Limits of the small-angle approximation to the radiative transport equation

The small-angle approximation to the radiative transport equation is used extensively in imaging models in which the transport medium is optically thick. The small-angle approximation is generally considered valid when the particles are very large compared with the wavelength, when the refractive-index ratio of the particle to the medium is close to 1, and when the optical thickness is not too large. We report results showing the limits of the validity of the small-angle approximation as a function of particle size and concentration for a particle-to-medium fixed refractive-index ratio of 1.196. This refractive-index ratio is comparable with that of minerals or diatoms suspended in water.     

Experimental investigation of the influence of the relative position of the scattering layer on image quality: the shower curtain effect

The imaging quality of optical systems in a turbid environment is influenced not only by the content of the turbid layer between the object and the optical receiver but also by the inhomogeneity of that medium. This is important, particularly when imaging is performed through clouds, nonhomogeneous layers of dust, or over vertical or slant paths through the atmosphere. Forward small-angle scattering influences image quality and blur more severely when the scattering layer is closer to the receiver. In this study it is the influence of the relative position of the scattering layer on the image quality and modulation transfer function (MTF) that is investigated. The scattering layer in controlled laboratory experiments consists of calibrated polystyrene particles of known size and quantity in a small cuvette. A point source was imaged by a computerized imaging system through a layer containing polystyrene particles, and the point-spread function (PSF) was recorded. The aerosol MTF was calculated using the measured PSF. The MTF was measured as a function of changing relative distance of the scattering layer from the receiver, whereas the object-plane-to-receiver distance was constant. The experimental results were compared to theoretical shower curtain effect models based on the solution from radiative transfer theory under the small-angle approximation. Although the general trend of the experimental results certainly agrees with the theoretical models, it could be that the small-angle approximation method might be of limited validity at such low spatial frequencies. Aggregation also causes some disagreement with predictions from theory.     

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.     

PARTICLE COUNTING OIL AND WATER EMULSIONS

Because of their speed and convenience, optical particle counters are widely used for particle size analysis of liquid samples. In some cases, both solid particles and emulsified water or oil may be present in a sample. Since emulsion droplets are counted as if they are solid particles, analysis and data interpretation for these samples are difficult. Until recently, no suitable method existed for distinguishing solid contaminants from emulsion droplets. This paper discusses a method which overcomes this limitation. Through the use of a surfactant-laden nonpolar dilution fluid, water is incorporated into reverse micelles too small to be seen by most optical particle counters. As a result, only solid contaminants are counted, and many problems associated with the analysis of emulsions are overcome. Results obtained from a wide range of oil and water emulsions are used to evaluate the merits and possible applications of the new technique.     

Comparison of near-forward light scattering on oceanic turbulence and particles

We examine and compare near-forward light scattering that is caused by turbulence and typical particulate assemblages in the ocean. The near-forward scattering by particles was calculated using Mie theory for homogeneous spheres and particle size distributions representative of natural assemblages in the ocean. Direct numerical simulations of a passive scalar with Prandtl number 7 mixed by homogeneous turbulence were used to represent temperature fluctuations and resulting inhomogeneities in the refractive index of water. Light scattering on the simulated turbulent flow was calculated using the geometrical-optics approximation. We found that the smallest temperature scales contribute the most to scattering, and that scattering on turbulence typically dominates over scattering on particles for small angles as large as 0.1 degrees . The scattering angle deviation that is due to turbulence for a light beam propagating over a 0.25-m path length in the oceanic water can be as large as 0.1 degrees . In addition, we carried out a preliminary laboratory experiment that illustrates the differences in the near-forward scattering on refractive-index inhomogeneities and particles.     

PARTICLE COUNTING OIL AND WATER EMULSIONS

ABSTRACT

Because of their speed and convenience, optical particle counters are widely used for particle size analysis of liquid samples. In some cases, both solid particles and emulsified water or oil may be present in a sample. Since emulsion droplets are counted as if they are solid particles, analysis and data interpretation for these samples are difficult. Until recently, no suitable method existed for distinguishing solid contaminants from emulsion droplets. This paper discusses a method which overcomes this limitation. Through the use of a surfactant-laden nonpolar dilution fluid, water is incorporated into reverse micelles too small to be seen by most optical particle counters. As a result, only solid contaminants are counted, and many problems associated with the analysis of emulsions are overcome. Results obtained from a wide range of oil and water emulsions are used to evaluate the merits and possible applications of the new technique.     

