Light scattering by randomly oriented spheroidal particles

Optical diffraction tomography for assessing single cell models in angular light scattering

Angularly resolved light scattering (ALS) has become a useful tool for assessing the size and refractive index of biological scatterers at cellular and organelle length scales. Sizing organelle populations with ALS relies on Mie scattering theory models, which require significant assumptions about the object, including spherical scatterers and a homogeneous medium. These assumptions may incur greater error at the single cell level, where there are fewer scatterers to be averaged over. We investigate the validity of these assumptions using 3D refractive index (RI) tomograms measured via optical diffraction tomography (ODT). We compute the angular scattering on digitally manipulated tomograms with increasingly strong model assumptions, including RI-matched immersion media, homogeneous cytosol, and spherical organelles. We also compare the tomogram-computed angular scattering to experimental measurements of angular scattering from the same cells to ensure that the ODT-based approach accurately models angular scattering. We show that enforced RI-matching with the immersion medium and a homogeneous cytosol significantly affects the angular scattering intensity shape, suggesting that these assumptions can reduce the accuracy of size distribution estimates.

Three-dimensional angular scattering simulations inform analysis of scattering from single cells

Significance

Organelle sizes, which are indicative of cellular status, have implications for drug development and immunology research. At the single cell level, such information could be used to study the heterogeneity of cell response to drugs or pathogens.

Aim

Angularly resolved elastic light scattering is known to be sensitive to changes in organelle size distribution. We developed a Mie theory-based simulation of angular scattering from single cells to quantify the effects of noise on scattering and size estimates.

Approach

We simulated randomly sampled organelle sizes (drawn from a log normal distribution), interference between different organelles' scattering, and detector noise. We quantified each noise source's effect upon the estimated mean and standard deviation of organelle size distributions.

Results

The results demonstrate that signal-to-noise ratio in the angular scattering increased with the number of scatterers, cell area, and exposure time and decreased with the size distribution width. The error in estimating the mean of the size distributions remained below 5% for nearly all experimental parameters tested, but the widest size distribution tested (standard deviation of 600 nm) reached 20%.

Conclusions

The simulator revealed that sparse sampling of a broad size distribution can dominate the mismatch between actual and predicted size parameters. Alternative estimation strategies could reduce the discrepancy.

Approximations for spherical scattering coefficients with negligible integral errors in parametric space

The solution of forward or inverse light scattering problems in astrophysical, biological, and atmospheric sensing applications is typically cost prohibitive for real-time applications. For example, given a probability density for the dimensions, refractive index, and wavelength, evaluating the expected scattering involves an integral over such parameters, and the number of scattering problems solved increases dramatically. In the case of dielectric and weakly absorbing spherical particles (both homogeneous and layered), we begin by highlighting a circular law that restricts scattering coefficients to a circle in the complex plane. Later, the Fraunhofer approximation of Riccati-Bessel functions is used to reduce the scattering coefficients into simpler nested trigonometric approximations. This results in relatively small errors of oscillatory signs that cancel out without a loss of accuracy in the integrals over scattering problems. Thus, the cost of evaluating the two spherical scattering coefficients for any mode is reduced by large factors ≈50, with a larger increase in the speed of the overall computation, as the approximations can be reused for multiple modes. We analyze the errors of the proposed approximation and present numerical results for a set of forward problems as a demonstration.

Grid-adaptive Fourier pseudospectral time domain model for the light scattering simulation of atmospheric nonspherical particles

PSTD (pseudospectral time domain) is recognized as one of the powerful models to accurately calculate the scattering properties of nonspherical particles. But it is only good at the computation in coarse spatial resolution, and large "staircase approximation error" will occur in the actual computation. To solve this problem, the variable dimension scheme is introduced to improve the PSTD computation, in which, the finer grid cells are set near the particle's surface. In order to ensure that the PSTD algorithm can be performed on non-uniform grids, we have improved the PSTD with the space mapping technique so that the FFT algorithm can be implemented. The performance of the improved PSTD (called "IPSTD" in this paper) is investigated from two aspects: for the calculation accuracy, the phase matrices calculated by IPSTD are compared with those well tested scattering models like Lorenz-Mie theory, T-matrix method and DDSCAT; for computational efficiency, the computational time of PSTD and IPSTD are compared for the spheres with different sizes. From the results, it can be found that, the IPSTD scheme can improve the simulation accuracy of phase matrix elements notably, especially in the large scattering angles; though the computational burden of IPSTD is larger than that of PSTD, its computational burden does not increase substantially.

