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.     

Modelling optical properties of soft tissue by fractal distribution of scatterers

Abstract

A knowledge of the local refractive index variations and size distribution of scatterers in biological tissue is required to understand the physical processes involved in light-tissue interaction. This paper describes a method for modelling the complicated soft tissue, based on the fractal approach, permitting numerical evaluation of the phase functions and four optical properties of tissue—scattering coefficient, reduced scattering coefficient, backscatter-ing coefficient, and anisotropy factor—by the use of the Mie scattering theory. A key assumption of the model is that refractive index variations caused by microscopic tissue elements can be treated as particles with size distribution according to the power law. The model parameters, such as refractive index, incident wavelength, and fractal dimension, that are likely to affect the predictions of optical properties are investigated. The results suggest that the fractal dimension used to describe how biological tissue can be approximated by particle distribution is highly dependent on how the continuous distribution is discretized. The optical properties of the tissue significantly depend on the refractive index of tissue, implying that the refractive index of the particles should be carefully chosen in the model in order accurately to predict the optical properties of the tissue concerned.     

Estimation of complex refractive index of polydisperse particulate systems from multiple-scattered ultraviolet-visible-near-infrared measurements

A method to extract the complex refractive index of spherical particles from a polydisperse suspension at concentrations where multiple light-scattering effects are significant is presented. The optical constants are estimated from total diffuse reflectance and transmittance measurements and inverting the measurements using the radiative transfer equation (RTE) and the Mie theory for scattering by polydisperse spherical particles. The method is tested by applying it to three different polydisperse polystyrene suspensions and extracting the optical constants of polystyrene particles in the wavelength range of 450-1200 nm. The effect of particle size, concentration, and polydispersity on the estimated values of the optical constants is also discussed.     

Determination of Particle Sizes and Crystalline Phases on Colloidal Silicon Nanoparticle Suspensions

1.IDtroductionLightscatteringpropertiesofsphericalparticlescanbedescribedbyMietheoryl1]whichcanbeaP-pliedtocolloidalparticlessuspendedinthegasorliquidphase.Withsomecarethetheorycanevenbeap-pliedtodrypowdersorparticlesonasolidsupport[2]lthoughitisstrictlyvalidonlyforisolatedsphericalparticles.Informationonparticlesizer,sizedistribu-tionandnumberdensitiesN(r),andrefractiveindexhcanberetrievedbyexperimentaldata.Theex-tinctioncoefficient7ofacolloidalsuspension,forex-ample,canbedeterminedfromthea…     

Determination of polar stratospheric cloud particle refractive indices by use of in situ optical measurements and T-matrix calculations

A new algorithm to infer structural parameters such as refractive index and asphericity of cloud particles has been developed by use of in situ observations taken by a laser backscattersonde and an optical particle counter during balloon stratospheric flights. All three main particles, liquid, ice, and a no-ice solid (NAT, nitric acid trihydrate) of polar stratospheric clouds, were observed during two winter flights performed from Kiruna, Sweden. The technique is based on use of the T-matrix code developed for aspherical particles to calculate the backscattering coefficient and particle depolarizing properties on the basis of size distribution and concentration measurements. The results of the calculations are compared with observations to estimated refractive indices and particle asphericity. The method has also been used in cases when the liquid and solid phases coexist with comparable influence on the optical behavior of the cloud to estimate refractive indices. The main results prove that the index of refraction for NAT particles is in the range of 1.37-1.45 at 532 nm. Such particles would be slightly prolate spheroids. The calculated refractive indices for liquid and ice particles are 1.51-1.55 and 1.31-1.33, respectively. The results for solid particles confirm previous measurements taken in Antarctica during 1992 and obtained by a comparison of lidar and optical particle counter data.     

Annealing of polymer films with embedded silver nanoparticles: Effect on optical properties

The influence of annealing time and of the silver over polymer ratio on the optical properties of the silver nanoparticles embedded in a poly(vinyl alcohol) matrix has been analyzed by spectroscopic ellipsometry in the visible/near-infrared spectral domains. The complex refractive index shows a localized absorption near 420 nm which can be attributed to localized surface plasmons. An atomic force microscopy topographic analysis shows that the particles were nearly spherical with an average size less than 20 nm, as confirmed by optical transmission measurements with polarized light. The size of the particles and their number respectively decreased and increased as the annealing time of the film increased, yielding a plasmon absorption band whose intensity is correlated to the silver nanoparticles density, estimated from their nearest-neighbour distance.     

