Iterative micro-tomography of biopsy samples from truncated projections with quantitative gray values.

Three-dimensional reconstruction from truncated two-dimensional projections cannot be solved analytically without prior knowledge of the sample or access to the non-truncated projections. To suppress reconstruction artifacts in region of interest (ROI) or local tomography, an iterative algorithm has been devised based on back-projection and re-projection, assuming an approximately cylindrical shape of the entire sample of general homogeneity, which is especially applicable for micro-tomography of biopsy samples from biological tissue. Tomographic reconstruction is iteratively refined by minimizing the mismatch between an empty ROI and the reconstruction from the difference between measured sinogram and forward projected ROI reconstruction. By numerical simulation and experimental demonstration, it is shown that the algorithm is not only able to reconstruct quantitative gray values, but also to reduce artifacts of peripheral glow, and may lead to increased image sharpness. The method is particularly suitable for examination of biopsy/autopsy-samples of soft tissue by micro/nano-computed tomography.

Holographic imaging with a hard x-ray nanoprobe: ptychographic versus conventional phase retrieval.

We have performed near-field x-ray imaging with simultaneous object and probe reconstruction. By an advanced ptychographic algorithm based on longitudinal and lateral translations, full-field images of nanoscale objects are reconstructed with quantitative contrast values, along with the extended wavefronts used to illuminate the objects. The imaging scheme makes idealizing assumptions on the probe obsolete, and efficiently disentangles phase shifts related to the object from the imperfections in the illumination. We validate this approach by comparison to the conventional reconstruction scheme without simultaneous probe retrieval, based on the contrast transfer function algorithm. To this end, a set of semiconductor nanowires with controlled chemical composition (InP core, insulating SiO2 layer, and indium tin oxide cover) is imaged using the quasi-point source illumination realized by the hard x-ray nanofocus (26 nm×39 nm spot size) of the ID16A Nano-Imaging beamline at the European Synchrotron Radiation Facility.

Reconstruction of wave front and object for inline holography from a set of detection planes.

We illustrate the errors inherent in the conventional empty beam correction of full field X-ray propagation imaging, i.e. the division of intensities in the detection plane measured with an object in the beam by the intensity pattern measured without the object, i.e. the empty beam intensity pattern. The error of this conventional approximation is controlled by the ratio of the source size to the smallest feature in the object, as is shown by numerical simulation. In a second step, we investigate how to overcome the flawed empty beam division by simultaneous reconstruction of the probing wavefront (probe) and of the object, based on measurements in several detection planes (multi-projection approach). The algorithmic scheme is demonstrated numerically and experimentally, using the defocus wavefront of the hard X-ray nanoprobe setup at the European Synchrotron Radiation Facility (ESRF).

Phase retrieval for object and probe using a series of defocus near-field images.

Full field x-ray propagation imaging can be severely deteriorated by wave front aberrations. Here we present an extension of ptychographic phase retrieval with simultaneous probe and object reconstruction suitable for the near-field diffractive imaging setting. Update equations used to iteratively solve the phase problem from a set of near-field images in view of reconstruction both object and probe are derived. The algorithm is tested based on numerical simulations including photon shot noise. The results indicate that the approach provides an efficient way to overcome restrictive idealizations of the illumination wave in the near-field (propagation) imaging.

Sub-5 nm hard x-ray point focusing by a combined Kirkpatrick-Baez mirror and multilayer zone plate.

Compound optics such as lens systems can overcome the limitations concerning resolution, efficiency, or aberrations which fabrication constraints would impose on any single optical element. In this work we demonstrate unprecedented sub-5 nm point focusing of hard x-rays, based on the combination of a high gain Kirkpatrick-Baez (KB) mirror system and a high resolution W/Si multilayer zone plate (MZP) for ultra-short focal length f. The pre-focusing allows limiting the MZP radius to below 2 µm, compatible with the required 5 nm structure width and essentially unlimited aspect ratios, provided by enabling fabrication technology based on pulsed laser deposition (PLD) and focused ion beam (FIB).