Forward scattering of a Gaussian beam by a nonabsorbing sphere

The forward scattering of a Gaussian laser beam by a spherical particle located along the beam axis is analyzed with the generalized Lorenz-Mie theory (GLMT) and with diffraction theory. Forwardscattering and near-forward-scattering profiles from electrodynamically levitated droplets, 51.6 μm in diameter, are also presented and compared with GLMT-based predictions. The total intensity in the forward direction, formed by the superposition of the incident and the scattered fields, is found to correlate with the particle-extinction cross section, the particle diameter, and the beam width. Based on comparison with the GLMT, the diffraction solution is accurate when beam widths that are approximately greater than or equal to the particle diameter are considered and when large particles that have an extinction efficiency near the asymptotic value of 2 are considered. However, diffraction fails to describe the forward intensity for more tightly focused beams. The experimental observations, which are in good agreement with GLMT-based predictions, reveal that the total intensity profile about the forward direction is quite sensitive to particle axial position within a Gaussian beam. These finite beam effects are significant when the ratio of the beam to the particle diameter is less than approximately 5:1. For larger beam-to-particle-diameter ratios, the total field in the forward direction is dominated by the incident beam.     

Extinction and the optical theorem. Part I. Single particles

We study the extinction caused by a single particle and present a conceptual phase-based explanation for the related optical theorem. Simulations of the energy flow caused by a particle's presence in a collimated beam of light demonstrate how the extinction process occurs. It is shown that extinction does not necessarily cause a reduction of the energy flow along the exact forward direction. Implications regarding the measurement of the single-particle extinction cross section are discussed. This work is extended to noninteracting and interacting multiparticle groups in Part II [J. Opt. Soc. Am. A25, pp. 1514 (2008)].     

Interbunch extinction measurement at the BNL AGS for the KOPIO experiment

The KOPIO experiment at the BNL AGS required an extracted proton beam in which a debunched, coasting beam is forced between empty longitudinal RF buckets to form microbunches. The goal of the measurement described here was to obtain a low background determination of the fraction of protons coming from the AGS slowly extracted beam at times between microbunches (interbunch extinction). The effect on interbunch extinction of variations in the RF cavity voltage, the momentum dispersion of the beam and the main guide field voltage-ripple was studied. It was found that there exists a broad range of operating parameters that could allow the AGS to produce microbunches with the interbunch extinction better than the KOPIO experiment requirement. Results obtained in this study gave interbunch extinctions better than 10⁻⁵ (1%) of KOPIO's upper limit.     

Effective phase function for light scattered by blood

The scattering process induced in blood by a collimated laser beam is theoretically investigated. An individual red blood cell (RBC) has a scattering phase function strongly peaked in the forward direction. For far-field experiments, the small scattering volumes can be considered as "macroscopic particles" characterized by an effective scattering phase function. Using the single-cell phase function as "input data" the angular distribution of light scattered at small angles by the whole scattering volume, containing RBCs in suspension, is calculated analytically. The angular dispersion of the light scattered by blood can be approximately described by the same formula used to characterize the light scattered by a single cell but with an effective, hematocrit-dependent anisotropy parameter.     

Optical and physical properties of stratospheric aerosols from balloon measurements in the visible and near-infrared domains. 1. Analysis of aerosol extinction spectra from the AMON and SALOMON balloonborne spectrometers

Aerosol extinction coefficients have been derived in the 375-700-nm spectral domain from measurement in the stratosphere since 1992, at night, at mid- and high latitudes from 15 to 40 km, by two balloonborne spectrometers, Absorption par les Minoritaires Ozone et NO(chi) (AMON) and Spectroscopie d'Absorption Lunaire pour l'Observation des Minoritaires Ozone et NO(chi) (SALOMON). Log-normal size distributions associated with the Mie-computed extinction spectra that best fit the measurements permit calculation of integrated properties of the distributions. Although measured extinction spectra that correspond to background aerosols can be reproduced by the Mie scattering model by use of monomodal log-normal size distributions, each flight reveals some large discrepancies between measurement and theory at several altitudes. The agreement between measured and Mie-calculated extinction spectra is significantly improved by use of bimodal log-normal distributions. Nevertheless, neither monomodal nor bimodal distributions permit correct reproduction of some of the measured extinction shapes, especially for the 26 February 1997 AMON flight, which exhibited spectral behavior attributed to particles from a polar stratospheric cloud event.     

