Nonabsorbing Particles Research Articles

Angular truncation errors in integrating nephelometry

Ideal integrating nephelometers integrate light scattered by particles over all directions. However, real nephelometers truncate light scattered in near-forward and near-backward directions below a certain truncation angle (typically 7°). This results in truncation errors, with the forward truncation error becoming important for large particles. Truncation errors are commonly calculated using Mie theory, which offers little physical insight and no generalization to nonspherical particles. We show that large particle forward truncation errors can be calculated and understood using geometric optics and diffraction theory. For small truncation angles (i.e., <10°) as typical for modern nephelometers, diffraction theory by itself is sufficient. Forward truncation errors are, by nearly a factor of 2, larger for absorbing particles than for nonabsorbing particles because for large absorbing particles most of the scattered light is due to diffraction as transmission is suppressed. Nephelometers calibration procedures are also discussed as they influence the effective truncation error.

Optical properties of irregularly shaped particles

The phase matrix of irregularly shaped randomly oriented large fractal particles is studied in the framework of the ray tracing approach for various refractive indices. The fractal particle model can be used for modelling local optical characteristics of various natural light scattering media with irregular particles, including oceanic water, crystalline clouds and solid aerosols. For nonabsorbing large particles the theory does not contain any fitting parameters except the refractive index of particles, which is either known (ice clouds) or has generally unknown distribution in a local volume of a scattering medium (dust aerosols and oceanic suspensions).

Generalized Lorenz-Mie theory for a spheroidal particle with off-axis Gaussian-beam illumination.

The beam-shape coefficients of arbitrary off-axis Gaussian beams in spheroidal coordinates are evaluated with a generalized Lorenz-Mie theory. The light-scattering properties of absorbing and nonabsorbing homogeneous spheroidal particles, such as the angular distribution of scattered intensity for a wide range of particles sizes and different complex refractive indices versus the magnitude and location of the beam waist, are investigated.

Optical closure for an aerosol column: Method, accuracy, and inferable properties applied to a biomass‐burning aerosol and its radiative forcing

During the Lindenberg Aerosol Characterization Experiment (LACE 98), airborne measurements of aerosol size distribution, fine‐particle concentration, particle absorption coefficient, backscatter coefficient, depolarization, and chemical composition as well as ground‐based measurements of spectral particle optical depth and of spectral backscatter and extinction coefficients were performed in the aerosol column above Lindenberg, Germany. We compare the measured optical parameters with calculations from the size distributions, which assume the aerosol to consist of sulfuric acid near the tropopause and mixtures of ammonium sulfate and soot in the remaining column. We obtain closure to within 25% for the optical depth of a column, which includes a biomass‐burning aerosol of North American origin, and infer a soot volume fraction of 35% for this aerosol. Assuming spheroidal particles of prolate shape and the average aspect ratio of the particles to be 1.3 in the biomass‐burning aerosol layer, the calculated depolarization agrees with the lidar measurement, whereas comparing the spectral backscatter coefficient shows the soot to be externally mixed with the nonabsorbing particles. With the two‐stream approximation, we estimate the local, instantaneous, cloud‐free radiative forcing of the biomass‐burning aerosol at the tropopause to −5.8 W/m2 with a corresponding optical depth of 0.09 at 710 nm wavelength and solar zenith angle of 56°. The radiative forcing for the biomass‐burning aerosol is as sensitive to a change in state of mixture, either external or internal, as to a change in surface albedo, ocean to coniferous forest.

Simulating the effects of multiple scattering on images of dense sprays and particle fields.

Most optical measurements in turbid media (including sprays, fogs, particulate and colloidal suspensions) assume single scattering of the detected photons. Multiple scattering introduces error, which has been quantified in very few systems. To quantify this error, we have written a flexible Monte Carlo photon transport simulation code capable of handling any three-dimensional geometry. Simulations of planar laser spray imaging with large, nonabsorbing particles show that up to 50% of the photons reaching the camera are multiply scattered. Because forward scattering dominates, the image is affected little. For particles with more absorption or with size closer to the wavelength of the light than those we have simulated, the effects are expected to be more serious.

