Defocus and probe-position coupling in electron ptychography

Shaohong Cao, Peng Li, Andrew M Maiden, John M Rodenburg

 Department of Electronic and Electrical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK.

One of the most promising applications of electron ptychography is the possibility of converting a conventional SEM, with a relatively poor stability envelope, into a high-resolution TEM. This is simply achieved by placing a transmission specimen in stage and a CCD camera placed below the specimen [1]. SEM ptychography does not need any image-forming lenses: the objective lens is only used to generate a conical illumination. Defocusing this into a large area allows for a large ptychographical step size and a very large field of view. High resolution is obtained by solving the phase problem for the high-angle scattered intensity (lying outside the Ronchigram) via iterative algorithms such as ePIE [2] and DM [3]. See Fig. 2a, where gold atomic fringes in gold nano particles on a carbon support film are clearly visible in a ptychographic reconstruction obtained from a conventional SEM (an FEI Quanta 600 SFEG at 30keV, data from [1]). We also solve for the illumination function, which in the case of conical illumination has a uniform curvature dependent on defocus.

A complication of electron (as opposed to visible light and X-ray) ptychography is that is normally necessary to solve also for the illumination positions [4] because of errors in the scan coils resulting from magnification calibration inaccuracy and hysteresis. However curvature in the illumination and probe shift are coupled. Figure 1 shows a simplified ray diagram. For any two specimen planes where the ratio of the shift distance () and the ratio of the feature size in the object () equals the ratio of the defocus (), the resulting Ronchigrams will behave identically as the probe is shifted. In fact in the presence of wave interference the correct solution is unique, but for probe position-searching algorithms that are necessarily guided by the Fourier error metric, the bright intensity of the Ronchigram dominates. When partial coherence is present (so that Fresnel effects in the Ronchigram are supressed) the problem is exacerbated, generally resulting in a distorted probe position lattice (Fig. 3), a wrong estimate of the defocus, and an inconsistent reconstruction in which lattice fringes are strongly delocalised. Of course, delocalisation renders the reconstruction entirely invalid, like an out-of-focus conventional TEM image.

We explore the coupled position-defocus stagnation problem based on both experimental and simulated data. We report progress on various methods that can resolve this important issue.

Acknowledgment: SC gratefully acknowledges financial support from Phase Focus Ltd and for access to the SEM data.

References:

[1] Humphry MJ, Kraus B, Hurst AC, Maiden AM and Rodenburg JM, Nature Communications, vol. 1733, no. 10.1038, 2012

[2] Maiden AM and Rodenburg JM, Ultramicroscopy, 109, (2009) 1256-1262

[3] Pierre Thibault P, et. al., Ultramicroscopy, 109 (2009) 338-343, 2009

[4] Maiden AM, et. al., Ultramicroscopy, 120 (2012) 64-72

Figures:

Figure 1: Ray diagram: see main text.

Figure 2: Example of a high resolution transmission electron ptychographic reconstruction obtained in a SEM.

Figure 3: Probe positions are stretched by the search algorithm [4] when coupled with a wrong (in this case, over large) defocus. The dashed squares in the corners show the stretched direction and the magnified stretches.

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