Regularized Newton Methods for X-ray Phase Contrast and General Imaging Problems

Like many other advanced imaging methods, x-ray phase contrast imaging and tomography require mathematical inversion of the observed data to obtain real-space information. While an accurate forward model describing the generally nonlinear image formation from a given object to the observations is often available, explicit inversion formulas are typically not known. Moreover, the measured data might be insufficient for stable image reconstruction, in which case it has to be complemented by suitable a priori information. In this work, regularized Newton methods are presented as a general framework for the solution of such ill-posed nonlinear imaging problems. For a proof of principle, the approach is applied to x-ray phase contrast imaging in the near-field propagation regime. Simultaneous recovery of the phase- and amplitude from a single near-field diffraction pattern without homogeneity constraints is demonstrated for the first time. The presented methods further permit all-at-once phase contrast tomography, i.e. simultaneous phase retrieval and tomographic inversion. We demonstrate the potential of this approach by three-dimensional imaging of a colloidal crystal at 95 nm isotropic resolution.Comment: (C)2016 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibite

Vesicle adhesion and fusion studied by small-angle x-ray scattering.

We have studied the adhesion state (also denoted by docking state) of lipid vesicles as induced by the divalent ions Ca2+ or Mg2+ at well-controlled ion concentration, lipid composition, and charge density. The bilayer structure and the interbilayer distance in the docking state were analyzed by small-angle x-ray scattering. A strong adhesion state was observed for DOPC:DOPS vesicles, indicating like-charge attraction resulting from ion correlations. The observed interbilayer separations of ∼1.6 nm agree quantitatively with the predictions of electrostatics in the strong coupling regime. Although this phenomenon was observed when mixing anionic and zwitterionic (or neutral) lipids, pure anionic membranes (DOPS) with highest charge density σ resulted in a direct phase transition to a multilamellar state, which must be accompanied by rupture and fusion of vesicles. To extend the structural assay toward protein-controlled docking and fusion, we have characterized reconstituted N-ethylmaleimide-sensitive factor attachment protein receptors in controlled proteoliposome suspensions by small-angle x-ray scattering

Nanosecond molecular relaxations in lipid bilayers studied by high energy resolution neutron scattering and in-situ diffraction

We report a high energy-resolution neutron backscattering study to investigate slow motions on nanosecond time scales in highly oriented solid supported phospholipid bilayers of the model system DMPC -d54 (deuterated 1,2-dimyristoyl-sn-glycero-3-phoshatidylcholine), hydrated with heavy water. Wave vector resolved quasi-elastic neutron scattering (QENS) is used to determine relaxation times $\tau$, which can be associated with different molecular components, i.e., the lipid acyl chains and the interstitial water molecules in the different phases of the model membrane system. The inelastic data are complemented both by energy resolved and energy integrated in-situ diffraction. From a combined analysis of the inelastic data in the energy and time domain, the respective character of the relaxation, i.e., the exponent of the exponential decay is also determined. From this analysis we quantify two relaxation processes. We associate the fast relaxation with translational diffusion of lipid and water molecules while the slow process likely stems from collective dynamics

Collective dynamics in phospholipid bilayers investigated by inelastic neutron scattering: Exploring the dynamics of biological membranes with neutrons

We present the first inelastic neutron scattering study of the short wavelength dynamics in a phospholipid bilayer. We show that inelastic neutron scattering using a triple-axis spectrometer at the high flux reactor of the ILL yields the necessary resolution and signal to determine the dynamics of model membranes. The results can quantitatively be compared to recent Molecular Dynamics simulations. Reflectivity, in-plane correlations and the corresponding dynamics can be measured simultaneously to gain a maximum amount of information. With this method, dispersion relations can be measured with a high energy resolution. Structure and dynamics in phospholipid bilayers, and the relation between them, can be studied on a molecular length scale

h→ggh\to gg and h→γγh\to\gamma\gamma with Anomalous Couplings at Next-to-Leading Order in QCD

We generalize the next-to-leading order QCD calculations for the decay rates of $h\to gg$ and $h\to\gamma\gamma$ to the case of anomalous couplings of the Higgs boson. We demonstrate how this computation can be done in a consistent way within the framework of an electroweak chiral Lagrangian, based on a systematic power counting. It turns out that no additional coupling parameters arise at NLO in QCD beyond those already present at leading order. The impact of QCD is large for $h\to gg$ and the uncertainties from QCD are significantly reduced at NLO. $h\to\gamma\gamma$ is only mildly affected by QCD; here the NLO treatment practically eliminates the uncertainties. Consequently, our results will allow for an improved determination of anomalous Higgs couplings from these processes. The relation of our framework to a treatment in Standard Model effective field theory is also discussed.Comment: Additional references included. 41 pages, 11 figures, 8 Table