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.     

Spatial quantum correlations in multiple scattered light

We predict a new spatial quantum correlation in light propagating through a multiple scattering random medium. The correlation depends on the quantum state of the light illuminating the medium, is infinite in range, and dominates over classical mesoscopic intensity correlations. The spatial quantum correlation is revealed in the quantum fluctuations of the total transmission or reflection through the sample and should be readily observable experimentally.     

Polarization properties of light multiply scattered by non-spherical Rayleigh particles

Multiple scattering of incoherent polarized light propagating through a random medium comprised of spheroidal Rayleigh particles is studied using Monte Carlo simulations. Two approaches are taken for the implementation of the simulation: the first uses individual realizations of particle orientation and the second, an accelerated method, averages over the particle orientation. These different methods produce results that are indistinguishable within statistical errors. The depolarization of light is examined in both transmission and backscatter for media comprised of spheroids of different polarizability ratios. In media containing spheroidal particles the depolarization is greater than that for spherical particles. Media containing prolate spheroids are more depolarizing than media comprising oblate particles of the same polarizability ratio. The extra depolarization due to asphericity is much less pronounced in the multiple scattering regime than for single scattering.     

Polarization properties of light multiply scattered by non-spherical Rayleigh particles

Abstract

Multiple scattering of incoherent polarized light propagating through a random medium comprised of spheroidal Rayleigh particles is studied using Monte Carlo simulations. Two approaches are taken for the implementation of the simulation: the first uses individual realizations of particle orientation and the second, an accelerated method, averages over the particle orientation. These different methods produce results that are indistinguishable within statistical errors. The depolarization of light is examined in both transmission and backscatter for media comprised of spheroids of different polarizability ratios. In media containing spheroidal particles the depolarization is greater than that for spherical particles. Media containing prolate spheroids are more depolarizing than media comprising oblate particles of the same polarizability ratio. The extra depolarization due to asphericity is much less pronounced in the multiple scattering regime than for single scattering.     

Heterodyne detection of multiply scattered monochromatic light with a multipixel detector

A new technique is presented for measuring the spectral broadening of light that has been multiply scattered from scatterers in motion. In our method the scattered light is detected by a heterodyne receiver that uses a CCD as a multipixel detector. We obtain the frequency spectrum of the scattered light by sweeping the heterodyne local oscillator frequency. Our detection scheme combines a high optical etendue (product of the surface by the detection solid angle) with an optimal detection of the scattered photons (shot noise). Using this technique, we measure, in vivo, the frequency spectrum of the light scattered through the breast of a female volunteer.     

Determination of g and mu using multiply scattered light in turbid media

We propose an inversion scheme to reconstruct the scattering coefficient mu and the anisotropy factor g that characterize the optical properties of a turbid medium. It is based on a theory for the scattering of light inside the medium from an angularly collimated light source. We demonstrate the feasibility of this method using light scattering data obtained from a Monte Carlo simulation.     

Mechanisms of ultrasonic modulation of multiply scattered incoherent light based on diffusion theory

An analytic equation interpreting the intensity of ultrasound-modulated scattering light is derived,based on diffusion theory and previous explanations of the intensity modulation mechanism.Furthermore,an experiment of ultrasonic modulation of incoherent light in a scattering medium is developed.This analytical model agrees well with experimental results,which confirms the validity of the proposed intensity modulation mechanism.The model supplements the existing research on the ultrasonic modulation mechanism of scattering light.     

Vector statistics of multiply scattered light in a random medium with large inhomogeneities

The distribution function of the scattered radiation intensity is calculated in the approximation of the basic polarization modes. In such an approximation, the distribution function is represented in terms of the degree of polarization of the initially circularly and linearly polarized waves transmitted by the sample. The effect of the difference of the decay rates for the circular and linear polarization modes on the statistics of the light waves that are multiply scattered in the medium with large inhomogeneities is analyzed.     

Average intensity of multiply scattered waves

The methods of the theory of multiple wave scattering are applied to a calculation of the mean intensity of radiation above a jagged rough surface under conditions such that shadowing and scattering form an intricate multipath structure on the part of the scalar field. The multiple wave scattering is described in the Twersky approximation, and a relationship of the given problem to the radiative transfer problem in an infinite plane-parallel layer is indicated. Expressions are derived for the coherent and incoherent components of the intensity at interior points of the layer, and the dependence of the mean value of the total intensity on the distance, radiation wavelength, and other parameters of the problem is analyzed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 85–90, May, 1984.     

Depolarization of multiply scattered light in transmission through a turbid medium with large particles

An approximate analytical method for solving the vector radiative transfer equation is proposed. The method is based on the assumption that single scattering of light by large-scale inhomogeneities occurs predominantly through small angles. The method is applied to calculate the polarization state of multiply scattered light. The results obtained are discussed for various turbid media.     

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.     

Doppler effect's contribution to ultrasonic modulation of multiply scattered coherent light: Monte Carlo modeling

Modulation of light by ultrasound in turbid media is investigated by modified public domain software based on the Monte Carlo algorithm. Apart from the recognized modulation mechanisms, originating in scatterers' displacements and refractive index modulation, an additional mechanism, evolving from Doppler shift during photon scattering, is considered. Comparison of the relative contributions from all three mechanisms to light modulation by ultrasound is performed for different medium scattering properties and ultrasound frequencies. Refractive index modulation remains the strongest mechanism for light modulation by ultrasound, but for high ultrasound frequencies and for large scattering coefficients the Doppler effect can become dominant.     