Application of constrained optimization to the design of quasi-rugate optical coatings

The constrained optimization approach is applied to the design of quasi-rugate optical coatings. These coatings are defined as multilayers with no thin layers where refractive index profiles resemble rugate-type refractive index profiles and where spectral properties are typical for rugate filters. It is shown that all design problems that are usually solved using rugate filters can be solved successfully in the frame of quasi-rugate optical coatings. Comparison between quasi-rugate and two-component multilayer designs is provided.     

Simultaneous retrieval of aerosol refractive index and particle size distribution from ground-based measurements of direct and scattered solar radiation

Ground-based sunphotometer observation of direct and scattered solar radiation is a traditional tool for providing data on aerosol optical properties. Spectral transmission and solar aureole measurements provide an optical source of aerosol information, which can be inverted for retrieval of microphysical properties (particle size distribution and refractive index). However, to infer these aerosol properties from ground-based remote-sensing measurements, special numerical inversion methods should be developed and applied. We propose two improvements to the existing inversion techniques employed to derive aerosol microphysical properties from combined atmospheric transmission and solar aureole measurements. First, the aerosol refractive index is directly included in the inversion procedure and is retrieved simultaneously with the particle size spectra. Second, we allow for real or effective instrumental pointing errors by including a correction factor for scattering angle errors as a retrieved inversion parameter. The inversion technique is validated by numerical simulations and applied to field data. It is shown that ground-based sunphotometer measurements enable one to derive the real part of the aerosol refractive index with an absolute error of 0.03-0.05 and to distinguish roughly between weakly and strongly absorbing aerosols. The aureole angular observation scheme can be refined with an absolute accuracy of 0.15-0.19 deg. Offset corrections to the scattering angle error are generally found to be small and consistently of the order of -0.17. This error magnitude is deduced to be due primarily to nonlinear field-of-view averaging effects rather than to instrumental errors.     

Optical fiber design and the trapping of Cerenkov radiation

Cerenkov radiation is generated in optical fibers immersed in radiation fields and can interfere with signal transmission. We develop a theory for predicting the intensity of Cerenkov radiation generated within the core of a multimode optical fiber by using a ray optic approach and use it to make predictions of the intensity of radiation transmitted down the fiber in propagating modes. The intensity transmitted down the fiber is found to be dominated by bound rays with a contribution from tunneling rays. It is confirmed that for relativistic particles the intensity of the radiation that is transmitted along the fiber is a function of the angle between the particle beam and the fiber axis. The angle of peak intensity is found to be a function of the fiber refractive index difference as well as the core refractive index, with larger refractive index differences shifting the peak significantly toward lower angles. The angular range of the distribution is also significantly increased in both directions by increasing the fiber refractive index difference. The intensity of the radiation is found to be proportional to the cube of the fiber core radius in addition to its dependence on refractive index difference. As the particle energy is reduced into the nonrelativistic range the entire distribution is shifted toward lower angles. Recommendations on minimizing the quantity of Cerenkov light transmitted in the fiber optic system in a radiation field are given.     

Modeling light scattering from Diesel soot particles

The Mie model is widely used to analyze light scattering from particulate aerosols. The Diesel particle scatterometer, for example, determines the size and optical properties of Diesel exhaust particles that are characterized by the measurement of three angle-dependent elements of the Mueller scattering matrix. These elements are then fitted by Mie calculations with a Levenburg-Marquardt optimization program. This approach has achieved good fits for most experimental data. However, in many cases, the predicted complex index of refraction was smaller than that for solid carbon. To understand this result and explain the experimental data, we present an assessment of the Mie model by use of a light-scattering model based on the coupled-dipole approximation. The results indicate that the Mie calculation can be used to determine the largest dimension of irregularly shaped particles at sizes characteristic of Diesel soot and, for particles of known refractive index, tables can be constructed to determine the average porosity of the particles from the predicted index of refraction.     

