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.     

Light scattering by a random distribution of particles embedded in absorbing media: diagrammatic expansion of the extinction coefficient

We address the problem of the modeling of the extinction coefficient into an absorbing medium, including a random distribution of identical scatterers of arbitrary size. We show that the extinction coefficient, including losses in the host medium, can be derived from a diagrammatic expansion arising from the rigorous multiple-scattering theory of electromagnetic waves in random media. While in previous approaches the contribution to the extinction coefficient due to the absorption in the host medium and due to the absorption and scattering by the particles were evaluated separately and heuristically, our approach is based on a derivation from first principles.     

Properties of a diffused photon-pair density wave in a multiple-scattering medium

A novel diffused photon-pair density wave (DPPDW) composed of correlated polarized photon pairs at different temporal frequencies and orthogonal linearly polarized states is proposed. A theory of DPPDWs is developed. A DPPDW selected by coherence gating and polarization gating that satisfies the diffusion equation has been verified experimentally. The sensitivity of amplitude and phase detection of the heterodyne signal has been improved by the properties of synchronized detection and common-path propagation of polarized pair photons in a multiple-scattering medium. Both reduced scattering coefficient micro2s' and absorption coefficient micro2alpha of the scattering medium in terms of the measured phase and amplitude of the heterodyne signal have been obtained. The detection sensitivity of micro2s' and micro2alpha and the properties of a DPPDW in a multiple-scattering medium are discussed and analyzed.     

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.     

Dynamic light scattering in subdiffusive regimes

For describing the fluctuating signal scattered from a multiple-scattering system, diffusive-wave spectroscopy makes use of a diffusion model that provides the path-length distribution of scattered waves for a specific geometry. Using the recently introduced optical path-length spectroscopy, we show that the diffusion model fails to describe wave propagation in the low-order multiple-scattering regime. We propose a new methodology with which to obtain information about the dynamic properties of nondiffusive scattering systems. We use optical path-length spectroscopy to obtain experimentally the path-length distribution of optical waves scattered from dynamic colloids, which are multiply scattering but not in the diffusion limit. The experimental results show that, with this new technique, the accuracy of dynamic measurements is significantly improved in subdiffusive scattering regimes.     

Average path-length parameter of diffuse light in scattering media

We use Monte Carlo simulations to study in detail the propagation of light in a plane-parallel medium containing scattering particles. In particular, we compute the forward and backward average path-length parameters (FAPP and BAPP, respectively) of four-flux radiative transfer models as functions of the optical depth. Strong dependence on the single scattering albedo and phase function asymmetry is found for both quantities. In general the values of the FAPP decrease with increasing absorption, whereas the opposite occurs for the BAPP. A similar effect is produced when changing from isotropic phase functions to phase functions with a large asymmetry in the forward direction. We present analytical results for the asymptotic values of the FAPP and BAPP as functions of albedo for the particular case of isotropic scattering. Our results differ markedly from the predictions obtained recently with two multiple-scattering models by Vargas and Niklasson [J. Opt. Soc. Am. A 14, 2243 (1997); Appl. Opt. 36, 3735 (1997)]. The differences found point out the intrinsic limitations of these models.     

Ballistic attenuation of low-coherence optical fields

Using a novel experimental geometry, we measured the ballistic attenuation of low-coherence optical fields propagating in multiple-scattering media. The high dynamic range and the angular filtering capability permit detecting the ballistic component through random media thicker than 20 mean free paths. Owing to the accuracy of the technique, we observe deviations from the standard Lambert-Beer law that are induced by the broad incident optical spectrum. We discuss the significance of these observations, their dependence on the type of scattering, and several potential applications.     

Quantifying Lipid Contents in Enveloped Virus Particles with Plasmonic Nanoparticles

Phosphatidylserine (PS) and monosialotetrahexosylganglioside (G_M1) are examples of two host‐derived lipids in the membrane of enveloped virus particles that are known to contribute to virus attachment, uptake, and ultimately dissemination. A quantitative characterization of their contribution to the functionality of the virus requires information about their relative concentrations in the viral membrane. Here, a gold nanoparticle (NP) binding assay for probing relative PS and G_M1 lipid concentrations in the outer leaflet of different HIV‐1 and Ebola virus‐like particles (VLPs) using sample sizes of less than 3 × 10⁶ particles is introduced. The assay evaluates both scattering intensity and resonance wavelength, and determines relative NP densities through plasmon coupling as a measure for the target lipid concentrations in the NP‐labeled VLP membrane. A correlation of the optical observables with absolute lipid contents is achieved by calibration of the plasmon coupling‐based methodology with unilamellar liposomes of known PS or G_M1 concentration. The performed studies reveal significant differences in the membrane of VLPs that assemble at different intracellular sites and pave the way to an optical quantification of lipid concentration in virus particles at physiological titers.     

