A Brief Review of Mueller Matrix Calculations Associated with Oceanic Particles

The complete Stokes vector contains much more information than the radiance of light for the remote sensing of the ocean. Unlike the conventional radiance-only radiative transfer simulations, a full Mueller matrix-Stokes vector treatment provides a rigorous and correct approach for solving the transfer of radiation in a scattering medium, such as the atmosphere-ocean system. In fact, radiative transfer simulation without considering the polarization state always gives incorrect results and the extent of the errors induced depends on a particular application being considered. However, the rigorous approach that fully takes the polarization state into account requires the knowledge of the complete single-scattering properties of oceanic particles with various sizes, morphologies, and refractive indices. For most oceanic particles, the comparisons between simulations and observations have demonstrated that the “equivalent-spherical” approximation is inadequate. We will therefore briefly summarize the advantages and disadvantages of a number of light scattering methods for non-spherical particles. Furthermore, examples for canonical cases with specifically oriented particles and randomly oriented particles will be illustrated

Efficient Implementation of the Invariant Imbedding T-Matrix Method and the Separation of Variables Method Applied to Large Nonspherical Inhomogeneous Particles

Three terms, ''Waterman's T-matrix method'', ''extended boundary condition method (EBCM)'', and ''null field method'', have been interchangeable in the literature to indicate a method based on surface integral equations to calculate the T-matrix. Unlike the previous method, the invariant imbedding method (IIM) calculates the T-matrix by the use of a volume integral equation. In addition, the standard separation of variables method (SOV) can be applied to compute the T-matrix of a sphere centered at the origin of the coordinate system and having a maximal radius such that the sphere remains inscribed within a nonspherical particle. This study explores the feasibility of a numerical combination of the IIM and the SOV, hereafter referred to as the IIMSOV method, for computing the single-scattering properties of nonspherical dielectric particles, which are, in general, inhomogeneous. The IIMSOV method is shown to be capable of solving light-scattering problems for large nonspherical particles where the standard EBCM fails to converge. The IIMSOV method is flexible and applicable to inhomogeneous particles and aggregated nonspherical particles (overlapped circumscribed spheres) representing a challenge to the standard superposition T-matrix method. The IIMSOV computational program, developed in this study, is validated against EBCM simulated spheroid and cylinder cases with excellent numerical agreement (up to four decimal places). In addition, solutions for cylinders with large aspect ratios, inhomogeneous particles, and two-particle systems are compared with results from discrete dipole approximation (DDA) computations, and comparisons with the improved geometric-optics method (IGOM) are found to be quite encouraging

Effect of the Inhomogeneity of Ice Crystals on Retrieving Ice Cloud Optical Thickness and Effective Particle Size

Spherical or spheroidal air bubbles are generally trapped in the formation of rapidly growing ice crystals. In this study the single-scattering properties of inhomogeneous ice crystals containing air bubbles are investigated. Specifically, a computational model based on an improved geometric-optics method (IGOM) has been developed to simulate the scattering of light by randomly oriented hexagonal ice crystals containing spherical or spheroidal air bubbles. A combination of the ray-tracing technique and the Monte Carlo method is used. The effect of the air bubbles within ice crystals is to smooth the phase functions, diminish the 22deg and 46deg halo peaks, and substantially reduce the backscatter relative to bubble-free particles. These features vary with the number, sizes, locations and shapes of the air bubbles within ice crystals. Moreover, the asymmetry factors of inhomogeneous ice crystals decrease as the volume of air bubbles increases. Cloud reflectance lookup tables were generated at wavelengths 0.65 m and 2.13 m with different air-bubble conditions to examine the impact of the bubbles on retrieving ice cloud optical thickness and effective particle size. The reflectances simulated for inhomogeneous ice crystals are slightly larger than those computed for homogenous ice crystals at a wavelength of 0.65 microns. Thus, the retrieved cloud optical thicknesses are reduced by employing inhomogeneous ice cloud models. At a wavelength of 2.13 microns, including air bubbles in ice cloud models may also increase the reflectance. This effect implies that the retrieved effective particle sizes for inhomogeneous ice crystals are larger than those retrieved for homogeneous ice crystals, particularly, in the case of large air bubbles

