Apparent optical properties of oceanic water: dependence on the molecular scattering contribution

The relationships between the apparent optical properties (AOP's) and the inherent optical properties (IOP's) of oceanic water bodies have been reinvestigated by solution of the radiative transfer equation. This reexamination deals specifically with oceanic case 1 waters (those for which phytoplankton and their associated particles or substances control their inherent optical properties). In such waters, when the chlorophyll content is low enough (in most of the entire ocean), the influence of molecular scattering by water molecules is not negligible, leading to a gradual change in the shape of the phase function. The effect of this change on the AOP's is analyzed. The effect of the existence of diffuse sky radiation in addition to the direct solar radiation on AOP-IOP relationships is also examined. Practical parameterizations are proposed to predict in case 1 waters, and at various depths, the vertical attenuation coefficient for downward irradiance (K(d)) as a function of the IOP's and solar angle. These parameterizations are valid for the spectral domain where inelastic scattering does not significantly occur (wavelengths below 590 nm).     

Method to determine the optical properties of turbid media

A novel method to determine the optical properties, namely, absorption coefficient, scattering coefficient, and anisotropy factor of turbid solutions, single constituent or multiconstituent, is presented. Turbid solutions of milk, ink, and a mixture of both were illuminated by a laser beam and measurements were carried out in scattered light. Experimental results were matched to the corresponding results of Monte Carlo simulation to obtain the optical properties of the turbid media.     

Noninvasive determination of the optical properties of two-layered turbid media

Light propagation in two-layered turbid media having an infinitely thick second layer is investigated in the steady-state, frequency, and time domains. A solution of the diffusion approximation to the transport equation is derived by employing the extrapolated boundary condition. We compare the reflectance calculated from this solution with that computed with Monte Carlo simulations and show good agreement. To investigate if it is possible to determine the optical coefficients of the two layers and the thickness of the first layer, the solution of the diffusion equation is fitted to reflectance data obtained from both the diffusion equation and the Monte Carlo simulations. Although it is found that it is, in principle, possible to derive the optical coefficients of the two layers and the thickness of the first layer, we concentrate on the determination of the optical coefficients, knowing the thickness of the first layer. In the frequency domain, for example, it is shown that it is sufficient to make relative measurements of the phase and the steady-state reflectance at three distances from the illumination point to obtain useful estimates of the optical coefficients. Measurements of the absolute steady-state spatially resolved reflectance performed on two-layered solid phantoms confirm the theoretical results.     

Influence of optical properties on two-photon fluorescence imaging in turbid samples

A numerical model was developed to simulate the effects of tissue optical properties, objective numerical aperture (N.A.), and instrument performance on two-photon-excited fluorescence imaging of turbid samples. Model data are compared with measurements of fluorescent microspheres in a tissuelike scattering phantom. Our results show that the measured two-photon-excited signal decays exponentially with increasing focal depth. The overall decay constant is a function of absorption and scattering parameters at both excitation and emission wavelengths. The generation of two-photon fluorescence is shown to be independent of the scattering anisotropy, g, except for g > 0.95. The N.A. for which the maximum signal is collected varies with depth, although this effect is not seen until the focal plane is greater than two scattering mean free paths into the sample. Overall, measurements and model results indicate that resolution in two-photon microscopy is dependent solely on the ability to deliver sufficient ballistic photon density to the focal volume. As a result we show that lateral resolution in two-photon microscopy is largely unaffected by tissue optical properties in the range typically encountered in soft tissues, although the maximum imaging depth is strongly dependent on absorption and scattering coefficients, scattering anisotropy, and objective N.A..     

Effect of refractive index on the measurement of optical properties in turbid media

Continuous-wave measurement-based methods offer a rapid cost-effective way to determine optical properties in turbid media. This method requires a measure of the refractive index of the medium, which is often unknown a priori. Whereas previous studies have reported that the refractive index has little impact on the measurement of optical properties, here we show a significant effect of refractive indices on measurements, using both simulations and experiments. In addition we propose a noniterative method to determine the refractive index of the medium. This method can also provide an optimal initial guess of the optical properties for the standard iterative method for determining optical properties in turbid media. Our method is confirmed by simulations and experiments with latex spheres and Intralipid suspensions.     

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.     

Effects of turbid media optical properties on object visibility in subsurface polarization imaging

We studied the effectiveness of using polarized illumination and detection to enhance the visibility of targets buried in highly scattering media. The effects of background optical properties including scattering coefficient, absorption coefficient, and anisotropy on image visibility were examined. Both linearly and circularly polarized light were used in the imaging. Three different types of target were investigated: scattering, absorption, and reflection. The experimental results indicate that target visibility improvement achieved by a specific polarization method depends on both the background optical properties and the target type. By analyzing all polarization images, it is possible to reveal certain information about target or the scattering background.     

