Uncertainties in measured and modelled asymmetry parameters of mineral dust aerosols

The error caused by the uncertainty in the refractive index in the determination of the asymmetry parameter g is studied for a variety of mineral dust aerosol samples at two different optical wavelengths. Lorenz–Mie computations for spherical model particles are compared with results based on laboratory-measured phase functions in conjunction with a commonly used extrapolation method. The difference between the g-value based on measurements and the g-value based on Lorenz–Mie simulations is generally on the same order of magnitude as the error caused by the uncertainty in the refractive index m. For larger effective radii the error in g related to the use of spherical model particles is even larger than that related to the uncertainty in m. This indicates that the use of spherical model particles can be among the major error sources in the determination of the asymmetry parameter of dust aerosols.     

A 3D implementation of ray tracing combined with diffraction on facets: Verification and a potential application

A 3D implementation of a new model of light scattering applicable to dielectric faceted objects is introduced. The model combines standard geometric optics with diffraction on individual facets. It can be applied to any faceted geometry. The model adds no significant computational overheads to classical geometric optics yet provides much improved results. Initial results for long hexagonal columns are compared to SVM and appear favourable. 2D scattering patterns are calculated for a hexagonal column in a fixed orientation and compared to those created by ice analogue crystals in the laboratory with close agreement. The comparison includes the observation of a guided wave propagating along the length of the column. The new model is then applied to a selection of geometries to illustrate how it could be used to aid particle characterization, particularly in the case of cirrus ice.     

Scattering from a long helix: Theory and simulation

We consider here the electromagnetic scattering by a long helical particle made from a thin (in comparison to the wavelength) wire. In contrast to several previous theoretical works, we adopt here the algorithm developed for scattering by a multi-layered fiber. In the present work, the helical particle is considered as a hollow cylinder with a thin non-homogeneous membrane for which periodical boundary conditions are imposed.     

Phase function of long helical particles at normal and oblique incidence

This paper studies characteristics of the electro-magnetic wave scattering by a long helical particle in cases of oblique incidence with different polarizations. The dependence of the resonant peaks and the phase function on the incidence angle is analyzed for different values of helix parameters. The analysis is based on the model developed by the authors and presented in previous publications.     

Shape modeling of mineral dust particles for light-scattering calculations using the spatial Poisson-Voronoi tessellation

We present a shape model of mineral dust particles for use in light-scattering calculations. A spatial Poisson-Voronoi tessellation was applied to simulate the aggregate structure and, therefore, the rough surface of the mineral particles. To develop the shape model, we took into account statistics of shape parameters derived from the cross-sectional areas, maximum dimensions, and perimeters of field-collected dust particles. Light-scattering properties of the modeled Voronoi aggregates were examined by the finite-difference time-domain (FDTD) method. The results of randomly oriented scattering properties agreed with previously reported laboratory measurements of mineral dust particles.     

团簇自然气溶胶散射相函数的数值分析

针对不同比例的灰尘和海盐团簇自然气溶胶,利用离散偶极子近似(DDA)法,通过考察成分的影响,使用波长为0.55 m,尺度参数变化范围为0.1~25时,研究了散射相函数和激光雷达比的影响,结果表明二者的变化趋势大体相同。尺度参数为13~24时,团簇自然气溶胶散射相函数有明显的后向散射加强,其中尺度参数为18附近,后向散射加强效应最明显。灰尘比海盐对散射相函数影响更大,二者的影响主要集中在尺度参数为15~25范围内,但除了散射角为180附近的后向外,影响的散射角方向略有不同。不同比例下的团簇自然气溶胶激光雷达比在尺度参数为3左右有最大值,其值约为180。在尺度参数为0.2~25范围内,成分对激光雷达比的影响不大,相对偏差小于10%,特别是尺度参数为0.5~2时的影响可以忽略,相对偏差小于1%。     

A T-matrix method and computer code for randomly oriented, axially symmetric coated scatterers

A computer code is described for the calculation of light-scattering properties of randomly oriented, axially symmetric coated particles, in the framework of the T-matrix theory. The underlying mathematical background is outlined briefly and convergence procedures are discussed. After outlining the input-output interaction between user and code, benchmark results are presented for two distinct shapes: coated, centered spheroids and offset coated spheres.     

