Serpentine Images

[Janne Desir]

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Serpentine is honoured to present a solo exhibition of recent works by American artist Barbara Kruger (b. 1945, Newark, New Jersey, USA). The exhibition will be presented at Serpentine South from 1st February to 17th March 2024 and in the public realm with Outernet Arts.

Titled Thinking of You. I Mean Me. I Mean You. the exhibition will feature a unique selection of installations, moving image works, and multiple soundscapes installed across the Serpentine building, bookshop, and outside banners, as well as on large-scale, immersive wraparound screens at Outernet Arts.

Architecture photographer Danica O. Kus has shared with us images of the 2014 Serpentine Gallery Pavilion, designed by Chilean architect Smiljan Radić. For a closer look at this unusual pavilion, inspired by Oscar Wilde's short story The Selfish Giant, check out all of Ms. Kus' images after the break.

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Scanning transmission electron microscopy (STEM) provides structural analysis with sub-angstrom resolution. But the pixel-by-pixel scanning process is a limiting factor in acquiring high-speed data. Different strategies have been implemented to increase scanning speeds while at the same time minimizing beam damage via optimizing the scanning strategy. Here, we achieve the highest possible scanning speed by eliminating the image acquisition dead time induced by the beam flyback time combined with reducing the amount of scanning pixels via sparse imaging. A calibration procedure was developed to compensate for the hysteresis of the magnetic scan coils. A combination of sparse and serpentine scanning routines was tested for a crystalline thin film, gold nanoparticles, and in an in-situ liquid phase STEM experiment. Frame rates of 92, 23 and 5.8 s-1 were achieved for images of a width of 128, 256, and 512 pixels, respectively. The methods described here can be applied to single-particle tracking and analysis of radiation sensitive materials.

Scanning transmission electron microscopy (STEM) has become the technique of choice for imaging, structure, and spectroscopy analysis with atomic level resolution1,2. The implementation of spherical aberration correctors (Cs-Corr STEM) has allowed for sub-angstrom resolution3; while the introduction of pixelated detectors has enabled the recovery of electron-phase information to even perform electric- and magnetic field measurements4,5. These technological advances have been accompanied by an increased beam current density, caused by the reduced electron probe, and increased dwell times TD, needed to record entire diffraction patterns at each scan position within a 2D array6. Yet, the exerted electron irradiation7 is the main limiting factor to investigating radiation sensitive materials such as oxides8, organic hybrids materials9 or biological specimens10. A further disadvantage of STEM is the relatively long image acquisition time (seconds), under typical pixel-by-pixel conditions, preventing fast in-situ observations, and the hindering of quantitative analysis as drift and scan distortions artifacts arise11.

The straightforward approach relies on scanning the next line immediately at the end of the current line but moving the beam towards the opposite direction. In that configuration, the trace and retrace signal would correspond to the odd and even rows within a square scan. An example of such a serpentine scan is shown in Fig. 2c, acquired with the same settings as Fig. 2a (6.1 fps). At certain speeds, trace and retrace signals can be completely out of phase, producing a pseudo-noisy image. This distortion arises from ferromagnetic hysteresis effects present in the scanning deflector coils of the microscope. As only the trace signal position is parametrized, the retrace values are assigned to the wrong nominal fast-axis position. The compensation process of odd and even rows would require the use of the former lines as a reference and the analysis of a well-defined periodic sample to rectify the elongation/contraction of the probe pathway.

At first glance, the scan presented in Fig. 2c seems worse than the expected raster scan. However, as observed from Fig. 3a (where even rows are displayed separately), it is noticeable that the atomic arrangement between the Si columns is being preserved. A closer inspection, given by the normalized intensity profiles of two consecutive line scans shown in Fig. 3b, highlights the mismatch between maxima, i.e., the column positions. A first approach to correcting for the scanning distortions would be to apply an offset to the retrace values to overlap both intensity profiles. Nevertheless, as demonstrated by the elongation of the atomic distances at higher acquisition frequencies (Fig. S1) and the remnant of artifacts under low TD, a shift is insufficient to correct for the serpentine scan distortions. To find the higher order distortion coefficients, prior knowledge of the Si lattice can be used. Rectification of non-periodical samples is unlikely as curvatures, gaps and features make every line scan unique. Regardless, even images of crystal lattices are prone to artifacts caused by beam damage, drift distortion and emission fluctuations11.

In order to avoid noise inhomogeneities and obtain sub-pixel resolution, the trace and retrace signals were represented as a one-harmonic Fourier series. As depicted in Fig. 3c, the fitting process allowed the visualization of the periodic lattice and normalized the intensity and spread of the data. If the trace signal is used as a reference signal, i.e., the nominal fast axis position vector, both trace and retrace intensity vector y can be expressed as:

where a0, a1 and b1 model the intercept and amplitude-based Fourier coefficients in the data, and the subscripts t and r are associated with the trace and retrace signals respectively. The transformation \(x_r = z_1 x_t^2 + z_2 x_t\), with rectification coefficients z1 (proportional) and z2 (offset), subordinates the retrace fast axis to the parametrized \(x_t\) to correct for compression effects. Once the minimization problem for the intensity vectors is solved, the rectification coefficients can be applied to obtain a rectified image such as in Fig. 3d, where the scan distortions have been corrected. However, some pixels at the edge of each line have been removed. The precise number of trimmed pixels depends mostly on TD.

Comparison between rectified-reconstructed and experimental STEM images. (a) Difference between Serpentine-reconstructions and Rectified-reconstructions of experimental sparse(1/3)-serpentine [110] Si images at different image size and TD. The color maps quantify the degree of misalignment (in pixels) between the postprocessed atom positions and the ideal lattice. (b) Comparison between raster, serpentine-reconstructions, and rectified-reconstructions of the AuNPs.

The benefit of these scanning schemes has thus far aimed to reduce acquisition times. Nonetheless, it is important to point out that these methods can be applied to low dose settings when compared with the raster scan approach. Due to the reduced times achieved, sensitive materials, prone to damage by not only the total electron dose but also the dose rate, could be imagined, while also reducing drift and charging effects as the electron irradiation becomes more spread out25.

In this work, we demonstrated the feasibility of combining two different electron beam scanning strategies to improve STEM acquisition. The implementation of serpentine scans required thorough calibration of the rectification coefficients in order to assess the behavioral responses of the scanning coils. The application of sub-sampling strategies served as a straightforward approach to reducing electron dose and image acquisition time when sparsity levels avoid oversampling, i.e., when the sample is periodic or the pxsz is small enough that redundancy exists. By eliminating flyback times and performing random walk scans, rectified-reconstructed STEM images were acquired at high speeds with a similar quality of standard raster scan images. The methods described herein have a direct application on the fields of low-dose imaging and single-particle tracking experiments in order to obtain reliable information on kinetic processes in liquid.

We would like to thank T. Dahmen for useful discussions, A. Bo for help with liquid TEM experiments, and E. Arzt for support through INM. The research was funded by the Deutsche Forschungsgemeinschaft project TFS-STEM.

N.J. and N.B. conceived the research and supervised the project. E.O. carried out the STEM experiments and the image analysis. D.N. applied the inpainting reconstruction algorithm to the sparse images. All authors reviewed and edited the final manuscript.

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