Features in coherent transmittance of a monolayer of particles

Coherent and incoherent transmittance values of a monolayer of particles are considered. Such a monolayer is a set of particles whose centers are located in the same plane. We set forth the conditions for the effect of coherent-transmittance quenching, which takes place as a result of the interference between incident and forward-scattered waves. Using the single-scattering approximation we determined size parameters and particle refractive indexes for this interference effect in the case of identical isotropic spherical particles. The influence of polydispersity and the fine structure of light-scattering characteristics on the quenching effect has been estimated. It is shown that the polydispersity destroys this interference effect only at large widths of particle-size distribution functions. The influence of multiple scattering on this effect is considered in the quasi-crystalline approximation. Multiple scattering results in increasing size parameters and decreasing particle concentration at which coherent transmittance quenching takes place in comparison with the case of single scattering. Our theoretical results for suspensions of latex particles in water are in fairly good agreement with the experimental results.     

Scattered light corrections to Sun photometry: analytical results for single and multiple scattering regimes

Analytical equations for the diffused scattered light correction factor of Sun photometers are derived and analyzed. It is shown that corrections are weakly dependent on the atmospheric optical thickness. They are influenced mostly by the size of aerosol particles encountered by sunlight on its way to a Sun photometer. In addition, the accuracy of the small-angle approximation used in the work is studied with numerical calculations based on the exact radiative transfer equation.     

Closed-form solution for the Wigner phase-space distribution function for diffuse reflection and small-angle scattering in a random medium

Within the paraxial approximation, a closed-form solution for the Wigner phase-space distribution function is derived for diffuse reflection and small-angle scattering in a random medium. This solution is based on the extended Huygens-Fresnel principle for the optical field, which is widely used in studies of wave propagation through random media. The results are general in that they apply to both an arbitrary small-angle volume scattering function, and arbitrary (real) ABCD optical systems. Furthermore, they are valid in both the single- and multiple-scattering regimes. Some general features of the Wigner phase-space distribution function are discussed, and analytic results are obtained for various types of scattering functions in the asymptotic limit s > 1, where s is the optical depth. In particular, explicit results are presented for optical coherence tomography (OCT) systems. On this basis, a novel way of creating OCT images based on measurements of the momentum width of the Wigner phase-space distribution is suggested, and the advantage over conventional OCT images is discussed. Because all previous published studies regarding the Wigner function are carried out in the transmission geometry, it is important to note that the extended Huygens-Fresnel principle and the ABCD matrix formalism may be used successfully to describe this geometry (within the paraxial approximation). Therefore for completeness we present in an appendix the general closed-form solution for the Wigner phase-space distribution function in ABCD paraxial optical systems for direct propagation through random media, and in a second appendix absorption effects are included.     

Use of optical scattering to discriminate particle types in coastal waters

The particulate scattering characteristics of coastal waters were examined at nine locations around the United States, including near-shore sites in the Gulf of Mexico and the Atlantic and Pacific oceans. The scattering measurements were used in conjunction with inversion models to estimate particle size distributions and bulk refractive indices of the suspended particles. The relationships between various scattering properties and chlorophyll concentration were also investigated and compared with previous relationships described for case I waters. Although the general patterns of scattering and particle characteristics in coastal waters were fairly consistent, fine-scale variability within the water column was substantial. Combining optical measurements with inversion techniques provided a more informative view of the environment and a better understanding of the nature of particle populations in the coastal ocean.     

Optical Probe for the In-Line Determination of Particle Shape, Size, and Velocity

