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.     

Multiple-scattering suppression by cross correlation

We describe a new method for characterizing particles in turbid media by cross correlating the scattered intensity fluctuations at two nearby points in the far field. The cross-correlation function selectively emphasizes single scattering over multiple scattering. The usual dynamic light-scattering capability of inferring particle size from decay rate is thus extended to samples that are so turbid as to be visually opaque. The method relies on single-scattering speckle being physically larger than multiple-scattering speckle. With a suitable optical geometry to select nearby points in the far field or equivalently slightly different scattering wave vectors (of the same magnitude), the multiple-scattering contribution to the cross-correlation function may be reduced and in some cases rendered insignificant. Experimental results demonstrating the feasibility of this approach are presented.     

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.     

Multiple-scattering effects on infrared scattering measurements used to characterize droplet size and volume fraction distributions in diesel sprays

We quantify the maximum error due to multiple-scattering effects for an infrared scattering droplet izing technique. Errors in Sauter mean diameters (SMDs) and liquid volume fractions were estimated lased on experimentally determined polarization properties of the scattered light. Light that is multiply scattered from spherical particles becomes randomly polarized, whereas singly scattered light from a spherical particle contains no cross-polarization scattering component. Therefore measurement of the cross-polarization component (in this case parallel) of the scattering signal is a measure of the multiply scattered light. A ratio of parallel to perpendicular polarized scattered light was experimentally determined and used to calculate an error due to multiple scattering. The infrared scattering measurements and polarization measurements used to quantify the multiple-scattering errors were applied to a typical diesel spray that was injected into three different background conditions: a room ambient condition; a room-temperature, high-pressure condition; and a combusting condition. Droplet SMD, liquid volume fraction, and multiple-scattering errors were determined for a number of locations within the spray; results indicate that the combusting case is negligibly affected by multiple scattering. However, the room ambient case exhibited notable errors due to multiple scattering near the centerline of the spray, and the high-pressure case demonstrated susceptibility to multiple scattering throughout all regions investigated. It is important to note, however, that multiple-scattering errors in many cases translate into relatively small effects on the reported droplet sizes.     

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.     

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.     

Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography

Optical diffraction tomography is an imaging technique that permits retrieval of the map of permittivity of an object from its scattered far field. Most reconstruction procedures assume that single scattering is dominant so that the scattered far field is linearly linked to the permittivity. In this work, we present a nonlinear inversion method and apply it to complex three-dimensional samples. We show that multiple scattering permits one to obtain a power of resolution beyond the classical limit imposed by the use of propagative incident and diffracted waves. Moreover, we stress that our imaging method is robust with respect to correlated and uncorrelated noise.     

Fluorescence correlation spectroscopy: an efficient tool for measuring size, size-distribution and polydispersity of microemulsion droplets in solution

Fluorescence correlation spectroscopy (FCS) is an ideal tool for measuring molecular diffusion and size under extremely dilute conditions. However, the power of FCS has not been utilized to its best to measure diffusion and size parameters of complex chemical systems. Here, we apply FCS to measure the size, and, most importantly, the size distribution and polydispersity of a supramolecular nanostructure (i.e., microemulsion droplets, MEDs) in dilute solution. It is shown how the refractive index mismatch of a solution can be corrected in FCS to obtain accurate size parameters of particles, bypassing the optical matching problem of light scattering techniques that are used often for particle-size measurements. We studied the MEDs of 13 different W(0) values from 2 to 50 prepared in a ternary mixture of water, sodium bis(2-ethylhexyl) sulfosuccinate (AOT), and isooctane, with sulforhodamine-B as a fluorescent marker. We find that, near the optical matching point of MEDs, the dynamic light scattering (DLS) measurements underestimate the droplet sizes while FCS estimates the accurate ones. A Gaussian distribution model (GDM) and a maximum-entropy-based FCS data fitting model (MEMFCS) are used to analyze the fluorescence correlation curves that unfold Gaussian-type size distributions of MEDs in solution. We find the droplet size varies linearly with W(0) up to ~20, but beyond this W(0) value, the size variation deviates from this linearity. To explain nonlinear variation of droplet size for W(0) values beyond ~20, we invoke a model (the coated-droplet model) that incorporates the size polydispersity of the droplets.     