Measurement of the local optical properties of turbid media by differential path-length spectroscopy

We report on the development of an optical-fiber-based diagnostic tool with which to determine the local optical properties of a turbid medium. By using a single fiber in contact with the medium to deliver and detect white light, we have optimized the probability of detection of photons scattered from small depths. The contribution of scattered light from greater depths to the signal is measured and subtracted with an additional fiber, i.e., a collection fiber, to yield a differential backscatter signal. Phantoms demonstrate that, when photons have large mean free paths compared with the fiber diameter, single scattering dominates the differential backscatter signal. When photons have small mean free paths compared with the fiber diameter, the apparent path length of the photons that contribute to the differential backscatter signal becomes approximately equal to 4/5 of the fiber diameter. This effect is nearly independent of the optical properties of the sample under investigation.     

Observation of the geometric amplitude factor in an optical system

Abstract

By manipulating the discrete optical levels inside an optical resonator, we obtain a classical realization of a twisted Landau-Zener model. We experimentally demonstrate the geometric amplitude factor in the transition amplitude that arises for this model. We consider in particular the region of parameter space addressed in the original study of the geometric amplitude factor by M. V. Berry [7].     

Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium

We have examined the possibility of determining the optical properties of a two-layer medium by using a diffusion approximation radiation transport model [Appl. Opt. 37, 779 (1998)]. Continuous-wave and frequency-domain (FD) low-noise Monte Carlo (MC) data were fitted to the model. Marquardt-Levenberg and a simulated annealing algorithm were used and compared as optimization techniques. Our particular choice of optical properties for the two-layer model was consistent with skin and underlying fat in the presence of an exogenous chromophore [Appl. Opt. 37, 1958 (1998)]. The results are therefore specific to this set of optical properties. It was found that the cw diffusion solution could never be used to estimate all optical properties reliably. The combined cw and FD solutions could not be used to estimate some of the top-layer optical properties to an accuracy of better than 10%, although the absorption and the transport scattering coefficients of the bottom layer could be estimated to within 7% and 0.5%, respectively. No improvement was found from simultaneously fitting MC data at three different modulation frequencies. These results point to the need for a more accurate radiation transfer model at small source-detector separations.     

Inverse hybrid technique for determining the optical properties of turbid media from integrating-sphere measurements

We have combined the Monte Carlo method with the small-angle approximation of the radiative transfer theory to derive the optical properties (the absorption coefficient, the scattering coefficient, and the anisotropy factor) of turbid materials from integrating-sphere measurements (the total transmittance and the diffuse reflectance) and the collimated transmittance. Unlike one-dimensional models, the technique accounts for the side losses of light at the edges of the sample. In addition, it enables the correction of the measured collimated signal for the contribution of multiply scattered light. On the other hand, the hybrid technique allows a significant reduction in calculation time compared with inverse methods based on a pure Monte Carlo technique. Numerical tests and experimental results from a phantom material (milk) as well as samples of biological tissue (porcine myocardium) confirmed the feasibility of applying this technique to the determination of the optical properties of turbid media.     

Effects of the surface boundary on the determination of the optical properties of a turbid medium with time-resolved reflectance

Solutions of the time-dependent diffusion equation were developed to take into account the depth of the source and the detector inside a semi-infinite medium. These solutions permitted an evaluation of optical properties at different depths below the surface by fitting time-resolved data. Measurements were performed on liquid optical phantoms with optical fibers for delivering and collecting light. A time-correlated single-photon-counting chain was used for electronic detection. The determination of optical properties underlines the continuity between the surface model and the infinite model and shows the depth at which the derived solutions can be applied.     

Fast algorithm to determine optical properties of a turbid medium from time-resolved measurements

After analytical expressions for the time-resolved reflectance are introduced from the diffusion approximation under the three most commonly used boundary conditions, a novel algorithm is demonstrated for determining the reduced scattering and the absorption coefficients from time-resolved reflectance (or backscatter) measurements at two positions on the surface of biotissue. The algorithm is straightforward and fast and involves only some simple mathematical operations, avoiding complicated iterative nonlinear fitting to the time-resolved curve. The derived reduced scattering coefficient is not affected by whatever boundary condition is applied. The algorithm was verified with time-resolved data from the Monte Carlo model. Both a semi-infinite medium and a turbid slab medium were tested. In contrast to the nonlinear fitting method, this algorithm allows both the scattering and the absorption coefficients to be determined to a high accuracy.     

Effect of the PVA (polyvinyl alcohol) concentration on the optical properties of Eu-doped YAG phosphors

The influence of the polyvinyl alcohol (PVA) concentration on the synthesis and structural, morphological and optical properties of Y₃Al₅O₁₃: Eu (Eu-doped YAG) was systematically investigated in this work. The final concentration of PVA in the preparation step influenced the crystallite size and also the degree of particle agglomeration in Eu-doped YAG phosphors. X-ray excited optical luminescence (XEOL) emission spectra results indicated typical Eu³⁺ emission lines and an abnormally intense ⁵D₀ → ⁷F₄. The intensity parameters Ω₂ and Ω₄ were calculated and indicated the PVA concentration affects the ratio Ω₂:Ω₄. X-ray absorption spectroscopy (XAS) results showed Eu valence did not change and the symmetry around the Eu³⁺ is influenced by the PVA concentration. XEOL-XAS showed the luminescence increases as a function of energy.     