Method for the determination of preferential orientation of marine particles from laser diffraction measurements

In situ laser diffractometry (LD) is increasingly used in oceanographic studies to estimate sediment transport, particle fluxes and to assess the concentration of marine phytoplankton. It enables an accurate characterization of the size distribution of suspended particles from the scattering signal produced by their interaction with a collimated laser beam. LD reliably reflects the sizes of suspensions dominated by nearly spherical particles; however, when complex particle morphologies dominate the suspension (e.g. phytoplankton) the resulting particle size distribution (PSD) may present significant variations attributed to different factors. In particular, the orientation of non-spherical particles - which abound in the sea - modifies LD measurements of PSDs. While this may be interpreted as a drawback for some studies (i.e. when precise measurement of the volume concentration is required), we propose that detailed analysis of this signal provides information on particle orientation. We use PDMS micropillars with prescribed elliptical cross-sections to experimentally determine the dependence between the spatial orientation of elongated particles and changes in the PSD measured with a LISST laser diffractometer. We show that LD can be used to adequately characterize the different dimensions of the non-spherical particles at specific orientations. Using this property, we describe and validate a method to infer the preferential orientation of particles in the sea. Our study opens new perspectives in the use of in-situ LD in ocean research.

Sensitivity study on the contribution of scattering by randomly oriented nonspherical hydrosols to linear polarization in clear to semi-turbid shallow waters

The influence of hydrosol nonsphericity on the polarization characteristics of light under water is investigated by combining accurate single-scattering models for randomly oriented spheroidal scatterers with a radiative transfer model that employs Stokes formalism and considers refraction of direct unpolarized solar radiation and 100% linearly polarized radiation at the air-water interface followed by single scattering. Variations in what we call the "linear polarization phase function" (the degree of linear polarization as a function of scattering angle and the angle of linear polarization as a function of scattering angle) are examined for a wide range of spheroid aspect ratios and complex refractive indices of hydrosols. Implications for polarization-sensitive marine organisms and for remote sensing of the marine environment are discussed.

Acoustic Characteristics of Biosynthetic Bubbles for Ultrasound Contrast Imaging

Biosynthetic bubbles produced by floating microorganisms, such as bacteria and algae, have recently attracted wide attention as novel ultrasound contrast agents owing to their significant potential in ultrasound imaging and acoustic reporter gene-based imaging. However, the acoustics properties of these bubbles are unclear. In this study, we developed a finite-element model to describe the oscillation of nonspherical biosynthetic bubbles composed of a gas core encapsulated in a protein shell. In this model, the elastic properties of the bubble shells were characterized in terms of the density, thickness, Young's modulus, and Poisson's ratio. Theoretical calculations were performed for a single bubble and an assembly of randomly oriented bubbles. Our results demonstrate that (1) there are many types of surface oscillation modes for nonspherical biosynthetic bubbles, and a systematic relationship exists between the surface modes and the resonance frequencies; (2) the bubble shell shape has a significant effect on the acoustic behavior; (3) the resonance frequency of an ellipsoidal bubble decreases with the decrease in its polar radius-to-equatorial axis ratio; and (4) the acoustic scattering of a randomly oriented suspension is isotropic at and below the first resonance frequency. Our findings provide physical insight into the biomedical applications of biosynthetic bubbles and can be used to optimize the acoustics properties of such bubbles.

Single scattering properties of non-spherical hydrosols modeled by spheroids

The single scattering properties of hydrosols play an important role in the study of ocean optics, ocean color remote sensing, and ocean biogeochemistry research. Measurements show that hydrosols can be of various sizes and shapes, suggesting general non-spherical models should be considered for the study of single scattering properties of hydrosols. In this work, light scattering by non-spherical hydrosols are modeled by randomly oriented spheroids with the Amsterdam discrete dipole approximation (ADDA) code. We have defined two new parameters to quantify the degree of optical non-sphericity (DONS) and investigated the dependence of DONS on refractive index, size, and aspect ratio. For particles with non-unitary aspect ratios, the magnitude of DONS increases as the refractive index and particle size increase. The dependence of the backscattering fraction on the non-sphericity, size, and refractive index of hydrosols is also studied. It is found that the backscattering fraction is larger for smaller particles as well as for particles with higher refractive indices. Absorptive hydrosols generally have a lower backscattering fraction than non-absorptive hydrosols. This study of light scattering by non-spherical hydrosols would lead to better radiative transfer models in ocean waters and new remote sensing techniques of hydrosol compositions.

