Physics-based multiplicative scatter correction approaches for improving the performance of calibration models

Light scattering effects pose a major problem in the estimation of chemical properties of particulate systems such as blood, tissue, and pharmaceutical solids. Recently, Martens et al. proposed an extended multiplicative signal correction (EMSC) approach where light-scattering effects were taken into account in an empirical manner. It is possible to include causal, first-principles mathematical models based on the physics of light scattering into the EMSC framework. This could lead to significant improvements in the separation of absorption and scattering effects. A preconditioning step prior to application of EMSC, whereby a transformation based on the physics of light scattering is used to convert the spectra into a form where the absorption and scattering effects are separable (an underlying assumption of EMSC), is proposed. Results indicate that the transformation followed by EMSC gives better calibration models than the direct application of EMSC to the absorbance spectra.     

Calculation of Mie derivatives

Analytical expressions are found for the derivatives of commonly used Mie scattering parameters, in particular the absorption and the scattering efficiencies, and for the angular intensity functions. These expressions are based on the analytical derivatives of the Mie scattering amplitudes a(n) and b(n) with respect to the particle size parameter and complex refractive index. In addition, analytical derivatives are found for the volume absorption and scattering coefficients, as well as for the intensity functions of a population of particles with log normal size distribution. These derivatives are given with respect to the total number density, to the median radius and spread of the distribution, and to the refractive index. Comparison between analytically and numerically computed derivatives showed the analytical version to be 2.5 to 6.5 times as fast for the single-particle and particle-distribution cases, respectively.     

Measurement of scattering properties of individual particles with a scanning flow cytometer

A hydrofocusing head with an optical cuvette has been developed for the flow cytometer to generate complete scatter patterns of single particles at scattering angles ranging from 10° to 120°. The scatter signal has been measured as a function of the angle (a flying indicatrix) by the use of particle motion within a scanning system of the flow cytometer by the use of a single photomultiplier. Scattering data measured with the flow cytometer have been compared with those calculated from Mie theory for latex particles. A calculation algorithm has been used to estimate the size and the refractive index of spherical particles from the scattering data measured.     

Retrieval of aerosol refractive index from extinction spectra with a damped harmonic-oscillator band model

A new method for the retrieval of the spectral refractive indices of micrometer-sized particles from infrared aerosol extinction spectra has been developed. With this method we use a classical damped harmonic-oscillator model of molecular absorption in conjunction with Mie scattering to model extinction spectra, which we then fit to the measurements using a numerical optimal estimation algorithm. The main advantage of this method over the more traditional Kramers-Kronig approach is that it allows the full complex refractive-index spectra, along with the parameters of the particle size distribution, to be retrieved from a single extinction spectrum. The retrieval scheme has been extensively characterized and has been found to provide refractive indices with a maximum uncertainty of approximately 10% (with a minimum of approximately 0.1%). Comparison of refractive indices calculated from measurements of a ternary solution of HNO3, H2SO4, and H2O with those published in J. Phys. Chem. A 104, 783 (2000) show similar differences as found by other authors.     

Patterns in the ripple structure of Mie scattering.

We study the ripple structure in the scattered intensity predicted by Mie scattering theory in the angular behavior of the scattered intensity for homogeneous, dielectric spheres. We find that for small values of the phase shift parameter rho = 2kR absolute value(m - 1), where k = 2 pi/lambda, R is the sphere radius, and m is the relative refractive index, the ripples are periodic with spacing equal to pi when plotted versus the dimensionless qR, where q = 2k sin(theta/2) and theta is the scattering angle. However, as rho increases, this outcome switches to nonuniform spacing of approximately pi cos(theta/2). The latter spacing is equivalent to a uniform spacing of pi/kR when plotted versus theta.     

Fluorophore-Decorated Mie Resonant Silicon Nanosphere for Scattering/Fluorescence Dual-Mode Imaging

Inorganic nanoparticles with multiple functions have been attracting attention as multimodal nanoprobes in bioimaging, biomolecule detection, and medical diagnosis and treatment. A drawback of conventional metallic nanoparticle-based nanoprobes is the Ohmic losses that lead to fluorescence quenching of attached molecules and local heating under light irradiation. Here, metal-free nanoprobes capable of scattering/fluorescence dual-mode imaging are developed. The nanoprobes are composed of a silicon nanosphere core having efficient Mie scattering in the visible to near infrared range and a fluorophore doped silica shell. The dark-field scattering and photoluminescence images/spectra for nanoprobes made from different size silicon nanospheres and different kinds of fluorophores are studied by single particle spectroscopy. The fluorescence spectra are strongly modified by the Mie modes of a silicon nanosphere core. By comparing scattering and fluorescence spectra and calculated Purcell factors, the fluorescence enhancement factor is quantitatively discussed. In vitro scattering/fluorescence imaging studies on human cancer cells demonstrate that the developed nanoparticles work as scattering/fluorescence dual-mode imaging nanoprobes.     

