Multiple-scattering Media Research Articles

Experimental verification of a theory for the time-resolved fluorescence spectroscopy of thick tissues

Fluorescence spectroscopy provides potential contrast enhancement for near-infrared tissue imaging and physiologically correlated spectroscopy. We present a fluorescence photon migration model and test its quantitative predictive capabilities with a frequency-domain measurement that involves a homogeneous multiple-scattering tissue phantom (with optical properties similar to those of tissue in the near infrared) that contains a fluorophore (rhodamine B). After demonstrating the validity of the model, we explore its ability to recover the fluorophore's spectral properties from within the multiple-scattering medium. The absolute quantum yield and the lifetime of the fluorophore are measured to within a few percent of the values measured independently in the absence of scattering. Both measurements are accomplished without the use of reference fluorophores. In addition, the model accurately predicts the fluorescence emission spectrum in the scattering medium. Implications of these absolute measurements of lifetime, quantum yield, concentration, and emission spectrum from within multiple-scattering media are discussed.

Imaging objects in tissuelike media with optical tagging and the diffuse photon differential transmittance.

In a proof-of-concept experiment, we optically tagged objects embedded in an inhomogeneous and multiple-scattering medium and measured the difference between the transmitted diffuse photons at two optical wave-lengths, one at and the other off a sharp absorption peak of the exogenous contrast agent. We demonstrated that the visibility of tagged objects was significantly enhanced in comparison with that of untagged objects. From our analysis it seems possible to use dual-wavelength differential transmittance spectrometry together with monoclonal-antibody-delivered optical contrast agents to detect tumors as small as 0.1-0.3 cm in size and embedded as deeply as a few centimeters beneath a tissue surface.

Imaging of dynamic heterogeneities in multiple-scattering media

A new method of visualizing objects with distinct internal dynamics of the constituent scattering particles embedded in a liquid multiple-scattering medium is presented. We report dynamic multiple-light-scattering experiments and a theoretical model, based on diffusing photon-density waves for concentrated colloidal suspensions in Brownian motion, as a background medium into which is inserted a capillary containing (i) the same suspension under flow, or (ii) suspensions of different particle sizes in Brownian motion. These model objects, with purely dynamic but no static scattering contrast, can be visualized by space-resolved measurements of the time autocorrelation function g2(t) of the scattered light intensity at the sample surface. Maximum contrast occurs at a parameter-dependent finite correlation time t. The physical origin of this effect is outlined. Our data are in excellent quantitative agreement with the model, with no adjustable parameter. © 1997 Optical Society of America. [S0740-3232(97)00701-1]

Theory of lasing in a multiple-scattering medium.

In several recent experiments, isotropic lasing action was observed in paints that contain rhodamine 640 dye molecules in methanol solution as gain media and titania particles as optical scatterers. These so-called paint-on laser systems are extraordinary because they are highly disordered systems. The microscopic mechanism for laser activity and the coherence properties of light emission in this multiple-light-scattering medium have not yet been elucidated. In this paper we derive the emission intensity properties of a model dye system with excited singlet and triplet electronic energy levels, which is immersed in a multiple-scattering medium with transport mean free path l*. Using physically reasonable estimates for the absorption and emission cross section for the singlet and triplet manifolds, and the singlet-triplet intersystem crossing rate, we solve the nonlinear laser rate equations for the dye molecules. This leads to a diffusion equation for the light intensity in the medium with a nonlinear intensity-dependent gain coefficient. Using this model we are able to account for nearly all of the experimentally observed properties of laser paint reported so far when l*\ensuremath{\gg}${\ensuremath{\lambda}}_{0}$, the emission wavelength. This includes the dependence of the peak intensity of amplified emission on the mean free path l*, the dye concentration \ensuremath{\rho}, and the pump intensity characteristics. Our model recaptures the collapse of the emission linewidth at a specific threshold pump intensity and describes how this threshold intensity varies with l*. In addition, our model predicts a dramatic increase in the peak intensity and a further lowering of the lasing threshold for the strong scattering limit l*\ensuremath{\rightarrow}${\ensuremath{\lambda}}_{0}$. This suggests a striking enhancement of the characteristics of laser paint near the photon localization threshold in a disordered medium. \textcopyright{} 1996 The American Physical Society.