A novel optical diffuser based on polymer micro-balls-filled nematic liquid crystal composite film

In this study, optical diffusers based on epoxy resin/thiol/nematic liquid crystal composites were prepared using different curing temperatures, curing times and curing agents (thiols). Additionally, the effects of the curing temperatures, the curing times and the thiols on the polymer ball microstructures and the optical properties of optical diffusers were investigated systematically. For applications of optical diffusers, the optimized curing temperature has been achieved by combining the high transmittance and high haze. A novel optical diffuser with ultrahigh transmittance (>94.0%), ultrahigh haze (>94.0%) and excellent diffusing ability has been obtained, of which the polymer morphology is single polymer micro-balls without aggregation.

A novel optical diffuser (transmission >94%, haze >94%) with the A6 polymer morphology has excellent light diffusing ability.

Liquid crystal-based Mueller matrix spectral imaging polarimetry for parameterizing mineral structural organization

Herein, we discuss the remote assessment of the subwavelength organizational structure of a medium. Specifically, we use spectral imaging polarimetry, as the vector nature of polarized light enables it to interact with optical anisotropies within a medium, while the spectral aspect of polarization is sensitive to small-scale structure. The ability to image these effects allows for inference of spatial structural organization parameters. This work describes a methodology for revealing structural organization by exploiting the Stokes/Mueller formalism and by utilizing measurements from a spectral imaging polarimeter constructed from liquid crystal variable retarders and a liquid crystal tunable filter. We provide results to validate the system and then show results from measurements on a mineral sample.

Effect of heterogeneity and shape on optical properties of urban dust based on three-dimensional modeling of individual particles

We show the effect of composition heterogeneity and shape on the optical properties of urban dust particles based on the three-dimensional spatial and optical modeling of individual particles. Using scanning electron microscopy/energy-dispersive X-ray spectroscopy (SEM/EDX) and focused ion beam (FIB) tomography, spatial models of particles collected in Los Angeles and Seattle accounted for surface features, inclusions, and voids, as well as overall composition and shape. Using voxel data from the spatial models and the discrete dipole approximation method, we report extinction efficiency, asymmetry parameter, and single-scattering albedo (SSA). Test models of the particles involved (1) the particle's actual morphology as a single homogeneous phase and (2) simple geometric shapes (spheres, cubes, and tetrahedra) depicting composition homogeneity or heterogeneity (with multiple spheres). Test models were compared with a reference model, which included the particle's actual morphology and heterogeneity based on SEM/EDX and FIB tomography. Results show particle shape to be a more important factor for determining extinction efficiency than accounting for individual phases in a particle, regardless of whether absorption or scattering dominated. In addition to homogeneous models with the particles' actual morphology, tetrahedral geometric models provided better extinction accuracy than spherical or cubic models. For iron-containing heterogeneous particles, the asymmetry parameter and SSA varied with the composition of the iron-containing phase, even if the phase was <10% of the particle volume. For particles containing loosely held phases with widely varying refractive indexes (i.e., exhibiting "severe" heterogeneity), only models that account for heterogeneity may sufficiently determine SSA.

Spectral attenuation and backscattering as indicators of average particle size

Measurements of the particulate beam attenuation coefficient at multiple wavelengths in the ocean typically exhibit a power law dependence on wavelength, and the slope of that power law has been related to the slope of the particle size distribution (PSD), when assumed to be a power law function of particle size. Recently, spectral backscattering coefficient measurements have been made using sensors deployed at moored observatories, on autonomous underwater vehicles, and even retrieved from space-based measurements of remote sensing reflectance. It has been suggested that these backscattering measurements may also be used to obtain information about the shape of the PSD. In this work, we directly compared field-measured PSD with multispectral beam attenuation and backscattering coefficients in a coastal bottom boundary later. The results of this comparison demonstrated that (1) the beam attenuation spectral slope correlates with the average particle size as suggested by theory for idealized particles and PSD; and (2) measurements of spectral backscattering also contain information reflective of the average particle size in spite of large deviations of the PSD from a spectral power law shape.

