Ptychographic phase reconstruction and aberration correction of STEM image using
4D
dataset recorded by pixelated detector
Authors: Sagawa Ryusuke , Yang Hao , Jones Lewys , Simson Martin , Huth Martin , Soltau Heike , Nellist Peter , Kondo Yukihito 
Published: December 2016

In scanning transmission electron microscopy (STEM), one can obtain a variety of STEM images such as bright‐field (BF) and annular dark‐field (ADF) STEM images by changing the shape of the scintillator. However, the intensity distribution of convergent beam electron diffraction (CBED) patterns at the detector plane is yet to be fully utilized. Meanwhile, direct electron detectors with fast frame rate have recently been commercialized and used in electron microscopy. Such detectors, when used for recording CBED pattern images for each STEM probe position, are called pixelated STEM detectors. With the obtained 4‐dimensional (4D) dataset, any shape of STEM detector can be synthesized in a post processing by a free selection of the integration area. Therefore, we can synthesize variety of STEM images such as differential phase contrast (DPC) and annular bright field (ABF) images, if we once record the image signal with a pixelated detector.
The 4D dataset can also be used for the advanced image processing techniques such as ptychography, which has been shown to provide high efficiency for reconstructing the phase image of an object [1,2]. Using ptychography, not only the phase contrast can be enhanced but also the effect of lens aberrations to the image such as defocus can be corrected by the post processing using the information collected by a pixelated detector.
Experiments were performed using an aberration corrected microscope (JEOL JEM‐ARM200F) equipped with a pixelated detector (pnDetector pnCCD), the fast direct electron detector, which can record images at a speed of 1,000 fps in a full frame mode (264 x 264 pixels). Binning or windowing can increase the speed. The camera was placed below the ADF detector to enable simultaneous recording.
Figure 1 shows STEM images of a monolayer graphene obtained at 80 kV. Fig. 1a shows an ADF image obtained with the probe current of approximately 0.2 pA and the dwell time for a pixel of 0.5 ms. Because of a combination of low dose and residual uncorrected aberrations, the lattice contrast of graphene is almost buried in the noise originated from 50 Hz commercial frequency. Fig. 1b shows a reconstructed phase image using ptychography. The image contrast is significantly improved compared to the simultaneous ADF image, but the contrast transfer of the image (see the Fourier transform displayed in the inset) is anisotropic, resulting in uncertain positions of carbon atoms. This is because there remains large two‐fold astigmatism and defocus in the image shown in Fig. 1(b), because we could not adjust those by observation of the ADF image due to the weak image signal. Fig. 1c is a phase image in which the aberrations are corrected through post processing using the same 4D dataset by applying correction functions in the spatial frequency domain. The image is no longer anisotropic and the carbon atomic positions can be unambiguously determined. Although the same amount of electron dose is used to form the ADF and the corrected phase images, the result clearly shows the benefit of ptychographic phase reconstruction in improving image signal to noise and being able to correct aberrations through post processing.
Figure 2 shows the ptychographic phase maps of the 4D dataset at a certain spatial frequency. With an aberration‐free electron probe, they would be flat phase on the two sidebands, and the phase difference between the bands be π. In Fig. 2a, the map of the original dataset, there is a phase gradient inside each sideband because the aberrations were present in the electron probe. Fig. 2b is the correction function that compensates for the aberration seen in Fig. 2a. Fig. 2c is the corrected phase map and corresponding to the image in Fig. 1c. Here, only defocus and two‐fold astigmatism are corrected but corrections of other higher order aberrations are in principle possible.
Figure 3 shows through focus images created in the same way as above. As we know the full information on the electron wave at the condenser aperture plane, we can induce any aberrations such as defocus.