Mie and Rayleigh modeling of visible-light scattering in neonatal skin

Reduced-scattering coefficients of neonatal skin were deduced in the 450-750-nm range from integrating-sphere measurements of the total reflection and total transmission of 22 skin samples. The reduced-scattering coefficients increased linearly at each wavelength with gestational maturity. The distribution of diameters d and concentration ρ(A) of the skin-sample collagen fibers were measured in histological sections of nine neonatal skin samples of varying gestational ages. An algorithm that calculates Mie scattering by cylinders was used to model the scattering by the collagen fibers in the skin. The fraction of the reduced-scattering coefficient μ(s)' that was attributable to Mie scattering by collagen fibers, as deduced from wavelength-dependent analysis, increased with gestational age and approached that found for adult skin. An assignment of 1.017 for n(rel), the refractive index of the collagen fibers relative to that of the surrounding medium, allowed the values for Mie scattering by collagen fibers, as predicted by the model for each of the nine neonatal skin samples to match the values for Mie scattering by collagen fibers as expected from the measurements of μ(s)'. The Mie-scattering model predicted an increase in scattering with gestational age on the basis of changes in the collagen-fiber diameters, and this increase was proportional to that measured with the integrating-sphere method.     

Patterns in Mie scattering: evolution when normalized by the Rayleigh cross section

An alternative to using the traditional scattering angle theta to describe light scattering from a uniform dielectric sphere is the dimensionless parameter qR, where R is the radius of the sphere, q = 2k sin(theta/2), and k is the wavenumber of the incident light. Simple patterns appear in the scattered intensity if qR is used in place of theta. These patterns are characterized by the envelopes approximating the scattered intensity distributions and are quantified by the phase-shift parameter rho = 2kR/m - 1/, where m is the real refractive index of the sphere. Here we find new patterns in these envelopes when the scattered intensity is normalized to the Rayleigh differential cross section. Mie scattering is found to be similar to Rayleigh scattering when p < 1 and follows simple patterns for p > 1, which evolve predictably as a function of p. These patterns allow us to present a unifying picture of the evolution of Mie scattering for changes in kR and m.     

Random media characterization using the analysis of diffusing light data on the basis of an effective medium model

The transport properties of dense random media such as rutile powder layers and polyball suspensions are analyzed in visible and near infrared on the basis of experimental data on coherent backscattering, diffuse transmittance, and low-coherence interferometry. The developed technique of retrieval of the transport parameters of examined scattering media allows the evaluation of the transport mean free path l* and the effective refractive index n(ef) of the medium without a priori knowledge of the optical properties of the scattering particles. It is found that with decreasing wavelength lambda(0) the value of localization parameter 2pin(ef)l*/lambda(0) of the studied rutile samples abruptly drops and approaches approximately 2.6 at 473 nm. This peculiarity is caused by the very large scattering efficiency of scatterers in the vicinity of the first Mie resonance.     

经典Mie散射的数值计算方法改进

在光散射颗粒测量技术中,Mie散射理论的计算非常重要。本文介绍一种改进的Mie散射数值计算方法,通过对Mie散射系数进行重新构造,找到参量来控制Mie计算的收敛和计算精度。对各有关参量选用合适、稳定的递推关系进行计算。数值计算结果表明该方法具有快速、稳定的优点,可以在极大的颗粒粒径和折射率范围内得到合理结果。     

An Approximation Method for the Backward Scattering of Light by a Soft Spherical Obstacle

Abstract

The optical analogue of a formula by Reading and Bassichis for the backscattering of a high-energy scalar wave by a square-well potential has been examined. In optical scattering, this corresponds to the problem of the back-scattering of light by a homogeneous spherical particle. Numerical checks with the Mie theory are presented for various values of the refractive index and size parameter. The formula is found to reproduce some scattering features extremely well for intermediate-size soft particles.     

Extended multiplicative signal correction as a tool for separation and characterization of physical and chemical information in Fourier transform infrared microscopy images of cryo-sections of beef loin

Extended multiplicative signal correction (EMSC) is used to separate and to characterize physical and chemical information in spectra from Fourier transform infrared (FT-IR) microscopy. This appears especially useful for applications in infrared spectroscopy where the scatter variance in spectra changes with the chemical variance in the sample set. In these cases the chemical information of specific bands that are assigned to functional groups is easier to interpret when the scatter information is removed from the spectra. We show that scatter (physical) information in FT-IR spectra of heat-treated beef loin is related to chemical changes due to heat treatment. This information is caused by textural changes induced by the heat treatment and expressed by physical effects as the optical path length. The chemical absorbance changes introduced in the FT-IR spectra due to heat treatment are shifts in the protein region of the infrared spectrum caused by changes in the secondary structure of the proteins. If the scatter and the chemical information is not separated properly, scatter information may erroneously be interpreted as chemical information.     

