Multiple-scattering in radar systems: a review

Although extensively studied within the lidar community, the multiple scattering phenomenon has always been considered a rare curiosity by radar meteorologists. Up to few years ago its appearance has only been associated with two- or three-body-scattering features (e.g. hail flares and mirror images) involving highly reflective surfaces. Recent atmospheric research aimed at better understanding of the water cycle and the role played by clouds and precipitation in affecting the Earth's climate has driven the deployment of high frequency radars in space. Examples are the TRMM 13.5 GHz, the CloudSat 94 GHz, the upcoming EarthCARE 94 GHz, and the GPM dual 13-35 GHz radars. These systems are able to detect the vertical distribution of hydrometeors and thus provide crucial feedbacks for radiation and climate studies. The shift towards higher frequencies increases the sensitivity to hydrometeors, improves the spatial resolution and reduces the size and weight of the radar systems. On the other hand, higher frequency radars are affected by stronger extinction, especially in the presence of large precipitating particles (e.g. raindrops or hail particles), which may eventually drive the signal below the minimum detection threshold. In such circumstances the interpretation of the radar equation via the single scattering approximation may be problematic. Errors will be large when the radiation emitted from the radar after interacting more than once with the medium still contributes substantially to the received power. This is the case if the transport mean-free-path becomes comparable with the instrument footprint (determined by the antenna beam-width and the platform altitude). This situation resembles to what has already been experienced in lidar observations, but with a predominance of wide- versus small-angle scattering events. At millimeter wavelengths, hydrometeors diffuse radiation rather isotropically compared to the visible or near infrared region where scattering is predominantly in the forward direction. A complete understanding of radiation transport modeling and data analysis methods under wide-angle multiple scattering conditions is mandatory for a correct interpretation of echoes observed by space-borne millimeter radars. This paper reviews the status of research in this field. Different numerical techniques currently implemented to account for higher order scattering are reviewed and their weaknesses and strengths highlighted. Examples of simulated radar backscattering profiles are provided with particular emphasis given to situations in which the multiple scattering contributions become comparable or overwhelm the single scattering signal. We show evidences of multiple scattering effects from air-borne and from CloudSat observations, i.e. unique signatures which cannot be explained by single scattering theory. Ideas how to identify and tackle the multiple scattering effects are discussed. Finally perspectives and suggestions for future work are outlined. This work represents a reference-guide for studies focused at modeling the radiation transport and at interpreting data from high frequency space-borne radar systems that probe highly opaque scattering media such as thick ice clouds or precipitating clouds.

The Heliospheric Imagers onboard the STEREO mission

Mounted on the sides of two widely separated spacecraft, the two Heliospheric Imager (HI) instruments onboard NASA’s STEREO mission view, for the first time, the space between the Sun and Earth. These instruments are wide-angle visible-light imagers that incorporate sufficient baffling to eliminate scattered light to the extent that the passage of solar coronal mass ejections (CMEs) through the heliosphere can be detected. Each HI instrument comprises two cameras, HI-1 and HI-2, which have 20° and 70° fields of view and are off-pointed from the Sun direction by 14.0° and 53.7°, respectively, with their optical axes aligned in the ecliptic plane. This arrangement provides coverage over solar elongation angles from 4.0° to 88.7° at the viewpoints of the two spacecraft, thereby allowing the observation of Earth-directed CMEs along the Sun – Earth line to the vicinity of the Earth and beyond. Given the two separated platforms, this also presents the first opportunity to view the structure and evolution of CMEs in three dimensions. The STEREO spacecraft were launched from Cape Canaveral Air Force Base in late October 2006, and the HI instruments have been performing scientific observations since early 2007. The design, development, manufacture, and calibration of these unique instruments are reviewed in this paper. Mission operations, including the initial commissioning phase and the science operations phase, are described. Data processing and analysis procedures are briefly discussed, and ground-test results and in-orbit observations are used to demonstrate that the performance of the instruments meets the original scientific requirements.

Development of orientation during electrospinning of fibres of poly(ε-caprolactone)

We explore the influence of a rotating collector on the internal structure of poly(ε-caprolactone) fibres electrospun from a solution in dichloroethane. We find that above a threshold collector speed, the mean fibre diameter reduces as the speed increases and the fibres are further extended. Small-angle and wide-angle X-ray scattering techniques show a preferred orientation of the lamellar crystals normal to the fibre axis which increases with collector speed to a maximum and then reduces. We have separated out the processes of fibre alignment on the collector and the orientation of crystals within the fibres. There are several stages to this behaviour which correspond to the situations (a) where the collector speed is slower than the fibre spinning rate, (b) the fibre is mechanically extended by the rotating collector and (c) where the deformation leads to fibre fracture. The mechanical deformation leads to a development of preferred orientation with extension which is similar to the prediction of the pseudo-affine deformation model and suggests that the deformation takes place during the spinning process after the crystals have formed.

