A variational approach to waveform design for synthetic aperture imaging

Abstract. We derive an optimal transmit waveform for filtered backprojectionbased synthetic-aperture imaging. The waveform is optimal in terms of minimising the mean square error (MSE) in the resulting image. Our optimization is performed in two steps: First, we consider the minimum-mean-square-error (MMSE) for an arbitrary but fixed waveform, and derive the corresponding filter for the filtered backprojection reconstruction. Second, the MMSE is further reduced by finding an optimal transmit waveform. The transmit waveform is derived for stochastic models of the scattering objects of interest (targets), other scattering objects (clutter), and additive noise. We express the waveform in terms of spatial spectra for the random fields associated with target and clutter, and the spectrum for the noise process. This approach results in a constraint that involves only the amplitude of the Fourier transform of the transmit waveform. Therefore, considerable flexibility is left for incorporating additional requirements, such as minimal variation of transmit amplitude and phase-coding

Polycontinuous geometries for inverse lipid phases with more than two aqueous network domains

Inverse bicontinuous cubic phases with two aqueous network domains separated by a smooth bilayer are firmly established as equilibrium phases in lipid/water systems. The purpose of this article is to highlight the generalisations of these bicontinuous geometries to polycontinuous geometries, which could be realised as lipid mesophases with three or more network-like aqueous domains separated by a branched bilayer. An analysis of structural homogeneity in terms of bilayer width variations reveals that ordered polycontinuous geometries are likely candidates for lipid mesophase structures, with similar chain packing characteristics to the inverse micellar phases (that once were believed not to exist due to high packing frustration). The average molecular shape required by global geometry to form these multi-network phases is quantified by the surfactant shape parameter, v/(al); we find that it adopts values close to those of the known lipid phases. We specifically analyse the 3etc(187 193) structure of hexagonal symmetry P63 /mcm with three aqueous domains, the 3dia(24 220) structure of cubic symmetry I 3d composed of three distorted diamond networks, the cubic chiral 4srs(24 208) with cubic symmetry P4232 and the achiral 4srs(5 133) structure of symmetry P42/nbc, each consisting of four intergrown undistorted copies of the srs net (the same net as in the QGII gyroid phase). Structural homogeneity is analysed by a medial surface approach assuming that the head-group interfaces are constant mean curvature surfaces. To facilitate future experimental identification, we provide simulated SAXS scattering patterns that, for the 4srs(24 208) and 3dia(24 220) structures, bear remarkable similarity to those of bicontinuous QGII-gyroid and QDII-diamond phases, with comparable lattice parameters and only a single peak that cannot be indexed to the well-established structures. While polycontinuous lipid phases have, to date, not been reported, the likelihood of their formation is further indicated by the reported observation of a solid tricontinuous mesoporous silicate structure, termed IBN-9, which formed in the presence of surfactants [Han et al., Nat. Chem., 2009, 1, 123]

X-ray attenuation models to account for beam hardening in computed tomography

We introduce a beam-hardening correction method for lab-based X-ray computed tomography (CT) by modifying existing iterative tomographic reconstruction algorithms. Our method simplifies the standard Alvarez-Macovski X-ray attenuation model [Phys. Med. Biol. 21, 733 (1976)] and is compatible with conventional (i.e., singlespectrum) CT scans. The sole modification involves a polychromatic projection operation, which is equivalent to applying a weighting that more closely matches the attenuation of polychromatic X-rays. Practicality is a priority, so we only require information about the X-ray spectrum and some constants relating to material properties. No other changes to the experimental setup or the iterative algorithms are necessary. Using reconstructions of simulations and several large experimental datasets, we show that this method is able to remove or reduce cupping, streaking, and other artefacts from X-ray beam hardening and improve the self-consistency of projected attenuation in CT. When the assumptions made in the simplifications are valid, the reconstructed tomogram can even be quantitative.Australian Research Council (LP150101040); partner company FEI (now Thermo-Fisher) through Linkage (Project LP150101040)

A bicontinuous mesophase geometry with hexagonal symmetry

We report that a specific realization of Schwarz's triply periodic hexagonal minimal surface is isotropic with respect to the Doi-Ohta interface tensor and simultaneously has minimal packing and stretching frustration similar to those of the commonly found cubic bicontinuous mesophases. This hexagonal surface, of symmetry P6(3)/mmc with a lattice ratio of c/a = 0.832, is therefore a likely candidate geometry for self-assembled lipid/surfactant or copolymer mesophases. Furthermore, both the peak position ratios in its powder diffraction pattern and the elastic moduli closely resemble those of the cubic bicontinuous phases. We therefore argue that a genuine possibility of experimental misidentification exists