High-resolution projection image reconstruction of thick objects by hard x-ray diffraction microscopy

Hard x-ray diffraction microscopy enables us to observe thick objects at high spatial resolution. The resolution of this method is limited, in principle, by only the x-ray wavelength and the largest scattering angle recorded. As the resolution approaches the wavelength, the thickness effect of objects plays a significant role in x-ray diffraction microscopy. In this paper, we report high-resolution hard x-ray diffraction microscopy for thick objects. We used highly focused coherent x rays with a wavelength of $\sim 0.1\text{nm}$ as an incident beam and measured the diffraction patterns of a $\sim 150\text{-nm}$-thick silver nanocube at the scattering angle of $\sim 3°$. We observed a characteristic contrast of the coherent diffraction pattern due to only the thickness effect and collected the diffraction patterns at nine incident angles so as to obtain information on a cross section of Fourier space. We reconstructed a pure projection image by the iterative phasing method from the patched diffraction pattern. The edge resolution of the reconstructed image was $\sim 2\text{nm}$, which was the highest resolution so far achieved by x-ray microscopy. The present study provides us with a method for quantitatively observing thick samples at high resolution by hard x-ray diffraction microscopy.

Figure 1

(Color online) Schematic layout of the relationship between the Ewald sphere and Fourier space: the spatial distribution of speckles across the $q_z=0$ plane is schematically drawn using a gray square. The rotation of the scattering object in real space corresponds to the rotation of the Ewald sphere around the origin of the Fourier space. When the sample is tilted, higher $q$ diffraction data in the $q_z\approx 0$ plane is observable, as shown by dotted lines.

Figure 2

(Color online) Schematic of the coherent x-ray diffraction experiment for collecting information on a cross section in Fourier space: focused coherent x rays with a wavelength of 0.1051 nm were radiated onto an isolated silver nanocube particle. To interrupt parasitic scattering x rays from the mirrors, guard slits were placed between the mirrors and the focus. Forward diffraction intensities were observed using a CCD detector. A direct x-ray beamstop was placed in front of the CCD detector. The incident x-ray angle was controlled by adjusting a two-axis rotational stage with angles of $\varphi$ and $\omega$.

Figure 3

(Color online) (a) Diffraction patterns of the silver nanocube at nine incident angles: each diffraction pattern is composed of an array of $1300\times 1340\text{pixels}$. (b) Diffraction pattern in the $q_z\approx 0$ plane derived from the nine diffraction patterns of (a). The total pixel number is $1611\times 1611$. $\mathit{q}$ is defined as $\left|\mathit{q}\right|=2\text{sin}\left(\Theta /2\right)/\lambda$, where $\Theta$ is the scattering angle and $\lambda$ is the x-ray wavelength.

Figure 4

(Color online) (a) Enlarged images of diffraction patterns at $\left(\varphi ,\omega \right)=\left(0°,0°\right)$ of Fig. 3a and the patched pattern displayed in Fig. 3b. Selected positions are indicated by white squares in Figs. 3a, 3b, respectively. Cross-sectional plots through the peak top of the specles of (a).

Figure 5

(Color online) (a) Projection image of the silver nanocube reconstructed from the diffraction pattern in Fig. 3b. (b) SEM image of an identical silver nanocube. Scale bars in (a) and (b) correspond to 100 nm. (c) Cross-sectional plot through line P in (a).