Measuring the light scattering and orientation of a spheroidal particle using in-line holography

The light scattering properties of a horizontally and vertically oriented spheroidal particle under laser illumination are experimentally investigated using digital in-line holography. The reconstructed wave field shows the bright singular points as a result of the condensed beam formed by a transparent spheroidal particle acting as a lens. The in-plane (θ) and out-of-plane (ϕ) rotating angles of an arbitrarily oriented spheroidal particle are measured by using these scattering properties. As a feasibility test, the 3D orientation of a transparent spheroidal particle suspended in a microscale pipe flow is successfully reconstructed by adapting the proposed method.

High-performance nanosensors based on plasmonic Fano-like interference: probing refractive index with individual nanorice and nanobelts

We propose two different configurations for which the Fano-like interference of longitudinal plasmon resonances occurring at individual metallic nanoparticles can be easily employed in refractive index sensing: a colloidal suspension of nanospheroids (nanorice) and a single nanowire with rectangular cross section (nanobelt) on top of a dielectric substrate. We numerically study the performance of the two in terms of their figures of merit, which are calculated under realistic conditions. For the case of nanorice, we explicitly incorporate the effect of size dispersity into the simulations. Our obtained results show that the application of the proposed configurations seems to be not only feasible but also very promising.

Mueller matrix measurements of algae with different shape and size distributions

The full Mueller matrix was measured to obtain the polarization state of the scattered light for a variety of algae with different shapes, wall compositions, sizes, and refractive indices. The experimental setup was a multiple laser Mueller matrix ellipsometer, by which measurements were performed for scattering angles from 16° to 160° sampled at every second degree for wavelengths of 473 nm and 532 nm. Previously, the polarization of light scattered from microalgae was investigated only for a few species, and the Mueller matrix was found to have little variation between the species. In our work a total of 11 algal species were investigated, representing diatoms, dinoflagellates, coccolithophorids, green algae, and a cryptophyte. The selection of species was made to obtain high variability in shape, size, cell wall, and refractive index. As in previous investigations, very small variations were found between species for most of the Mueller matrix elements, but noticeable variations were found for M(11), (M(12)+M(21))/2 and (M(33)+M(44))/2.

Laboratory measurements of light beam depolarization on turbulent convective flow

Laboratory measurements of light beam depolarization by a turbulent flow, corresponding to oceanic turbulence within the oceanic mixed layer, show that the depolarization rate (1x10(-5)?m(-1) to 3x10(-3)?m(-1)) correlates with turbulence strength and is consistent with polarized lidar observations [Opt. Express, 16, 1196 (2008)OPEXFF1094-408710.1364/OE.16.001196]. These results imply that one should be able to characterize oceanic turbulence with polarimetric oceanic lidar measurements.

Optical caustics observed in light scattered by an oblate spheroid

The electromagnetic fields scattered when a plane wave is incident on an oblate spheroid in the side-on orientation may be calculated using a generalization of Mie theory, and the results may be decomposed in a Debye series expansion. A number of optical caustics are observed in the computed scattered intensity for the one internal reflection portion of the Debye series for scattering angles in the vicinity of the first-order rainbow, and are analyzed in terms of the rainbow, transverse cusp, and hyperbolic umbilic caustics of catastrophe optics. The specific features of these three caustics are described, as is their assembly into the global structure of the observed caustics for spheroid scattering. It is found that, for a spheroid whose radius is an order of magnitude larger than the wavelength of the incident light, the interference structure accompanying the transverse cusp and hyperbolic umbilic caustics is only partially formed.

Depolarization ratios of single ice particles assuming finite circular cylinders

Results of the depolarization ratio (delta) of single ice particles in fixed orientations are presented to determine whether discrimination between nonspherical ice crystals (causing depolarization) and spherical water droplets (inducing no depolarization) can be made. A T-matrix method is used to compute delta over a range of particle diameters from 0.13 to 4 microm and aspect ratios chi=d/h (d is the diameter and h the height of the particle) from 0.3 to 3, where ice crystals are assumed to have a circular cylindrical shape. The depolarization ratio is primarily dependent on the orientation of the particle. Some orientations return no depolarization, whereas others generate values reaching almost delta=1. Considering the depolarization averaged over all orientations, a dependence of delta with the particle size is observed where values close to 0.25 are reached. No strong influence of the aspect ratio on the depolarization for a given particle size of 2 mum is evident, as values remain in a range between 0.2 and 0.3.

