Ptychography

1) Method to scan a specimen with a defocused convergent electron probe (Fig. (a))
A specimen is illuminated with a defocused convergent electron probe to broaden the illumination area. The probe is scanned on the specimen so that the adjacent illumination areas are partially overlapped to each other. The scan points of the probe are normally a few 10 points × a few 10 points or less depending on the scanning area and probe size. The procedure to obtain a structure image (phase image) by means of this type of ptychography is as follows:
The initial specimen function is assumed equal to 1 and the probe function is assumed to be a box function. The specimen exit-wave function (a product of the specimen and probe functions) is Fourier-transformed to obtain a diffraction pattern, the intensities of which are replaced by those of the pattern acquired experimentally. The updated diffraction pattern is then transformed back to an image in the real space by an inverse Fourier transform, which gives a new revised exit-wave function for this probe position. The probe function obtained is replaced with the correct function or the original one. And the above procedure is repeated. Then, the calculation moves to the next position. Aforementioned procedure is repeated until the difference of the calculated and experimental diffraction patterns becomes sufficiently small.
The resultant structural image (phase image) of the specimen is shown in Fig. (c). The present method is similar to conventional incoherent diffractive imaging. It should be however noted that non-unique solution problem arising in diffractive imaging is overcome due to the additional constraint, in which the specimen function in the overlapping region of the adjacent illumination areas have to be the same in the calculation for the diffraction patterns recorded. Furthermore, the issue of a limited field of view is cleared by scanning technique.

2) Method to scan a specimen with a focused convergent electron probe (Fig. (b))
A specimen is illuminated with a focused convergent electron probe．The convergent beam electron diffraction (CBED) pattern is recorded as a 2D image. The probe is scanned two dimensionally on the specimen. Scan points of the probe becomes a huge four-dimensional (4D) data set (2D CBED patterns +2D scan points), normally exceeding a few 10 thousands points.
The procedure for reconstructing a high-contrast structure image is as follows. First, the 4D data set RK (2D scan points R + 2D CBED patterns K) is Fourier-transformed with respect to the 2D scan points R to obtain another 4D data set QK (2D spatial frequencies Q + 2D CBED patterns K). In the overlapping area (K’) of the transmitted disc and a neighboring diffracted disc of the CBED pattern for a certain 2D spatial frequency q, the intensity of the Fourier component q of the structure appears (bottom of Fig. (b)). To improve the signal-to-noise ratio of the structure image (phase image) to be obtained, the intensities outside the interference area (K’) are set to be 0 (zero). And the sign (phase) of the intensities in the interference area (K'') located symmetrically with respect to the transmitted disc is reversed. By this processing, the intensities of the two areas (K’ and K''), which are normally canceled out when integrating, can be added positively or enhanced. Then, the intensities of the two areas (K’ and K'') of the 2D CBED pattern (bottom of Fig. (b)) are integrated for each spatial frequency component q of the 4D data set QK, so that a 2D spatial frequency pattern Q' is created. Finally, this 2D spatial frequency pattern Q' is inverse-Fourier transformed to obtain the structure image (phase image) of the specimen (Fig. (d)).

(Proofread by Dr. Peng Wang, Nanjing University)

Fig. 1
(a) Ptychography in which a specimen is scanned with a defocused convergent electron probe so that adjacent illumination areas are partially overlapped to each other. The illumination area is about a few nm to a few 10 nm in diameter. The number of the scan points is normally a few 10 times a few 10 or less.
(b) Ptychography in which a specimen is scanned with a focused convergent electron probe (probe diameter: about 0.3 nm or less). The number of the scan points is a few 100 times a few 100 (the total number exceeding a few 10 thousands) like the case of ordinary STEM. A high-speed and high-sensitivity camera (pixelated STEM detector) is used to obtain a series of the CBED patterns.
(c) Structure image (Phase image) of a mono-layer of MoS₂ reconstructed by the defocus method (a). (Data courtesy: Dr. Peng Wang, Nanjing University)
(d) Structure image (Phase image) of a mono-layer graphene reconstructed by the focus method (b).

Fig. 2 Comparison of a reconstructed structure image (phase) obtained by Ptychography in which a specimen is scanned with a convergent probe and a simultaneously-obtained ABF image of a mono-layer graphene acquired at an accelerating voltage of 200 kV.
(a) Structure image (phase) of graphene reconstructed from 4D data set. Here, the atomic sites appear bright.
(b) Ordinal ADF image simultaneously acquired with the 4D data set.
Comparison of the two images elucidates that the reconstructed structure image (phase) has a higher signal-to-noise ratio and provides higher contrast than those of the ADF image.