A laboratory optical probe was developed to simultaneously determine the following particle characteristics: circularity, particle projection area, equivalent diameter of a circle, length of the particle outline or perimeter, maximum chord length, aspect ratio, and particle velocity. Using the projection area and the perimeter, the particle shape factor circularity can be determined. The aspect ratio was approximated by the ratio of the equivalent diameter to the maximum chord length. The basic measuring principle is multi-point scanning of the particle shadow image by a line of optical fibers. In addition, the particle velocity can be measured by a differential spatial filter of optical fibers. These fibers are step index fibers with a core diameter of 64 µm and cladding of 70 µm. The shadow image of a single particle was generated by a parallel laser beam. The uncertainty of the measured circularity and aspect ratio was investigated by using metal wires with diameters of 0.12 to 0.5 mm as test particles with known circularity and aspect ratio. The standard deviations were 1.9% for the circularity and 15.5% for the approximated aspect ratio. In addition, the optical probe system was investigated by measurements of solid particles with different shapes. As an example, the results of sand, marjoram seed, and metallic oxide particles are shown. Using 1000 sand particles, the correlation between equivalent diameter and particle velocity could be demonstrated. The presented configuration of the optical probe is applicable in the size range of 0.1 to 0.9 mm and up to a particle velocity of 5 m/s.     

Optical Probe for the In-Line Determination of Particle Shape,Size, and Velocity

A laboratory optical probe was developed to simultaneously determine the following particle characteristics: circularity, particle projection area, equivalent diameter of a circle, length of the particle outline or perimeter, maximum chord length, aspect ratio, and particle velocity. Using the projection area and the perimeter, the particle shape factor circularity can be determined. The aspect ratio was approximated by the ratio of the equivalent diameter to the maximum chord length. The basic measuring principle is multi-point scanning of the particle shadow image by a line of optical fibers. In addition, the particle velocity can be measured by a differential spatial filter of optical fibers. These fibers are step index fibers with a core diameter of 64 µm and cladding of 70 µm. The shadow image of a single particle was generated by a parallel laser beam. The uncertainty of the measured circularity and aspect ratio was investigated by using metal wires with diameters of 0.12 to 0.5 mm as test particles with known circularity and aspect ratio. The standard deviations were 1.9% for the circularity and 15.5% for the approximated aspect ratio. In addition, the optical probe system was investigated by measurements of solid particles with different shapes. As an example, the results of sand, marjoram seed, and metallic oxide particles are shown. Using 1000 sand particles, the correlation between equivalent diameter and particle velocity could be demonstrated. The presented configuration of the optical probe is applicable in the size range of 0.1 to 0.9 mm and up to a particle velocity of 5 m/s.     

Appearance of the Sun and the Moon seen through clouds

If the Sun can be seen at all through thin clouds it usually has a sharp edge, although occasionally it appears fuzzy, especially through altostratus, but rarely, if ever, through fog. Experiments with suspensions of polystyrene spheres of different sizes and optical thicknesses suggest that the range of cloud optical thicknesses over which a fuzzy Sun is seen increases with particle size. Nonsphericity, turbulence, and cloud horizontal inhomogeneity are not necessary for fuzziness. A possible explanation for what is observed is that, for a given optical thickness, the modulation contrast function of a cloud decreases more rapidly with increasing frequency the greater the particle size. Consequently the transition from optical thicknesses for which contrast is above the contrast threshold at all spatial frequencies to optical thicknesses for which contrast is below the threshold at high frequencies is sufficiently gradual to permit fuzziness of the Sun to be observed through clouds of constantly changing opt cal thickness.     

Microfluidic sorting with a moving array of optical traps

Optical sorting was demonstrated by selective trapping of a set of microspheres (having specific size or composition) from a flowing mixture and guiding these in the desired direction by a moving array of optical traps. The approach exploits the fact that whereas the fluid drag force varies linearly with particle size, the optical gradient force has a more complex dependence on the particle size and also on its optical properties. Therefore, the ratio of these two forces is unique for different types of flowing particles. Selective trapping of a particular type of particles can thus be achieved by ensuring that the ratio between fluid drag and optical gradient force on these is below unity whereas for others it exceeds unity. Thereafter, the trapped particles can be sorted using a motion of the trapping sites towards the output. Because in this method the trapping force seen by the selected fraction of particles can be suitably higher than the fluid drag force, the particles can be captured and sorted from a fast fluid flow (about 150 μm/s). Therefore, even when using a dilute particle suspension, where the colloidal trafficking issues are naturally minimized, due to high flow rate a good throughput (about 30 particles/s) can be obtained. Experiments were performed to demonstrate sorting between silica spheres of different sizes (2, 3, and 5 μm) and between 3 μm size silica and polystyrene spheres.     

