Experimental 3D Metrology

You have 8 hours of wall-clock time for this task. Your machine has 4 CPU cores, 12 GiB of RAM and 1 T4 GPU. When the time is up, you are stopped and your work is graded as it stands.

Recover the three-dimensional structure of the crystalline silicon channel and its surrounding amorphous gate oxides from the experimental electron diffraction scan in /app/data/measurements.h5. The array /intensity has dimensions (256, 256, 128, 128): two scan axes followed by two detector axes. Values are detector ADU. Acquisition calibration is in /app/data/calibration.json.

The reconstruction should resolve the silicon lattice through the depth of the device, so that the positions and roughness of the channel's interfaces with the oxides, and the lattice strain near them, can be measured at each depth.

Write /app/phase.npy, a real-valued NumPy array containing your recovered slice phase in radians, positive where the projected potential is higher. It must have 40 slices in beam propagation order, with 10 Å slice spacing, beginning at the specimen entrance. Use the calibrated lateral pixel size specified in the calibration file, with equal lateral sampling along both axes. Each lateral dimension may be 850–1400 pixels; include the illuminated specimen region. Use float32 or float64 with finite values throughout, no object arrays, and save it as a plain .npy file under 330 MB. The volume may differ from the specimen by one global lateral translation and any combination of right-angle rotations and reflections of the lateral axes, but its slices must stay in depth order and share one lateral registration.

Keep scripts and intermediate results under /app; only /app/phase.npy is kept when you finish.