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

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

Phase retrieval beyond the homogeneous object assumption for X-ray in-line holographic imaging

X-ray near field holography has proven to be a powerful 2D and 3D imaging technique with applications ranging from biomedical research to material sciences. To reconstruct meaningful and quantitative images from the measurement intensities, however, it relies on computational phase retrieval which in many cases assumes the phase-shift and attenuation coefficient of the sample to be proportional. Here, we demonstrate an efficient phase retrieval algorithm that does not rely on this homogeneous-object assumption and is a generalization of the well-established contrast-transfer-function (CTF) approach. We then investigate its stability and present an experimental study comparing the proposed algorithm with established methods. The algorithm shows superior reconstruction quality compared to the established CTF-based method at similar computational cost. Our analysis provides a deeper fundamental understanding of the homogeneous object assumption and the proposed algorithm will help improve the image quality for near-field holography in biomedical application

Simultaneous high-resolution scanning Bragg contrast and ptychographic imaging of a single solar cell nanowire

Simultaneous scanning Bragg contrast and small-angle ptychographic imaging of a single solar cell nanowire are demonstrated, using a nanofocused hard X-ray beam and two detectors. The 2.5 microm-long nanowire consists of a single-crystal InP core of 190 nm diameter, coated with amorphous Si$_{O}$2 and polycrystalline indium tin oxide. The nanowire was selected and aligned in real space using the small-angle scattering of the 140 x 210 nm X-ray beam. The orientation of the nanowire, as observed in small-angle scattering, was used to find the correct rotation for the Bragg condition. After alignment in real space and rotation, high-resolution (50 nm step) raster scans were performed to simultaneously measure the distribution of small-angle scattering and Bragg diffraction in the nanowire. Ptychographic reconstruction of the coherent small-angle scattering was used to achieve sub-beam spatial resolution. The small-angle scattering images, which are sensitive to the shape and the electron density of all parts of the nanowire, showed a homogeneous profile along the nanowire axis except at the thicker head region. In contrast, the scanning Bragg diffraction microscopy, which probes only the single-crystal InP core, revealed bending and crystalline inhomogeneity. Both systematic and non-systematic real-space movement of the nanowire were observed as it was rotated, which would have been difficult to reveal only from the Bragg scattering. These results demonstrate the advantages of simultaneously collecting and analyzing the small-angle scattering in Bragg diffraction experiments