Multiple-scattering effects on infrared scattering measurements used to characterize droplet size and volume fraction distributions in diesel sprays

We quantify the maximum error due to multiple-scattering effects for an infrared scattering droplet izing technique. Errors in Sauter mean diameters (SMDs) and liquid volume fractions were estimated lased on experimentally determined polarization properties of the scattered light. Light that is multiply scattered from spherical particles becomes randomly polarized, whereas singly scattered light from a spherical particle contains no cross-polarization scattering component. Therefore measurement of the cross-polarization component (in this case parallel) of the scattering signal is a measure of the multiply scattered light. A ratio of parallel to perpendicular polarized scattered light was experimentally determined and used to calculate an error due to multiple scattering. The infrared scattering measurements and polarization measurements used to quantify the multiple-scattering errors were applied to a typical diesel spray that was injected into three different background conditions: a room ambient condition; a room-temperature, high-pressure condition; and a combusting condition. Droplet SMD, liquid volume fraction, and multiple-scattering errors were determined for a number of locations within the spray; results indicate that the combusting case is negligibly affected by multiple scattering. However, the room ambient case exhibited notable errors due to multiple scattering near the centerline of the spray, and the high-pressure case demonstrated susceptibility to multiple scattering throughout all regions investigated. It is important to note, however, that multiple-scattering errors in many cases translate into relatively small effects on the reported droplet sizes.

Light extinction and absorption by arbitrarily oriented finite circular cylinders by use of geometrical path statistics of rays

From the geometrical path statistics of rays in an anomalous-diffraction theory (ADT) [Opt. Lett. 28, 179 (2003)] closed-form expressions for the geometrical path distribution of rays and analytical formulas for the optical efficiencies of finite circular cylinders oriented in an arbitrary direction with respect to the incident light are derived. The characteristics of the shapes of the cylinders produce unique features in the geometrical path distributions of the cylinders compared with spheroids. Gaussian ray approximations, which depend only on the mean and the mean-squared geometrical paths of rays, of the optical efficiencies of finite circular cylinders and spheroids are compared with the exact optical efficiencies in ADT. The influence of the difference in shape between cylinders and spheroids on the optical efficiencies in ADT is illustrated by their respective geometrical path distributions of rays.

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.

Bridging technique for calculating the extinction efficiency of arbitrary shaped particles

A general bridging technique is developed to calculate the extinction efficiency of particles by combining the extended Rayleigh-Debye approximation and the modified anomalous diffraction theory. Comparisons with the exact methods are performed for spheres, spheroids, infinite cylinders, and finite cylinders. The overall features of the extinction efficiencies calculated from the new, to our knowledge, bridging method are in agreement with those calculated from the exact methods. Also discussed are accuracy of the new method and its domain of applicability. The new technique can be potentially applied to particles of virtually any shapes and sizes.

Extinction-to-backscatter ratio of Asian dust observed with high-spectral-resolution lidar and Raman lidar

Extinction-to-backscatter ratio or lidar ratio is a key parameter in the issue of backscatter-lidar inversions. The lidar ratio of Asian dust was observed with a high-spectral-resolution lidar and a combined Raman elastic-backscatter lidar during the springs of 1998 and 1999. The measured values range from 42 to55 sr in most cases, with a mean of 51 sr. These values are significantly larger than those predicted by the Mie computations that incorporate measured Asian dust size distributions and a range of refractive index with a typical value of 1.55-0.005i. The enhancement of lidar ratio is mostly due to the nonsphericity of dust particles, as indicated by the T-matrix calculations for spheroid particles and a number of other theoretical studies. In addition, possible contamination of urban aerosols may also contribute somewhat in optically thin cases. Mie theory, although it can well describe spherical particle scattering, will not be sufficient to represent the scattering characteristics of irregular particles such as Asian dust, especially in directions larger than approximately 90 degrees when the size parameter is large.

Characterizing Mammalian cells and cell phantoms by polarized backscattering fiber-optic measurements

Fiber-optic, polarized elastic-scattering spectroscopy techniques are implemented and demonstrated as a method for determining both scatterer size and concentration in highly scattering media. Measurements of polystyrene spheres are presented to validate the technique. Measurements of biological cells provide an estimate of the average effective scatterer radius of 0.5-1.0 mum. This average effective scatterer size is significantly smaller than the nucleus. In addition, to facilitate use of polarization techniques on biological cells, polarized angular dependent scattering from cell suspensions was measured. The light scattering from cells has properties similar to those of small spheres.

