Abstract:The reconstruction problem in in-line X-ray Phase-Contrast Tomography is usually approached by solving two independent linearized sub-problems: phase retrieval and tomographic reconstruction. Both problems are often ill-posed and require the use of regularization techniques that lead to artifacts in the reconstructed image. We present a novel reconstruction approach that solves two coupled linear problems algebraically. Our approach is based on the assumption that the frequency space of the tomogram can be divided into bands that are accurately recovered and bands that are undefined by the observations. This results in an underdetermined linear system of equations. We investigate how this system can be solved using three different algebraic reconstruction algorithms based on Total Variation minimization. These algorithms are compared using both simulated and experimental data. Our results demonstrate that in many cases the proposed algebraic algorithms yield a significantly improved accuracy over the conventional L2-regularized closed-form solution. This work demonstrates that algebraic algorithms may become an important tool in applications where the acquisition time and the delivered radiation dose must be minimized.

We evaluate several basic electrodynamic processes as modified by the presence of a very strong magnetic field, exceeding B Q ≡ m 2 /e = 4.4 × 10 13 G. These results are needed to build models of dissipative phenomena outside magnetars and some other neutron stars. Differential and total cross sections and rates are presented for electronphoton scattering, the annihilation of an electron-positron pair into two photons, the inverse process of two-photon pair creation, and single-photon pair creation into the lowest Landau state. The relative importance of these interactions changes as the background magnetic field grows in strength. The particle phase space relevant for a given process may be restricted by single-photon pair creation, which also opens up efficient channels for pair multiplication, e.g. in combination with scattering. Our results are presented in the form of compact formulae that allow for relativistic electron (positron) motion, in the regime where Landau excitations can be neglected (corresponding to 10 3 B Q B B Q for moderately relativistic motion along the magnetic field). Where a direct comparison is possible, our results are tested against earlier calculations, and a brief astrophysical context is provided. A companion paper considers electron-positron scattering, scattering of electrons and positrons by ions, and relativistic electron-ion bremsstrahlung.

State-of-the-art techniques for phase retrieval in propagation based X-ray phase-contrast imaging are aiming to solve an underdetermined linear system of equations. They commonly employ Tikhonov regularization − an L2-norm regularized deconvolution scheme − despite some of its limitations. We present a novel approach to phase retrieval based on Total Variation (TV) minimization. We incorporated TV minimization for deconvolution in phase retrieval using a variety of the most common linear phase-contrast models. The results of our TV minimization was compared with Tikhonov regularized deconvolution on simulated as well as experimental data. The presented method was shown to deliver improved accuracy in reconstructions based on a single distance as well as multiple distance phase-contrast images corrupted by noise and hampered by errors due to nonlinear imaging effects.

The photon spectrum emitted by a transrelativistic pair plasma is calculated in the presence of an ultrastrong magnetic field, and is shown to bear a remarkable resemblance to the rising hard X-ray spectra of quiescent magnetars. This emission is powered by pair annihilation which, in contrast with a weakly magnetized pair plasma, shows an extended low-frequency tail similar to bremsstrahlung. Cross sections for electron–positron annihilation/scattering, two-photon pair creation, and photon-e ± scattering are adopted from our earlier ab initio quantum electrodynamic calculations in the regime  ≫ B ≫ B Q. Careful attention is given to the u-channel scattering resonance. Magnetospheric arcades anchored in zones of intense crustal shear and reaching about twice the magnetar radius are identified as the sites of the persistent hard X-ray emission. We deduce a novel and stable configuration for the magnetospheric circuit, with a high plasma density sustained by ohmic heating and in situ pair creation. Pairs are sourced nonlocally by photon collisions in zones with weak currents, such as the polar cap. Annihilation bremsstrahlung extends to the optical–IR band, where the plasma cutoff is located. The upper magnetar atmosphere experiences strong current-driven growth of ion-acoustic turbulence, which may limit positron diffusion. Coherent optical–IR emission is bounded near the observed flux by induced scattering. This model accommodates the rapid X-ray brightening of an activating magnetar, concentrated thermal hotspots, and the subdominant thermal X-ray emission of some active magnetars. Current injection is ascribed to continuous magnetic braiding, as seen in the global yielding calculations of Thompson, Yang, and Ortiz.

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