A data-analysis method for decomposing synchronization variability of anticipatory systems into stochastic and deterministic components

Synchronization has been shown to be a valuable concept in the field of nonlinear dynamics and dynamical systems in general. Deviation from perfect synchronization results from an interplay of deterministic coupling forces and stochastic fluctuating forces. When the exact details of these two sources of variance are unknown, it becomes useful to estimate them directly from data. To this end, we develop a data analysis method for estimating parameters associated with these deterministic and stochastic components. The method relies on separating their respective contributions to synchronization error. We focus on the case where a slave system synchronizes with the future of a master system, so-called anticipating synchronization.     

Light scattering modeling of small feldspar aerosol particles using polyhedral prisms and spheroids

The use of simplified particle shapes for modeling scattering by irregularly shaped mineral-dust particles is studied using polyhedral prisms and spheroids as model particles. Simulated phase matrices averaged over shape and size distributions at wavelength 633 nm are compared with a laboratory-measured phase matrix of feldspar particles with known size distribution with effective radius of . When an equi-probable shape distribution is assumed, prisms and oblate spheroids agree with measurements to a similar degree, whereas prolate spheroids perform markedly better. Both spheroids and prisms perform much better than spheres. When an automatic fitting method is applied for finding optimal shape distributions, it is found that the most elongated spheroids are most important for good fits, whereas nearly-spherical spheroids are generally of very little importance. The phase matrices for the different polyhedral prisms, on the other hand, are found to be similar, thus their shape-averaged phase matrices are insensitive to the shape distribution assumed. For spheroids, a simple parameterization for the shape distribution, where weights increase with increasing departure from spherical shape, is proposed and tested. This parameterization improves the fit of most phase matrix elements attained with an equi-probable shape distribution, and it performs particularly well for reproducing the measured phase function.     

Light scattering by large Saharan dust particles: Comparison of modeling and experimental data for two samples

Light scattering by large mineral-dust particles with small-scale surface roughness is investigated by comparing model simulations with laboratory-measured scattering matrices of two distinct dust samples collected from the Sahara desert. The samples have been chosen on the basis of their large effective radii, and the simulations are based on their measured size distributions. Size parameters larger than about 30 are modeled using a modified ray-optics model RODS (Ray optics with diffuse and specular interactions), while smaller particles are simulated with a T-matrix model. RODS allows us to mimic the surface roughness of large dust particles by covering the particle surface by a thin layer of external scatterers with specific single-scattering properties. The Gaussian-random-sphere geometry is used for the shapes of large dust particles. Small particles are modeled as an axial-ratio distribution of spheroids with smooth surfaces. One of the samples consists wholly of large particles and its scattering matrix can be reproduced very well by the RODS model, except for the phase function. The incorporation of wavelength-scale roughness is, however, necessary for good fits. The other sample, consisting of both small and large particles, proves more challenging to match with simulations. The analysis indicates, however, that the difficulties arise at least partially from the small-particle contribution, while RODS results are consistent with the measurements. Further, the results imply that the agreement with measurements would improve if roughness could also be accounted for in the small-particle simulations. Overall, the RODS method seems promising for modeling the optical properties of mineral-dust particles much larger than the wavelength.     

A data-analysis method for identifying differential effects of time-delayed feedback forces and periodic driving forces in stochastic systems

In this work a method is developed for analyzing time series of periodically driven stochastic systems involving time-delayed feedback. The proposed data-analysis method yields dynamical models in terms of stochastic delay differential equations. On the basis of these dynamical models differential effects of driving forces and time-delayed feedback forces can be identified.     

