nodeology.ai

Ptychography simulator

An interactive simulator of ePIE, the iterative phase-retrieval engine behind ptychographic imaging.

Coherent sourceA coherent monochromatic beam, laser, visible-light, electron, or X-ray. Well-defined phase across the wavefront is what makes downstream phase retrieval possible.
Sample, probe at rjThe probe P illuminates a patch of the unknown complex object O at scan position r_j. Adjacent positions overlap; that redundancy is the source of phase information.
Detector, far fieldThe far-field detector records intensity only, |F{P · O}|². Phase is destroyed at this step; the algorithm has to recover it from the overlap between scan positions.
Data acquisition
drag to orbit, scroll to zoom
Ground truth, object
Diffraction pattern
Reconstructed object
Reconstructed probe
Probe
Overlap
Noise
5×
Acquiring
—
Data error‖√I − |Ψ|‖
—
Convergence
—
Drop overlap to 50%. Convergence stalls; overlap carries the phase information.
Switch noise to high. The data error settles to a non-zero floor instead of going to zero.
Use a 32 px probe. More scan positions, sharper features, but each frame carries less information.
The ePIE loop
  1. 1
    Exit wave at position j
    ψj(r)=P(r) O(r−rj)\psi_j(\mathbf{r}) = P(\mathbf{r})\,O(\mathbf{r} - \mathbf{r}_j)
  2. 2
    Fraunhofer propagation
    Ψj(k)=F{ψj(r)}\Psi_j(\mathbf{k}) = \mathcal{F}\{\psi_j(\mathbf{r})\}
  3. 3
    Modulus constraint (measurement)
    Ψj′(k)=Ij(k) Ψj(k)∣Ψj(k)∣\Psi'_j(\mathbf{k}) = \sqrt{I_j(\mathbf{k})}\,\dfrac{\Psi_j(\mathbf{k})}{|\Psi_j(\mathbf{k})|}
  4. 4
    Inverse propagation
    ψj′(r)=F−1{Ψj′(k)}\psi'_j(\mathbf{r}) = \mathcal{F}^{-1}\{\Psi'_j(\mathbf{k})\}
  5. 5
    Object update
    O←O+α P∗(r)max⁡∣P∣2(ψj′−ψj)O \leftarrow O + \alpha\,\dfrac{P^*(\mathbf{r})}{\max|P|^2}\bigl(\psi'_j - \psi_j\bigr)
  6. 6
    Probe update
    P←P+β O∗(r−rj)max⁡∣O∣2(ψj′−ψj)P \leftarrow P + \beta\,\dfrac{O^*(\mathbf{r} - \mathbf{r}_j)}{\max|O|^2}\bigl(\psi'_j - \psi_j\bigr)