Experimental and theoretical study of light scattering by individual mature red blood cells by use of scanning flow cytometry and a discrete dipole approximation

Elastic light scattering by mature red blood cells (RBCs) was theoretically and experimentally analyzed by use of the discrete dipole approximation (DDA) and scanning flow cytometry (SFC), respectively. SFC permits measurement of the angular dependence of the light-scattering intensity (indicatrix) of single particles. A mature RBC is modeled as a biconcave disk in DDA simulations of light scattering. We have studied the effect of RBC orientation related to the direction of the light incident upon the indicatrix. Numerical calculations of indicatrices for several axis ratios and volumes of RBC have been carried out. Comparison of the simulated indicatrices and indicatrices measured by SFC showed good agreement, validating the biconcave disk model for a mature RBC. We simulated the light-scattering output signals from the SFC with the DDA for RBCs modeled as a disk-sphere and as an oblate spheroid. The biconcave disk, the disk-sphere, and the oblate spheroid models have been compared for two orientations, i.e., face-on and rim-on incidence, relative to the direction of the incident beam. Only the oblate spheroid model for rim-on incidence gives results similar to those of the rigorous biconcave disk model.     

Scattering by a dense finite layer of infinite cylinders at oblique incidence

This paper presents the scattering solution for a finite dense layer of cylinders irradiated by an arbitrarily polarized plane wave at a general incident direction. The theoretical formulation utilizes the effective field approach and quasi-crystalline approximation to derive the governing equations for the propagation constant and amplitudes of the effective waves. The finite layer thickness gives rise to effective waves propagating in both the forward and backward directions inside the dense medium. Formulas are developed for the far-field coherent and incoherent scattered intensities, as well as the extinction and scattering cross sections of the dense layer. The forward peak of the incoherent scattered intensity is shown to be shifted to the propagating direction of the effective waves. The influence of incident direction, layer thickness, and solid volume fraction on the scattering properties is illustrated by means of a numerical example.     

Cross-type optical particle separation in a microchannel

A continuous, real-time optical particle separation, which was previously delineated theoretically, is successfully implemented experimentally for the first time. In this method, particles suspended in a flowing fluid are irradiated with a laser beam propagating in a direction perpendicular to direction of fluid flow. Upstream of the laser beam, the particles move parallel to the direction of fluid flow. When the particles pass through the laser beam, the scattering force pushes them in the direction of laser beam propagation, causing the particles to be displaced perpendicular to the fluid flow direction. This displacement, known as the retention distance, depends on the particle size and the laser beam parameters. Finally, the particles escape from the laser beam and maintain their retention distances as they move downstream. In the present work, the trajectories and retention distances of polystyrene latex microspheres with three distinct diameters were monitored and measured using cross-type optical particle separation. The measured retention distances for different-sized particles were in good agreement with theoretical predictions.     

Tungsten source integrated cavity output spectroscopy for the determination of ambient atmospheric extinction coefficient

Broadband integrated cavity output spectroscopy (ICOS) utilizing an incoherent tungsten lamp as a spectroscopic source is described. This novel approach has been termed W-ICOS. The technique has been applied to make quantitative measurements of Rayleigh scattering by carbon dioxide between 570 and 590 nm and to make measurements of aerosol and atmospheric extinction. Minimum detectable extinction coefficients (kext) made in a 94 cm optical cavity ranged between 3.4 and 35 Mm(-1) depending on the level of signal averaging employed. The level of sensitivity achieved should allow measurements on static gas samples and regular, quantitative measurements of the atmospheric extinction coefficient.     

Light Scattering by Commercial Sugar Solutions

Using a direct measure of scattered light, it was found that commercial sugar solutions scatter light predominantly in a forward direction. The scattering at angles less than 30° was as much as one hundred times that at right angles to the incident beam.It was found that the light scattering by commercial sugar solutions is inversely dependent on wavelength to a power of between 2 and 3, and that severe multiple scattering occurs when the turbidity of the solution is larger than 2×10⁻¹cm⁻¹ at 436 mµ. The scattering of commercial sugar solutions is compared with that of highly purified sucrose.A method is discussed that will enable a good approximation of the turbidity of commercial sugar solutions to be made from a single forward scattering measurement at an angle of about 20° with respect to the incident light beam. A correction for scattered light in transmission measurements of these solutions is also introduced.     

