Talbot-Lau Grating Interferometry (X-ray phase-contrast imaging) L1-074
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
Three X-ray gratings (G0 source grating, G1 phase grating, G2 analyzer grating) encode phase and small-angle scattering as a spatially modulated moire pattern. Phase stepping (typically 8 steps) of one grating recovers three contrast images per pixel: absorption (A), differential phase (phi), and dark-field (visibility V).
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 400
Well-conditioned linear Fourier extraction of three contrast channels from K phase-stepped frames (K >= 3 required; K = 8 typical for noise averaging). Stability dominated by grating alignment and vibration; dark-field channel degrades when visibility V < 0.15.
Solvability C
- Solver class:
- Fourier demodulation (analytical), weighted least-squares, TV-regularized ADMM for A/phi/V fusion, learned (TalbotNet)
- Convergence rate q:
- 2
- Complexity:
- O(K * H * W) for Fourier extraction