Scattering amplitude of absorbing and nonabsorbing spheroidal particles in the WKB approximation

This work is devoted to a theoretical study of scattering of light by absorbing and nonabsorbing oriented spheroidal particles in the Wentzel–Kramers–Brillouin (WKB) approximation. Within the framework of the scattering theory, we investigate the form factor and the scattering amplitude for this approximation. The Rayleigh–Gans–Debye theory (RGD), the diffraction approximation (DA), and the anomalous diffraction (AD) are treated as particular cases for nonabsorbing spheroids. To illustrate our formalism, we analyze some numerical examples.

Calibration of Polarization-Sensitive and Dual-Angle Laser Light Scattering Methods Using Standard Latex Particles

A polarization-sensitive laser light scattering (PSLLS) method and a dual-angle laser light scattering (DALLS) method have been studied for in situ measurement of submicrometer hydrosol and aerosol particles. By using standard monodisperse polystyrene latex particles suspended in water and air as test particles, calibration of systems built based on the above methods have been performed. The effects of light scattered by agglomerated aerosol particles (multiplets) were corrected by considering the fraction of multiplets as determined with an aerosol measurement technique using a differential mobility analyzer. The change in the measured intensities of scattered light with particle diameter was then determined by calculations based on Mie theory. It was shown that the PSLLS system can determine particle diameters as small as ∼60 nm for the test hydrosol particles and ∼100 nm for test aerosol particles, respectively. The DALLS system can determine smaller diameters than the PSLLS system for test particles with no light absorption. The change in scattered light intensities with particle diameter was also investigated by theoretical calculations with various refractive indexes and scattering angles. The PSLLS and DALLS systems promise to become routine measurement tools for absorbing and nonabsorbing particles, respectively.

Mie scattering efficiency of a large spherical particle embedded in an absorbing medium

The Mie scattering calculations are usually performed for non-absorbing spherical particles embedded in a non-absorbing medium. We consider a case of an absorbing sphere placed in an absorbing medium. We find, by numerical calculation for large size parameter of the order of 10 4, that the scattering efficiency of a spherical particle in an absorbing medium approaches the reflectance of a plane surface at perpendicular incidence.

Rheooptical determination of aspect ratio and polydispersity of nonspherical particles

AbstractA rheooptical method proposed rapidly determines the aspect ratio and polydispersity of small axisymmetric, nonspherical particles. The time evolution of the average orientation angle of optically isotropic, nonabsorbing particles upon inception of a shear flow was monitored by a polarization modulation method by using dilute suspensions of the particles. Since the orientation angle is a geometric property of the particles, no arbitrary assumptions on the scattering mechanism had to be made to analyze the data. The period of the damped oscillatory response of the orientation angle is related to the average aspect ratio. In the limit of strong flows the damping only depends on dispersion in particle shape. An analytical expression to relate the polydispersity of the equivalent hydrodynamic aspect ratio to the damping function is presented, as well as the applicability of the technique by studying the hydrodynamic aspect ratio and associated polydispersity in a sample containing ellipsoidal hematite particles.

Estimate of the aerosol properties over the ocean with POLDER

The wide field of view imaging spectroradiometer Polarization and Directionality of the Earth's Reflectance (POLDER) developed by Centre National d'Etudes Spatiales and operated aboard the Japanese heliosynchronous platform Advanced Earth Observation Satellite (ADEOS) from October 30, 1996, to June 30, 1997, provided the first global systematic measurements of the spectral, directional, and polarized characteristics of the solar radiation reflected by the Earth/atmosphere system. These original observational capabilities offer an opportunity to enhance the characterization of several components of the global environment, especially the oceanic and terrestrial vegetal primary production, the aerosol physical and optical properties, and the tridimensional structure and microphysics of clouds. Here we examine the remote sensing of aerosols over the oceans. In a first step the aerosol optical thickness and Ångström exponent are derived from the radiance measurements. In a second step the polarization measurements are used for the retrieval of the aerosol refractive index. The inversion algorithm assumes spherical, nonabsorbing particles with monomodal lognormal size distribution. The adequacy of this modeling is discussed for a representative set of aerosol observations. Successful retrieval is generally achieved in the presence of small aerosols with Ångström exponent larger than ∼1.0. For such particles, polarization may provide information on the particle refractive index. As the Ångstrom exponent of the particle decreases, the data fitting residual errors increase, especially in polarized light, which prevents the retrieval of the aerosol refractive index. The trends of the discrepancies point out two shortcomings of the aerosol modeling. The theoretical results systematically underestimate the contribution of small polarizing particles in the polarization measurements for side‐scattering angles ranging from 80° to 120°. This indicates very probably that aerosol models have to follow bimodal size distribution. On the other hand, the systematic trend of the directional behavior of the upward radiance and the lack of significant rainbow effect in the measurements result probably from nonsphericity of some large aerosols. Confirmation of these points requires improved analysis of the POLDER data.