Simultaneous measurement of thickness and refractive index based on rotation incidence angle

A method for simultaneous measurement of geometric thickness and refractive index of an optical wafer is presented. By using a fiber optic Mach–Zehnder interferometer (MZI) with a free space, the transmission spectrum of a MZI for the optical wafer at different incidence angle is interrogated, and the geometric thickness and the refractive index of the optical wafer are measured simultaneously. With the transmission spectrum, we can obtain a clear interferogram with a high visibility no matter how small the measurement range of the refractive index. Therefore the proposed technique possesses a broad measurement range and low cost. The experimental results show that the maximum errors of the geometric thickness and the refractive index are only 0.007?mm and 0.008, respectively, and that a broad measurement from 1.316 to 3.503 can be achieved.     

Multiscale patterning of plasmonic metamaterials

The interaction of light with surface plasmons--collective oscillations of free electrons--in metallic nanostructures has resulted in demonstrations of enhanced optical transmission, collimation of light through a subwavelength aperture, negative permeability and refraction at visible wavelengths, and second-harmonic generation from magnetic metamaterials. The structures that display these plasmonic phenomena typically consist of ordered arrays of particles or holes with sizes of the order of 100 nm. However, surface plasmons can interact with each other over much longer distances, so the ability to organize nanoscale particles or holes over multiple length scales could lead to new plasmonic metamaterials with novel optical properties. Here, we present a high-throughput nanofabrication technique-soft interference lithography-that combines the ability of interference lithography to produce wafer-scale nanopatterns with the versatility of soft lithography, and use it to create such plasmonic metamaterials. Metal films perforated with quasi-infinite arrays of 100-nm holes were generated over areas greater than 10 cm(2), exhibiting sharp spectral features that changed in relative amplitude and shifted to longer wavelengths when exposed to increased refractive index environments. Moreover, gold nanohole arrays patterned into microscale patches exhibited strikingly different transmission properties; for instance, patches of nanoholes displayed narrow resonances (<14.5 nm full-width-at-half-maximum) that resulted in high refractive index sensitivities far exceeding those reported previously. Soft interference lithography was also used to produce various infinite and finite-area arrays of nanoparticles, including patterns that contained optically distinct particles side by side and arrays that contained both metallic and dielectric materials.     

Determination of thickness, refractive index, and thickness irregularity for semiconductor thin films from transmission spectra

A simplified theoretical model has been proposed to predict optical parameters such as thickness, thickness irregularity, refractive index, and extinction coefficient from transmission spectra. The proposed formula has been solved for thickness and thickness irregularity in the transparent region, and then the refractive index is calculated for the entire spectral region by use of the interference fringes order. The extinction coefficient is then calculated with the exact formula in the transparent region, and an appropriate model for the refractive index is used to solve for the extinction coefficient in the absorption region (where the interference fringes disappear). The proposed model is tested with the theoretical predicted data as well as experimental data. The calculation shows that the approximations used for solving a multiparameter nonlinear equation result in no significant errors.     

Optical properties of soda-lime float glass from spectroscopic ellipsometry

Optical properties of soda-lime glass manufactured by the float process were investigated using spectroscopic ellipsometry and intensity transmission measurements. Thickness and optical properties of surface layers on the air and tin sides were determined with ellipsometry. The tin side surface layer shows a graded refractive index with a non-linear profile. Intensity transmission data were used to quantify absorption in the bulk glass. Transmission-mode generalized ellipsometry characterized residual birefringence in the bulk glass. Birefringence effects on ellipsometric delta data were corrected using a simple empirical offset with 1/wavelength dependence. A general optical model for soda-lime glass is presented which can be used for subsequent analysis of coated soda-lime glass and other transparent substrates.     

Determining the refractive index and average thickness of AsSe semiconducting glass films from wavelength measurements only

The dispersive refractive index n(λ) and thickness d of chalcogenide glass thin films are usually calculated from measurements of both optical transmission and wavelength values. Many factors can influence the transmission values, leading to large errors in the values obtained for n(λ) and d. Anovel optical method is used to derive n(λ) and d for AsSe semiconducting glass thin films deposited by thermal evaporation in the spectral region where k(2) ? n(2), using only wavelength values. This entails obtaining two transmission spectra: one at normal incidence and another at oblique incidence. The procedure yields values for the refractive index and average thickness of thermally evaporated chalcogenide films to an accuracy better than 3%.     

