Neutron sub-micrometre tomography from scattering data

Abstract

Neutrons are valuable probes for various material samples across many areas of research. Neutron imaging typically has a spatial resolution of larger than 20 µm, whereas neutron scattering is sensitive to smaller features but does not provide a real-space image of the sample. A computed-tomography technique is demonstrated that uses neutron-scattering data to generate an image of a periodic sample with a spatial resolution of ∼300 nm. The achieved resolution is over an order of magnitude smaller than the resolution of other forms of neutron tomography. This method consists of measuring neutron diffraction using a double-crystal diffractometer as a function of sample rotation and then using a phase-retrieval algorithm followed by tomographic reconstruction to generate a map of the sample's scattering-length density. Topological features found in the reconstructions are confirmed with scanning electron micrographs. This technique should be applicable to any sample that generates clear neutron-diffraction patterns, including nanofabricated samples, biological membranes and magnetic materials, such as skyrmion lattices.

Keywords: computed tomography; nanoscience; nanostructures; neutron diffraction; neutron scattering; phase retrieval.

Figure 1

(a) The experimental setup. A λ = 4.4 Å neutron beam passes through a monochromator crystal, then through a phase grating whose effect is measured by an analyzer crystal and a ³He proportional counter. (b) From the measured diffraction intensity, the position-space phase is retrieved, providing the phase sinogram, which is then used to reconstruct the scattering-length density of the grating.

Figure 2

SEM micrographs of the phase gratings (left column) compared with their neutron tomographic reconstructions (middle column). Also shown is an overlay (right column) of the outline of the reconstruction over the SEM. The good agreement between the SEM micrographs and the reconstructions indicates that the shape of the gratings is uniform over a large range. The walls of Grating-2 and Grating-3 are shown to be very straight, while the sloped walls of Grating-1 appear in both the SEM micrograph and the reconstruction. Edge highlights are added to the reconstructions for clarity.

Figure 3

The outline of the entire reconstruction process. The raw data are filtered and deconvolved from the average diffraction spectrum of the maximum and minimum measured sample-rotation angles. The output is passed into an alternating projections algorithm for each sample rotation angle β, with the previous solution seeding the next step in β. A filtered back projection of the sinogram creates the reconstructed scattering-length density. The high-fidelity portion of the reconstruction is made into a binary image, Radon transformed back into a sinogram and compared with the original sinogram over the relevant range. The sinogram error is minimized with respect to the aspect ratio of the reconstruction. See text for details.

Figure 4

Results of the phase-retrieval algorithm and tomographic reconstruction with the FFT of a Radon-transformed image as inputs. A comparison of reconstructions after truncating past nth order (rows) with the phase of left intact (left column) and with the phase retrieved (right column).