Estimation of optical properties of turbid media: experimental comparison of spatially and temporally resolved reflectance methods

We compare two methods for the optical characterization of turbid media. The estimates of the absorption and reduced scattering coefficients (mu(a) and mu(')(s)) by a spatially resolved method and a time-resolved method are performed on tissue-like phantoms. Aqueous suspension of microspheres and Intralipid are used as scattering media with the addition of ink as an absorber. mu(')(s) is first measured on weakly absorbing media. The robustness of these measurements is then tested with respect to a variation of mu(a). The spatially resolved method gave more accurate estimates for mu(')(s) whereas the time-resolved method gave better results for mu(a) estimates.     

Hyperspectral diffuse reflectance imaging for rapid, noncontact measurement of the optical properties of turbid materials

We present a method and technique of using hyperspectral diffuse reflectance for rapid determination of the optical properties of turbid media. A hyperspectral imaging system in line scanning mode was used to acquire spatial diffuse reflectance profiles from liquid phantoms made up of absorbing dyes and fat emulsion scatterers over the spectral range of 450-1000 nm instantaneously. The hyperspectral reflectance data were analyzed by using a steady-state diffusion approximation model for semi-infinite homogeneous media. A calibration procedure was developed to compensate the nonuniform instrument response of the imaging system, and a curve-fitting algorithm was used to extract absorption and reduced scattering coefficients (mua and mus', respectively) for the phantoms in the wavelength range from 530 to 900 nm. The hyperspectral imaging system gave good measures of mua and mus' for the phantoms with average fitting errors of 12% and 7%, respectively. The hyperspectral imaging technique is fast, noncontact, and easy to use, which makes it especially suitable for measurement of the optical properties of turbid liquid and solid foods.     

Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media

Monte Carlo simulations and experiments in tissue phantoms were used to empirically develop an analytical model that characterizes the reflectance spectrum in a turbid medium. The model extracts the optical properties (scattering and absorption coefficients) of the medium at small source-detector separations, for which the diffusion approximation is not valid. The accuracy of the model and the inversion algorithm were investigated and validated. Four fiber probe configurations were tested for which both the source and the detector fibers were tilted at a predetermined angle, with the fibers parallel to each other. This parallel-fiber geometry facilitates clinical endoscopic applications and ease of fabrication. Accurate extraction of tissue optical properties from in vivo spectral measurements could have potential applications in detecting, noninvasively and in real time, epithelial (pre)cancers.     

Speckle properties of the logarithmically transformed signal in optical coherence tomography

We discuss the statistical properties of speckle of the logarithmically transformed signal in optical coherence tomography (OCT) both theoretically and experimentally. OCT signals of Intralipid solution with different volume particle concentrations ρ (correspondingly, scattering coefficient μ(s) ranges from 1.25 to 25.11 mm(-1)) were measured and analyzed under two different focusing conditions [numerical apertures (NAs) of the objective lens of 0.13 and 0.25]. We found that the effect of the speckle noise can be suppressed by displaying OCT images in the logarithmic scale and by using the objective lens with a higher NA. We also found that the speckle properties are correlated with the scattering properties of the sample, which may be used to characterize the scattering properties of biological tissue. The simulated OCT image and the in vitro OCT image of a rat liver are used as examples to demonstrate the feasibility of the method.     

Apparent and inherent optical properties of turbid estuarine waters: measurements, empirical quantification relationships, and modeling

Spectral measurements of remote-sensing reflectance (Rrs) and absorption coefficients carried out in three European estuaries (Gironde and Loire in France, Tamar in the UK) are presented and analyzed. Typical Rrs and absorption spectra are compared with typical values measured in coastal waters. The respective contributions of the water constituents, i.e., suspended sediments, colored dissolved organic matter, and phytoplankton (characterized by chlorophyll-a), are determined. The Rrs spectra are then reproduced with an optical model from the measured absorption coefficients and fitted backscattering coefficients. From Rrs ratios, empirical quantification relationships are established, reproduced, and explained from theoretical calculations. These quantification relationships were established from numerous field measurements and a reflectance model integrating the mean values of the water constituents' inherent optical properties. The model's sensitivity to the biogeochemical constituents and to their nature and composition is assessed.     

Dynamic 193-nm optical properties of water

Previous assumptions that water is not a 193-nm chromophore during ArF excimer laser tissue ablation are based on room-temperature data and ignore spectroscopic literature that suggests a strong temperature dependence of far-ultraviolet water absorption. By the use of a Q-switched Er:YAG laser as a pump source and an ArF excimer laser as a probe source, thermal generation and relaxation of 193-nm water absorption were characterized under nonequilibrium high-temperature and high-pressure conditions. At volumetric energy densities as small as 2 kJ/cm(3) relative to room temperature, the 193-nm absorption coefficient of water was measured to increase by more than 5 orders of magnitude. These results are consistent with the hypothesis that the absorption of 193-nm radiation by water may play a role in ArF excimer laser ablation of tissue.