Adaptive probe correction with electrostatic phase plate

Abstract text (incl. figure legends and references)

Introduction

Scherzer theorem [1] states that to correct spherical aberration of an electron optical system, one needs either electromagnetic lenses that break rotational symmetry, time variant fields, or the existence of space charge. While the effectiveness of the first solution has been widely proven, we implemented the last one as an alternative. In this project, an electrostatic phase plate that creates local electric potential is installed in the microscope, altering the phase of the electron wave. In this manner, the phase plate compensates aberrations to some degree and increases the resolving power of the probe. With this principle, an adaptive aberration correction method is proposed.

Objectives

To correct the electron probe using phase plate without measuring the aberrations, but through maximizing a chosen quality indicator computed from annular dark field (ADF) images instead.

Methods

Multiple algorithms are used to search for the best phase configuration, all of them aim to minimize specific loss functions that are coupled with different scanning modes. For line scans, the standard deviation of the intensity is used, while for raster scans, other loss functions can be added, such as BRISQUE image quality assessment [2] and symmetry analysis of the probe.

The optimization goes in two steps. In the first step, the resulting image with different phase configurations is acquired by changing the voltage of the phase elements either grouped in rings or as lobes (Fig. 1). To avoid local minima, simulated annealing is used to search rather widely in the space of possible phase configurations. In the second step, gradient descend is applied with complete freedom of possible phase configuration allowed by the phase plate in order to further improve the result from the first step, and thus less symmetric aberrations and local variations in the phase response of the phase plate can be corrected.

Results

The simulated results (Fig. 1) of the probe and ADF images formed with a circular aperture, phase plate, and corrected phase plate at different stages of the process. The contrast and resolving power increase at each stage, accompanied by sharpening of the probe intensity profile.

Conclusion

An automatic probe correction scheme with phase plate is presented and experimentally realized on the microscope. Comparing the ADF image generated with the phase plate before and after the process clearer atomic features are observed, even with the unavoidable tail spread-out imposed by the finite fill factor of the phase plate [3]. The project shows a promising method for the probe correction of a less critical optical system and also a significant progress in fully automating electron microscopy experiments.

Reference

[1] O, Scherzer. "Über einige fehler von elektronenlinsen." Zeitschrift für Physik 101.9 (1936): 593-603.

[2] A. Mittal, et al. "Blind/referenceless image spatial quality evaluator." 2011 conference record of the forty fifth asilomar conference on signals, systems and computers. IEEE, 2011.

[3] F. Vega Ibáñez, et al. "Can a Programmable Phase Plate serve as an Aberration Corrector in the Transmission Electron Microscope (TEM)?." arXiv e-prints (2022): arXiv-2205.

Fig. 1 The probe shape at different stage of probe correction and their corresponding ADF image. The probe gradually converges to a sharp point with increasing resolving power. The sample shown is gold [1 1 1] on amorphous carbon.