Scattering of a spheroidal particle illuminated by a gaussian beam

An approach to expanding a Gaussian beam in terms of the spheroidal wave functions in spheroidal coordinates is presented. The beam-shape coefficients of the Gaussian beam in spheroidal coordinates can be computed conveniently by use of the known expression for beam-shape coefficients, g(n), in spherical coordinates. The unknown expansion coefficients of scattered and internal electromagnetic fields are determined by a system of equations derived from the boundary conditions for continuity of the tangential components of the electric and magnetic vectors across the surface of the spheroid. A solution to the problem of scattering of a Gaussian beam by a homogeneous prolate (or oblate) spheroidal particle is obtained. The numerical values of the expansion coefficients and the scattered intensity distribution for incidence of an on-axis Gaussian beam are given.

Asymptotic solutions for optical properties of large particles with strong absorption

The transverse wave condition is not applicable to the refracted electromagnetic wave within the context of geometrical optics when absorption is involved. Either the TM or the TE wave condition can be assumed for the wave to locally satisfy the electromagnetic boundary condition in a ray-tracing calculation. The assumed wave mode affects both the reflection and the refraction coefficients. As a result, nonunique solutions for these coefficients are inevitable. In this study the appropriate solutions for the Fresnel reflection-refraction coefficients are identified in light-scattering calculations based on the ray-tracing technique. In particular, a 3 x 2 refraction or transmission matrix is derived to account for the inhomogeneity of the refracted wave in an absorbing medium. An asymptotic solution that completely includes the effect of medium absorption on Fresnel coefficients is obtained for the scattering properties of a general polyhedral particle. Numerical results are presented for hexagonal plates and columns with both preferred and random orientations.

Fourier analysis of light scattered by elongated scatterers

Biological stimulation of living cells is sometimes associated with morphological changes. A practical method is developed to monitor cell stimulation by means of their conformational changes through interpretation of the pattern of light scattered from a cell population. For this purpose a mathematical model is suggested that predicts the power spectrum from a population of elliptic objects with a given eccentricity. A computer simulation of that model is presented together with supporting experimental results of the simulation. The predicted and the measured spectra are in good agreement. This technique was applied to elongated cells that become circular on exposure to a human hormone, indicating the potential applicability of the method in biology and medicine. The method and the apparatus presented in this study could be applied to bioassays of cell systems that respond to a variety of stimulants and to trace quantitatively the structural changes that occur during biological processes.

Scattering of electromagnetic waves by spheroidal particles: a novel approach exploiting the T matrix computed in spheroidal coordinates

A method other than the extended-boundary-condition method (EBCM) to compute the T matrix for electromagnetic scattering is presented. The separation-of-variables method (SVM) is used to solve the electromagnetic scattering problem for a spheroidal particle and to derive its T matrix in spheroidal coordinates. A transformation is developed for transforming the T matrix in spheroidal coordinates into the corresponding T matrix in spherical coordinates. The T matrix so obtained can be used for analytical calculation of the optical properties of ensembles of randomly oriented spheroids of arbitrary shape by use of an existing method to average over orientational angles. The optical properties obtained with the SVM and the EBCM are compared for different test cases. For mildly aspherical particles the two methods yield indistinguishable results. Small differences appear for highly aspherical particles. The new approach can be used to compute optical properties for arbitrary values of the aspect ratio. To test the accuracy of the expansion coefficients of the spheroidal functions for arbitrary arguments, a new testing method based on the completeness relation of the spheroidal functions is developed.