Effect of aerosol microphysical properties on polarization of skylight: sensitivity study and measurements

We analyze the sensitivity of the degree of linear polarization in the Sun's principal plane as a function of aerosol microphysical parameters: the real and imaginary parts of the refractive index, the median radius and geometric standard deviation of the bimodal size distribution (both fine and coarse modes), and the relative number weight of the fine mode at a wavelength of 675 nm. We use Mie theory for single-scattering simulations and the doubling-adding method with the inclusion of polarization for multiple scattering. It is shown that the behavior of the degree of linear polarization is highly sensitive to both the small mode of the bimodal size distribution and the real part of the refractive index of aerosols, as well as to the aerosol optical thickness; whereas not all parameters influence the polarization equally. A classification of the importance of the input parameters is given. This sensitivity study is applied to an analysis of ground-based polarization measurements. For the passive remote sensing of microphysical and optical properties of aerosols, a ground-based spectral polarization measuring system was built, which aims to measure the Stokes parameters I, Q, and U in the visible (from 410 to 789 nm) and near-infrared (from 674 to 995 nm) spectral range with a spectral resolution of 7 nm in the visible and 2.4 nm in the near infrared. We compare polarization measurements taken with radiative transfer simulations under both clear- and hazy-sky conditions in an urban area (Cabauw, The Netherlands, 51.58 degrees N, 4.56 degrees E). Conclusions about the microphysical properties of aerosol are drawn from the comparison.     

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.     

Numerical evaluation of droplet sizing based on the ratio of fluorescent and scattered light intensities (LIF/Mie technique)

The dependence of fluorescent and scattered light intensities from spherical droplets on droplet diameter was evaluated using Mie theory. The emphasis is on the evaluation of droplet sizing, based on the ratio of laser-induced fluorescence and scattered light intensities (LIF/Mie technique). A parametric study is presented, which includes the effects of scattering angle, the real part of the refractive index and the dye concentration in the liquid (determining the imaginary part of the refractive index). The assumption that the fluorescent and scattered light intensities are proportional to the volume and surface area of the droplets for accurate sizing measurements is not generally valid. More accurate sizing measurements can be performed with minimal dye concentration in the liquid and by collecting light at a scattering angle of 60° rather than the commonly used angle of 90°. Unfavorable to the sizing accuracy are oscillations of the scattered light intensity with droplet diameter that are profound at the sidescatter direction (90°) and for droplets with refractive indices around 1.4.     

基于Mie散射理论的微球体颗粒数值模拟计算和实验研究

应用Mie散射理论,在散射角0～π范围内,模拟微球体颗粒的散射光强度与粒径大小的变化关系,分析了相对折射率的大小对散射光强度的影响;在实验装置条件下,分别模拟了散射光强度与粒径大小的变化关系及2um、5um、10um三种粒子的散射光强度与波长的变化关系。实验验证了数值模拟与实验结果基本一致,也证明实验中粒子散射遵从Mie散射理论模型。     

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.     

纳米及微米磁性颗粒在长波长下的光散射特性分析

根据Mie散射理论,分析计算了纳米级、微米级磁性颗粒的光散射特性。针对目前在导航、遥控及雷达等行业广泛应用的纳米、微米磁性颗粒,在Mie散射系数中引入磁导率变量,对比分析了磁性与非磁性颗粒、吸收性与非吸收性颗粒的散射特性规律。数值计算结果表明,磁导率的变化对具有吸收性磁性颗粒的散射特性造成影响,随着磁导率的增大,颗粒的散射光强及吸收性能将逐渐增大,同时磁导率增大对颗粒散射特性的影响将会受到复折射率实部的制约。     

两种方法测量大气气溶胶折射率的对比分析

针对气溶胶折射率在分析大气气溶胶光学特性中的重要性,介绍两种综合利用黑碳仪、浊度计、光学粒子计数器和微脉冲激光雷达测量大气气溶胶折射率的新方法。两种方法都是根据球形粒子的Mie散射理论计算大气气溶胶的折射率,使用以上两种方法对厦门地区气溶胶折射率进行了计算和对比分析,证明了它们的合理性,分析了它们的测量精度和误差来源。