Determination of Ice Cloud Models Using MODIS and MISR Data

Representation of ice clouds in radiative transfer simulations is subject to uncertainties associated with the shapes and sizes of ice crystals within cirrus clouds. In this study, we examined several ice cloud models consisting of smooth, roughened, homogeneous and inhomogeneous hexagonal ice crystals with various aspect ratios. The sensitivity of the bulk scattering properties and solar reflectances of cirrus clouds to specific ice cloud models is investigated using the improved geometric optics method (IGOM) and the discrete ordinates radiative transfer (DISORT) model. The ice crystal habit fractions in the ice cloud model may significantly affect the simulations of cloud reflectances. A new algorithm was developed to help determine an appropriate ice cloud model for application to the satellite-based retrieval of ice cloud properties. The ice cloud particle size retrieved from Moderate Resolution Imaging Spectroradiometer (MODIS) data, collocated with Multi-angle Imaging Spectroradiometer (MISR) observations, is used to infer the optical thicknesses of ice clouds for nine MISR viewing angles. The relative differences between view-dependent cloud optical thickness and the averaged value over the nine MISR viewing angles can vary from 0.5 to 0.5 and are used to evaluate the ice cloud models. In the case for 2 July 2009, the ice cloud model with mixed ice crystal habits is the best fit to the observations (the root mean square (RMS) error of cloud optical thickness reaches 0.365). This ice cloud model also produces consistent cloud property retrievals for the nine MISR viewing configurations within the measurement uncertainties

Validation of Quasi-Invariant Ice Cloud Radiative Quantities with MODIS Satellite-Based Cloud Property Retrievals

Similarity relations applied to ice cloud radiance calculations are theoretically analyzed and numerically validated. If t(1v) and t(1vg) are conserved where t is optical thickness, v the single-scattering albedo, and g the asymmetry factor, it is possible that substantially different phase functions may give rise to similar radiances in both conservative and non-conservative scattering cases, particularly in the case of large optical thicknesses. In addition to theoretical analysis, this study uses operational ice cloud optical thickness retrievals from the Moderate Resolution Imaging Spectroradiometer (MODIS) Level 2 Collection5 (C5) and Collection 6 (C6) cloud property products to verify radiative similarity relations. It is found that, if the MODIS C5 and C6 ice cloud optical thickness values are multiplied by their respective (1wg)factors, the resultant products referred to as the effective optical thicknesses become similar with their ratio values around unity. Furthermore, the ratios of the C5 and C6 ice cloud effective optical thicknesses display an angular variation pattern similar to that of the corresponding ice cloud phase function ratios. The MODIS C5 and C6 values of ice cloud similarity parameter, defined as [(1w)(1(exp. 1/2)wg)]12, also tend to be similar

Platform effects on optical variability and prediction of underwater visibility

We present hydrographic and optical data collected concurrently from two different platforms, the R/P FLoating Instrument Platform and the R/V Kilo Moana, located about 2km apart in the Santa Barbara Channel in California. We show that optical variability between the two platforms was due primarily to platform effects, specifically the breakdown of stratification from mixing by the hull of R/P FLIP. Modeled underwater radiance distribution differed by as much as 50% between the two platforms during stratified conditions. We determine that the observed optical variability resulted in up to 57% differences in predicted horizontal visibility of a black target

Light backscattering polarization patterns from turbid media: theory and experiment

We present both experimental measurements and Monte-Carlo-based simulations of the diffusely backscattered intensity patterns that arise from illuminating a turbid medium with a polarized laser beam. It is rigorously shown that, because of axial symmetry of the system, only seven elements of the effective backscattering Mueller matrix are independent. A new numerical method that allows simultaneous calculation of all 16 elements of the two-dimensional Mueller matrix is used. To validate our method we compared calculations to measurements from a turbid medium that consisted of polystyrene spheres of different sizes and concentrations in deionized water. The experimental and numerical results are in excellent agreement

Observation of precursorlike behavior of femtosecond pulses in a dye with a strong absorption band

Journals published by the American Physical Society can be found at http://publish.aps.org/Recent interest in Sommerfeld-Brillouin optical precursors has brought attention to the possibility of optical precursor observation in bulk matter. We investigate the possible formation of optical precursors in an organic dye solution with a sharp absorption band and anomalous dispersion at a wavelength of approximately 800 nm. We explore this regime experimentally with sub-10-fs pulses with a central wavelength of approximately 800 nm from a Ti : sapphire oscillator. The pulses are passed through a thin layer of the dye solution and characterized by interferometric autocorrelation. The obtained autocorrelation traces are compared with simulations, and we observe important dispersion effects on the shape of the propagated pulses, including precursorlike behavior in their time evolution