Retrieval of volcanic and man-made stratospheric aerosols from orbital polarimetric measurements.

Stratospheric aerosols that are caused by a major volcanic eruption can serve as a valuable test of global climate models, as well as severely complicate tropospheric-aerosol monitoring from space. In either case, it is highly desirable to have accurate global information on the optical thickness, size, and composition of volcanic aerosols. We report sensitivity study results, which reveal the implications of making precise multi-angle photopolarimetric measurements in a 1.378-µm spectral channel residing within a strong water-vapor absorption band. We demonstrate that, under favorable conditions, such measurements would enable near-perfect retrievals of the optical thickness, effective radius, and refractive index of stratospheric aerosols. Besides enabling accurate retrievals of volcanic aerosols, such measurements can also be used to monitor man-made particulates injected in the stratosphere for geoengineering purposes.

Multiple scattering of polarized light by particles in an absorbing medium.

We study multiple scattering of light by particles embedded in an absorbing host medium using a recently developed single-scattering and vector radiative-transfer methodology directly based on the Maxwell equations. The first-principles results are compared with those rendered by the conventional heuristic approach according to which the single-scattering properties of particles can be computed by assuming that the host medium is nonabsorbing. Our analysis shows that the conventional approach yields very accurate results in the case of aerosol and cloud particles suspended in an absorbing gaseous atmosphere. In the case of air bubbles in water, the traditional approach can cause large relative errors in reflectance, but only when strong absorption in the host medium makes the resulting reflectance very small. The corresponding polarization errors are substantially smaller.

Far-field Lorenz-Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm.

A recently developed FORTRAN program computing far-field optical observables for spherical particles in an absorbing medium has exhibited numerical instability arising when the product of the particle vacuum size parameter and the imaginary part of the refractive index of the host becomes sufficiently large. We offer a simple analytical explanation of this instability and propose a compact numerical algorithm for the stable computation of Lorenz-Mie coefficients based on an upward recursion formula for spherical Hankel functions of a complex argument. Extensive tests confirm an excellent accuracy of this algorithm approaching machine precision. The improved public-domain FORTRAN program is available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html.

Retrieval of microphysical characteristics of particles in atmospheres of distant comets from ground-based polarimetry.

We summarize unique aperture data on the degree of linear polarization observed for distant comets C/2010 S1, C/2010 R1, C/2011 KP36, C/2012 J1, C/2013 V4, and C/2014 A4 with heliocentric distances exceeding 3 AU. Observations have been carried out at the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences (Nizhnij Arkhyz, Russia) during the period from 2011 to 2016. The measured negative polarization proves to be significantly larger in absolute value than what is typically observed for comets close to the Sun. We compare the new observational data with the results of numerical modeling performed with the T-matrix and superposition T-matrix methods. In our computer simulations, we assume the cometary coma to be an optically thin cloud containing particles in the form of spheroids, fractal aggregates composed of spherical monomers, and mixtures of spheroids and aggregate particles. We obtain a good semi-quantitative agreement between all polarimetric data for the observed distant comets and the results of numerical modeling for the following models of the cometary dust: (i) a mixture of submicrometer water-ice oblate spheroids with aggregates composed of submicrometer silicate monomers; and (ii) a mixture of submicrometer water-ice oblate spheroids and aggregates consisting of both silicate and organic monomers. The michrophysical parameters of these models are presented and discussed.

Electromagnetic scattering by spheroidal volumes of discrete random medium.

We use the superposition T-matrix method to compare the far-field scattering matrices generated by spheroidal and spherical volumes of discrete random medium having the same volume and populated by identical spherical particles. Our results fully confirm the robustness of the previously identified coherent and diffuse scattering regimes and associated optical phenomena exhibited by spherical particulate volumes and support their explanation in terms of the interference phenomenon coupled with the order-of-scattering expansion of the far-field Foldy equations. We also show that increasing nonsphericity of particulate volumes causes discernible (albeit less pronounced) optical effects in forward and backscattering directions and explain them in terms of the same interference/multiple-scattering phenomenon.

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media.

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first-principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.

