Electron Ptychography

• Each diffraction pattern → non-convex set
  • Problem: reconstruct probe $\hat{\mathcal{P}}$ and object $\hat{\mathcal{O}}$ from diffraction intensities $I$

$$\begin{aligned} \psi_j(\boldsymbol{r}) &= \hat{\mathcal{P}}(\boldsymbol{r}) \times \hat{\mathcal{O}}(\boldsymbol{r}-\boldsymbol{R}_j) \\ I_j(\boldsymbol{k}) &= \left| \mathcal{F}\left[\psi_j(\boldsymbol{r})\right]\right|^2 \end{aligned}$$

• Rich literature of reconstruction algorithms:
  • "Fourier" projection
    • Reconstructed probe and object accurately reproduce measured intensities
  • "Overlap" projection
    • Reconstructed probe and object are self-consistent with adjacent scanning positions

Interactive Extended Ptychographic Iterative Engine Simulation