Optical properties of highly scattering media determined from changes in attenuation, phase, and modulation depth

The optical properties of scattering media determine the attenuation (A) and the transit time (?t?) of light reflected from the medium as well as the phase (?) and modulation depth (M) of an intensity-modulated lightwave. Our primary finding is that the ratio of changes in A, ?, and M is approximately independent of the scattering properties and gives a good estimate of the absorption coefficient. These changes can be induced either by small changes in the absorption coefficient of the medium, by the tuning of the wavelength, or by changes in the light source-detector distance. The application for the in vivo monitoring of hemoglobin and oxyhemoglobin concentrations in human tissue is discussed.     

Metallic colloid wavelength-ratiometric scattering sensors

Gold and silver colloids display strong colors as a result of electron oscillations induced by incident light, which are referred to as the plasmon absorption. This absorption is dependent on colloid-colloid proximity, which has been the basis of absorption assays using colloids. We now describe a new approach to optical sensing using the light scattering properties of colloids. Colloid aggregation was induced by avidin-biotin interactions, which shifted the plasmon absorption to longer wavelengths. We found the spectral shift results in changes in the scattering at different incident wavelengths. By measuring the ratio of scattered intensities at two incident wavelengths, this measurement was made independent of the total colloid concentration. The high scattering efficiency of the colloids resulted in intensities equivalent to fluorescence when normalized by the optical density of the fluorophore and colloid. This approach can be used in a wide variety of assay formats, including those commonly used with fluorescence detection.     

Multiple light scattering in laser particle sizing

Multiple light scattering is an important issue in modern laser diffraction spectrometry. Most laser particle sizers do not account for multiple light scattering in a disperse medium under investigation. This causes an underestimation of the particle sizes in the case of high concentrations of scatterers. The retrieval accuracy is improved if the measured data are processed with multiple-scattering algorithms that treat multiple light scattering in a disperse medium. We evaluate the influence of multiple light scattering on light transmitted by scattering layers. The relationships among different theories to account for multiple light scattering in laser particle sizing are considered.     

Determination of optical coefficients of biological tissue from a single integrating-sphere

The detection of interactions between light and tissue can be used to characterize the optical properties of the tissue. The development is described of a method that determines optical coefficients of biological tissue from a single optical reflectance spectrum measured with an integrating-sphere. The experimental system incorporated a DH-2000 deuterium tungsten halogen light source, a USB4000-VIS-NIR miniature fiber optic spectrometer and an integrating-sphere. Fat emulsion and ink were used to mimic the scattering and absorbing properties of tissue in the tested sample. The measured optical reflectance spectrums with different scattering and absorbing properties were used to train a back-propagation neural network (BPNN). Then the neural network (BPNN) was used to determine the optical coefficients of biological tissue from a single optical reflectance spectrum measured with an integrating-sphere. Tests on tissue-simulation phantoms showed the relative errors of this technique to be 7% for the reduced scattering coefficient and 15% for the absorption coefficients. The optical properties of human skin were also measured in vivo.     

Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium

The conventional Lorenz-Mie formalism is extended to the case for a coated sphere embedded in an absorbing medium. The apparent and inherent scattering cross sections of a particle, derived from the far field and near field, respectively, are different if the host medium is absorptive. The effect of absorption within the host medium on the phase-matrix elements associated with polarization depends on the dielectric properties of the scattering particle. For the specific cases of a soot particle coated with a water layer and an ice sphere containing an air bubble, the phase-matrix elements -P12/P11 and P33/P11 are unique if the shell is thin. The radiative transfer equation for a multidisperse particle system embedded within an absorbing medium is discussed. Conventional multiple-scattering computational algorithms can be applied if scaled apparent single-scattering properties are applied.     

Coupled atmosphere/canopy model for remote sensing of plant reflectance features

Solar radiative transfer through a coupled system of atmosphere and plant canopy is modeled as a multiple-scattering problem through a layered medium of random scatterers. The radiative transfer equation is solved by the discrete-ordinates finite-element method. Analytic expressions are derived that allow the calculation of scattering and absorption cross sections for any plant canopy layer from measurable biophysical parameters such as the leaf area index, leaf angle distribution, and individual leaf reflectance and transmittance data. An expression for a canopy scattering phase function is also given. Computational results are in good agreement with spectral reflectance measurements directly above a soybean canopy, and the concept of greenness- and brightness-transforms of Landsat MSS data is reconfirmed with our computed results. A sensitivity analysis with the coupled atmosphere/canopy model quantifies how satellite-sensed spectral radiances are affected by increased atmospheric aerosols, by varying leaf area index, by anisotropic leaf scattering, and by non-Lambertian soil boundary conditions. Possible extensions to a 2-D model are also discussed.     