Yet another look at light scattering from particles in absorbing media

We examine the scattering properties of particles contained in absorbing media. Rather than consider energy fluxes through arbitrary integrating spheres, we examine the extinction from its fundamental definition: the energy removed from the plane wave, or incident beam. The resulting energy received by a detector contains two terms: one the result of the incident beam traversing through the medium that would have occurred if the particle were not present, and a correction term due to the presence of the particle. Both terms have the same dependence on the pathlength that the beam travels between two arbitrarily located parallel planes and are independent of where the particle is located within the medium. The result is that the definition of the extinction cross section is not dependent on a reference plane or the particle location within the medium.     

Finite-difference time-domain solution of light scattering and absorption by particles in an absorbing medium

The three-dimensional (3-D) finite-difference time-domain (FDTD) technique has been extended to simulate light scattering and absorption by nonspherical particles embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition is used to truncate the computational domain. When computing the single-scattering properties of a particle in an absorbing dielectric medium, we derive the single-scattering properties including scattering phase functions, extinction, and absorption efficiencies using a volume integration of the internal field. A Mie solution for light scattering and absorption by spherical particles in an absorbing medium is used to examine the accuracy of the 3-D UPML FDTD code. It is found that the errors in the extinction and absorption efficiencies from the 3-D UPML FDTD are less than approximately 2%. The errors in the scattering phase functions are typically less than approximately 5%. The errors in the asymmetry factors are less than approximately 0.1%. For light scattering by particles in free space, the accuracy of the 3-D UPML FDTD scheme is similar to a previous model [Appl. Opt. 38, 3141 (1999)].     

An inverse light scattering technique for morphological characterization of irregular particles based on the Gaussian-random-sphere model

The Gaussian-random-sphere model is employed for morphological characterization of nonspherical, irregular particles using an inverse light scattering technique. The synthetic measurement data consist of reduced scattering spectra caused by an aggregate of irregular particles randomly oriented in turbid media and are generated using the discrete dipole approximation. The proposed method simultaneously retrieves the concentration and shape parameters of particles using the data collected at multiple wavelengths. The performance of the inverse algorithm is tested using noise-corrupted data, in which up to 50% noise may be added to the observed scattering spectra.     

Error analysis of Raman differential absorption lidar ozone measurements in ice clouds

A formalism for the error treatment of lidar ozone measurements with the Raman differential absorption lidar technique is presented. In the presence of clouds wavelength-dependent multiple scattering and cloud-particle extinction are the main sources of systematic errors in ozone measurements and necessitate a correction of the measured ozone profiles. Model calculations are performed to describe the influence of cirrus and polar stratospheric clouds on the ozone. It is found that it is sufficient to account for cloud-particle scattering and Rayleigh scattering in and above the cloud; boundary-layer aerosols and the atmospheric column below the cloud can be neglected for the ozone correction. Furthermore, if the extinction coefficient of the cloud is ?0.1 km(-1), the effect in the cloud is proportional to the effective particle extinction and to a particle correction function determined in the limit of negligible molecular scattering. The particle correction function depends on the scattering behavior of the cloud particles, the cloud geometric structure, and the lidar system parameters. Because of the differential extinction of light that has undergone one or more small-angle scattering processes within the cloud, the cloud effect on ozone extends to altitudes above the cloud. The various influencing parameters imply that the particle-related ozone correction has to be calculated for each individual measurement. Examples of ozone measurements in cirrus clouds are discussed.     

