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E39 · Electron wavefront

Electron Ptychography: Recover Phase from Overlap

Record a scanning diffraction dataset and iterate a phase estimate against its stored counts.

Interactive modelElectron Ptychography: Recover Phase from Overlap
Recorded frame count—\text{—}
Total recorded electrons—\text{—}
Recorded incident electrons per frame—\text{—}
Adjacent intensity overlap—\text{—}
Maximum cumulative incident fluence—\text{—}
Completed iterations—\text{—}
Measured amplitude relative RMS—\text{—}
Committed probe calibration error—\text{—}
Experiment target—\text{—}

Physics tutorial

Electron Ptychography: Recover Phase from Overlap

BackgroundRecord a scanning diffraction dataset and iterate a phase estimate against its stored counts.

Why it mattersWhat does overlap add to a diffraction intensity measurement?

Start with the essentials

Focus question
What does overlap add to a diffraction intensity measurement?
One-sentence intuition
Compare conjugate planes without confusing prediction and measurement.

Core mathematical model

Stored diffraction counts

Ψj=F ⁣[P Oj]Cj∼Poisson⁡ ⁣(N∣Ψj∣2)\begin{aligned}\Psi_j&=\mathcal F\!\left[P\,O_j\right]\\C_j&\sim\operatorname{Poisson}\!\left(N|\Psi_j|^2\right)\end{aligned}

Known probe and positions define each exit-wave patch. Complete discrete detector sampling conserves the expected electrons for a unit-modulus object.

Object-only PIE update

Ψjc=Cj/N eiarg⁡ΨjOj←Oj+βP∗max⁡∣P∣2(ψjc−ψj)\begin{aligned}\Psi_j^c&=\sqrt{C_j/N}\,e^{i\arg\Psi_j}\\O_j&\leftarrow O_j+\beta\frac{P^*}{\max|P|^2}(\psi_j^c-\psi_j)\end{aligned}

Use beta 0.7 and project each updated object pixel to unit modulus. The independently calibrated probe is fixed.

Measured-amplitude residual

R=∑j,k(∣Ψj,k∣−Cj,k/N)2∑j,kCj,k/NR=\sqrt{\frac{\sum_{j,k}(|\Psi_{j,k}|-\sqrt{C_{j,k}/N})^2}{\sum_{j,k}C_{j,k}/N}}

The residual measures agreement with recorded amplitudes; sparse scans can fit well while leaving phase unconstrained.

Common difficulties

Scientific boundary

Typical misconceptionA low residual or sharp calculated probe certifies an experimental image.

Better mental modelCoherent 200 kV single-slice pure-phase teaching object. Object-only PIE uses an independently calibrated finite Gaussian probe, known integer scan positions and unit-modulus prior. No joint probe retrieval, multislice scattering, position refinement, partial coherence, damage, background or real-material resolution claim. Reconstructed phase has an arbitrary constant; displayed phase is relative to the illuminated-region mean. Small residual alone does not certify a unique or correct object. Angles and specimen size are enlarged schematically.

Run the experiment

  1. 01

    Predict redundancy

    Choose the scan step, probe width and per-frame electron budget.

    What to observe: Smaller steps increase both redundancy and cumulative dose at fixed per-frame counts.
  2. 02

    Record the scan

    Acquire the dataset; browse stored diffraction frames.

    What to observe: Changing acquisition sliders does not rewrite the stored frames.
  3. 03

    Iterate the phase estimate

    Choose iteration count and assumed probe calibration, then reconstruct.

    What to observe: Only recorded counts, positions and calibration constrain the object update.
  4. 04

    Test a failure

    Compare sparse, low-count and incorrect-probe examples before checking the target.

    What to observe: Small residual can coexist with an incorrect or weakly constrained phase.