Coupling between mesogenic units and polymer backbone in side-chain liquid crystal polymers and elastomers

The levels of alignment of the mesogenic units and of the polymer backbone trajectory for polyacrylate based nematic side-chain liquid crystal polymers and elastomers were evaluated by using wide angle X-ray and small angle neutron scattering procedures. The X-ray scattering measurements show that substantial levels of preferred orientation of the mesogenic units may be introduced through magnetic fields for uncrosslinked polymers and through mechanical extension for liquid crystal elastomers. Small angle neutron scattering measurements show that for highly aligned samples an anisotropic polymer backbone trajectory is observed in which the envelope is slightly extended by ∼ 10% in the direction parallel to the axis of alignment of the mesogenic units. The sense of this coupling differs from that recorded for other uncrosslinked side-chain liquid crystal polymers. Possible mechanisms to account for this anisotropy and its relationship to the properties of liquid crystal elastomers are discussed. The observed deformation behaviour of the liquid crystal elastomer is non-affine and this appears to confirm the dominating influence of the liquid crystal order of the side chains on the mechanical properties of these novel networks.

Measurement of molecular orientation in thermotropic liquid crystalline polymers

Procedures for obtaining molecular orientational parameters from wide angle X-ray scattering patterns of samples of thermotropic liquid crystalline polymers are presented. The methods described are applied to an extrusion-aligned sample of a random copolyester of poly(ethylene terephthalate) (PET) and p-acetoxybenzoic acid. Values of the orientational parameters are obtained from both the interchain and intrachain maxima in the scattering pattern. The differences in the values so derived suggest some level of local rotational correlation

The determination of molecular orientation in uniaxially compressed PMMA by X-ray scattering

A procedure is presented for obtaining full molecular orientation information from wide angle X-ray scattering patterns of deformed non-crystalline polymers. The method is based on the analysis of experimental and calculated scattering patterns into their spherical harmonics. The results obtained for PMMA are compared with values predicted by the pseudo affine and affine deformation schemes.

The effect of annealing on the local structure of glassy polycarbonate

Annealing of polycarbonate glasses at temperatures belowTg leads to an increase in yield stress and a drop in the impact strength. Although such behaviour may be related to the corresponding reduction in free volume upon annealing, variations in the wide-angle X-ray scattering curves indicate some modification to the local structure. The area of an intrachain peak at s ∼ 0.7 Å−1 is monitored with respect to annealing temperature and time. It is proposed that the variations may be described by an increasing level of interlocking or (nesting) between neighbouring chain segments, a process which is a natural consequence of the molecular shape of polycarbonate.

A two-dimensional X-ray scattering system for in-situ time-resolving studies of polymer structures subjected to controlled deformations

A two-dimensional X-ray scattering system developed around a CCD-based area detector is presented, both in terms of hardware employed and software designed and developed. An essential feature is the integration of hardware and software, detection and sample environment control which enables time-resolving in-situ wide-angle X-ray scattering measurements of global structural and orientational parameters of polymeric systems subjected to a variety of controlled external fields. The development and operation of a number of rheometers purpose-built for the application of such fields are described. Examples of the use of this system in monitoring degrees of shear-induced orientation in liquid-crystalline systems and crystallization of linear polymers subsequent to shear flow are presented.

WAXS studies of global molecular orientation induced in nematic liquid crystals by simple shear flow

Global molecular orientation function coefficients for the nematic liquid crystal 4-cyano 4'-nn -pentylbiphenyl (5CB) in shear flow are presented, being extracted from 2-dimensional Wide-Angle X-ray Scattering data. A linear increase in orientation parameter P2 is observed with a logarithmic increase in shear rate. It is proposed that this arises from an increased number of LC directors aligning to the shear axis. Upon cessation of shear flow, the anisotropy is seen to relax away completely, over a time scale which is inversely proportional to the previously applied shear rate.

The development of organized structures in polyethylene crystallized from a sheared melt, analyzed by WAXS and TEM

The development of global orientation and morphological features in linear polyethylene crystallizing from a sheared melt are studied using in-situ time-resolving wide angle X-ray scattering (WAXS) and ex-situ transmission electron microscopy. It is found that samples subjected to a shear rate above a critical value of ~1s-1 result in macroscopically oriented structures in the crystallized sample. This critical shear rate appears to be independent of the differences in molecular weight distribution of the samples studied although the morphologies which develop are sensitive to quite small differences in molecular weight distributions. The presence of shish kebabs in the morphology is shown to differ markedly according to variations in the upper molecular weight fraction of the molecular weight distribution, even though the resulting global orientation does not. The WAXS also reveals that areas which evidence no row nucleated structures still realize high degrees of molecular orientation. It is proposed that the formation of shish kebab or lamellar morphologies in these samples is dependent on the critical density of contiguous elongated crystallization nuclei rather than any specific global criteria.

