Quantitative 3D imaging of highly distorted micro-crystals using Bragg ptychography

Abstract

Bragg coherent diffraction imaging (BCDI) fails to reliably retrieve phases in micro-crystals exhibiting strong strain inhomogeneities, which restricts its applicability. Here we show that three-dimensional Bragg ptychography (3DBP) overcomes this limitation by enabling stable inversion for large lattice distortions. Using a combination of experimental measurements and numerical tests, we compare the performance limits of the two approaches and demonstrate that 3DBP tolerates lattice distortions more than six times larger than BCDI. We also establish the sensitivity of both methods on a weakly distorted crystal, for which 3DBP yields smoother amplitude and phase fields with reduced short-length-scale artifacts. 3DBP thus provides a reliable route for imaging micro-crystals with large lattice distortions, expanding the scope of coherent X-ray Bragg microscopy to strongly deformed systems.

Figures (4)

• Figure 1: Experimental setup. (a) 3DBP set-up including a fully illuminated Fresnel zone plate (FZP), an order sorting aperture (OSA), the sample installed vertically on a piezo-stage and a rotation stage ($\theta$). The position of the sample is shifted downstream the focal plane to increase the illumination spot onto the sample. The diffracted intensity pattern is measured with a 2D detector placed in the far field. The same configuration is used to produced the curved-beam BCDI data set presented in Supplemental Materials, section S2 Supplemental_Materials. (b) Same set-up optimized for the plane-wave BCDI acquisition. The aperture of the FZP is strongly reduced to enlarge the spot size at the focal plane, producing a locally flat illumination over an area much larger than the particle size. (c, d) Retrieved wave-fields at the sample position for configurations (a) and (b), respectively. (e, f) Scanning electron microscopy image of the weakly and highly distorted particles, respectively. In (f) the white arrow points towards a faint contrast visible at the surface of the particle.
• Figure 2: 3D imaging of a weakly distorted particle. (a, b) 3D reconstructions of the weakly strained crystal showing the isosurface of the amplitude, colored with the reconstructed phase, for BCDI and 3DBP respectively. (c, d), (e, f) and (g, h) 2D cross sections of the retrieved amplitudes, phase (in radians) and strain, respectively. From (c) to (h), the top and bottom rows correspond to BCDI and 3DBP reconstruction, respectively. (i) Diffraction pattern measurement from the plane wave BCDI data set. (j) Simulation of the BCDI diffraction pattern calculated from the plane wave BCDI reconstruction and (k) from the 3DBP reconstruction.
• Figure 3: Quantitative 3D imaging of a highly distorted micro-crystal. (a, b) 3D reconstructions of the highly distorted crystal showing the iso-surface of the amplitude, colored with the reconstructed phase, obtained from 3DBP and BCDI, respectively. (c, d, e, f) 2D cross-sections of the amplitude, phase, strain and lattice tilt for the 3DBP reconstruction. (g, h) 2D cross-section of the amplitude and phase for the BCDI reconstruction. (i) Diffraction pattern measurement from the plane wave BCDI data set and (j) BCDI diffraction pattern simulated by using the particle retrieved with the 3DBP data. Phase maps are in radians. In (i, j) intensity unit is photon counts on logarithmic scale.
• Figure 4: Limits of BCDI and 3DBP methods assessed from numerical simulations. Normalized cross-correlation values $C$ obtained by comparing the reconstruction result to the ground truth when the phase distortion parameter $\alpha$ increases from 0.1 to 1 (top plot) and from 1 to 10 (bottom plot). The $\alpha =1$ value corresponds to the distortion level of the highly distorted particle of Fig. \ref{['fig:2']}. Black circles and red squares correspond to BCDI and 3DBP results, respectively. The dashed lines are guides to the eye. On the top and bottom of the plot, 2D cross-sections of the BCDI and 3DBP retrieved amplitudes are shown, respectively, for some of the $\alpha$ values.