Pumping Current Noise in Ballistic Nanostructures: Acoustoelectric Current in a Point Contact

We consider current noise in a non-biased ballistic nanostructure irradiated by an AC field, which is assumed to be a stationary random process to imitate time averaging in the experiment. The AC field creates a current, which contains DC and AC components, the latter vanishing after time averaging. Correspondingly, the correlator describing current noise has two contributions. The first contribution to it is responsible for the fluctuations of the DC current. These fluctuations happen because of electron inelastic transitions between scattering states. Transitions agitated by the thermal bath lead to a thermal noise spectrum, which disappears at zero temperature; its magnitude is renormalized compared to equilibrium. Transitions initiated by the AC field lead to a noise spectrum, which is a convolution of the thermal one and that of the AC field. The magnitude of this noise is proportional to the power of the AC field and is finite at zero temperature. The second contribution to the noise correlator is due to fluctuations of the AC current. This noise does not depend on temperature, and its spectrum reproduces that of the AC field.     

Closed-form solution for the Wigner phase-space distribution function for diffuse reflection and small-angle scattering in a random medium

Within the paraxial approximation, a closed-form solution for the Wigner phase-space distribution function is derived for diffuse reflection and small-angle scattering in a random medium. This solution is based on the extended Huygens-Fresnel principle for the optical field, which is widely used in studies of wave propagation through random media. The results are general in that they apply to both an arbitrary small-angle volume scattering function, and arbitrary (real) ABCD optical systems. Furthermore, they are valid in both the single- and multiple-scattering regimes. Some general features of the Wigner phase-space distribution function are discussed, and analytic results are obtained for various types of scattering functions in the asymptotic limit s > 1, where s is the optical depth. In particular, explicit results are presented for optical coherence tomography (OCT) systems. On this basis, a novel way of creating OCT images based on measurements of the momentum width of the Wigner phase-space distribution is suggested, and the advantage over conventional OCT images is discussed. Because all previous published studies regarding the Wigner function are carried out in the transmission geometry, it is important to note that the extended Huygens-Fresnel principle and the ABCD matrix formalism may be used successfully to describe this geometry (within the paraxial approximation). Therefore for completeness we present in an appendix the general closed-form solution for the Wigner phase-space distribution function in ABCD paraxial optical systems for direct propagation through random media, and in a second appendix absorption effects are included.     

Elemental characterisation of aluminium used in reactors by optical emission spectroscopic methods

Using AC spark, AC arc and DC arc excitations in optical emission spectroscopic systems, the Al metal used in reactors can be characterised for its minor or trace element composition. The best precision of ± 6% is obtained with an AC spark in which the rod sample is taken as a self electrode and elements Cu, Fe, Mn, Si and Ti are determined in the concentration range 0·01–1%. The oxide powder sample with DC arc excitation provides best minimum detection limits of 10 ppm in general and 21 trace elements are determined by it. The AC arc method also uses oxide powder standards prepared synthetically and determines B and Mg in addition to the elements determined in AC spark excitation with a precision of ±9%.     

Multiple-scattering transmission and an effective average photon path length of a plane-parallel beam in a homogeneous medium

A two-stream radiative transfer model is used to derive expressions for the multiple-scattered transmitted flux (including single-scattering contributions) and the total effective average photon path length on transmission of a normally incident plane-parallel beam on a homogeneous layer characterized by the optical depth, the single-scattering albedo, and the asymmetry parameter of the scatterers. The results are simple analytical expressions that are useful for modifying the Beer-Lambert transmission law for a thick scattering medium in which the multiple-scattering contribution to the transmission is not negligible.     

Imaging with diffusing light: an experimental study of the effect of background optical properties

The overall image quality and diagnostic potential of time-resolved transmittance imaging depend on sensitivity to optical contrast, capacity to discriminate scattering from absorption contributions, and spatial resolution. We have investigated experimentally the effects of the optical properties of the background medium on the overall image quality of optical imaging based on fitting the experimental data to the solution of the diffusion equation and on time gating. Images were acquired from phantoms with different background optical properties, while the optical contrast between inhomogeneities and background is kept constant. Data were collected every 0.2 cm over a 6 cm x 6 cm area from realistic tissue phantoms containing cylindrical inhomogeneities (1 cm high and 1 cm in diameter) embedded in a 5-cm-thick turbid slab. The optical coefficients of the background were varied in the ranges of 5-15 cm(-1) for transport scattering and 0.02-0.08 cm(-1) for absorption. The optical contrast for the inclusions was kept at values of -50% and +50% for the scattering and -75% and +300% for the absorption. The results show that both high scattering and high absorption are beneficial.     

Multiple-scattering-based lidar retrieval: method and results of cloud probings

Recent developments in the search for a practical method of exploiting the multiple-scattering contributions to lidar returns are consolidated in a robust retrieval algorithm. The theoretical basis is the small-angle diffusion approximation. This implies that the algorithm is limited to media of sufficient optical thickness to generate measurable multiple scattering and to geometries for which the receiver's footprint diameter is less than the scattering mean free path. The primary retrieval products are the range-resolved extinction coefficient and the effective particle diameter from which secondary products such as the particle volume mixing ratio and the extinction at other wavelengths can be calculated. We recall briefly earlier validation tests and present new data and analysis that demonstrate and quantify the solutions' accuracy. The results show that systematic lidar probings with the proposed multiple-scattering technique can provide valuable physical information on cloud formation and evolution.