Near-field speckle-scanning-based x-ray imaging

The x-ray near-field speckle-scanning concept is an approach recently introduced to obtain absorption, phase, and dark-field images of a sample. In this paper, we present ways of recovering from a sample its ultrasmall-angle x-ray scattering distribution using numerical deconvolution. We also show how to access the 2D phase gradient signal from random step scans, the latter having the potential to elude the flat-field correction error. Each feature is explained theoretically and demonstrated experimentally at a synchrotron x-ray facility.

Figure 1

First image recorded during the scan with (a) and without an object (b) inserted in the beam. (c) Experimental setup for the data collection.

Figure 2

(a) Geometry for the scanning x-ray speckle imaging technique with constant steps. (b) Example of a reference speckle pattern built from the intensity values read in the yellow pixel during the scan. (c) Corresponding pattern recorded in the same pixel during a scan with the sample in the beam. (d) Scattering distribution obtained by deconvolution of (b) with (c).

Figure 3

Image modes of a blueberry sample obtained with the method of Sec. 3: (a) transmission image $T$, (b)–(c) horizontal and vertical wave front gradients $\mathbf{\nabla }W·{\mathbf{e}}_{\mathbf{x}/\mathbf{y}}$, (d) phase reconstruction $\varphi$, and (e) scattering image $Df$. Images obtained using the method of Sec. 4: (f)–(g) horizontal and vertical wave front gradients $\mathbf{\nabla }W·{\mathbf{e}}_{\mathbf{x}/\mathbf{y}}$. Higher moments of the scattering distribution: (i) $\sqrt{M_{20}}$, (j) $\sqrt{M_{02}}$, (k) $\sqrt[3]{M_{30}}$, (l) $\sqrt[3]{M_{03}}$, and (h) $\sqrt[4]{M_{40}}$.

Figure 4

The two possible geometries for the technique with the membrane placed either (a) upstream or (b) downstream from the investigated object. The refraction angle of the (dashed) red ray passing through the sample is denoted $\alpha$ and the (plain) blue ray shows the ray falling in the same detector pixel when no sample is in the beam.

Figure 5

Array of the $5\times 5$ central scatter images organized by their angular vector $\alpha =s_s\mathbf{p}/d$.

Figure 6

Geometry of the concept. (a) Data vector ${\mathbf{i}}_{\mathbf{r}}$ built from $N$ images with the sample in the beam. (b) Set of reference vectors $\left\{{\omega }_{\mathbf{r}+\mathbf{h}}\right\}$ in the reference data. (c) Correlation factor map of $\rho ({\mathbf{i}}_{\mathbf{r}},{\omega }_{\mathbf{r}}+\mathbf{h})$.

Figure 7

Random step processing scheme. (a) Horizontal and (b) vertical differential wave front gradients. (c) Phase, (d) transmission, and (e) scattering reconstruction images. (f) Intensity plot along the lines marked in (c)–(e).

Figure 8

(a)–(b) Correct transmission and phase images of a juniper cone. (c) Horizontal phase gradient calculated searching the location of vectors from the sample scan across the reference scan. (d) Output of the reciprocal calculation, searching reference vector locations across the sample scan. (e)–(f) Zoom in the small subset drawn on the above images. (f) Absolute difference between the values of two magnified image subsets: $\mathrm{\Delta }=\text{(e)–(f)}$.