A review of optical measurements at the aerosol and cloud chamber AIDA

This paper provides a survey of recent studies on the optical properties of aerosol and cloud particles that have been conducted at the AIDA facility of Forschungszentrum Karlsruhe (Aerosol Interactions and Dynamics in the Atmosphere). Reflecting the broad accessible temperature range of the AIDA chamber which extends from ambient temperature down to 183 K, the investigations feature a broad diversity of research topics, such as the wavelength-dependence of the specific absorption cross sections of soot and mineral dust aerosols at room temperature, depolarization and infrared extinction measurements of ice crystal clouds generated at temperatures below 235 K, and the optical properties of polar stratospheric cloud constituents whose formation was studied in chamber experiments at temperatures well below 200 K. After reviewing the AIDA research activity of the past decade and introducing the optical instrumentation of the AIDA facility, this paper presents illustrative examples of ongoing and already published work on optical measurements of soot aerosols, mineral dust particles, and ice crystal clouds.     

Fast and accurate radiance calculations using truncation approximation for anisotropic scattering phase functions

The phase function for solar light scattering by large particles such as cloud droplets is strongly anisotropic due to very strong peaking in the forward direction. This creates numerical difficulties when attempting to calculate accurate reflected and transmitted radiances, which are important for remote sensing of atmospheric and surface properties. A popular approach uses the delta function to approximate the forward-scattering peak in a fraction of energy and a limited number of polynomial terms or a geometrically truncated function for the remaining fraction (so-called truncation approximations). This article compares and discusses several methods for fast and accurate calculations using truncation approximations. When using a single truncation approximation for all scattering orders, large biases appear in directions near the solar and anti-solar points. As shown here, high accuracy can be obtained using different truncation approximations depending on the order of scattering. Of particular importance is the use of phase functions close to the exact phase functions for the first few orders of scattering. Applying the method in combination with the Monte Carlo (MC) method, in which the truncation fraction for a scattering order depends on the scattering angle at the previous scattering event, obtains accurate radiance calculations under almost all geometrical and optical conditions, including in directions near the solar point. Because the method also reduces computational noise due to the MC sampling of radiance, it is useful for fast and accurate radiance calculations for cloudy atmospheres.     

T-matrix method and its applications to electromagnetic scattering by particles: A current perspective

This note serves as a short introduction to the reprint of our article “T-matrix computations of light scattering by nonspherical particles: a review” (JQSRT 1996; 55:535-75). We first discuss the motivation for writing that article and explain its historical context. This is followed by a short overview of more recent developments.     

Performance of discrete dipole approximation for prediction of amplitude and phase of electromagnetic scattering by particles

Electromagnetic scattering provides useful signatures for nonintrusive particle characterization. Scattered wave which carries characteristic information about particles is identified completely by its intensity, polarization state and phase. Recent developments in measurement techniques have enabled measurement of phase of the scattered wave which is a source of additional information about particles. In the present study, accuracy of discrete dipole approximation (DDA) in predicting amplitude and phase of scattered wave is investigated via publicly available DDSCAT code by Draine and Flatau, which is a well-established tool for DDA and has found wide range of applications in the literature due to its flexibility. DDSCAT routine is modified to enable accurate computation of phase of complex amplitude scattering matrix (ASM) elements as well as their magnitude. DDA method was implemented by using lattice dispersion relation for dipole polarizabilities, generalized prime factor algorithm for fast-Fourier transformation and pre-conditioned bi-conjugate gradient method with stabilization for the solution of the complex linear system of equations. Accuracy of ASM elements predicted by DDA is assessed on single sphere problems with various size parameters and refractive indices by validation against Mie theory solutions. Excellent agreement between predictions and exact solutions proves the reliability of the modified DDSCAT code for prediction of amplitude and phase of scattered electromagnetic wave. Applicability conditions and requirements of the present DDA application to ensure accurate prediction of complete set of scattering parameters are mapped for single spheres, on an extensive domain of size parameters and refractive indices. A correlation is presented to estimate the magnitude and phase errors associated with given size parameter, refractive index and cubic lattice subdivision. Assessment of computational time requirements for different optical constants shows that implementation of DDA with the present specifications is unfeasible for size parameters larger than 4 when Re(m)>2 and Im(m)<0.1 at the same time, due to slow convergence rate.     