Speckle correlations in the light scattered from weakly rough random metal surfaces

Abstract

Diagrammatic perturbation theory and computer simulation methods are used to compute the angular intensity correlation function C(q, k|q′,k′)=([I(q|k) - (I(q|k))] × [I(q′|k′) - (I(q′|k′))]) for p-polarized light scattered from a weakly rough, one-dimensional random metal surface. I(q|k) is the squared modulus of the scattering matrix for the system, and q, q′ and k, k′ are the projections on the mean scattering surface of the wavevectors of the scattered and incident light, respectively. Contributions to C include: (a) short-range memory effect and time-reversed memory effect terms, C ⁽¹⁾; (b) an additional short-range term of comparable magnitude C ⁽¹⁰⁾; (c) a long-range term C ⁽²⁾; (d) an infinite-range term C ⁽³⁾; and (e) a term C ^(1.5) that along with C ⁽²⁾ displays peaks associated with the excitation of surface plasmon polaritons. The diagrammatic methods are also extended to treat the angular intensity correlation function for the scattering of p to p, p to s, s to p, and s to s polarizations of light from a two-dimensional randomly rough surface. These correlations are again described in terms of C ⁽¹⁾, C ⁽¹⁰⁾, C ^(1.5), C ⁽²⁾, and C ⁽³⁾ contributions to C for the two-dimensional surfaces. Short-range memory and time-reversed memory effects are observed in the two-dimensional C ⁽¹⁾ correlations, and peaks associated with the excitation of surface polaritons are observed in the two-dimensional C ^(1.5) and C ⁽²⁾ correlations. Most of the results for the one- and two-dimensional systems are presented for incident electromagnetic plane waves. In addition, results for one-dimensional systems are presented for incident electromagnetic beams of finite width. Some of the results for one-dimensional surfaces are corroborated by means of computer simulation techniques.     

Probability distribution of singly and multiply scattered light near the critical point of a binary mixture

The probability density function p(I) is theoretically and experimentally investigated in the case of single, double, and multiple light scattering near a second-order transition (demixing of the binary mixture nitrobenzene and n-hexane). Experimentally we find no differences between the statistics of singly, doubly or multiply scattered light, and as expected from theory, p(I) shows an exponential variation. These results justify the use of either heterodyne or homodyne techniques for studying single or multiple scattering close to a critical point. We also describe a particularly simple way of determining whether homodyne or heterodyne detection occurs.     

Calculation of angular distribution of multiply scattered ions

A SCAT program is developed for calculation of the angular distribution of multiply scattered ions in the case of various interaction potentials. The accuracy attained is higher than that obtained with the well-known Meyer and Sigmund programs. The influence of the interaction potential on the angular distribution of multiply scattered ions is analyzed. A good agreement between the angular distribution calculated by the SCAT program and the experimental data and the results of simulation by the Monte Carlo method is observed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 103–107, August, 1993.     

Quantum and classical correlations in tripartite Gaussian states of light

We demonstrate an optical scheme involving two interlinked nonlinear interactions taking place simultaneously in a second-order nonlinear crystal. The three-mode output state is fully inseparable and endowed with perfect photon-number correlations among the generated fields. In order to discriminate between classical and quantum correlations we evaluate the quantum noise reduction, i.e. compare the fluctuations of the difference photocurrent between one mode and the sum of the other two with those coming from three uncorrelated coherent states. Preliminary results indicate that our scheme may achieve three-mode sub-shot noise correlations with current technology.     

High angle phase modulated low coherence interferometry for path length resolved Doppler measurements of multiply scattered light

We describe an improved method for coherence domain path length resolved measurements of multiply scattered photons in turbid media. An electro-optic phase modulator sinusoidally modulates the phase in the reference arm of a low coherence fiber optic Mach-Zehnder interferometer, at a high phase modulation angle. For dynamic turbid media this results in Doppler broadened phase modulation interference peaks at the modulation frequency and its multiples. The signal to noise ratio is increased by almost one order or magnitude for large modulation angles and the shape of the spectral peaks resulting from the interference of Doppler shifted sample waves and reference light is not changed. The path length dependent Doppler broadening is compared with the theoretical predictions in the single scattered and diffusive regimes. The experimentally measured optical path lengths are validated with the Monte Carlo technique.     

Speckle correlations in the light scattered from a weakly rough one-dimensional random metal surface

Perturbation theory is used to compute the angular-intensity correlation function C(q, k|q(?), k(?)) = ?[I(q|k) - ?I(q|k)?][I(q(?)|k(?)) - ?I(q(?)|k(?))]? for p-polarized light scattered from a weakly rough, one-dimensional random metal surface. I(q|k) is the squared modulus of the scattering matrix for the system, and q , q(?) and k , k(?) are the projections on the mean scattering surface of the wave vectors of the scattered and the incident light, respectively. Contributions to C include (a) short-range memory effect and time-reversed memory effect terms, C((1)) ; (b) an additional short-range term of comparable magnitude C((10)) ; (c) a long-range term C((2)) ; (d) an infinite-range term C((3)) ; and (e) a new term C((1.5)) that along with C((2)) displays peaks associated with the excitation of surface polaritons. These new features arise when the factorization approximation is not made in calculating the correlation function C .