Anomalous diffraction theory for arbitrarily oriented finite circular cylinders and comparison with exact T-matrix results

A general method is developed to formulate extinction and absorption efficiency for nonspherical particles at arbitrary and random orientations by use of anomalous diffraction theory (ADT). An ADT for finite circular cylinders is evaluated as an example. Existing ADT's for infinite cylinders at arbitrary orientations and for finite cylinders at the normal incidence are shown to be special cases of the new formulation. ADT solutions for finite cylinders are shown to approach the rigorous T-matrix results when the refractive indices approach unity. The importance of some physical processes that are neglected in the ADT approximation are evaluated by comparisons between ADT and rigorous calculations for different particle geometries. For spheres, van de Hulst's ADT and Mie theory are used, whereas the ADT that we present and T-matrix calculations are used for cylinders of different diameter-to-length ratios. The results show that the differences in extinction between ADT and exact solutions generally decrease with nonsphericity. A similar decrease occurs for absorption at wavelengths of relatively strong absorption. The influence of complex refractive index is evaluated. Our results suggest that ADT may provide a useful approximation in parameterization and remote sensing of cirrus clouds in the Christiansen bands where the real part of the refractive index approaches unity and/or where relative absorption is strong.

Treatment of polarization in laser remote sensing of ocean water

We review existing experimental data and methods for calculating the Mueller matrix of ocean water for use as input in a simulation model applicable to laser remote sensing. Calculations of the Mueller matrix are made for scattering media of different refractive indices, shapes, and size distributions. Dependencies of the backscattering depolarization ratio as a function of the particle refractive index are presented, and we demonstrate the potential importance of polarization in bathymetric sensing.

Mueller matrices and information derived from linear polarization lidar measurements: theory

A Mueller matrix M is developed for a single-scattering process such that G(theta, phi) = T (phi(a))M T (phi(p))u, where u is the incident irradiance Stokes vector transmitted through a linear polarizer at azimuthal angle phi(p), with transmission Mueller matrix T (phi(p)), and G(theta, phi) is the polarized irradiance Stokes vector measured by a detector with a field of view F, placed after an analyzer with transmission Mueller matrix T (phi(a)) at angle phi(a). The Mueller matrix M is a function of the Mueller matrix S (theta) of the scattering medium, the scattering angle (theta, phi), and the detector field of view F. The Mueller matrixM is derived for backscattering and forward scattering, along with equations for the detector polarized irradiance measurements (e.g., cross polarization and copolarization) and the depolarization ratio. The information that can be derived from the Mueller matrix M on the scattering Mueller matrixS (theta) is limited because the detector integrates the cone of incoming radiance over a range of azimuths of 2pi for forward scattering and backscattering. However, all nine Mueller matrix elements that affect linearly polarized radiation can be derived if a spatial filter in the form of a pie-slice slit is placed in the focal plane of the detector and azimuthally dependent polarized measurements and azimuthally integrated polarized measurements are combined.

Ice-crystal absorption: a comparison between theory and implications for remote sensing

The problem of the disagreement between cirrus crystal sizes determined remotely and by in situ measurements is shown to be due to inappropriate application of Mie theory. We retrieved the absorption optical depth at 8.3 and 11.1 mum from 11 tropical anvil cirrus clouds, using data from the High Resolution Infrared Radiation Sounder (HIRS). We related the absorption optical depth ratio between the two wavelengths to crystal size (the size was defined in terms of the crystal median mass dimension) by assuming Mie theory applied to ice spheres and anomalous diffraction theory (ADT) applied to hexagonal columns, hexagonal plates, bullet rosettes, and aggregates (polycrystals). The application of Mie theory to retrievals yielded crystal sizes approximately one third those obtained with ADT. The retrievals of crystal size by use of HIRS data are compared with measurements of habit and crystal size obtained from in situ measurements of tropical anvil cirrus particles. The results of the comparison show that ADT provides the more realistic retrieval. Moreover, we demonstrate that at infrared wavelengths retrieval of crystal size depends on assumed habit. The reason why Mie theory predicts smaller sizes than ADT is shown to result from particle geometry and enhanced absorption owing to the capture of photons from above the edge of the particle (tunneling). The contribution of particle geometry to absorption is three times greater than from tunneling, but this process enhances absorption by a further 35%. The complex angular momentum and T-matrix methods are used to show that the contribution to absorption by tunneling is diminished as the asphericity of spheroidal particles is increased. At an aspect ratio of 6 the contribution to the absorption that is due to tunneling is substantially reduced for oblate particles, whereas for prolate particles the tunneling contribution is reduced by 50% relative to the sphere.