A single director switching mode for monodomain liquid crystal elastomer

We report rotation of a single director in a nematic monodomain, acrylate based side-chain elastomer which was subjected to mechanical fields applied at angles in the range to the director, , present at the time of network formation. Time and spatially resolving wide angle X-ray scattering, together with polarised light microscopy measurements revealed a pronounced, almost discontinuous switching mode at a critical extension as the strain was applied at angles approaching to , whereas a more continuous rotation was seen when the strain was applied at more acute angles. This director reorientation was more or less uniform across the complete sample and was accompanied by a modest decrease in orientation parameter . At strains sufficient to induce switching there was some continuous distribution of director orientations with fluctuations of 10 although there was no evidence for any localised director inhomogenities such as domain formation. The observed deformation behaviour of these acrylate-based nematic monodomains was in accord with the predictions of a theory developed by Bladon et al., in that the complete set of data could be accounted for through a single parameter describing the chain anisotropy. The experimentally deduced chain anisotropy parameter was in broad agreement with that obtained from small-angle neutron scattering procedures, but was somewhat greater than that obtained by spontaneous shape changes at the nematic-isotropic transition.

Extracting quantitative structural parameters for disordered polymers from neutron scattering data

The organization of non-crystalline polymeric materials at a local level, namely on a spatial scale between a few and 100 a, is still unclear in many respects. The determination of the local structure in terms of the configuration and conformation of the polymer chain and of the packing characteristics of the chain in the bulk material represents a challenging problem. Data from wide-angle diffraction experiments are very difficult to interpret due to the very large amount of information that they carry, that is the large number of correlations present in the diffraction patterns.We describe new approaches that permit a detailed analysis of the complex neutron diffraction patterns characterizing polymer melts and glasses. The coupling of different computer modelling strategies with neutron scattering data over a wide Q range allows the extraction of detailed quantitative information on the structural arrangements of the materials of interest. Proceeding from modelling routes as diverse as force field calculations, single-chain modelling and reverse Monte Carlo, we show the successes and pitfalls of each approach in describing model systems, which illustrate the need to attack the data analysis problem simultaneously from several fronts.

SANS/WANS time-resolving neutron scattering studies of polymer phase transitions using NIMROD

We use new neutron scattering instrumentation to follow in a single quantitative time-resolving experiment, the three key scales of structural development which accompany the crystallisation of synthetic polymers. These length scales span 3 orders of magnitude of the scattering vector. The study of polymer crystallisation dates back to the pioneering experiments of Keller and others who discovered the chain-folded nature of the thin lamellae crystals which are normally found in synthetic polymers. The inherent connectivity of polymers makes their crystallisation a multiscale transformation. Much understanding has developed over the intervening fifty years but the process has remained something of a mystery. There are three key length scales. The chain folded lamellar thickness is ~ 10nm, the crystal unit cell is ~ 1nm and the detail of the chain conformation is ~ 0.1nm. In previous work these length scales have been addressed using different instrumention or were coupled using compromised geometries. More recently researchers have attempted to exploit coupled time-resolved small-angle and wide-angle x-ray experiments. These turned out to be challenging experiments much related to the challenge of placing the scattering intensity on an absolute scale. However, they did stimulate the possibility of new phenomena in the very early stages of crystallisation. Although there is now considerable doubt on such experiments, they drew attention to the basic question as to the process of crystallisation in long chain molecules. We have used NIMROD on the second target station at ISIS to follow all three length scales in a time-resolving manner for poly(e-caprolactone). The technique can provide a single set of data from 0.01 to 100Å-1 on the same vertical scale. We present the results using a multiple scale model of the crystallisation process in polymers to analyse the results.

Mobile-to-mobile MIMO transmit-receive diversity systems: analysis and performance in three-dimensional double-correlated channels

Mobile-to-mobile (M-to-M) communications are expected to play a crucial role in future wireless systems and networks. In this paper, we consider M-to-M multiple-input multiple-output (MIMO) maximal ratio combining system and assess its performance in spatially correlated channels. The analysis assumes double-correlated Rayleigh-and-Lognormal fading channels and is performed in terms of average symbol error probability, outage probability, and ergodic capacity. To obtain the receive and transmit spatial correlation functions needed for the performance analysis, we used a three-dimensional (3D) M-to-M MIMO channel model, which takes into account the effects of fast fading and shadowing. The expressions for the considered metrics are derived as a function of the average signal-to-noise ratio per receive antenna in closed-form and are further approximated using the recursive adaptive Simpson quadrature method. Numerical results are provided to show the effects of system parameters, such as distance between antenna elements, maximum elevation angle of scatterers, orientation angle of antenna array in the x–y plane, angle between the x–y plane and the antenna array orientation, and degree of scattering in the x–y plane, on the system performance. Copyright © 2011 John Wiley & Sons, Ltd.

Performance analysis of MIMO MRC in 3D mobile-to-mobile double-correlated channels

In this paper, we consider multiple-input multiple- output (MIMO) maximal ratio combining (MRC) systems and assess the system performance in terms of average symbol error probability (SEP), outage probability and ergodic capacity in double-correlated Rayleigh-and-Lognormal fading channels. In order to derive the receive and transmit correlation functions needed for the performance analysis, a three-dimensional (3D) MIMO mobile-to-mobile (M-to-M) channel model, which takes into account the effects of fast fading and shadowing is used. Numerical results are provided to show the effects of system parameters, such as maximum elevation angle of scatterers, orientation angle of antenna array in the x-y plane, angle between x-y plane and the antenna array orientation, and degree of scattering in the x-y plane, on the system performance.