Stationary phase method and delay times for relativistic and non-relativistic tunneling particles

The stationary phase method is frequently adopted for calculating tunneling phase times of analytically-continuous Gaussian or infinite-bandwidth step pulses which collide with a potential barrier. This report deals with the basic concepts on deducing transit times for quantum scattering: the stationary phase method and its relation with delay times for relativistic and non-relativistic tunneling particles. After reexamining the above-barrier diffusion problem, we notice that the applicability of this method is constrained by several subtleties in deriving the phase time that describes the localization of scattered wave packets. Using a recently developed procedure - multiple wave packet decomposition - for some specifical colliding configurations, we demonstrate that the analytical difficulties arising when the stationary phase method is applied for obtaining phase (traversal) times are all overcome. In this case, we also investigate the general relation between phase times and dwell times for quantum tunneling/scattering. Considering a symmetrical collision of two identical wave packets with an one-dimensional barrier, we demonstrate that these two distinct transit time definitions are explicitly connected. The traversal times are obtained for a symmetrized (two identical bosons) and an antisymmetrized (two identical fermions) quantum colliding configuration. Multiple wave packet decomposition shows us that the phase time (group delay) describes the exact position of the scattered particles and, in addition to the exact relation with the dwell time, leads to correct conceptual understanding of both transit time definitions. At last, we extend the non-relativistic formalism to the solutions for the tunneling zone of a one-dimensional electrostatic potential in the relativistic (Dirac to Klein-Gordon) wave equation where the incoming wave packet exhibits the possibility of being almost totally transmitted through the potential barrier. The conditions for the occurrence of accelerated and, eventually, superluminal tunneling transmission probabilities are all quantified and the problematic superluminal interpretation based on the non-relativistic tunneling dynamics is revisited. Lessons concerning the dynamics of relativistic tunneling and the mathematical structure of its solutions suggest revealing insights into mathematically analogous condensed-matter experiments using electrostatic barriers in single- and bi-layer graphene, for which the accelerated tunneling effect deserves a more careful investigation.     

Programmable aperture microscopy: A computational method for multi-modal phase contrast and light field imaging

We demonstrate a simple and cost-effective programmable aperture microscope to realize multi-modal computational imaging by integrating a programmable liquid crystal display (LCD) into a conventional wide-field microscope. The LCD selectively modulates the light distribution at the rear aperture of the microscope objective, allowing numerous imaging modalities, such as bright field, dark field, differential phase contrast, quantitative phase imaging, multi-perspective imaging, and full resolution light field imaging to be achieved and switched rapidly in the same setup, without requiring specialized hardwares and any moving parts. We experimentally demonstrate the success of our method by imaging unstained cheek cells, profiling microlens array, and changing perspective views of thick biological specimens. The post-exposure refocusing of a butterfly mouthpart and RFP-labeled dicot stem cross-section is also presented to demonstrate the full resolution light field imaging capability of our system for both translucent and fluorescent specimens.     

Kinematics and backgrounds for HAPPEX measurements

Measurements and systematic errors of the 4-momentum transfer squared (Q²) and backgrounds for the 2005 HAPPEX runs are described.     

Accelerating the calculations of binary detour phase method by integrating both CUDA and Matlab programming for GPU's parallel computations

The availability of state of art GPGPU cards can play a promising role in accelerating the calculations of computer generated holograms (CGH) where one of the main problems of generating such holograms is the need for massive amount of calculations. Both CUDA and Matlab can be used alone to fulfill this purpose but using both at the same time gives a number of benefits. This paper is dedicated to present a performance study of applying Fermi-Architecture CUDA-enabled GPGPU card for speeding up the calculations of binary detour phase holograms using both Matlab and CUDA programming.