Numerical analysis of a path-length-resolved spectrum of time-varying scattered light field

The path-length-resolved power spectrum of a time-varying scattered light field measured by a time-of-flight method or low-coherence interferometry is evaluated by a new numerical simulation algorithm. The path-length-resolved power spectrum is theoretically derived by combining diffusing-wave-spectroscopy theory and radiative-transfer theory. The proposed algorithm, using the Monte Carlo method, is used to determine the scattering configurations and numerically calculate the power spectrum. The path-length distribution, path-length-dependent scattering order distribution, and path-length-resolved power spectrum are demonstrated numerically over all scattering orders. The resultant power spectra agree with experimental results measured by the low-coherence-dynamic-light-scattering method.     

Forward average path-length parameter in four-flux radiative transfer models

The optical properties of films containing spherical particles in a nonabsorbing matrix have been modeled by using a four-flux radiative transfer theory. The forward average path-length parameter takes into account the different path lengths for collimated and diffuse components of the radiation field. This parameter, whose value was known only in special cases, has been used previously as a fitting quantity. We establish a method for evaluating the forward average path-length parameter in a rigorous way. Single-scattering parameters are evaluated from the Lorenz-Mie theory, and multiple-scattering effects are taken into account by means of an extended Hartel's theory.     

Single-walled carbon nanotubes as excitonic optical wires

Although metallic nanostructures are useful for nanoscale optics, all of their key optical properties are determined by their geometry. This makes it difficult to adjust these properties independently, and can restrict applications. Here we use the absolute intensity of Rayleigh scattering to show that single-walled carbon nanotubes can form ideal optical wires. The spatial distribution of the radiation scattered by the nanotubes is determined by their shape, but the intensity and spectrum of the scattered radiation are determined by exciton dynamics, quantum-dot-like optical resonances and other intrinsic properties. Moreover, the nanotubes display a uniform peak optical conductivity of approximately 8 e(2)/h, which we derive using an exciton model, suggesting universal behaviour similar to that observed in nanotube conductance. We further demonstrate a radiative coupling between two distant nanotubes, with potential applications in metamaterials and optical antennas.     

Multiple-scattering suppression in dynamic light scattering based on a digital camera detection scheme

We introduce a charge-coupled device (CCD) camera-based detection scheme in dynamic light scattering that provides information on the single-scattered autocorrelation function even for fairly turbid samples. It is based on the single focused laser beam geometry combined with the selective cross-correlation analysis of the scattered light intensity. Using a CCD camera as a multispeckle detector, we show how spatial correlations in the intensity pattern can be linked to single- and multiple-scattering processes. Multiple-scattering suppression is then achieved by an efficient cross-correlation algorithm working in real time with a temporal resolution down to 0.02 s. Our approach allows access to the extensive range of systems that show low-order scattering by selective detection of the singly scattered light. Model experiments on slowly relaxing suspensions of titanium dioxide in glycerol were carried out to establish the validity range of our approach. Successful application of the method is demonstrated up to a scattering coefficient of more than micro(S) = 5 cm(-1) for the sample size of L = 1 cm.     

Near-field intensity correlations of scattered light

We show that the two-point correlation function in the near field of scattered light is simply related to the scattered intensity distribution. We present a new, to our knowledge, optical scheme to measure the correlation function in the near field, and we describe a processing technique that permits the subtraction of stray light on a statistical basis. We present experimental data for solutions of latex spheres, and we show that this novel technique is a powerful alternative to static light scattering.     

