Correlation transfer and diffusion of ultrasound-modulated multiply scattered light

We develop a temporal correlation transfer equation (CTE) and a temporal correlation diffusion equation (CDE) for ultrasound-modulated multiply scattered light. These equations can be applied to an optically scattering medium with embedded optically scattering and absorbing objects to calculate the power spectrum of light modulated by a nonuniform ultrasound field. We present an analytical solution based on the CDE and Monte Carlo simulation results for light modulated by a cylinder of ultrasound in an optically scattering slab. We further validate with experimental measurements the numerical calculations for an actual ultrasound field. The CTE and CDE are valid for moderate ultrasound pressures and on a length scale comparable with the optical transport mean-free path. These equations should be applicable to a wide spectrum of conditions for ultrasound-modulated optical tomography of soft biological tissues.     

Auto-correlation Properties of Scattering Light in Ultrasound-modulated Random Media

In this paper, the auto-correlation properties of scattering light in random media modulated by ultrasound were studied. The expression of temporal auto-correlation function of scattering light amplitude in the ultrasound-modulated media was presented. The results show that the auto-correlation function is modulated as the ultrasound is introduced into the media and the modulation amplitude decays with correlation time. The influences of ultrasound amplitude, Brownian diffusion coefficient, scattering and absorption coefficients on auto-correlation function were discussed. The auto-correlation imaging of an object hidden in random media was also studied by the use of Monte Carlo simulations.     

Auto-correlation Properties of Scattering Light in Ultrasound-modulated Random Media

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Multiple-scattering suppression in dilute and concentrated colloidal dispersions

Summary We describe the design and operation of an improved two-colour dynamic light scattering (TCDLS) equipment which effectively suppresses multiple scattering and allows the study of the Brownian dynamics of optically turbid samples. The technique operates by cross correlating scattered light of two different colours. With the appropriate scattering geometry, only singly scattered light contributes to the time-dependent part of the measured intensity cross-correlation function thus allowing straightforward interpretation of the data. To test the performance of the instrument we have studied several dilute colloidal suspensions, which, although dilute enough that free diffusion of the particles can be assumed, ranged from quite transparent to distinctly turbid. We have confirmed that the measured cross-correlation functions accurately reflect only single scattering even in the presence of strong multiple scattering. As a first application of the technique, we have performed light scattering measurements on concentrated suspensions of PMMA particles in cis-decalin. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Analysis of light propagation in highly scattering media by path-length-assigned Monte Carlo simulations

Numerical analysis of optical propagation in highly scattering media is investigated when light is normally incident to the surface and re-emerges backward from the same point. This situation corresponds to practical light scattering setups, such as in optical coherence tomography. The simulation uses the path-length-assigned Monte Carlo method based on an ellipsoidal algorithm. The spatial distribution of the scattered light is determined and the dependence of its width and penetration depth on the path-length is found. The backscattered light is classified into three types, in which ballistic, snake, and diffuse photons are dominant.     

Similarity effects in multiple scattering of coherent radiation: Phenomenology and experiments

Based on phenomenological concepts of statistics of effective optical paths for multiple scattering of coherent radiation, an analysis is carried out of similarity effects observed for the dependences of statistical moments of the scattered field on the relaxation parameters with a dimension of reciprocal length. Within the framework of the diffusion approximation, expressions are obtained that describe the autocorrelation function of fluctuations of the scattered-field amplitude, the degree of polarization, and the normalized intensity of scattered light for media with a finite absorption length in the case of forward scattering of coherent radiation in a plane layer of an isotropic scattering medium. The results of the analysis show the similarity of the dependences of these quantities on the corresponding spatial scales. Experiments with model scattering media (aqueous suspensions of polystyrene spherical particles) supported the existence of similarity effects in multiple scattering. An experimental study was made of the relation between the characteristic depolarization length and the transport length for multiple scattering of coherent radiation in a plane layer. The effective value of the radiation diffusion coefficient providing the best agreement between the experimental and the calculated values of parameters of the scattered field is shown to be independent of the absorption coefficient of a medium.     

Beam radiated from quasi-homogeneous uniformly polarized electromagnetic source scattering on quasi-homogeneous media

We study the coherence properties of the field generated by beam radiated from quasi-homogeneous (QH) electromagnetic source scattering on QH media. Formulas for the spectral density and spectral degree of coherence of the three dimensional scattered field are derived. The results show under assumption that the diagonal correlation coefficients of the source are proportional to each other, the far field of the scattered light satisfy two reciprocity relations analogous to that in the scalar case, that, the spectral density is proportional to the convolution of the spectral density of the source and the spatial Fourier transform of the correlation coefficient of the scattering potential; the spectral degree of coherence is proportional to the convolution of the diagonal correlation coefficients and the strength of the scattering potential.     