Analysis of a diffuse-photon-density wave in multiple-scattering media in the presence of a small spherical object

We present a general analysis of the sensitivity of a diffuse photon density wave in a homogeneous multiple-scattering medium to the presence of a small spherical object. From our calculations in both infinite and semi-infinite geometry we derive the charge and dipole coefficients that typify the object’s most significant response.

Moments of multiple scattering

We present an analytical technique that solves exactly, and in closed form, for the first and second moments of the spatial and angular positions of photon distributions in a multiple-scattering medium. The analysis leads to simple analytic expressions for these moments, both conditioned on the number of scatterings and summed over all scattering events. The conventional results for small-angle forward scattering, and for the diffusion regime, are recovered in the appropriate limiting cases.

Propagation through optically thick media

An analytic model for propagation of an optical pulse through an optically thick multiple-scattering medium such as a cloud is developed. Both a narrow collimated and a broad Gaussian beam are considered incident at the entrance of the medium, which is assumed to be a plane-parallel slab of infinite horizontal extent. Analytic expressions are derived for the radiance and power received by an on-axis receiver at any distance beyond the exit plane of the medium. Calculations with these expressions are compared with published Monte Carlo results for an infinite-plane, π/2-field-of-view receiver at the exit plane of the medium. Calculated and simulated results show excellent agreement for optical thickness beyond approximately 20.

Enhanced backscattering from a volume-scattering medium behind a phase screen

The enhanced-backscattering (EBS) phenomenon is investigated for the case in which a phase screen is placed close to a multiple-scattering medium. This situation results in a narrowing of the EBS peak that depends on the strength and the position of the phase screen. The resulting enhancement peak is essentially the sum of two contributions: the EBS produced by the multiple-scattering medium in the absence of the phase screen and the enhancement obtained when the multiple-scattering medium is replaced by a plane mirror.

Photon migration in the presence of a single defect: a perturbation analysis

We present an analytical perturbation analysis for studying the sensitivity of diffusive photon flux to the addition of a small spherical defect object in multiple-scattering media such as human tissues. As a first simple application of our perturbation method, we derive analytically the photon migration path distributions and the shapes of the so-called banana regions in which the photon migration paths are concentrated. We then derive analytically the sensitivity of detected photon flux densities to the inclusion of small spherical defects in the multiple-scattering medium for both single-source and two-source configurations, at both steady-state (dc) and frequency-modulation conditions, and compare the results with Monte Carlo simulations.

Intensity Distributions of Waves Transmitted through a Multiple Scattering Medium.

The distributions of the angular transmission coefficient and of the total transmission are calculated for multiple scattered waves. The calculation is based on a mapping to the distribution of eigenvalues of the transmission matrix. The distributions depend on the profile of the incoming beam. The distribution function of the angular transmission has a stretched exponential decay. The total-transmission distribution grows log-normally whereas it decays exponentially.

Frequency-domain method for measuring spectral properties in multiple-scattering media: methemoglobin absorption spectrum in a tissuelike phantom

We have measured the optical absorption and scattering coefficient spectra of a multiple-scattering medium (i.e., a biological tissue-simulating phantom comprising a lipid colloid) containing methemoglobin by using frequency-domain techniques. The methemoglobin absorption spectrum determined in the multiple-scattering medium is in excellent agreement with a corrected methemoglobin absorption spectrum obtained from a steady-state spectrophotometer measurement of the optical density of a minimally scattering medium. The determination of the corrected methemoglobin absorption spectrum takes into account the scattering from impurities in the methemoglobin solution containing no lipid colloid. Frequency-domain techniques allow for the separation of the absorbing from the scattering properties of multiple-scattering media, and these techniques thus provide an absolute measurement of the optical absorption spectra of the methemoglobin/lipid colloid suspension. One accurately determines the absolute methemoglob in absorption spectrum in the frequency domain by extracting the scattering and absorption coefficients from the phase shift Φ and average light intensity DC (or Φ and the amplitude of the light-intensity oscillations AC) data with relationships provided by diffusion theory, but one determines it less accurately by using the Φ and modulation M (M ≡ AC/DC) data and the diffusion theory relationships. In addition to the greater uncertainty in the absorption and scattering coefficients extracted from the Φ and M data, the optical parameters extracted from the Φ and M data exhibit systematically inaccurate behavior that cannot be explained by random noise in the system. Possible reasons for the systematically lower accuracy of the methemoglobin absorption spectrum obtained from Φ and M data are discussed.

