Numerical study of light scattering by a boundary-layer flow

Temperature inhomogeneities in free, isotropic turbulence have the effect of scattering light in near-forward angles. We investigate numerically modifications of free turbulence by a rigid wall and its effect on the propagation of light through turbulence. The wall is a 5 cm optical window placed at the leading edge of an instrument towed with speeds of 0.1 and 1 m/s in free turbulence. The turbulent flow field presents inhomogeneities of an embedded passive scalar (Pr = 7, temperature in water), which are modified by the boundary layer developing on the window. We find that the developing laminar boundary layer has a negligible effect on light scattering for the investigated geometry when considered in terms of the volume-scattering function (differential cross section). This indicates that the boundary layer is not an obstacle for optical measurements of turbulence.     

Light scattering on oceanic turbulence

Turbulent inhomogeneities of fluid flow have the effect of scattering light in near-forward angles, thus providing an opportunity to use optics to quantify turbulence. Here we report measurements of the volume-scattering function in the range of 10(-7) to 10(-3) rad using a wave-front sensing technique. The total scattering coefficient b, due to scattering on turbulent inhomogeneities, is between 1 and 10 m(-1) under typical oceanographic conditions. The numerical calculations of turbulent volume-scattering functions compare well with the laboratory measurement. These results suggest that optical measurements at small angles are affected by turbulence-related scattering, and their effects can be well modeled with numerical calculations.     

The Eikonal Approximation to Near-forward Light Scattering from Homogeneous Spheres

The eikonal approximation and modified eikonal approximation are considered for near-forward light scattering from transparent homogeneous spheres of diameter 0·2-5·0 μm. Numerical comparisons with the exact theory are presented for values of relative refractive indices of less than 1·15. The implications of these results for sizing spherical particles are briefly discussed.     

In situ particle size measurements using a two-color laser scattering technique

We have developed a technique using light scattered from individual particles in the near-forward direction to measure particle size in the range of 10-200 microm. This technique uses the Mie scattering theory to relate the measured light intensity to particle size based on calibration techniques employing pinholes and water droplets of known size. We have applied a unique two-color optical arrangement to minimize the edge effect which can cause incorrect size measurements for particles that pass through the edge of the laser beam focal volume. In this paper we describe our experimental technique and the results of size measurements obtained with this technique for water droplets and pulverized coal particles.     

Detection of biological particles by the use of circular dichroism measurements improved by scattering theory

Light scattered from optically active spheres was theoretically analyzed for biodetection. The circularly polarized signal of near-forward scattering from circularly dichroic spheres was calculated. Both remote and point biodetection were considered. The analysis included the effect of a circular aperture and beam block at the detector. If the incident light is linearly polarized, a false signal would limit the sensitivity of the biodetector. If the incident light is randomly polarized, shot noise would limit the sensitivity. Suggested improvements to current techniques include a beam block, precise angular measurements, randomly polarized light, index-matching fluid, and larger apertures for large particles.     

Optical turbulence on underwater image degradation in natural environments

It is a well-known fact that the major degradation source on electro-optical imaging underwater is from scattering by particles of various origins and sizes. Recent research indicates that, under certain conditions, the apparent degradation could also be caused by the variations of index of refraction associated with temperature and salinity microstructures in the ocean and lakes. The combined impact has been modeled previously through the simple underwater imaging model. The current study presents the first attempts in quantifying the level of image degradation due to optical turbulence in natural waters in terms of modulation transfer functions using measured turbulence dissipation rates. Image data collected from natural environments during the Skaneateles Optical Turbulence Exercise are presented. Accurate assessments of the turbulence conditions are critical to the model validation and were measured by two instruments to ensure consistency and accuracy. Optical properties of the water column in the field were also measured in coordination with temperature, conductivity, and depth. The results show that optical turbulence degrades the image quality as predicted and on a level comparable to that caused by the particle scattering just above the thermocline. Other contributing elements involving model closure, including temporal and spatial measurement scale differences among sensors and mitigation efforts, are discussed.     

Observations and calculations of light scattering from clusters of spheres

Two-dimensional angular optical scattering (TAOS) patterns from clusters of polystyrene latex spheres are measured in the near-forward and near-backward directions. In both cases, the scattering pattern contains a rich and complicated structure that is the result of the interaction and interference of light among the primary particles. Calculations are made for aggregates that are similar to those generated experimentally and also demonstrate the rich structure in the scattering pattern. A comparison of the experimental and theoretical TAOS patterns gives good qualitative agreement.     

用激光散射法测量大颗粒时使用衍射理论的误差

从实验数据，物理和几何光学的定性分析及Ｍｉｅ理论的严格计算等三个方面证明了即便是远远大于光波长的颗粒的散射光场，其实际光能分布与衍射理论给出的结果之间也有不可忽略的误差：表现为较大散射角上实际的散射光能远大于衍射理论光能。按照衍射理论的计算结果，这一误差等效于１μｍ左右的颗粒产生的光能分布。如果颗粒对光具有吸收性，则误差将显著减少。     

The effect of clustering of particles on Rayleigh scattering of radiation in a turbulent flow

The effect of clustering of particles under conditions of homogeneous isotropic turbulence on Rayleigh scattering of radiation is analyzed. It is demonstrated that, similarly to the diagnostics of molecular structure of liquid using X-ray scattering, the radial distribution function of macroscopic particles, which characterizes the clustering phenomenon, may be determined by way of measuring the intensity of scattering of infrared or microwave radiation. An approximate relation for clustering coefficient is obtained, which may be employed for estimating the increase in reflected radiation of microwave radar from cumulus clouds owing to turbulent clustering of water drops in the cloud.     