人造水雾粒度测试及红外消光因子计算分析

在大型半密闭空间内发生具有不同粒度分布的水雾体系,用喷雾激光粒度仪测试粒度分布规律并采用Van Der Hulst公式计算不同大小水雾粒子对红外辐射的散射效率因子、吸收效率因子和消光效率因子。结果表明:试验条件下水雾粒子的平均直径在5~65μm范围内。计算结果显示:水雾粒子对3～5、8～14μm红外辐射的消光作用主要取决于散射效应而非吸收效应。当水雾粒子的直径大于等于红外辐射的波长时,水雾体系对该波长红外辐射能够产生较强的消光效果。综合分析水雾体系的稳定性和消光特性,直径在3~30μm之间的水雾粒子对3～5、8～14μm红外辐射的衰减效果更为明显。     

Corrections to facilitate planar imaging of particle concentration in particle-laden flows using Mie scattering, part 1: collimated laser sheets

Planar nephelometry is a laser-based technique of imaging the light scattered from particles to provide information about the local number density of these particles. In many seeded flows of practical interest, such as pulverized coal flames, particle loadings are sufficiently high for the incident laser beam to be severely attenuated. Measurements in these flows are therefore difficult, and limited data are available under these conditions. Laser attenuation experiments were conducted in suspensions of spherical particles in water at various concentrations. This is used to formulate a calibration for the effects of diffuse scattering and laser sheet extinction. A model for the distribution of light through a heavily seeded, light-scattering medium is also developed and is compared with experimental results. It is demonstrated that the scattered signal may be considered proportional to the local particle concentration multiplied by the incident laser power. The incident laser power varies as a function of the attenuation by obscurement. This correction for planar nephelometry images thus extends the technique to provide pseudoquantitative data for instantaneous particle concentration measurements.     

Light scattering of ultrafine silica particles by VUV synchrotron radiation

Vacuum ultraviolet (VUV) light scattering from ultrafine silica particles is studied with an aerosol instrument recently established at the Advanced Light Source (ALS) in Berkeley. Silica particles, size-selected by a differential mobility analyzer, are introduced into vacuum through a set of aerodynamic lenses to form a particle beam. The scattered photons from the crossing area of the VUV synchrotron beam and particle beam are detected with a rotatable VUV photon detector. The angular distributions of scattered photons (ADSP) originating from 70, 100, 200 nm diameter silica particles are measured with 145.9 and 118.1 nm synchrotron radiation. These angular distributions show strong forward scattering. The measured ADSPs are consistent with simulation of Mie scattering. The refractive indices of silica particles, 2.6 + 1.1i and 1.6 + 0.0001i for 118.1 and 145.9 nm, respectively, are obtained by fitting the measured ADSPs; the least average percentage deviations are 18% and 6%, respectively. The scattered fluxes at widely different wavelengths (visible versus VUV) also exhibit clear size sensitivity. Under comparable experimental conditions of photon fluxes and detection efficiencies, limits of particle size detection of 70 and 250 nm are obtained, respectively, when using 118.1 and 532 nm illumination. As anticipated, VUV scattering is a more sensitive probe for ultrafine particles, which will find application in detection of these ubiquitous species beyond the confines of a laboratory.     

Multiple scattering in optical coherence microscopy

We show that the multiple-scatter rejection provided by optical coherence microscopy (low-coherence interferometry) can be incomplete in optically turbid media and that multiple scattering manifests itself in two distinct ways. Multiple small-angle scattering results in an effective probe field that is stronger than expected from a first-order beam extinction model, but that contains a distorted wave front that enhances the apparent reflectance of small structures relative to those that are larger than the unscattered incident beam. Multiple wide-angle scattering produces a broad diffuse haze that reduces the contrast of subsequent features.     

Differences arising in the determination of the atmospheric extinction coefficient by transmission and target reflectance measurements

Measurements of the optical extinction at a wavelength of 1.06 microm have been made in water droplet clouds. The extinction coefficient has been measured in the laboratory using two different methods simultaneously. In the first, measurements of the transmitted signal attenuation over a known path length were used. In the second the extinction coefficient was derived from the two-way attenuation of the signal reflected from a target on the opposite side of the cloud from the laser source and detector. It is found that in general the two values of the coefficient derived differ considerably, and the magnitude of the difference depends on the cloud density, the target size, and the system's optical parameters. The difference is shown to originate in the off-axis forward scattering caused by the cloud droplets, and the implications of the results on the measurement of the atmospheric extinction by reflection (lidar) techniques are discussed.