DEVELOPMENT AND APPLICATION OF A SPECTRAL LIGHT ABSORPTION PHOTOMETER FOR AEROSOL AND HYDROSOL SAMPLES

A multi-wavelength photometer for several particulate black carbon sample substrates and sample sizes was developed and calibrated with synthetic soot samples and samples of external mixtures of soot and non-absorbing particles. With this photometer a 13 month series of daily continental aerosol samples with aerodynamic diameters below 3.2 μ m was analysed to determine black carbon concentrations and spectral absorption coefficients in the range 0.45– 1 μ m wavelength. Gravimetric mass and sulphate were analysed on the same samples. Additionally, continuous SO 2 and meteorological data were available at the sampling site. Together with concurrent size distribution data this data set provides the information for subsequent radiative transfer modelling of the radiative forcing of the light absorbing aerosol over the study area. A strong break in the time series of mass concentrations and composition clearly demonstrated the effect of new German emission regulations concerning large combustion sources. The fact that this compositional change had no effect on black carbon concentrations confirms previous studies findings indicating that black carbon over Central Europe is more related to traffic sources than to power plants.

Light backscattering by fine non-absorbing suspended particles

In this paper, light backscattering measurements with fine silica, alumina, titanium dioxide and polystyrene latex particle suspensions for solids volume fraction φ between 10 −6 and 0.3 are presented. For small φ, the measured normalized backscattered intensity can be expressed as a power law of φ with an exponent of about 0.85±0.05. Even for the smallest examined φ, multiple scattering takes place as is proved by Monte Carlo simulations and analytical calculations. For high φ, the total inverse transport mean l̃* −1 free path is found to be the determining parameter. Comparison between experimental data and the diffusion approximation of the radiative transfer theory reveals good agreement for l̃* −1>10 cm −1. In this case, a mean particle diameter can be determined supposing a particle size distribution (PSD) and knowing the volume fraction and relative refractive index of the particles.

Applicability of quasi-static and Rayleigh approximations for spheroidal particles

Expressions are obtained for the efficiency of absorption and scattering of radiation by uniform spheroids in the quasi-static approximation and the region of their applicability is studied. The prolate and oblate nonabsorbing particles with refractive indices 1.1≤n≤10 and axial ratios 1.1≤a/b≤100 were studied. The approximation expressions are found for the particle size at which the efficiency factors are calculated in the quasi-static approximation with an accuracy of 1%.

Extinction of light in dispersive media with high particle concentrations: applicability limits of the interference approximation

We investigated the limits of applicability of the interference approximation (ITA), which is often used to calculate light fields in dispersive media with high particle concentrations. We analyzed the conditions under which the use of the ITA leads to an error in calculation of the dispersive-medium extinction coefficient ∊ equal to 10%, 15%, and 25%. The analysis was carried out by comparing the values of ∊ calculated in the ITA with the results of the calculation of ∊ in a much more exact quasi-crystalline approximation (QCA). The validity of the QCA in estimating the error of the ITA is shown by comparing the values of ∊ calculated in the ITA and the QCA with experimental data [J. Opt. Soc. Am.72, 1317 (1982)]. Our investigation shows that the ITA can be used only at relatively small values of the particle size parameter x. When the relative refractive index of the particles is n≳1.8, the applicability of the ITA is limited to the case in which the particle size parameter x⩽xmax≈1.5. A decrease in n leads to an increase in xmax, and for nonabsorbing particles at n≲1.3,xmax is approximately proportional: 1/(n-1). An increase in the imaginary part of the relative refractive index of the particles κ leads to a decrease in xmax. The smaller the n, the greater the dependence of xmax on κ.

