Ptychography (scanning coherent diffraction with probe overlap) L1-070
Unclaimed Principle — open for contribution
This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.
To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.
Forward model E
Ptychography acquires J overlapping far-field diffraction intensities I_j as a coherent probe P scans across a complex object O on a regular or random grid. Each intensity is the phaseless squared magnitude of the Fourier transform of the product probe*object patch. The high inter-patch overlap (60-80%) creates redundancy that jointly constrains probe and object phases.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 8000
Non-convex phaseless recovery; Hayes ambiguity (global phase, conjugate flip, constant offset) resolved by overlap redundancy and probe structure. Oversampling sigma >= 2 per dim combined with overlap >= 0.6 guarantees local-minimum convergence for iterative projection solvers.
Solvability C
- Solver class:
- iterative projection (ePIE, PIE, rPIE, DM), proximal (ADMM-ptycho), Wirtinger-flow, learned (PtychoNN, PtychoDV)
- Convergence rate q:
- 1.5
- Complexity:
- O(J * K^2 * log K) per epoch (J scan positions, K-pixel diffraction patterns)