Dynamic Light Scattering Measurement of Nanometer Particles in Liquids

Dynamic light scattering (DLS) techniques for studying sizes and shapes of nanoparticles in liquids are reviewed. In photon correlation spectroscopy (PCS), the time fluctuations in the intensity of light scattered by the particle dispersion are monitored. For dilute dispersions of spherical nanoparticles, the decay rate of the time autocorrelation function of these intensity fluctuations is used to directly measure the particle translational diffusion coefficient, which is in turn related to the particle hydrodynamic radius. For a spherical particle, the hydrodynamic radius is essentially the same as the geometric particle radius (including any possible solvation layers). PCS is one of the most commonly used methods for measuring radii of submicron size particles in liquid dispersions. Depolarized Fabry-Perot interferometry (FPI) is a less common dynamic light scattering technique that is applicable to optically anisotropic nanoparticles. In FPI the frequency broadening of laser light scattered by the particles is analyzed. This broadening is proportional to the particle rotational diffusion coefficient, which is in turn related to the particle dimensions. The translational diffusion coefficient measured by PCS and the rotational diffusion coefficient measured by depolarized FPI may be combined to obtain the dimensions of non-spherical particles. DLS studies of liquid dispersions of nanometer-sized oligonucleotides in a water-based buffer are used as examples.     

Feasibility of glucose monitoring based on Brownian dynamics in time-domain optical coherence tomography

Our purpose is to investigate the feasibility of Brownian motion in time-domain optical coherence tomography (OCT) incorporated with wavelet power spectrum to monitor glucose concentration in Intralipid solution. The results show that the standard deviation (SD) of frequency in the superficial layer of single scattering region, linearly proportional to Brownian diffusion coefficient, is independent of the depth. Our preliminary results demonstrate that average SD of frequency in the single scattering region is inversely proportional to the glucose concentration in Intralipid solution, since the Brownian diffusion coefficient is a function of concentration. Thus the average SD of frequency in OCT signal is capable of differentiating the glucose concentration.     

Coherent transverse speckle dynamics in the case of probing of stationary bulk scattering media by a laser with frequency deviation

A coherent transverse dynamics of scattered speckle fields that arises upon propagation of tunable laser radiation through stationary optically inhomogeneous bulk media has been discovered. The dynamic photochromic speckle effect can be observed experimentally if the deviation of the laser radiation frequency is comparable with or greater than the effective phase delays arising upon scattering of waves in a random or partly organized medium. It was found experimentally that, with an increase in the frequency tuning range of a probing laser diode (λ = 650 nm) or a compact YAG:Nd laser (λ = 532 μm), which can reach hundreds of gigahertz for multiply scattering bulk media from several millimeters to two centimeters thick (fluoroplastic phantoms), the two-dimensional correlation coefficient of speckle structures decreased monotonically, and the characteristic drop for thicker structures was observed at smaller frequency detunings.     

Propagation of polarized light in media with large discrete inhomogeneities

An approximate analytical method of solution of the vector radiative-transfer equation for an optically isotropic medium with large-scale inhomogeneities is proposed. The method is based on an assumption about the distinct anisotropy of single scattering. The method was used to calculate the polarization characteristics of light multiply scattered in a monodisperse medium with large spherical particles.     

Mechanisms of ultrasonic modulation of multiply scattered coherent light: a Monte Carlo model

A Monte Carlo model of the ultrasonic modulation of multiply scattered coherent light in scattering media is provided. The model is based on two mechanisms: the ultrasonic modulation of the index of refraction, which causes a modulation of the optical path lengths between consecutive scattering events, and the ultrasonic modulation of the displacements of scatterers, which causes a modulation of optical path lengths with each scattering event. Multiply scattered light accumulates modulated optical path lengths along its path. Consequently, the intensity of the speckles that are formed by the multiply scattered light is modulated. The contribution from the index of refraction is comparable with the contribution from displacement when the acoustic-wave vector is less than a critical fraction of the transport mean free path and becomes increasingly greater than the contribution from displacement beyond this critical point. This Monte Carlo model agrees well with an independent analytical model for isotropically scattering media. Both mechanisms are coherent phenomena, requiring the use of a coherent light source.     

Analysis of non-ergodic behaviour in spatio-temporal coherence properties of speckle light

Spatio-temporal coherence properties of light scattered by rough surfaces that leads to speckle fluctuations are analysed. It is demonstrated that the scattered light is non-ergodic with the disorder due to the scattering process. Although the mutual coherence matrix vanishes with isotropic polarization fluctuations, it is shown that spatio-temporal coherence properties can be described with interference experiments that can be obtained between different speckles of the scattered light. For non-singular scattering processes, the maximal value of the modulus of the Wolf degree of coherence is analysed in the spatial time domain. This approach is also applied to totally unpolarized incident light with an isotropic and spatially independent scattering process. The mean value and the standard deviation of the Wolf degree of coherence are then determined from the coherence properties of the incident light.     