Controlling the optical path length in turbid media using differential path-length spectroscopy: fiber diameter dependence

We have characterized the path length for the differential path-length spectroscopy (DPS) fiber optic geometry for a wide range of optical properties and for fiber diameters ranging from 200 microm to 1000 microm. Phantom measurements show that the path length is nearly constant for scattering coefficients in the range 5 mm(-1)< micros <50 mm(-1) for all fiber diameters and that the path length is proportional to the fiber diameter. The path length decreases with increasing absorption for all fiber diameters, and this effect is more pronounced for larger fiber diameters. An empirical model is formulated that relates the DPS path length to total absorption for all fiber diameters simultaneously.     

Optical extinction by closely spaced parallel cylinders inside a finite dielectric slab

The formulation for the extinction and scattering cross sections of closely spaced parallel infinite cylinders in a dielectric medium of finite thickness is presented. We consider the general case of dissimilar refractive indices for the half-spaces on both sides of the slab, and the diameter and refractive index of each cylinder can be different. The formulation accounts for the coherent scattering between the cylinders and scattering of the multiply reflected internal waves inside the slab. Discontinuity in the refractive index across the dielectric slab interfaces results in boundary reflections that modify the angular distribution of the scattered intensity in both forward and backward directions. The extinction cross section, which is derived by a formal application of the optical theorem, is shown to consist of both a forward and a backward component. The general solution is applied to obtain the formulas for the cases of cylinders in front of a reflecting plane, cylinders inside a semi-infinite dielectric medium, and cylinders in free space.     

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.     

Irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: Raman-scattering effects

We modify an algorithm for retrieving the absorption (a) and backscattering (b(b)) coefficient profiles in natural waters by inverting profiles of downwelling and upwelling irradiance so as to include the presence of Raman scattering. For a given wavelength of interest, lambda, the light field at the appropriate Raman excitation wavelength lambda(e) is first inverted to obtain the Raman source function at lambda. Starting from estimates of the inherent optical properties at lambda, the contribution to the irradiances at lambda from Raman scattering is then estimated and subtracted from the total irradiances to obtain the elastically scattered irradiances. We then inverted the elastically scattered irradiances to find new estimates of a and b(b) using our original method [Appl. Opt. 37, 3886 (1998)]. The algorithm then operates iteratively: The new estimates are used with the Raman source function to derive a new estimate of the Raman contribution, etc. Sample results are provided that demonstrate the working of the algorithm and show that the absorption and scattering coefficients can be retrieved with accuracies similar to those in the absence of Raman scattering down to depths at which the light field is significantly perturbed by it, e.g., with ~90% of the upwelling light field originating from Raman scattering.     

Pulsed light field of a point source in a scattering medium

Pulsed radiation propagating through a layer of a scattering medium undergoes distortions caused by multiple scattering. The results of numerical calculations of pulse waveforms for media with different scattering phase functions are presented. It is demonstrated that the scattered radiation waveform is not described by diffusion theories even for sufficiently large optical thicknesses (tau approximately 10-20) but is described, as a rule, by a bimodal distribution. Only when the optical thickness significantly increases (tau>100-150), the photon distribution over the free paths acquires the unimodal diffusion form.     

Enhanced specular peaks in diffuse light scattering from weakly rough metal surfaces

We employ Monte Carlo techniques based on the reduced Rayleigh equations to study an enhanced specular peak that appears in the light scattered from weakly rough metal surfaces. This peak is not associated with the specular reflection but instead appears, with finite angular width, at the specular angle of the mean diffusely scattered intensity. As is the case with backscattering enhancement, the specular peak arises from the interference of contributions of multiple-scattering processes related to surface plasmon polariton excitation. We demonstrate that the specular peak is seen clearly for surface roughness that has a conventional Gaussian power spectrum. Further, we show that the peak appears more distinctly for roughness whose power spectrum has a new rectangular form, which is proposed here with the intent of better isolation of the scattering processes essential to the specular peak. Finally, for a pair of rough surfaces that have appropriately correlated surface roughness, it is found that the cross correlation of scattered amplitudes presents a well-isolated specular peak, which directly demonstrates the constructive interference that produces the effect.