Laser-assisted removal of particles on silicon wafers

Laser cleaning is one of the new promising dry cleaning techniques considered by semiconductor companies to replace wet cleans in the near future. A dry laser cleaning tool was tested that uses an inert gas jet to remove particles lifted off by the action of a DUV excimer laser. A model was developed to simulate the cleaning process and analyze the influence of experimental parameters on laser cleaning efficiency. The best cleaning efficiencies obtained with 1.0 μm SiO2, ∼0.3 μm Si3N4, and 0.3 μm SiO2 particles deposited on Si wafers were 84±8%, 33±4%, and 12±7%, respectively. This is in qualitative agreement with theoretical calculations showing the existence of a size threshold for the removal of nonabsorbing particles by dry laser cleaning. Among the process parameters tested to optimize the process efficiency, fluence showed the highest influence on removal efficiency, before the number of laser pulses and the laser repetition rate. The use of high fluences was limited by the damaging of the wafer surface, which was not homogeneous on a macroscopic scale. The optimum number of laser pulses per unit area depended on the type of particle. The laser repetition rate had no significant influence on cleaning efficiency and can be used to reduce process time. The influence of capillary condensation on the process was demonstrated by the higher removal efficiency of 0.3 μm SiO2 and Si3N4 particles, 88±6% and 78%, respectively, upon exposure of wafers to air saturated with moisture prior to laser processing. This was attributed to the explosive evaporation of capillary condensed water, similar to the mechanism proposed for liquid assisted laser cleaning.

Derivation of aerosol properties from satellite measurements of backscattered ultraviolet radiation: Theoretical basis

We discuss the theoretical basis of a recently developed technique to characterize aerosols from space. We show that the interaction between aerosols and the strong molecular scattering in the near ultraviolet produces spectral variations of the backscattered radiances that can be used to separate aerosol absorption from scattering effects. This capability allows identification of several aerosol types, ranging from nonabsorbing sulfates to highly UV‐absorbing mineral dust, over both land and water surfaces. Two ways of using the information contained in the near‐UV radiances are discussed. In the first method, a residual quantity, which measures the departure of the observed spectral contrast from that of a molecular atmosphere, is computed. Since clouds yield nearly zero residues, this method is a useful way of separately mapping the spatial distribution of UV‐absorbing and nonabsorbing particles. To convert the residue to optical depth, the aerosol type must be known. The second method is an inversion procedure that uses forward calculations of backscattered radiances for an ensemble of aerosol models. Using a look‐up table approach, a set of measurements given by the ratio of backscattered radiance at 340–380 nm and the 380 nm radiance are associated, within the domain of the candidate aerosol models, to values of optical depth and single‐scattering albedo. No previous knowledge of aerosol type is required. We present a sensitivity analysis of various error sources contributing to the estimation of aerosol properties by the two methods.

The dependence of phase functions of large transparent particles on their refractive index and shape

A new, fast ray tracing code for calculating local optical characteristics of light-scattering media with large particles was created. The dependences of phase functions of nonabsorbing particles on their shape and refractive index were investigated. It was found that the position of the primary rainbow can be used to retrieve the aspect ratio of spheroidal particles.

Computation of the internal field of a large spherical particle by use of the geometrical-optics approximation

We obtain the internal electric field of an illuminated liquid droplet using geometrical optics. The approximation includes the phase effects of various components. We compare the geometrical-optics solution with the Mie theory solution for a nonabsorbing particle with a size parameter of alpha = 500 and an index of refraction of n = 1.332.

Light transmission by a monolayer of particles: comparison of experimental data with calculation as a single-scattering approximation

The laws of light transmission by particle monolayers are investigated. The results of measurement of coherent transmission for monolayers formed by large nonabsorbing particles are presented. The obtained results are compared to the calculation in the single-scattering approximation. Good agreement between experimental and calculated data is shown.

Applicability conditions of the Kubelka–Munk theory

The description of optical properties of light-scattering materials has made extensive use of radiative transfer models. One of the most successful and simplest models is that of Kubelka and Munk (KM). With this model, optical properties of particulate films under diffuse illumination can be predicted from effective absorption and scattering coefficients of the material. We consider the applicability conditions of this kind of model. An extended KM model for the case of perpendicular collimated illumination is compared with results from a more general four-flux approach, and the differences between them are characterized in terms of a correction factor that depends on particle scattering and absorption, concentration of the scatterers, and film thickness. It is proved formally that the extended KM model under perpendicular illumination is a good approximation for the cases of optically thick films that contain weakly or nonabsorbing particles.