Response of phase Doppler anemometer systems to nonspherical droplets

The Phase Doppler Anemometer (PDA) technique measures particle diameter assuming sphericity. A means for detecting nonsphericity has usually been implemented in commercial PDA systems to avoid sizing errors if the sphericity assumption is not valid. In the present research the response of standard and planar PDA systems is examined experimentally in more detail by passing nonspherical droplets of known shape through the measurement volume. The effectiveness of nonsphericity detection schemes can be evaluated, and furthermore the influence of the droplet oscillations on the frequency and phase evolution of individual signals can be quantified. The light scattering from such particles has been simulated by using geometric optics, and the computed response of standard and planar PDA systems agrees well with the experimental observations. We conclude with some remarks concerning the possibilities of characterizing the nonsphericity with PDA systems.

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.

Scattering of light by polydisperse, randomly oriented, finite circular cylinders

We use the T-matrix method, as described by Mishchenko [Appl. Opt. 32, 4652 (1993)], to compute rigorously light scattering by finite circular cylinders in random orientation. First we discuss numerical aspects of T -matrix computations specific for finite cylinders and present results of benchmark computations for a simple cylinder model. Then we report results of extensive computations for polydisperse, randomly oriented cylinders with a refractive index of 1.53 + 0.008i, diameter-to-length ratios of 1/2, 1/1.4, 1, 1.4, and 2, and effective size parameters ranging from 0 to 25. These computations parallel our recent study of light scattering by polydisperse, randomly oriented spheroids and are used to compare scattering properties of the two classes of simple convex particles. Despite the significant difference in shape between the two particle types (entirely smooth surface for spheroids and sharp rectangular edges for cylinders), the comparison shows rather small differences in the integral photometric characteristics (total optical cross sections, single-scattering albedo, and asymmetry parameter of the phase function) and the phase function. The general patterns of the other elements of the scattering matrix for cylinders and aspect-ratio-equivalent spheroids are also qualitatively similar, although noticeable quantitative differences can be found in some particular cases. In general, cylinders demonstrate much less shape dependence of the elements of the scattering matrix than do spheroids. Our computations show that, like spheroids and bispheres, cylinders with surface-equivalent radii smaller than a wavelength can strongly depolarize backscattered light, thus suggesting that backscattering depolarization for nonspherical particles cannot be universally explained by using only geometric-optics considerations.

Use of sky brightness measurements from ground for remote sensing of particulate polydispersions

The software code SKYEAD.pack for retrieval of aerosol size distribution and optical thickness from data of direct and diffuse solar radiation is described; measurements are carried out with sky radiometers in the wavelength range 0.369-1.048 µm. The treatment of the radiative transfer problem concerning the optical quantities is mainly based on the IMS (improved multiple and single scattering) method, which uses the delta-M approximation for the truncation of the aerosol phase function and corrects the solution for the first- and second-order scattering. Both linear and nonlinear inversion methods can be used for retrieving the size distribution. Improved calibration methods for both direct and diffuse radiation, the data-analysis procedure, the results from the proposed code, and several connected problems are discussed. The results can be summarized as follows: (a) the SKYRAD.pack code can retrieve the columnar aerosol features with accuracy and efficiency in several environmental situations, provided the input parameters are correctly given; (b) when data of both direct and diffuse solar radiation are used, the detectable radius interval for aerosol particles is approximately from 0.03 to 10 µm; (c) besides the retrieval of the aerosol features, the data-analysis procedure also permits the determination of average values for three input parameters (real and imaginary aerosol refractive index, ground albedo) from the optical data; (d) absolute calibrations for the sky radiometer are not needed, and calibrations for direct and diffuse radiation can be carried out with field data; (e) the nonlinear inversion gives satisfactory results in a larger radius interval, without the unrealistic humps that occur with the linear inversion, but the results strongly depend on the first-guess spectrum; (f) aerosol features retrieved from simulated data showed a better agreement with the given data for the linear inversion than for the nonlinear inversion.

Ray scattering by an arbitrarily oriented spheroid. II. Transmission and cross-polarization effects

Transmission of an arbitrarily polarized plane wave by an arbitrarily oriented spheroid in the short-wavelength limit is considered in the context of ray theory. The transmitted electric field is added to the diffracted plus reflected ray-theory electric field that was previously derived to obtain an approximation to the far-zone scattered intensity in the forward hemisphere. Two different types of cross-polarization effects are found. These are (a) a rotation of the polarization state of the transmitted rays from when they are referenced with respect to their entrance into the spheroid to when they are referenced with respect to their exit from it and (b) a rotation of the polarization state of the transmitted rays when they are referenced with respect to the polarization state of the diffracted plus reflected rays.