interactive ptychography

How the measurement works

A focused electron probe illuminates a small region of the sample. The probe is intentionally defocused so that neighboring scan positions overlap, and every region of the sample is measured many times from slightly different illumination conditions. At each of the 15 by 15 scan positions we record the far-field diffraction pattern, giving a four-dimensional dataset: two scan dimensions and two diffraction dimensions.

The simulation uses a 300 kV beam, an adjustable convergence semiangle (10 to 40 mrad), and a strongly defocused probe (200 Å of overfocus to 200 Å of underfocus). Larger convergence angles reach higher scattering angles and sharpen the depth resolution; more defocus spreads the illumination over more of the sample. The sample is a five-fold twinned decahedral nanoparticle embedded in an amorphous carbon substrate. Every diffraction pattern is computed live with the multislice algorithm for the given probe conditions.

How the reconstruction works

Ptychography recovers the complex-valued object and probe from the recorded diffraction intensities alone. We parameterize the object as a stack of complex slices and use the same multislice model in the forward direction, comparing the modeled far-field intensity against the measurement.

The solver minimizes the amplitude error between modeled and measured diffraction patterns using mini-batch gradient descent. Each iteration:

1. picks a small random batch of probe positions,
2. back-propagates the residual through the multislice model to get the gradient with respect to every object slice, and
3. takes an Adam step.

This is the same pixelated multislice approach used in quantEM, with the probe assumed known and starting from a blank object.

The depth resolution of ptychography is limited to roughly twice the wavelength divided by the square of the convergence angle, which is tens of ångströms here. You can see this in the reconstructed slice stack: the nanoparticle and substrate blur across neighboring slices, including the empty padding slices above and below the sample.

Going further: deep generative priors

Pixel-based reconstructions like this one are sensitive to noise and need careful regularization, especially in 3D. In my recent work we replace the pixel grids with deep generative priors, neural networks that parameterize the object and probe inside the same differentiable multislice model. This improves noise robustness, convergence speed, and depth regularization. Read more about the project or see the paper on arXiv.

To run these algorithms yourself, see the quantEM diffractive imaging tutorials.