Nanoscale Imaging with Resonant Coherent X Rays: Extension of Multiple-Wavelength Anomalous Diffraction to Nonperiodic Structures

The methodology of multiple-wavelength anomalous diffraction, widely used for macromolecular structure determination, is extended to the imaging of nonperiodic nanostructures. We demonstrate the solution of the phase problem by a combination of two resonantly recorded coherent scattering patterns at the carbon $K$ edge (285 eV). Our approach merges iterative phase retrieval and x-ray holography approaches, yielding unique and rapid reconstructions. The element, chemical, and magnetic state specificity of our method further renders it widely applicable to a broad range of nanostructures, providing a spatial resolution that is limited, in principle, by wavelength only.

Figure 1

Schematic experimental setup for MAD phasing: The sample (SEM image) is illuminated with a monochromatized and spatially coherent source (red). MAD phasing exploits the energy-dependent interference of the $R$ exit wave (red) with the non-$R$ exit wave (blue). The interference patterns recorded with a CCD detector reveal notable changes around the carbon $K$ edge. The center portions of two intensity maps are shown on a logarithmic scale. The corresponding OCs for the selected energies are indicated in the plot.

Figure 2

MAD phasing results: (a) the amplitudes $|A_N|$ and (b) $|A_R|$. Intensities are shown on the same logarithmic scale. (c) The phase relation $\Delta \varphi$ is obtained from the interference of the two components. $800\times 800$ pixels are shown corresponding to $0.153{\mathrm{nm}}^{-1}$.

Figure 3

Top: The diagram represents the iterative RPR method implementing the MAD phases $\Delta \varphi$ as reciprocal space constraints between the $R$ and non-$R$ amplitudes. Bottom: The normalized convergence error is plotted against the iteration for a set of reconstructions with varying OCs. The insets show the progressing $R$ structure determination and the non-$R$ part (circular aperture).

Figure 4

(Top left) The final $R$ structure of the polystyrene spheres and (top right) a magnified portion with adjusted linear contrast is presented. The 90 nm spheres are clearly resolved. The phase stability (bottom) suggests that image resolution is not better than 25 nm limited by the statistics at higher $q$.