Correlation spectroscopy measurements of particle size using an optical fiber probe

We propose measuring the size of particles suspended in a liquid by light beating spectroscopy of scattered light using an optical fiber probe inserted into a medium and consisting of three multimode optical fibers. One of them is used to transmit light, the other two — to transmit scattered light to a unit providing its spatial coherence and further to a photodetector. In very turbid media, the multiple-to-single light-scattering spectral line width ratio is determined by the ratio of line widths in two collecting optical fibers. Then the particle size is determined by the spectrum of multiple rather than single scattering.     

Slow diffusion of light in a cold atomic cloud

We study the diffusive propagation of multiply scattered light in an optically thick cloud of cold rubidium atoms illuminated by a quasiresonant laser beam. In the vicinity of a sharp atomic resonance, the energy transport velocity of the scattered light is almost 5 orders of magnitude smaller than the vacuum speed of light, reducing strongly the diffusion constant. We verify the theoretical prediction of a frequency-independent transport time around the resonance. We also observe the effect of the residual velocity of the atoms at long times.     

Ultrasound detection through turbid media

Optical coherence-domain reflectometry and laser-based ultrasound detection have been combined with the use of adaptive optics to detect ultrasound through turbid media. The dynamic hologram in a photorefractive quantum-well device performs as a coherence gate that eliminates multiply scattered background. Quadrature homodyne detection conditions are selected by the choice of center wavelength of the pulse spectrum, requiring no active stabilization or feedback. A depth resolution of 30 microm was achieved, with a pulse duration of nominally 120 fs for ultrasound detection through turbid media up to optical thicknesses of 11 mean free scattering lengths.     

M-mode swept source optical coherence tomography for quantification of salt concentration in blood: An in vitro study

We report the use of M-mode swept source optical coherence tomography (SS-OCT) for measuring sodium chloride (NaCl) salt concentrations in liquid phantoms and in drawn whole blood based on temporal dynamics of light scattering. The Brownian motion of scattering particle is affected due to the change in viscosity of liquid. An autocorrelation function was determined from the power spectrum of SS-OCT signal and then was fit by mono and double exponential function to obtain decorrelation time. These translational decorrelation times corresponding to translational diffusion coefficients enabled us to find the controlled viscosity of the medium. The viscosities of the media were compared with literature values and a fair/excellent agreement was observed. Thus, the technique has ability to quantify the salt levels in terms of viscosity in nonflowing medium suspensions and many research routes necessary to determine its potential for in-vivo applications.     

Polarization preservation in diffusive scattering from in vivo turbid biological media: effects of tissue optical absorption in the exact backscattering direction

There is considerable recent interest in using polarized light to investigate turbid biological media. Although tissue multiple scattering randomizes incident polarization states, there are circumstances when appreciable degree of polarization can be observed in diffusive scattering. In this study, we use polarization modulation and synchronous detection to examine in the exact backscattering direction the polarization properties of diffusely reflected visible light from hands of human volunteers of varying pigmentation levels. The surviving polarization fraction increases with increasing pigmentation, likely due to preferential loss of highly scattered, long-pathlength photons; this mechanism lowers the average pathlength traversed by the detected light and hence increases the measured polarization preservation. This behavior is contrasted with the overall diffuse reflectance intensity, whose magnitude decreases with increasing absorption. These experiments demonstrate the important influences of medium optical properties on the polarization characteristics of multiply scattered light, which must be further investigated to enable quantitative polarization evaluation of turbid media such as biological tissues.     

Effect of the spatial distribution of probe beam on the results of measurements of the disperse composition of nanoparticles by dynamic light scattering method

The model of dynamic scattering on a finite ensemble of Brownian particles in liquid is considered. It is shown that an artifact characteristic relaxation time appears in the autocorrelation function of the scattered light intensity, which is much longer than the correlation time controlled by particle diffusion in the scattering volume.     

Modeling of Multiple Scattering Effects in Fraunhofer Diffraction Particle Size Analysis

A model for the direct problem of calculating the forward scattering signature of a multiple scattering medium is presented. The new formulation is optimized for integration into schemes for reconstructing the particle size distribution from laser diffraction (forward scattering) signatures obtained from optically thick media. The analysis is valid for media where the particle sizes and interparticle spacings are large (relative to the wavelength and the particle size, respectively) such that Fraunhofer diffraction theory adequately describes the properties of the forward scattered light from individual scattering events. The simulated performance of laser diffraction particle sizing instruments was then studied using predictions of the scattered light signatures which would be measured by laser diffraction instrument under multiple scattering conditions. The results were compared with experimental data and theoretical calculations based on other models.