X-ray Bragg magnifier microscope as a linear shift invariant imaging system: image formation and phase retrieval

Tofu: a fast, versatile and user-friendly image processing toolkit for computed tomography

Tofu is a toolkit for processing large amounts of images and for tomographic reconstruction. Complex image processing tasks are organized as workflows of individual processing steps. The toolkit is able to reconstruct parallel and cone beam as well as tomographic and laminographic geometries. Many pre- and post-processing algorithms needed for high-quality 3D reconstruction are available, e.g. phase retrieval, ring removal and de-noising. Tofu is optimized for stand-alone GPU workstations on which it achieves reconstruction speed comparable with costly CPU clusters. It automatically utilizes all GPUs in the system and generates 3D reconstruction code with minimal number of instructions given the input geometry (parallel/cone beam, tomography/laminography), hence yielding optimal run-time performance. In order to improve accessibility for researchers with no previous knowledge of programming, tofu contains graphical user interfaces for both optimization of 3D reconstruction parameters and batch processing of data with pre-configured workflows for typical computed tomography reconstruction. The toolkit is open source and extensive documentation is available for both end-users and developers. Thanks to the mentioned features, tofu is suitable for both expert users with specialized image processing needs (e.g. when dealing with data from custom-built computed tomography scanners) and for application-specific end-users who just need to reconstruct their data on off-the-shelf hardware.

Fast Fresnel propagation through a set of inclined reflecting planes applicable for X-ray imaging

We present a fast and accurate method for wave propagation through a set of inclined reflecting planes. It is based on the coordinate transformation in reciprocal space leading to a diffraction integral, which can be calculated only by using two 2D Fast Fourier Transforms and one 2D interpolation. The method is numerically tested, and comparisons with standard methods show its superiority in both computational speed and accuracy. The direct application of this method is found in the X-ray phase contrast imaging using the Bragg magnifier-an optics consisting of crystals asymmetrically diffracting in Bragg geometry.

Phase retrieval for arbitrary Fresnel-like linear shift-invariant imaging systems suitable for tomography

We present a generalization of the non-iterative phase retrieval in X-ray phase contrast imaging applicable for an arbitrary linear shift-invariant (LSI) imaging system with a non-negligible amount of free space propagation (termed as Fresnel-like). Our novel approach poses no restrictions on the propagation distance between optical elements of the system. In turn, the requirements are only demanded for the transfer function of the optical elements, which should be approximable by second-order Taylor polynomials. Furthermore, we show that the method can be conveniently used as an initial guess for iterative phase retrieval, resulting in faster convergence. The proposed approach is tested on synthetic and experimentally measured holograms obtained using a Bragg magnifier microscope - a representative of Fresnel-like LSI imaging systems. Finally, the algorithm is applied to a whole micro-tomographic scan of a biological specimen of a tardigrade, revealing morphological details at the spatial resolution of 300 nm - limiting resolution of the actual imaging system.

Single-distance phase retrieval algorithm for Bragg Magnifier microscope

We present an improved, single-distance phase retrieval algorithm applicable for holographic X-ray imaging of biological objects for an in-line germanium Bragg Magnifier Microscope (BMM). The proposed algorithm takes advantage of a modified shrink-wrap algorithm for phase objects, robust unwrapping algorithm as well as other reasonable constraints applied to the wavefield at the object and the detector plane. The performance of the algorithm is analyzed on phantom objects and the results are shown and discussed. We demonstrated the suitability of the algorithm for the phase retrieval on a more complex biological specimen Tardigrade, where we achieved successful phase retrieval from only a single hologram. The spatial resolution obtained by Fourier spectral power method for biological objects is ∼ 300 nm, the same value as obtained from the reconstructed test pattern. Our results achieved using the new algorithm confirmed the potential of BMM for in-vivo, dose-efficient single-shot imaging of biological objects.

Laboratory-based multi-modal X-ray microscopy and micro-CT with Bragg magnifiers

We report on the successful demonstration of X-ray phase contrast microscopy and micro computed tomography (CT) with a Bragg magnifier microscope (BMM) in a laboratory setup. The Bragg magnifiers, constituted by two channel-cut crystals in asymmetric diffraction, produced a 15X magnification of the X-ray beam, thus enabling high resolution imaging to be attained. The angular sensitivity of the crystals was used to implement analyzer-based phase contrast imaging: acquiring images at different angular positions and the three parametric images (apparent absorption, differential phase and scattering) have been obtained. Micro-CT, with resolution of about 5 μm is demonstrated with the same system. The main limitations, as well as the ways to mitigate them, are discussed with the aid of the experimental data. The technique demonstrated herein extends high-resolution, multi-modal, x-ray imaging and micro-CT to compact laboratory setups, with the potential of broadening the reach of these techniques outside the community of synchrotron users.

Development of variable-magnification X-ray Bragg optics

A novel X-ray Bragg optics is proposed for variable-magnification of an X-ray beam. This X-ray Bragg optics is composed of two magnifiers in a crossed arrangement, and the magnification factor, M, is controlled through the azimuth angle of each magnifier. The basic properties of the X-ray optics such as the magnification factor, image transformation matrix and intrinsic acceptance angle are described based on the dynamical theory of X-ray diffraction. The feasibility of the variable-magnification X-ray Bragg optics was verified at the vertical-wiggler beamline BL-14B of the Photon Factory. For X-ray Bragg magnifiers, Si(220) crystals with an asymmetric angle of 14° were used. The magnification factor was calculated to be tunable between 0.1 and 10.0 at a wavelength of 0.112 nm. At various magnification factors (M ≥ 1.0), X-ray images of a nylon mesh were observed with an air-cooled X-ray CCD camera. Image deformation caused by the optics could be corrected by using a 2 × 2 transformation matrix and bilinear interpolation method. Not only absorption-contrast but also edge-contrast due to Fresnel diffraction was observed in the magnified images.