Radiation pressure cross sections and optical forces over negative refractive index spherical particles by ordinary Bessel beams

When impinged by an arbitrary laser beam, lossless and homogeneous negative refractive index (NRI) spherical particles refract and reflect light in an unusual way, giving rise to different scattered and internal fields when compared to their equivalent positive refractive index particles. In the generalized Lorenz-Mie theory, the scattered fields are dependent upon the Mie scattering coefficients, whose values must reflect the metamaterial behavior of an NRI scatterer, thus leading to new optical properties such as force and torque. In this way, this work is devoted to the analysis of both radial and longitudinal optical forces exerted on lossless and simple NRI particles by zero-order Bessel beams, revealing how the force profiles are changed whenever the refractive index becomes negative.     

Modeling the optical properties of mineral particles suspended in seawater and their influence on ocean reflectance and chlorophyll estimation from remote sensing algorithms

The optical properties of mineral particles suspended in seawater were calculated from the Mie scattering theory for different size distributions and complex refractive indices of the particles. The ratio of the spectral backscattering coefficient to the sum of the spectral absorption and backscattering coefficients of seawater, b(b)(lambda)/[a(lambda) + b(b)(lambda)], was analyzed as a proxy for ocean reflectance for varying properties and concentrations of mineral particles. Given the plausible range of variability in the particle size distribution and the refractive index, the general parameterizations of the absorption and scattering properties of mineral particles and their effects on ocean reflectance in terms of particle mass concentration alone are inadequate. The variations in the particle size distribution and the refractive index must be taken into account. The errors in chlorophyll estimation obtained from the remote sensing algorithms that are due to the presence of mineral particles can be very large. For example, when the mineral concentration is 1 g m(-3) and the chlorophyll a concentration is low (0.05 mg m(-3)), current global algorithms based on a blue-to-green reflectance ratio can produce a chlorophyll overestimation ranging from approximately 50% to as much as 20-fold.     

Inverse Radiation Problem for Determination of Optical Constants of Fly-Ash Particles

In this paper, a technique for determining the optical constants of fly-ash particles from spectral transmittance measurements is presented. Combined with the precise Mie theory and the Kramers–Kronig (KK) relation, the complex refractive index was estimated by the spectral transmittance distribution of a cloud of fly-ash particles in potassium bromide (KBr) pellets. The unique and multi-value problems are thoroughly investigated. Particular attention is given to the error analysis of the inverse procedure including the influence of the experimental precision, the numerical simulation of the KK relation, scattering theory, and the single-scattering approximation. Good agreement was obtained between the inverse simulation results and the known optical properties of ash particles available in the literature. At the same time, an experimental analysis for two kinds of ash particles is also presented, and their spectral complex refractive indices in the range (1.0–25 μm) are determined by the inverse model used in the present work.     

Discontinuous Galerkin method for the forward modelling in optical diffusion tomography

We propose a discontinuous Galerkin discretization scheme for the forward modelling in optical diffusion tomography in highly scattering media to facilitate dynamic mesh adaptation for complex domains. In addition, the numerical method is also shown to effectively deal with inhomogeneities in optical properties and refractive index mismatch at material interfaces. The accuracy of the method is demonstrated over a model concentric spherical layers problem where the discontinuous Galerkin method is compared against an analytical solution. Copyright © 2010 John Wiley & Sons, Ltd.     

Validating the assumption to the interference approximation by use of measurements of absorption efficiency and hindered scattering in dense suspensions

Frequency domain photon migration (FDPM) measurements were employed to accurately quantify optical properties of both the suspending fluid and particles within dense polystyrene suspensions of 143- or 226-nm mean diameter at varying concentrations (5-30% by volume). The measured absorption coefficients varied linearly with particle volume fraction whereas the isotropic scattering coefficients varied nonlinearly in agreement with the prediction that utilizes the hard-sphere structure factor model. These results validate the interference approximation of light scattering to describe light propagation accurately within dense suspensions. Furthermore, owing to the accuracy of FDPM absorption measurements, the imaginary refractive indices for both particles and their suspending fluid were determined and were found to compare favorably with literature values.