Electromagnetic scattering by fully ordered and quasi-random rigid particulate samples.

In this paper we have analyzed circumstances under which a rigid particulate sample can behave optically as a true discrete random medium consisting of particles randomly moving relative to each other during measurement. To this end, we applied the numerically exact superposition T-matrix method to model far-field scattering characteristics of fully ordered and quasi-randomly arranged rigid multiparticle groups in fixed and random orientations. We have shown that, in and of itself, averaging optical observables over movements of a rigid sample as a whole is insufficient unless it is combined with a quasi-random arrangement of the constituent particles in the sample. Otherwise, certain scattering effects typical of discrete random media (including some manifestations of coherent backscattering) may not be accurately replicated.

Demonstration of numerical equivalence of ensemble and spectral averaging in electromagnetic scattering by random particulate media.

The numerically exact superposition T-matrix method is used to model far-field electromagnetic scattering by two types of particulate object. Object 1 is a fixed configuration that consists of N identical spherical particles (with N=200 or 400) quasi-randomly populating a spherical volume V having a median size parameter of 50. Object 2 is a true discrete random medium (DRM) comprising the same number N of particles randomly moving throughout V. The median particle size parameter is fixed at 4. We show that if Object 1 is illuminated by a quasi-monochromatic parallel beam then it generates a typical speckle pattern having no resemblance to the scattering pattern generated by Object 2. However, if Object 1 is illuminated by a parallel polychromatic beam with a 10% bandwidth then it generates a scattering pattern that is largely devoid of speckles and closely reproduces the quasi-monochromatic pattern generated by Object 2. This result serves to illustrate the capacity of the concept of electromagnetic scattering by a DRM to encompass fixed quasi-random particulate samples provided that they are illuminated by polychromatic light.

Linear depolarization of lidar returns by aged smoke particles.

We use the numerically exact (superposition) T-matrix method to analyze recent measurements of the backscattering linear depolarization ratio (LDR) for a plume of aged smoke at lidar wavelengths ranging from 355 to 1064 nm. We show that the unique spectral dependence of the measured LDRs can be modeled, but only by assuming expressly nonspherical morphologies of smoke particles containing substantial amounts of nonabsorbing (or weakly absorbing) refractory materials such as sulfates. Our results demonstrate that spectral backscattering LDR measurements can be indicative of the presence of morphologically complex smoke particles, but additional (e.g., passive polarimetric or bistatic lidar) measurements may be required for a definitive characterization of the particle morphology and composition.

Adhesion of mineral and soot aerosols can strongly affect their scattering and absorption properties.

We use the numerically exact superposition T-matrix method to compute the optical cross sections and the Stokes scattering matrix for polydisperse mineral aerosols (modeled as homogeneous spheres) covered with a large number of much smaller soot particles. These results are compared with the Lorenz-Mie results for a uniform external mixture of mineral and soot aerosols. We show that the effect of soot particles adhering to large mineral particles can be to change the extinction and scattering cross sections and the asymmetry parameter quite substantially. The effect on the phase function and degree of linear polarization can be equally significant.

Light scattering by wavelength-sized particles "dusted" with subwavelength-sized grains.

The numerically exact superposition T-matrix method is used to compute the scattering cross sections and the Stokes scattering matrix for polydisperse spherical particles covered with a large number of much smaller grains. We show that the optical effect of the presence of microscopic dust on the surfaces of wavelength-sized, weakly absorbing particles is much less significant than that of a major overall asphericity of the particle shape.

Coherent backscattering by polydisperse discrete random media: exact T-matrix results.

The numerically exact superposition T-matrix method is used to compute, for the first time to our knowledge, electromagnetic scattering by finite spherical volumes composed of polydisperse mixtures of spherical particles with different size parameters or different refractive indices. The backscattering patterns calculated in the far-field zone of the polydisperse multiparticle volumes reveal unequivocally the classical manifestations of the effect of weak localization of electromagnetic waves in discrete random media, thereby corroborating the universal interference nature of coherent backscattering. The polarization opposition effect is shown to be the least robust manifestation of weak localization fading away with increasing particle size parameter.