Quantitative x-ray phase nanotomography

X-ray ptychographic computed tomography has recently emerged as a nondestructive characterization tool for samples with representative sizes of several tens of micrometers, yet offering a resolution currently lying in but not limited to the 100-nm range. Here we evaluate the quantitativeness of this technique using a model sample with a known structure and density, and we discuss its sensitivity as a function of resolution. Additionally, we show an example application for the determination of the mass density of individual $2-\mu$m-sized SiO${}_2$ microspheres with a relative error of 2$\%$. The accuracy and sensitivity demonstrated in this paper will enable quantitative imaging, segmentation, and identification of different phases in complex materials at the nanoscale.

Figure 1

(a) Sketch of the experimental setup for ptychographic tomography. At each incidence angle coherent diffraction patterns are recorded and the projected complex transmission function can be reconstructed. Example of amplitude (b) and phase (c) of a single projection of a test sample consisting of two spheres.

Figure 2

(a) 3D isosurface representation of the tomographic reconstruction of a test sample. (b) 2D slice of the tomogram in (a), scale bar $5\mu$m. (c) Spherical slice of the tomogram in (a) showing a region with milled letters on the surface of the sample. (d) SEM image of the same region shown in (c). Scale bars in (c) and (d) are $1\mu$m.

Figure 3

(a) Histogram of a region in the sample of approximately ${\left(2.8\mu \text{m}\right)}^3$ size marked with a square in Fig. 2b. (b) The circles show the relative error of the histogram ${\sigma }_r$ as a function of the voxel side length $r$, obtained by binning the voxels within this region. The line shows a fit to the data (see text for details).

Figure 4

(a) 3D rendering of the ptychographic tomogram of a sample consisting of $2-\mu$m-diam SiO${}_2$ microspheres in a glass capillary. We show in yellow (dark gray) an isosurface representation of the microspheres, while the capillary is shown in a semitransparent light gray color. (b) 2D section through the tomogram shown in (a). (c) 2D section of the same tomogram perpendicular to the section shown in (b) at the position of the line. (d) Line profile indicated by a dashed line in (c) reveals the refractive index distribution within a particle and the capillary wall.