimes practical reasons for using tapered waveguides, but detailed propagation solutions are known for only a few specific taper functions. The parabolic taper is perhaps the most important special case, and the solution-generating techniques that we generalize are used to obtain analytic solutions for this case.     

Explosion propagation in inert porous media

Porous media are often used in flame arresters because of the high surface area to volume ratio that is required for flame quenching. However, if the flame is not quenched, the flow obstruction within the porous media can promote explosion escalation, which is a well-known phenomenon in obstacle-laden channels. There are many parallels between explosion propagation through porous media and obstacle-laden channels. In both cases, the obstructions play a duel role. On the one hand, the obstruction enhances explosion propagation through an early shear-driven turbulence production mechanism and then later by shock-flame interactions that occur from lead shock reflections. On the other hand, the presence of an obstruction can suppress explosion propagation through momentum and heat losses, which both impede the unburned gas flow and extract energy from the expanding combustion products. In obstacle-laden channels, there are well-defined propagation regimes that are easily distinguished by abrupt changes in velocity. In porous media, the propagation regimes are not as distinguishable. In porous media the entire flamefront is affected, and the effects of heat loss, turbulence and compressibility are smoothly blended over most of the propagation velocity range. At low subsonic propagation speeds, heat loss to the porous media dominates, whereas at higher supersonic speeds turbulence and compressibility are important. This blending of the important phenomena results in no clear transition in propagation mechanism that is characterized by an abrupt change in propagation velocity. This is especially true for propagation velocities above the speed of sound where many experiments performed with fuel-air mixtures show a smooth increase in the propagation velocity with mixture reactivity up to the theoretical detonation wave velocity.     

Wave propagation in anisotropic layered media

The determination of the natural modes of wave propagation in an anisotropic layered medium requires the solution of a transcendental eigenvalue problem that is usually approached numerically with the aid of search techniques. Such computations require great effort. The method presented in this paper provides an alternate solution to this problem in terms of a quadratic eigenvalue problem involving tridiagonal matrices, for which the eigenvalues can be found with great speed and accuracy. The technique is then illustrated by means of an example involving a cross-anisotropic Gibson solid.     

Wave propagation in unsaturated porous media

We present a simple macroscopical three-phase model describing wave propagation in partially saturated porous media. The model consists of a continuous non-wetting phase and a continuous wetting phase and is an extension of classical biphasic (Biot-type) models. The framework is based on kinematics, balance equations and well-known constitutive equations for single- and multi-phase continua. The final set of linearised equations gives information about the physical behaviour of three compressional waves and one shear wave. Among others, information about phase velocities, damping and displacements of the single constituents can be determined for arbitrary variations of input parameters like saturation or angular frequency (ω). The physical processes are investigated and explained by an example of Massilon sandstone filled with air and water. For the quasi-static limit case, i.e. \({\omega \mapsto 0}\) , the results of the model are identical with the phase velocity obtained with the well-known Gassmann–Wood limit. The model focuses on systems with a liquid and a gas phase. It is shown that the grain compressibility can be neglected in this case, and the amount of material parameters as well as the complexity reduces significantly compared to other three-phase approaches. This makes the well-adapted model suitable for direct application in the vadose zone or partially saturated laboratory samples with a gas phase and a liquid phase. The final model is characterised by low computational effort, general validity for application from geophysics over engineering up to biomedicine and flexibility for use of extended empirical and theoretical relationships.     

Narrow-beam propagation in a two-dimensional scattering medium

The problem of narrow-beam propagation in a medium with highly anisotropic scattering is considered within radiative transfer theory. A novel solution of the radiative transfer equation within small-angle approximation, accounting for the path length spread, is presented. A new stable numerical algorithm for the simulation of a narrow beam is developed and applied to a narrow beam in a two-dimensional scattering medium. A truly three-dimensional version of the proposed approach is formulated.     

Computer simulation of forward wave propagation in soft tissue

A method for simulating forward wavefront propagation in heterogeneous tissue is discussed. The intended application of this method is for the study of aberration produced when performing ultrasound imaging through a layer of soft tissue. A one-way wave equation that permits smooth variation in all acoustically important variables is derived. This equation also describes tissue exhibiting nonlinear elasticity and arbitrary frequency-dependent relaxation. A numerical solution to this equation is found by means of operator splitting and propagation along the spatial depth coordinate. The numerical solution is accurate when compared to analytical solutions for special cases, and when compared to numerical solutions of the full wave equation by other methods. The presented implementation provides a fast numerical method for studying the impact of aberration in medical ultrasound imaging through soft tissue--both on the transmitted beam and the nonlinearly generated harmonic beam.     

Spatial coherence in strongly scattering media

We study the spatial coherence of an optical beam in a strongly scattering medium confined in a slab geometry. Using the radiative transfer equation, we study numerically the behavior of the transverse spatial coherence length in the different transport regimes. Transitions from the ballistic to the diffusive regimes are clearly identified.     

Edge contribution to forward scattering by spheres

Edge functions T1 and T2, which describe the polarization-dependent edge contribution to forward scattering by spheres, are derived from the exact Mie solution. All the relative refractive indices and the 64 < x < 2048 size parameter range are considered. The edge functions significantly improve the approximation methods that can be used to calculate forward-scattering patterns. For m close to 1, an asymptotic approximation is used. Otherwise, the familiar geometrical optics approximation and the similar physical optics approximation for glory rays are used. Both geometrical and physical optics equations can be deduced from the above-mentioned asymptotic approximation.