Multiple-scattering-based lidar retrieval: method and results of cloud probings

Recent developments in the search for a practical method of exploiting the multiple-scattering contributions to lidar returns are consolidated in a robust retrieval algorithm. The theoretical basis is the small-angle diffusion approximation. This implies that the algorithm is limited to media of sufficient optical thickness to generate measurable multiple scattering and to geometries for which the receiver's footprint diameter is less than the scattering mean free path. The primary retrieval products are the range-resolved extinction coefficient and the effective particle diameter from which secondary products such as the particle volume mixing ratio and the extinction at other wavelengths can be calculated. We recall briefly earlier validation tests and present new data and analysis that demonstrate and quantify the solutions' accuracy. The results show that systematic lidar probings with the proposed multiple-scattering technique can provide valuable physical information on cloud formation and evolution.     

Phase inversion of particle-stabilized materials from foams to dry water

Small particles attached to liquid surfaces arise in many products and processes, including crude-oil emulsions and food foams and in flotation, and there is a revival of interest in studying their behaviour. Colloidal particles of suitable wettability adsorb strongly to liquid-liquid and liquid-vapour interfaces, and can be sole stabilizers of emulsions and foams, respectively. New materials, including colloidosomes, anisotropic particles and porous solids, have been prepared by assembling particles at such interfaces. Phase inversion of particle-stabilized emulsions from oil in water to water in oil can be achieved either by variation of the particle hydrophobicity (transitional) or by variation of the oil/water ratio (catastrophic). Here we describe the phase inversion of particle-stabilized air-water systems, from air-in-water foams to water-in-air powders and vice versa. This inversion can be driven either by a progressive change in silica-particle hydrophobicity at constant air/water ratio or by changing the air/water ratio at fixed particle wettability, and has not been observed in the corresponding systems stabilized by surfactants. The simplicity of the work is that this novel inversion is achieved in a single system. The resultant materials in which either air or water become encapsulated have potential applications in the food, pharmaceutical and cosmetics industries.     

Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community

We describe an approach to modeling the ocean's inherent optical properties (IOPs) that permits extensive analyses of IOPs as the detailed composition of suspended particulate matter is varied in a controlled manner. Example simulations of the IOP model, which includes 18 planktonic components covering a size range from submicrometer viruses and heterotrophic bacteria to microplanktonic species of 30-mum cell diameter, are discussed. Input data to the model include the spectral optical cross sections on a per particle basis and the particle-number concentration for each individual component. This approach represents a significant departure from traditional IOP and bio-optical models in which the composition of seawater is described in terms of a few components only or chlorophyll concentration alone. The simulations illustrate how the separation and understanding of the effects of various types of particle present within a water body can be achieved. In an example simulation representing an oligotrophic water body with a chlorophyll a concentration of 0.18 mg m(-3), the planktonic microorganisms altogether are the dominant particulate component in the process of light absorption, but their relative contribution to light scattering is smaller than that of nonliving particles. A series of simulations of water bodies with the same chlorophyll a concentration but dominated by different phytoplankton species shows that composition of the planktonic community is an important source of optical variability in the ocean.     

大颗粒交联聚苯乙烯白球的聚合工艺

研究了大颗粒交联聚苯乙烯白球的制备工艺,着重探讨了搅拌速度、反应温度、分散剂类型及用量、引发剂用量、致孔剂的用量、搅拌桨的大小与位置高低等因素对其粒径大小及分布的影响,确定了产品粒径主要位于1.5mm～3.5mm范围内的聚合工艺条件为:油相/水相的体积比为2∶1,聚乙烯醇的含量为3%,磷酸钙的用量为0.45%,过氧化二苯甲酰用量为0.9%,固体石蜡的用量为24%,实行分段控制搅拌速度、分段控温,同时要求搅拌桨位于油层以下1cm～2cm处。     

Small-angle Light Scattering by Spherulites in the Anomalous Diffraction Approximation

Using the anomalous-diffraction (AD) light-scattering approximation, a relationship is derived between the scattering matrix of an object and its full Jones' matrix. This allows scattering to be calculated for dielectric objects having any kind of optical anisotropy, e.g. birefringent or optically active particles. The theory is used to calculate the small-angle light scattering (SALS) by a spherulite placed between two linear polarizers. Serious disagreements are found between the AD theory and the currently accepted theory of SALS based on the Rayleigh-Gans-Debye approximation.     

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.