Hollow Electron Ptychographic Diffractive Imaging

We report a method for quantitative phase recovery and simultaneous electron energy loss spectroscopy analysis using ptychographic reconstruction of a data set of “hollow” diffraction patterns. This has the potential for recovering both structural and chemical information at atomic resolution with a new generation of detectors.

Figure 1

Schematic illustration of the experimental setup used. (a) Optical configuration used for ptychographic data acquisition. ($\alpha$ is the probe convergence semiangle and $\beta$ is the semiangle of the hollow region of detector.) (b) HAADF image of ${\mathrm{MoS}}_2$ oriented along the [001] direction. The region enclosed in the red box was subsequently reconstructed using the ePIE algorithm. (c) Projected atomic model of ${\mathrm{MoS}}_2$ displayed along the [001] direction.

Figure 2

(a)–(e) Binary masks applied to diffraction patterns with hollow inner angles of (a) 0, (b) 5, (c) 10, (d) 15, and (e) 20 mrad and an outer angle of 24 mrad, which is equal to the convergence semiangle $\alpha$. Diffraction patterns calculated from the object function reconstructed from (f)–(j) experimental and (k)–(o) simulated data set with different hollow inner angles corresponding to the masks shown in (a)–(e), respectively. All diffraction patterns were obtained after 50 reconstruction iterations. The 20-mrad scale bar applies to all data in (a)–(o).

Figure 3

(a) ADF image of monolayer ${\mathrm{MoS}}_2$. (b) Conventional ptychographic (Con Ptycho, full diffraction pattern) and (c) Hollow ptychographic (Hol5 Ptycho, $\beta =5\mathrm{mrad}$) reconstructed phases from the same sample in the region enclosed by the red square in Fig. 1, respectively. The top-right and bottom-right insets in (a)–(c) are the corresponding experimental unit-cell averaged and simulated results, respectively. The 1-nm and 1-Å scale bars apply to (a)–(c) and their corresponding insets, respectively. (d)–(f) Power spectra of (a)–(c). The pink, white, yellow, and red circles mark (100), (110), (200), and (300) reflections corresponding to spacings of 273, 158, 136, and 91 pm, respectively.

Figure 4

(a) Root mean square error (RMSE) as a function of hollow inner angle $\beta$ for various step sizes and position errors. Solid lines represent step sizes of 0.204 Å (-filled inverted triangle-), 0.408 Å (-filled circle-), and 0.612 Å (-filled rectangle-) without the introduction of a probe position error. Same color dotted lines represent the results with 2-pixel random error introduced at the probe positions. (b)–(g) Reconstructed phases for the conditions marked by the dashed vertical line in (a). The 1-nm scale bar applies to all images in (b)–(g). The associated power spectra are insets to (b)–(g), respectively. The yellow and white circles mark (200) and (110) reflections corresponding to spacings of 136 and 158 pm, respectively.