Surface reflections and multiple scattering in one, two, and three dimensions

Surface reflections in multiple-scattering media are treated theoretically for the coherent backscattering of light, the optical memory effect, time correlations in dynamical systems, and frequency correlations in static systems. A finite number of surface reflections and a finite separation between the surface of the scattering medium and the reflecting surface are included in the theory and are found to induce a variety of new effects. Simple, closed-form expressions are given for one, two, and three dimensions. The theory is found to be in good accord with recent experiments on the coherent backscattering of light.

Analytical solution to the optical transfer function of a scattering medium with large particles

A new analytical expression for the optical transfer function of multiple-scattering media such as clouds, mists, and dust aerosols is given in terms of their microphysical characteristics. The geometrical optics approximation is used to find local optical parameters of a scattering medium, including the simple approximation of the phase function, which is the key to the solution of the problem considered here. The optical transfer function is taken within a small-angle approximation of the radiative transfer theory. A comparison with Monte Carlo data shows a fairly satisfactory accuracy of our analytic formulas.

Effects due to geometry and boundary conditions in multiple light scattering.

Light propagation is measured through a multiple-scattering medium, and the scattering mean-free path is measured for different densities of scatterers. We analyze the effect of detector orientation relative to the light source, an effect of the anisotropy of the photon current. We compare light propagation in an infinite geometry to reflectance in a backscattering experiment. We compare to models for the boundary conditions applicable at the interface between the scattering medium and the adjacent free medium. These consist of linear combinations of absorbing and reflecting boundary conditions.

Location of objects in multiple-scattering media

When a small object is placed in a multiple-scattering medium the stationary diffusion equation can be used to derive the disturbance in the transmitted and backscattered light intensity. The diffusion equation will describe the intensity outside and inside the object. The object is characterized by a size, a diffusion constant, and an absorption length. In this way absorbing objects as well as nonabsorbing objects can be treated. The results are derived for two and three dimensions. Experiments are performed on suspended titanium dioxide particles in glycerine, wherein objects could be placed. There is good agreement between theory and experiment. This work shows that with the use of continuous light sources, it may be possible to recover the location of objects accurately inside a diffusive scattering medium.

Angular intensity and polarization dependence of diffuse transmission through random media

A simple theoretical model involving only a single sample parameter, the depolarization ratio ρ for linearly polarized normally incident and normally scattered light, is developed to describe the angular intensity and all other polarization-dependent properties of diffuse transmission through multiple-scattering media. Initial experimental results that tend to support the theory are presented. Results for diffuse reflection are also described.

Properties of photon density waves in multiple-scattering media

Amplitude-modulated light launched into multiple-scattering media, e.g., tissue, results in the propagation of density waves of diffuse photons. Photon density wave characteristics in turn depend on modulation frequency (omega) and media optical properties. The damped spherical wave solutions to the homogeneous form of the diffusion equation suggest two distinct regimes of behavior: (1) a high-frequency dispersion regime where density wave phase velocity V(p) has a radicalomega dependence and (2) a low-frequency domain where V(p), is frequency independent. Optical properties are determined for various tissue phantoms by fitting the recorded phase (?) and modulation (m) response to simple relations for theappropriate regime. Our results indicate that reliable estimates of tissue like optical properties can be obtained, particularly when multiple modulation frequencies are employed.

Numerical method for studying the detectability of inclusions hidden in optically turbid tissue

We introduce an efficient numerical method for studying the detectability of absorptive inclusions in a multiple-scattering optical medium. Use of the method is demonstrated by the forward calculation of integrated and time-gated photon intensities. Schemes for positioning the light source above an inclusion and otherwise determining the location of a hidden object, involving either reflected or transmitted reemissions, are discussed as examples. They are investigated for several illustrative models, and images are calculated as a function of the size and shape of the inclusion.

Surface correlations in multiple-scattering media.

Analytical forms for the short-range correlations present at the surface of a multiple-scattering medium are derived from diffusion theory

Time-reversal symmetry and image reconstruction through multiple-scattering media

Imaging through a multiple scatterer by using the time-reversal symmetry of double passage is analyzed, and a comparison is made with previous work for phase screens. An ensemble average over scatterer positions and a coherently reflecting object are assumed. The depolarization of the light as the result of multiple scattering and the means of separating the light that is returned by the object from the light that is returned by the random medium are discussed. Imaging through a single realization of the random medium is also considered.