Quantitative light-scattering angular correlations of conglomerate particles

A quantitative analysis of the fluctuations in the scattering associated with micrometer-size glycerol droplets that contain spherical latex inclusions are performed. Scattering intensities at two angles (the near-forward and the near-backward directions) are measured as functions of time. We analyze these signals using two techniques. We find that calculated autocorrelation time constants associated with these signals are not consistent with current models based on interference of light scattering from latex inclusions that exhibit Stokes-Einstein diffusion. The intensity fluctuations at different scattering angles display extended periods of both positive and negative correlations with characteristic time constants of the order of seconds. The time constants associated with the cross correlations provide information on the physical parameters of the inclusions.     

Application of the small-angle approximation to ocean water types

The small-angle approximation to the radiative transport equation is applied to particle suspensions that emulate ocean water. A particle size distribution is constructed from polystyrene and glass spheres with the best available data for particle size distributions in the ocean. A volume scattering function is calculated from the Mie theory for the particles in water and in oil. The refractive-index ratios of particles in water and particles in oil are 1.19 and 1.01, respectively. The ratio 1.19 is comparable to minerals and nonliving diatoms in ocean water, and the ratio 1.01 is comparable to the lower limit for microbes in water. The point-spread functions are measured as a function of optical thickness for both water and oil mixtures and compared with the point-spread functions generated from the small-angle approximation. Our results show that, under conditions that emulate ocean water, the small-angle approximation is valid only for small optical thicknesses. Specifically, the approximation is valid only for optical thicknesses less than 3.     

Electromagnetic phase differences in the coherent backscattering enhancement mechanism for random media consisting of large nontransparent spheres

Phase curves of intensity are calculated for light scattering in media randomly packed with large nontransparent spheres (x=125), the surfaces of which reflect according to the Fresnel equations. We consider three values of refractive index: m = 0.73 + i5.93 (metal Al), 1.6 + i1.72 (metal Fe), and 1.5 + i0.1 (black glass). We use a Monte Carlo ray-tracing approach. Different kinds of electromagnetic phase differences of reciprocal trajectories are investigated for the second and third orders of scattering; the highest orders give comparatively small contributions due to the backward-scattering indicatrix of large nontransparent spheres. We find that the main electromagnetic phase difference between the direct and time-reversal (reciprocal) trajectories is the outer phase difference that depends only on the relative positions of the first and last points of the ray reflections and the phase angle. The inner phase difference is connected with the changing path length of the ray inside the medium. This depends on the particle size and the phase angle that is the angle between the source and receiver from the scatterer, i.e., 180 degrees minus the scattering angle. The inner phase difference can give oscillations in the phase curve consisting of second-order components if the medium consists of strictly monodisperse spheres. Usually the coherent backscattering enhancement is calculated ignoring the shadow-hiding effect. We show that accounting for the shadowing of the reciprocal trajectory is important for the formation of the backscattering effect. The third-order scattering surge is a superposition of wide and narrow opposition spikes that correspond to two different types of scattering trajectories, closed and opened ones. The first type is due to scattering by two particles; the second one corresponds to scattering by three particles.     

Measurement of the Mueller matrix for ocean water

The normalized light scattering polarization matrix has been measured for ocean water using an electrooptic light scattering polarimeter. Measurements were done on samples from the Atlantic and Pacific Oceans and the Gulf of Mexico. The polarization effects in the matrices were found to have, in general, a form which is similar to polarization effects in the Rayleigh scattering approximation; for example, all off-diagonal matrix elements except S12 and S21 were zero. Mueller matrix elements were calculated using a Mie computer code and compared to the measured matrices for ocean water. A simple one-component distribution was found to produce a reasonably good fit.     

Estimation of scattering error in spectrophotometric measurements of light absorption by aquatic particles from three-dimensional radiative transfer simulations

We present an approach based on three-dimensional Monte Carlo radiative transfer simulations for estimating scattering error in measurements of light absorption by aquatic particles with a typical laboratory double-beam spectrophotometer. The scattering error is calculated by combining the weighting function describing the angular distribution of photon losses that are due to scattering on suspended particles with the volume scattering function of particles. We applied this method to absorption measurements made on marine phytoplankton, a diatom Thalassiosira pseudonana and a cyanobacterium Synechococcus. Assuming that the scattering phase function is described by the Henyey-Greenstein formula, we determined the backscatter probability of phytoplankton, which yields the best correction for scattering error at a light wavelength of 750 nm, where true absorption is null. The backscattering ratio estimated for both phytoplankton species is significantly higher than previously reported data based on Mie-scattering calculations for homogeneous spheres. Depending on the type of particles, the corrected absorption spectra obtained with our method may be similar or significantly different from spectra obtained with the null-point correction based on wavelength-independent scattering error.     

Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle

The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate the scattering diagram in all directions from 0 degrees to 180 degrees. The intensities of the scattered field calculated by the EGOA are compared with those calculated by the generalized Lorenz-Mie theory, and good agreement is found. The surface wave effect in Gaussian beam scattering is also qualitatively analyzed by introducing a flux ratio factor. The approach proposed is particularly important to the further extension of the geometrical-optics approximation to the scattering of large spheroidal particles.     

Application of dynamic light scattering to the study of small marine particles

Small particles ranging from approximately 0.1 μm to several micrometers in size, which include detrital material, bacteria, and other planktonic microorganisms, make a significant contribution to light scattering in the upper ocean. The scattering properties of these particles are strongly dependent on their size, which is difficult to measure in the submicrometer range with commonly used electronic resistive counters and microscopic techniques. We examined the size of small marine particles by application of the dynamic light scattering (DLS) method. In this method the time-dependent autocorrelation function of scattered intensity by particles undergoing Brownian motion provides information about the size of particles. The samples were collected in clear oceanic waters off the coast of Southern California. The mean hydrodynamic diameter of particles, determined from the DLS measurements at a scattering angle of 45°, was 0.54μ m. This indicates that the major contribution to scattering at this angle comes rom submicrometer particles. We also described an inverse method for estimating the general slope of the size distribution of small marine particles from the mean hydrodynamic diameter. This method is based on calculations of the size distribution weighted by distribution from Mie theory and assumes that a power-law approximation represents the actual particle scattered intensity. These calculations suggested that particulate assemblage in our seawater samples was best characterized by a differential size distribution with a slope of -4.35. This estimation was supported by independent measurements of particle size distribution and the spectral beam attenuation coefficient taken from the same samples as those used for the DLS measurements. We also demonstrated that multiangle DLS measurements may be used to determine the representative value of the refractive index of particles.     

Correlated light scattering by a dense distribution of condensation droplets on a window pane

An analytical model of the scattering structure factor for an assembly of noninteracting hard disks has recently appeared in the literature [Phys. Rev. A 42, 5978-5989 (1990)]. We employ this model to calculate correlated light scattering by monodispersions and binary mixtures of condensation droplets on a window pane. We find that an area fraction of ? ≥ 0.6 is required for producing the near-forward direction scattering suppression and that a moderately wide polydispersion of droplet sizes is capable of producing the experimentally observed bright ring of colored light.     

Sensitivity of the backscattering Mueller matrix to particle shape and thermodynamic phase

The Mueller matrix (M) corresponding to the phase matrix in the backscattering region (scattering angles ranging from 175 degrees to 180 degrees) is investigated for light scattering at a 0.532-microm wavelength by hexagonal ice crystals, ice spheres, and water droplets. For hexagonal ice crystals we assume three aspect ratios (plates, compact columns, and columns). It is shown that the contour patterns of the backscattering Mueller matrix elements other than M11, M44, M14, and M41 depend on particle geometry; M22 and M33 are particularly sensitive to the aspect ratio of ice crystals. The Mueller matrix for spherical ice particles is different from those for nonspherical ice particles. In addition to discriminating between spherical and nonspherical particles, the Mueller matrix may offer some insight as to cloud thermodynamic phase. The contour patterns for large ice spheres with an effective size of 100 microm are substantially different from those associated with small water droplets with an effective size of 4 microm.     

Can cirrus clouds produce glories?

A vague glory display was photographed over central Utah from an airplane beginning its descent through a cirrus cloud layer with an estimated cloud top temperature of -45 and -55 degrees C. Photographic analysis reveals a single reddish-brown ring of 2.5-3.0 degrees radius around the antisolar point, although a second ring appeared visually to have been present over the brief observation period. Mie and approximate nonspherical theory scattering simulations predict a population of particles with modal diameters between 9 and 15 mum. Although it is concluded that multiple-ringed glories can be accounted for only through the backscattering of light from particles that are strictly spherical in shape, the poor glory colorization in this case could imply the presence of slightly aspherical ice particles. The location of this display over mountainous terrain suggests that it was generated by an orographic wave cloud, which we speculate produced numerous frozen cloud droplets that only gradually took on crystalline characteristics during growth.     

Online laser light scattering coupled with imaging for pressurized capillary gel filtration

A system combining pressurized capillary gel filtration with online laser light scattering and microscopic imaging, particularly suitable for biological applications, has been developed. Structural information of eluted materials in the gel filtration provides important clues about their behavior and how they interact with light. It also reveals that the dispersion of the column packing materials is the major limiting factor in the improvement of detectability. Surprisingly, it is found that eluted lysozymes actually scatter light coherently with two distinctive features: a very strong scattering characteristic of constructive interference and a very weak scattering consistent with destructive interference. A variation of the incident angle by 2 degrees of the laser beam caused a swing between the two features. Albumins and large blue dextran particles scatter light simply as individual particles.